Major element diffusion in garnet and the exsolution of majoritic garnet from aluminous enstatite in Earth's Upper Mantle

Majo elemen di usion in ga ne and he exsolu ion o majo i ic ga ne om aluminous ens a i e in Ea h's Uppe Man le Disse a ion Von de Fakul ä ü Biologie, Chemie und Geowissenscha en de Uni e si ä Bay eu h zu E langung de Wü de eines Dok o s de Na u wissenscha en - D . e . na . - o geleg on Willem Louis an Mie lo Gebo en in Leidschendam / die Niede lande Bay eu h, 2011 Diese Disse a ion wu de am Baye ischen Geoins i u , Uni e si ä Bay eu h im Zei aum on Janua 2008 bis Mai 2011 un e de Be euung on P o . D . Falko Langenho s ange e ig . Volls ändige Abd uck de on de Fakul ä ü Chemie, Biologie und Geowissenscha en de Uni e si ä Bay eu h genehmig en Disse a ion zu E langung des G ades eines Dok o s de Na u wissenscha en (D . e . na .). Disse a ion einge eich am: 25.05.2011 Zulassung du ch die P ü ungskommission: 11.07.2011 Wissenscha liches Kolloquiem: 26.07.2011 P ü ungsausschuss: P o . D . Falko Langenho s (E s gu ach e ) P o . D . Da id Rubie (Zwei gu ach e ) P o . D . Jö gen Senke (Vo si z) P o . D . Tomoo Ka su a P o . D . Klaus Bi ze Acknowledgemen s I would like o hank he Eu opean Commission o p o iding he unding o he p esen ed PhD p ojec unde he Ma ie Cu ie Resea ch T aining Ne wo k 'C us o Co e– he a e o subduc ed ma e ial' (MRTN-CT-2006- 035957). I would like o hank my supe iso du ing o my PhD, Falko Langenho s , o his pa ience and help in eaching me, he many ui ul discussions and he in aluable eedback he ga e me, which signi ican ly imp o ed he quali y o he disse a ion. Dan F os , Da id Rubie, Nobuyoshi Miyajima, Flo ian Heidelbach, Hans Kepple , Ca he in McCammon, Guðmundu Guð innson and De le K auße I would like o hank o hei ad ise and ins uc ions on using he di e en kinds o equipmen ha was used o p oduce esul s p esen ed in his disse a ion. My scien i ic p oduc i i y was g ea ly inc eased by he me iculous p epa a ion wo k done by Uwe Di mann, Hube Schulze, S e an Übelhack and Heinz Fische in he wo kshops. Thei wo k is g ea ly app ecia ed! Lydia Kison-He zing, Pe a Buche , and S e an Keyssne I hank o hei help in sol ing adminis a i e and o he p oblems no di ec ly ela ed o my scien i ic wo k. I would like o hank all my colleagues and iends a he Baye isches Geoins i u o c ea ing a g ea en i onmen o wo k in and he nice social li e ou side BGI. I also wan o hank my iends in Holland, ha hey a e he e o me and i is always nice o see hem again! To conclude I would like o hank my amily o all he help and suppo hey p o ided h ough all o my li e, wi hou hem I would no be whe e I would be now. Table o con en s 1 In oduc ion 1.1 Phase ela ions in he Ea h's T ansi ion Zone 1.2 Di usion kine ics o he majo elemen s in Ea h's man le 1.2.1 Oli ine 1.2.2 High p essu e polymo phs o oli ine 1.2.3 Pe o ski e (MgSiO3) 1.2.4 Magnesiowüs i e 1.2.5 Ga ne s 1.2.6 Py oxenes 1.3 Reac ion kine ics in Ea h’s man le 1.4 Goals o his PhD s udy 1.5 Re e ences 2 Ga ne s and di usion kine ics 2.1 Ga ne s and majo i e, a high p essu e polymo ph o ens a i e 2.1.1 Ga ne 2.1.2 Majo i e 2.1.3 Majo i ic ga ne and UHP ocks 2.2 Di usion in mine als 2.2.1 The di e en di usion coe icien s 2.2.2 Fick's laws 2.2.3 P essu e and empe a u e dependence 2.2.4 Vacancies and oxygen ugaci y 2.2.5 Mul i-componen models 2.3 Re e ences 3 Expe imen al and analy ical echniques 3.1 High p essu e – high empe a u e expe imen s 3.1.1 The Mul i-an il appa a us 3.2 T ansmission elec on mic oscopy 3.2.1 Sample p epa a ion 3.2.2 Basic p inciples o he TEM 3.2.3 Elas ic sca e ing wi hin he specimen 3.2.4 Inelas ic sca e ing – Ene gy dispe si e spec oscopy 3.2.5 Elec on ene gy loss spec oscopy 3.3 The elec on mic op obe 3.4 Re e ences 1 1 5 5 7 8 10 11 14 15 18 19 28 28 28 29 30 32 32 33 33 34 35 37 41 41 42 47 47 50 51 54 58 60 63 4 Nume ical modeling o di usion phenomena 4.1 Plana 1-D mul i-componen di usion 4.2 Di usion in a sphe ical o cylind ical geome y 4.3 Re e ences 5 Di usion o he majo i e componen in ga ne 5.1 In oduc ion 5.1.1 Di usion in mine als 5.2 Expe imen al me hods 5.2.1 S a ing ma e ials 5.2.2 Appa a us and p essu e cell 5.3 Analy ical me hods 5.4 Resul s 5.4.1 Cha ac e iza ion o he samples a e he expe imen s 5.4.2 Tempe a u e dependence 5.4.3 P essu e dependence 5.4.4 Magnesium – i on in e di usion 5.4.5 Almandine – (Mg) majo i e di usion 5.5 Discussion 5.5.1 Homogeniza ion o he uppe man le 5.5.2 Rheology o ga ne in he ansi ion zone 5.5.3 Compa ison wi h p e ious expe imen al da a 5.5.4 E ec o majo i e con en on di usi i y o he elemen s 5.6 Conclusions 5.7 Re e ences Appendix 5.1: Radia ion damage co ec ion Appendix 5.2: Quan i ica ion o he EDS analyses Appendix 5.3:P ecision o TEM EDS measu emen s Appendix 5.4: Majo i ic ga ne – Do a Mai a py ope di usion couple p o iles 6 Exsolu ion o ga ne om o hopy oxene 6.1 In oduc ion 6.2 Expe imen al se up 6.3 Analy ical se up 6.4 Resul s 6.4.1 De e mina ion o he ens a i e polymo ph 6.4.2 Mic os uc u e 6.4.3 Majo i ic ga ne p ecipi a es 6.4.4 Di usion o Al in high clinoens a i e 6.5 Discussion 66 66 69 71 72 72 72 74 74 76 76 78 78 82 83 84 85 88 89 89 92 92 94 95 98 100 100 102 104 104 105 106 107 107 107 109 111 112 6.5.1 Py oxene mic os uc u e 6.5.2 Ga ne p ecipi a es 6.5.3 Aluminium di usi i y in clinoens a i e 6.6 Conclusions 6.7 Re e ences 112 114 115 116 118 Summa y Majo i e is a high p essu e polymo ph o ens a i e wi h he ga ne s uc u e. The amoun o ens a i e ha can be dissol ed in ga ne as a majo i e componen inc eases signi ican ly wi h p essu e, and he e o e, majo i ic ga ne is hough o be a majo cons i uen o he Ea h's ansi ion zone. The anspo p ope ies o majo i ic ga ne a e, howe e , no well cons ained a he momen . The magni ude o he di usi i y o he majo i e componen in ga ne in luences ou unde s anding o he homogeniza ion ime scale o Ea h's man le. This is impo an in subduc ion zone se ings, whe e he subduc ing oceanic c us will o m a majo i e inhomogenei y in he ansi ion zone because o i s highe aluminium con en . Reac ion kine ics in he d y ansi ion zone a e di usion con olled and he e o e an imp o ed da ase on he di usi i y o he majo i e componen in ga ne will enable us o be e unde s and he o ole o disequilib ium in subduc ion zones. This disse a ion he e o e epo s he esul s o di usion expe imen s on ga ne . Slow di usion kine ics o he majo i e componen in ga ne will also will hampe he dissolu ion o py oxene in ga ne and py oxene will he e o e be me as ably p ese ed du ing subduc ion. Na u al py oxenes always con ain aluminium, which is expec ed o cause exsolu ion o a ga ne phase du ing subduc ion. The e o e, high p essu e and empe a u e expe imen s ha e been conduc ed on aluminous ens a i e, o simula e his p ocess, o which he esul s a e also p esen ed in his disse a ion. Di usion expe imen s ha e been conduc ed wi h di usion couples o majo i ic ga ne – Do a Mai a py ope, Do a Mai a py ope and Ö z al almandine and Ö z al almandine and majo i ic ga ne in a mul i-an il p ess be ween 1400 – 1900 °C and 12 – 20 GPa. The di usion expe imen s wi h he majo i ic ga ne – Do a Mai a py ope ga ne couples show ha he di usion o he majo i e componen in ga ne is e y slow, compa able o he di usi i y o silicon in wadsleyi e and ingwoodi e. The ac i a ion ene gy, ac i a ion olume and he p e- exponen ial o di usion o he majo i e componen in ga ne we e de e mined o be 241 ± 54 kJ mol-1, 3.3 ± 0.1 cm3 mol-1 and 2.3 x 10-7 cm2 s-1, espec i ely. The di usi i y o he majo i e componen in ga ne was de e mined o be 2-3 o de s o magni ude slowe han he sel -di usi i y o Mg, Fe and Ca in ga ne a he same condi ions. Compa ison wi h di usion da a on wadsleyi e and ingwoodi e shows ha he di usi i y o he majo i e componen in ga ne is e y simila o ha o he silicon sel -di usi i y in he high-p essu e polymo phs o oli ine. Ano he se o di usion expe imen s was conduc ed wi h Ö z al almandine – majo i ic ga ne di usion couples. The di usion p o iles ob ained om hese expe imen s a e s ongly asymme ic, and indica e ha he e is an inc eased ace -di usi i y o Mg and Fe by one o de o magni ude in majo i ic ga ne pa o he di usion couple. The inc eased di usi i y o Mg and Fe in majo i ic ga ne appea s o be an in insic p ope y o majo i ic ga ne , which can be explained by he ac ha he oc ahed al si es sho cu he di usion pa h h ough he ga ne s uc u e. In almandine he oc ahed al si es a e all occupied by aluminium, whe eas in he majo i ic ga ne a p opo ion o he oc ahed al si es a e also occupied by Mg and Fe. To de e mine whe he solid s a e di usion can homogenize he man le he di usion dis ance o he majo i e componen in ga ne , assuming g ain bounda y di usion is he dominan di usion mechanism, has been calcula ed. The esul s show ha wi hin he ange o empe a u es p e ailing in he ansi ion zone, majo i e is able o di use 5 – 15 m on he ime scale o he age o he Ea h. Solid s a e di usion is hus no able o homogenize he man le. Ano he impo an ques ion is whe he o no di usion o he majo i e componen in ga ne is as enough o enable py oxene o dissol e in ga ne , hus o ming majo i ic ga ne in he subduc ing oceanic slab. A ini e di e ence code has been de eloped o assess his ques ion ha models di usion in a sphe ical g ain and di usion con olled g ow h o a sphe ical g ain. The esul s show ha du ing he subduc ion p ocess all py oxene can be dissol ed in ga ne in he case o he li hosphe ic man le pa o he slab. The oceanic c us shows howe e a di e en esul , due o i s lowe empe a u e, and only a small amoun o py oxene can be dissol ed in o ga ne . Me as able phases will hus be p ese ed in he subduc ing oceanic c us du ing he subduc ion p ocess. Na u al py oxenes con ain small amoun s o aluminium. Du ing subduc ion py oxene is hough o dissol e in o ga ne . Howe e , as he di usion expe imen s epo ed in his hesis show, he e is a signi ican delay in he dissolu ion o py oxene in ga ne as esul o he limi ed di usi i y o he majo i e componen in ga ne . The e o e, ga ne will exsol e om py oxene be o e py oxene is dissol ed in o ga ne , because he aluminium solubili y in py oxene dec eases wi h inc easing p essu e. Expe imen s wi h Do a Mai a py ope – Tanzania ens a i e couples ha e been conduc ed a 1700 °C and 15 GPa o simula e he p ocess o subduc ion in o he ansi ion zone. The eco e ed samples e eal in low clinoens a i e ex ensi e winning on (100) and a high densi y o s acking aul s on (100) wi h displacemen ec o R = [½ ½ w]. F om c ys al s uc u e conside a ions one inds ha w is mos likely ½. The s acking aul plane in combina ion wi h he displacemen ec o can be explained by he phase ans o ma ion o HP high clinoens a i e o low clinoens a i e. The opo ac ic ela ionship be ween he majo i ic ga ne p ecipi a es and he low clinoens a i e hos was also de e mined. Though he e is no a unique opo ac ic ela ionship, mos o he ga ne p ecipi a es ha e hei <111> di ec ion pa allel o he [001] di ec ion in low clinoens a i e. The lack o a unique opo ac ic ela ion is p obably due o a lack o an oxygen close packing di ec ion in ga ne . The obse ed dominan opo ac ic ela ionship is he e o e in e p e ed as he esul o he low di usi i y o silicon and is hus a opo ac ic ela ion con olled by kine ics. F om he aluminium di usion p o iles measu ed in low clinoens a i e, he di usi i y o Al in high clinoens a i e was de e mined o be a leas 6 x 10-11 cm2 s-1 a 1700 °C and 15 GPa. Compa ison wi h da a in diopside shows he e is a disc epancy be ween di usion da a a high p essu e and a low p essu e, which migh indica e a s ong dependence o Al di usi i y in clinopy oxene on Ca con en s o a change in di usion mechanism. The esul s o he expe imen s conduc ed in his PhD s udy show ha he low di usi i y o componen s in he Ea h may se e ely hampe eac ion kine ics in he Ea h in he case whe e mass anspo is equi ed. To be e unde s and dynamics o he Ea h i would he e o e be use ul s udy he ole o di usion in o he phase ansi ions in he Ea h whe e mass anspo is equi ed. Zusammen assung Majo i is eine Hochd uck-Modi ika ion on Ens a i mi G ana s uk u . Mi s eigendem D uck nimm de Ens a i -Gehal , de als Majo i -Komponen e in G ana gelös sein kann, deu lich zu, weswegen e mu e wi d, dass majo i ische G ana eine Haup komponen e in de Übe gangszone de E de is . Dennoch sind die T anspo eigenscha en on majo i ischem G ana noch nich genau bekann . Vom Ausmaß des Di usions e mögens des majo i ischen An eils in G ana häng unse Ve s ändnis om zei lichen Ablau de Homogenisa ion des E dman els ab. Dieses spiel in Subduk ionszonen eine wich ige Rolle, wo die subduzie e ozeanische K us e au g und ih es höhe en Aluminium-Gehal s eine Majo i -Inhomogeni ä in de Übe gangszone bilde . Da Reak ionsabläu e in eine ockenen Übe gangszone di usionskon ollie sind, we den e besse e Da en übe das Di usions e hal en de majo i ischen Komponen e in G ana dazu bei agen, Ungleichgewich e in Subduk ionszonen besse zu e s ehen. Die E gebnisse solche Di usions- Expe imen e we den in diese Disse a ion o ges ell . Eine langsame Di usion de Majo i -Komponen e in G ana behinde die Au lösung on Py oxen in G ana , wodu ch Py oxen wäh end des Subduk ionsp ozesses me as abil e hal en bleib . Na ü liche Py oxen en häl imme Aluminium, das sich wäh end de Subduk ion als G ana -Phase en misch . Um diesen P ozess zu simulie en, wu den Hochd uck- und Hoch empe a u -Expe imen e an Aluminium- eichem Ens a i du chge üh . Die E gebnisse we den eben alls in diese Disse a ion p äsen ie . Di usionsexpe imen e wu den an den olgenden Di usions-Paa en du chge üh : (1) majo i ische G ana – Do a Mai a-Py op, (2) Do a Mai a-Py op und Ö z al-Almandin und (3) Ö z al-Almandin und majo i ische G ana in eine Mul i-An il-P esse bei Tempe a u en on 1400 – 1900 °C und D ücken on 12 – 20 GPa du chge üh . Jene Expe imen e mi Paa en on majo i ischem G ana – Do a Mai a-Py op zeigen, dass die Di usion de majo i ischen Komponen e in G ana seh langsam ons a en geh , e gleichba mi dem Di usions e mögen on Silizium in Wadsleyi und Ringwoodi . Die Ak i i ä sene gie, das Ak i i ä s olumen und de p äexponen ielle Fak o de Di usion de majo i ischen Komponen e in G ana be agen 241 ± 54 kJ mol-1, beziehungsweise 3.3 ± 0.1 cm3 mol-1 und 2.3 x 10-7 cm2 s-1. Das Di usions e mögen de majo i ischen Komponen e in G ana is 2 bis 3 G ößeno dnungen langsame als die Selbs di usion on Mg, Fe und Ca in G ana un e denselben Bedingungen. Ve gleiche mi den Di usionsda en on Wadsleyi und Ringwoodi zeigen, dass das Di usions e mögen de Majo i -Komponen e in G ana de Selbs di usion on Silizium in den Hochd uck-Polymo phen on Oli in seh ähnlich is . Eine wei e e Reihe on Di usionsexpe imen en wu de an Di usionspaa en on Ö z al-Almandin und majo i ischem G ana du chge üh . Die aus diesen Expe imen en he o gegangenen Di usionsp o ile sind s a k asymme isch und belegen ein um eine G ößeno dnung e höh es Di usions e mögen on Spu en on Mg F os 2008), making majo i ic ga ne he second mos abundan phase in he ansi ion zone a e he high p essu e polymo phs o oli ine, wadsleyi e and ingwoodi e ( igu e 1.2). The mine alogy o he bulk pa o Ea h’s man le can be desc ibed by he sys em CaO – MgO – Al2O3 – SiO2 (CMAS-sys em). I on mainly exchanges wi h magnesium and he e o e a ec s he size o he s abili y ields o he phases in ol ed and he dep h ange o e which phase ansi ion occu s (Akaogi e al. 1989, Ka su a and I o 1989, F os 2003). The p esence o i on gene ally does no lead o he appea ance o new phases. The addi ion o CaO and Al2O3 o he sys em leads o he s abili y o clinopy oxene and ga ne a lowe p essu es. High p essu e expe imen s in he CMS-sys em ha e shown ha he HP high-clinoens a i e phase men ioned abo e, howe e , does no o m a solid-solu ion wi h he diopside (CaMgSi2O6) ich clinopy oxenes s able a lowe p essu e and a e hus wo dis inc phases (Gaspa ik 1990). The mu ual solubili y o HP-clinoens a i e and he clinopy oxene jadei e (NaAlSi2O6) is signi ican ly highe , howe e in he ansi ion zone he solubili y o jadei e in HP-clinoens a i e is also educed o i ually ze o (Gaspa ik 1989, 1990). The b eakdown o diopsidic clinopy oxene abo e 17 – 18 GPa ( igu e 1.3) esul s in he o ma ion o a majo i e ich ga ne (En80Di20 when he composi ion is exp essed as py oxene end-membe s) in equilib ium wi h calcium pe o ski e a empe a u es abo e 1400 °C, and he o ma ion o a calcium pe o ski e + s isho i e + wadsleyi e / ingwoodi e below 1400 °C. The calcium con en o he ga ne phase is howe e s ongly dependen on empe a u e and p essu e and inc eases wi h inc easing empe a u e and dec easing p essu e (Canil 1994, Ogu i e al. 1997). Gaspa ik (1989, 1990) obse ed he o ma ion o a new non-quenchable phase as b eakdown p oduc o diopside wi h a close o diopside s oichiome y a p essu es abo e 14 GPa, which is howe e no con i med by o he s udies and no c ys al s uc u e de e mina ion o his new phase was a emp ed by he 3 Figu e 1.1: Phase diag am o he Mg2Si2O4 – Fe2SiO4 join a 1600 °C. Modi ied a e Ka su a and I o (1989). au ho s. Simila b eakdown o ga ne a high empe a u es and p essu es is obse ed o sodium bea ing py oxenes. On he jadei e – ens a i e join a 1650 °C, pu e jadei e ans o ms o a ga ne s uc u e abo e 21 GPa (Gaspa ik 1990).The sodium a om is inco po a ed in a dodecahed al si e and he addi ional silicon a om is inco po a ed in an oc ahed al si e (Ringwood and Majo 1971). Liu (1978) howe e , showed ha a lowe empe a u es (1000 °C) jadei e disp opo iona es o s isho i e + calcium- e i e s uc u ed NaAlSiO4 abo e 24 GPa. The s abili y o ga ne s wi h a calcic and sodic clinopy oxene s oichiome y a high p essu e and empe a u e indica es ha , like ens a i e, he majo ock- o ming clinopy oxene end-membe s diopside and jadei e can be dissol ed in o ga ne in he ansi ion zone, also bea ing in mind ha calcium can be inco po a ed in ga ne as a g ossula componen . Since MORBs ha e a ela i e high aluminium, calcium and sodium con en , his has impo an consequences o he subduc ed oceanic c us in he ansi ion zone. I i une and Ringwood (1986) and I i une e al. (1993) pe o med high-p essu e expe imen s in a mul i-an il p ess on ma e ials wi h a MORB composi ion, o which he oceanic c us is made. These expe imen s showed ha i ually all py oxene will be dissol ed in o ga ne in he ansi ion zone, o ming a ga ne i e assemblage consis ing o ~ 90 ol. % o ga ne be ween 15 GPa and 20 GPa ( igu e 1.2). Ga ne a hese condi ions ha e a s ong majo i e componen (up o ~ 40%). A p essu es abo e 21 GPa (a 1200 °C) majo i ic ga ne s a s o exsol e i s Ca4Si4O12 componen as calcium pe o ski e. A p essu es abo e ~25 GPa an Al- ich phase wi h a calcium- e i e s uc u e s a s o exsol e om ga ne (I i une and Ringwood 1993, Hi ose e al. 1999). A ~ 27 GPa he emaining majo i ic ga ne ans o ms o Mg-pe o ski e (Hi ose e al. 1999, Ono e al. 2001). In he subduc ed oceanic c us , majo i ic ga ne is hus a dominan phase be ween 15 GPa and 27 GPa. 4 Figu e 1.2: a) Mine alogy o he man le assuming a py oli e composi ion (F os 2008) and b) a MORB composi ion, he subduc ed oceanic c us (I i une & Ringwood 1993), as unc ion o p essu e. ab 1.2 Di usion kine ics o he majo elemen s in Ea h's man le The di usion o a oms in mine als con ol a numbe p ocesses in he Ea h's in e io and p ope ies o he Ea h in which geologis s a e in e es ed in. Among hese a e he eac ion kine ics du ing phase ans o ma ions, especially when hey equi e long- ange anspo o he componen s (Pu nis 1992), o de – diso de phase ansi ions (Sipling and Yund 1973, Ca pen e 1982), e-equilib a ion o me amo phic assemblages and i s geo he mo-ba ome ic applica ions (Lasaga 1983, Lasaga and Jiang 1995), geoch onology (Dodson 1973) and heology o phases in he Ea h's in e io (Wee man e al. 1978, Poi ie 1985). This sec ion will gi e a sho e iew o di usion da a on mine als ele an o he Ea h's man le. 1.2.1 Oli ine As al eady poin ed ou abo e, oli ine is he mos abundan phase in Ea h's uppe man le. I has he e o e been he ocus o a g ea numbe o s udies. Buening and Buseck (1973) and Misene (1974) pe o med pionee ing wo k on he in e di usion o magnesium and i on in oli ine. They showed ha di usion in his sys em is highly asymme ic and di usion down he c-axis in oli ine is up o one o de o magni ude as e han down he a- o b-axis. The highly asymme ic p o iles indica ed ha he i on con en is o g ea in luence on he Mg-Fe in e di usi i y in oli ine. Buening and Buseck (1973) a gued he e o e, ha he inc eased in e di usi i y can be a ibu ed o a acancy p ocess whe e he oxida ion o i on in he oli ine s uc u e in oduces ex insic acancies and he eby inc eases he Mg-Fe in e di usi i y in oli ine. This was also la e con i med by o he s udies, whe e acancy concen a ions in oli ine as unc ion o oxygen ugaci y we e de e mined (Nakamu a and Schmalz ied 1983, Tsai and Dieckmann 2002) and whe e he Fe-Mg in e di usi i y as unc ion o oxygen ugaci y was obse ed o inc ease in a simila way as he acancy concen a ions (Chak abo y 1997, Dohmen e al. 2007). 5 Figu e 1.3: Phase diag am o diopside showing he b eakdown abo e ~ 18 GPa. A e Ogu i e al. (1997). Buening and Buseck (1973) also ound a change in slope in he log10 DFe-Mg s. ecip ocal empe a u e plo a ound 1125 °C and men ioned ha a change in Fe-Mg in e di usion mechanism in oli ine, om an ex insic mechanism a low empe a u es o an in insic mechanism a high empe a u es, migh cause such a kink. A ( en a i ely in e p e ed) simila in insic – ex insic ansi ion has been obse ed o Co – Mg in e di usion in oli ine a 1300 °C by Mo ioka (1980). The in e p e a ion as in insic – ex insic di usion egime ansi ion o he obse ed kink ansi ion has been con es ed by Chak abo y (1997), who claimed ha he kink obse ed by Buening and Buseck (1973) was p obably due o he se up o hei expe imen s. A mo e ecen s udy, whe e he oxygen was mo e ca e ully con olled, showed ha a ansi ion om one ex insic o a di e en ex insic mechanism was p esen a an oxygen ugaci y o 10-10 Pa and 900 °C. A lowe oxygen ugaci ies Fe-Mg in e di usion is independen o he oxygen ugaci y, whe eas a high oxygen ugaci ies Fe-Mg in e di usion becomes dependen on oxygen ugaci y. The e is also a sligh inc ease in he ac i a ion ene gy o Fe-Mg in e di usion om ~201 kJ mol-1 in he O2 dependen egime o ~ 220 kJ mol-1 in he O2 independen egime (Dohmen and Chak abo y 2007, Dohmen e al. 2007). Di usion s udies ha e also been o in e es because hey shed mo e ligh upon he heological p ope ies o he ma e ials o Ea h's man le. The wo de o ma ion mechanism ha a e deemed o be he mos impo an in he Ea h's man le, i.e. disloca ion c eep and di usion c eep, a e bo h con olled by he di usi i y o he mine al cons i uen s (Ranalli and Fische 1984, Ranalli 2001). The slowes di using species, usually oxygen o silicon in silica es, will hen con ol he heological p ope ies. The e o e, a numbe o expe imen s ha e been pe o med in he pas on he oxygen and silicon di usi i y in oli ine. Jaoul e al. (1980) pe o med di usion expe imen s de e mining he oxygen sel di usi i y in o s e i e. They de e mined he oxygen sel -di usi i y o be 5 o de o magni ude slowe han ha o Mg-Fe in e di usion a he 1500 K and oom p essu e. They also showed, ha o i on- ee o s e i e, he oxygen sel -di usi i y is independen o he oxygen ugaci y. Houlie e al. (1988) pe o med silicon and oxygen ace -di usion expe imen s a 1300 °C a a pO2 anging om 10-4 Pa o 10 Pa in a na u al San Ca los oli ine c ys al. Al hough hey we e no able o de e mine whe he he e was a dependence o silicon and oxygen ace -di usi i y on he oxygen ugaci y o no , hey showed ha silicon is he slowes di using ca ion in na u al oli ine, abou 1 – 2 o de s o magni ude slowe han oxygen. A compa ison o he di e en s udies ha ha e been pe o med on na u al oli ines, shows ha he ac i a ion ene gy o di usion o oxygen in oli ine, ~300 – 320 kJ mol-1 (Jaoul e al. 1980, 1983, Gé a d and Jaoul 1989), only Rye son e al. (1989) p oduced a lowe ac i a ion ene gy o 266 kJ mol-1, is highe han ha o Fe-Mg in e di usion which is ~200 – 220 kJ mol-1 (Misene 1974, Chak abo y 1997, Dohmen e al. 2007). Houlie e al. (1990) measu ed an ac i a ion ene gy o silicon sel -di usion o 291 kJ mol-1, whe eas Dohmen e al. (2002b) de e mined he ac i a ion ene gy o silicon sel -di usion o be 531 kJ mol-1. The la e asc ibes he ela i e low ac i a ion ene gy o Houlie e al. (1990) o he ac ha di usion p o iles o silicon di usion in oli ine a e e y sho and close o he limi s o ins umen al p ecision and analyses, which causes an appa en b oadening o he di usion p o iles. Dohmen e al. (2002) ook his in o accoun in hei s udy, which would gi e a simila ac i a ion ene gy o he wise. The esul s om Dohmen e al. (2002) 6 co espond be e o expe imen al de o ma ion da a on oli ine (Mei and Kohls ed 2000, Ka a o and Jung 2003). Excep o Misene (1974), he p e iously men ioned expe imen s we e all conduc ed a oom p essu es. Clea ly, since di usi i y is gene ally p essu e-dependen , i can no be simply assumed ha hese di usion coe icien s a e ep esen a i e o he Ea h's in e io , whe e p essu e a e in he GPa ange. The ac i a ion olume o Fe-Mg in e di usion in oli ine was de e mined by se e al au ho s o be ~5.0 – 5.5 cm3 mol-1 (Misene 1974, Fa be e al. 2000, Holzap el e al. 2007). This alue co esponds well o he alue o Mg ace di usion in oli ine (~ 5 cm3 mol-1) calcula ed using a omis ic modeling by Béjina e al (2009). The g oup a ound Jaoul (Be an-Al a ez e al. 1992, Jaoul e al. 1995) and Chak abo y e al. (1999) de e mined lowe ac i a ion olumes o Fe-Mg in e di usion, howe e he in e di usion da a by he Jaoul g oup is anomalously high (Dohmen e al. 2007) and he da a by Chak abo y e al (1999) was ob ained using misaligned c ys als in he di usion couples, which ga e an appa en educ ion in he Fe-Mg in e di usi i y a high p essu es (Holzap el e al. 2007). In con as o Fe-Mg in e di usion in oli ine a high p essu e, high p essu e da a on silicon is a he sca ce and on oxygen is absen . The e ec o p essu e on he ace di usi i y o silicon in oli ine was s udied by Béjina e al (1997, 1999). Thei esul s indica ed ha he ac i a ion olume o silicon ace -di usion in oli ine is negligible. Figu e 1.4 displays he magni ude o he di e en ionic di usi i ies in oli ine. 1.2.2 High p essu e polymo phs o oli ine Because wadsleyi e and ingwoodi e compose ~60 ol. % o he Ea h's ansi ion zone, hey ha e been he ocus o se e al s udies. Chak abo y e al (1999) conduc ed Fe-Mg in e di usion expe imen s on di usion couples consis ing o oli ine couples and wadsleyi e couples. Thei esul s indica ed ha Fe-Mg in e di usion in wadsleyi e is oughly 2 o de s o magni ude as e han in oli ine. This obse a ion was con i med by Fa be e al (2000) in hei expe imen s, who al eady obse ed a simila phenomenon on he Mg2SiO4 – Ni2SiO4 join ea lie , whe e Mg-Ni in e di usion in he high p essu e phases whe e obse ed o be h ee o de s o magni ude as e han in he oli ine phase (Fa be e al. 1994). Kubo e al. (2004), howe e , exp essed conce ns abou he e ec o wa e in wadsleyi e, since i g ea ly enhances he Fe-Mg in e di usi i y and wadsleyi e is known o ha e a high wa e solubili y (Inoue e al. 1995, Kohls ed e al. 1996). Holzap el e al. (2009) pe o med mo e di usion expe imen on nominally d y wadsleyi e and showed ha when one akes in o accoun he e ec o O2, H2O and i on con en s o oli ine and wadsleyi e in he wo phase egion in he ansi ion zone, he Fe-Mg in e di usi i y is expec ed o be 7 o de s o magni ude as e in wadsleyi e han in oli ine. In he same s udy hey also combined all da a published on Fe-Mg in e di usion in wadsleyi e o calcula e an ac i a ion 229 kJ mol-1, which is simila o ha o oli ine, and an ac i a ion olume o 13.9 kJ mol-1, signi ican ly g ea e han ha o oli ine. In hei di usion expe imen s Fa be e al. (2000) simul aneously de e mined he Fe-Mg in e di usi i y o oli ine, wadsleyi e and ingwoodi e. They showed ha he Fe-Mg in e di usi i y is e y simila in wadsleyi e and ingwoodi e. Because o he g ea simila i y be ween bo h s uc u es, his is in line wi h expec a ions. 7 The silicon and oxygen sel -di usi i y in wadsleyi e ha e been de e mined by Simojuku e al. (2004, 2009). Compa ison wi h Fe-Mg in e di usion in wadsleyi e da a (Holzap el e al. 2009) shows ha like in oli ine, di usion o silicon and oxygen in he high p essu e polymo phs o oli ine is 5 – 6 o de s o magni ude slowe han Fe-Mg in e di usion ( igu e 1.4). They de e mined an ac i a ion en halpy o di usion in oli ine o 291 kJ mol-1 and 409 kJ mol-1 o oxygen and silicon, espec i ely. This di e ence in ac i a ion en halpy o di usion be ween oxygen and silicon leads o a change o silicon being he slowes di using species below 1800 °C o oxygen being he slowes di using species abo e 1800 °C a 16 GPa. In hei expe imen s hey we e also able o de e mine he g ain bounda y di usi i y o silicon and wadsleyi e. Thei esul s show ha g ain bounda y is 4 – 5 o de s o magni ude as e han olume di usion a he expe imen al condi ions. The ac i a ion ene gies o g ain bounda y di usion hey de e mined o be o silicon ~ 80 kJ mol-1 lowe han ha o olume di usion in bo h wadsleyi e and ingwoodi e and o oxygen o be 50 kJ mol-1 smalle in wadsleyi e and 120 kJ mol-1 smalle in ingwoodi e han o olume di usion. 1.2.3 Pe o ski e (MgSiO3) Magnesium-silica e pe o ski e (he ea e pe o ski e) is he dominan phase in he lowe man le, whe e i cons i u e ~ 80 % o he o al olume(Fique 2001). The e o e i will con ol o a la ge ex en he heological 8 Figu e 1.4 : a) I on – magnesium in e di usi i y in wadsleyi e and oli ine. (1) wadsleyi e 13 GPa (Holzap el e al. 2009) (2) wadsleyi e15 GPa (Holzap el e al. 2009) (3) wadsleyi e 16 GPa (Holzap el e al. 2009) (4) wadsleyi e 17 GPa (Holzap el e al. 2009) (5) oli ine 1 a m (Dohmen e al. 2007) (6) oli ine 15 GPa (Holzap el e al. 2009; Dohmen e al. 2007), open ci cle: Kubo e al. (2004), solid ci cle:Chak abo y e al. (1999), open squa e: Fa be e al. (2000), solid squa e: Holzap el e al. (2009) b) Oxygen and silicon di usion in oli ine and i s high p essu e polymo phs. (1) Si, oli ine 1 a m (Dohmen, Chak abo y, e al. 2002) (2) Si, ingwoodi e 22 GPa (Shimojuku e al. 2009) (3) Si, wadsleyi e 16 GPa (Shimojuku e al. 2009) (4) O, ingwoodi e 22 GPa (Shimojuku e al. 2009) (5) O, wadsleyi e 16 GPa (Shimojuku e al. 2009) (6) O, oli ine 1 a m (Dohmen, Chak abo y, e al. 2002). A e Chak abo y (2010). a b p ope ies o he lowe man le. Since pe o ski e is only s able a high p essu es (abo e ~ 22 GPa), conduc ing di usion expe imen s on pe o ski e is challenging and expe imen ally epo ed di usion coe icien s a e sca ce. Yamazaki e al. (2000) we e he i s o epo on silicon sel -di usion in pe o ski e. They de e mined ha he ac i a ion en halpy o silicon sel -di usion in pe o ski e is ~ 336 kJ mol-1, which o silicon is a a he low alue conside ing ha he expe imen s we e conduc ed a 25 GPa. The na u e o hei expe imen s also made i possible o de e mine he g ain bounda y di usi i y o silicon, showing ha i was ~4 o de o magni ude as e han olume di usion. The ac i a ion en halpy o g ain bounda y di usion was de e mined o be e y simila o he ac i a ion en halpy o olume di usion, implying ha g ain bounda y di usion may play an impo an ole independen o empe a u e. Holzap el e al. (2005) measu ed he Fe-Mg in e di usi i y in pe o ski e be ween 22 GPa and 26 GPa be ween 1700 °C and 2000 °C. They de e mined ha he Fe-Mg in e di usion coe icien is h ee o de s o magni ude slowe han in oli ine a 12 GPa and is o he same o de magni ude as ha o silicon sel -di usion epo ed by Yamazaki e al. (2000). This is a a he su p ising esul , since in he o he dominan phases p esen in he Ea h's in e io , Fe-Mg in e di ussion is se e al o de s o magni ude as e han silicon sel -di usion. In he same s udy hey also de e mined he ac i a ion en halpy o Fe-Mg in e di usion in pe o ski e o be ~414 kJ mol-1, which is sligh ly g ea e beyond expe imen al e o han ha o silicon sel -di usion. Dobson e al. (2008) pe o med silicon and oxygen ace -di usion expe imen s simila o he expe imen s om Yamazaki e al. (2000). Fo silicon, hey basically con i med he ace -di usi i ies measu ed by Yamazaki e al. (2000). The oxygen di usi i y was de e mined o be abou wo o de s o magni ude as e han silicon di usion, al hough i has a a he la ge ac i a ion en halpy o oxygen di usion o ~500 kJ mol-1, which is signi ican ly g ea e han he ac i a ion en halpy o Si de e mined by Yamazaki e al (2000). Due o he ela i e la ge e o s on he di usion coe icien s o bo h Fe-Mg in e di usion (Holzap el e al. 2005) and oxygen di usion (Dobson e al. 2008) i is no possible o de e mine whe he he ac i a ion en halpy o one is g ea e han he o he . Due o he di icul ies in conduc ing expe imen s a high p essu es i is gene ally e y di icul o measu e accu a e ac i a ion olumes o di usion in pe o ski e. People ha e he e o e eso ed o a omis ic me hods he de e mine he di usi i y o he majo elemen s in pe o ski e. Ea lie a omis ic s udies we e able o calcula e mig a ion en halpies o magnesium and oxygen easonably well, when di usion in he ex insic egime was assumed o magnesium di usion and ei he he in insic and ex insic egime o oxygen di usion (W igh and P ice 1993, Dobson 2003, Ka ki and Khanduja 2007, Dobson e al. 2008). They ailed howe e in ep oducing he mig a ion en halpy o silicon di usion. Ammann e al. (2009) pe o med a mo e ho ough sea ch o he silicon saddle poin , which de ines he ac i a ion ene gy o di usion. They ound a mo e easonable alue o he ac i a ion en halpy o silicon di usion o abou 453 kJ mol-1, a 26.2 GPa. I o and To umi (2010) ook a di e en app oach using molecula dynamics simula ion ha does no make any assump ions abou he loca ion o he saddle poin and ob ained an ac i a ion en halpy a 25 GPa o silicon di usion in pe o ski e o ~ 332 kJ mol-1, hough hei simula ion we e pe o med a empe a u es (~ 3900 °C – 9 5600 °C) well abo e he Ea h's geo he m. The ac i a ion olumes o silicon di usion in pe o ski e de e mined by he abo e men ioned a omis ic s udies a e usually below 3.5 cm3 mol-1 a lowe man le condi ions and dec eases wi h inc easing p essu e. Ac i a ion olumes o magnesium di usion a e sligh ly highe han hose o silicon di usion. I can hus be concluded ha Fe-Mg in e di usion is anomalously sluggish in pe o ski e, and i migh be he a e limi ing p ocess in de o ma ion du ing di usion c eep o disloca ion c eep. In his case he e migh be a s ong dependence o he heological p ope ies o he lowe man le on he oxygen ugaci y, since he numbe o i on and magnesium acancies is usually dependen on he oxida ion s a e o he man le. 1.2.4 Magnesiowüs i e Magnesiowüs i e o e ope iclase (Mg,Fe1-x)O is he second mos abundan phase in Ea h's lowe man le, cons i u ing abou 20 ol.% o he lowe man le. Though no he mos abundan phase in he lowe man le, as a weak phase i may s ill play a signi ican ole in de e mining he heological beha iou o he lowe man le (S e on e al. 2001, Heidelbach e al. 2003). Again he mobili y and hus di usi i y o i on, magnesium and oxygen in magnesiowüs i e will play an impo an ole in de e mining he heological p ope ies o his mine al. As wi h he o he p e iously men ioned mine als Mg-Fe in e di usion p o iles in magnesiowüs i e a e usually highly asymme ic (Rigby and Cu le 1965, Blank and Pask 1969, Mackwell e al. 2005). This is no su p ise, as wüs i e is one o he classical examples exhibi ing non-s oichiome y due o oxida ion o di alen i on. Though he ea lie s udy by Rigby and Cu le (1965) showed no dependence o he ac i a ion ene gy o Fe-Mg in e di usion in magnesiowüs i e on i on con en , Blank and Pask (1969) showed he e was a posi i e exponen ial dependence o he ac i a ion en halpy on he i on concen a ion in magnesiowüs i e. This was subsequen ly also con i med by o he s udies, whe e he e ec oughly amoun s o a dec ease o he ac i a ion en halpy o 1.0 – 1.3 kJ mol-1 pe mola pe cen o FeO. (Chen and Pe e son 1980, Sa a and Go o 1982, Holzap el e al. 2003, Yamazaki and I i une 2003, Mackwell e al. 2005). The ac i a ion ene gy o Fe-Mg in e di usion in hese s udies was de e mined o be ~210 kJ mol-1. Di e en s udies ha e also shown he e is a D = D' O21/n dependence o he Fe-Mg in e di usi i y on he oxygen ugaci y, o which n is in he ange o 5 -6 o geological ele an composi ions (Chen and Pe e son 1980, Sa a and Go o 1982, Mackwell e al. 2005). This indica es ha oxida ion o e ous i on in magnesiowüs i e is balanced by he o ma ion o acancies on he me al si es (see also chap e 2). No many di usion expe imen s ha e been conduc ed a p essu es ele an o he Ea h's lowe man le. Holzap el e al. (2003) and Yamazaki and I i une (2003) pe o med Fe-Mg in e di usion expe imen s a condi ions ele an o he uppe pa o he lowe man le. Bo h s udies epo ed di e en ac i a ion olumes o Fe-Mg in e di usion, 3.3 cm3 mol-1 was epo ed in he o me and 1.8 cm3 mol-1 in he la e s udy. Mackwell e al. (2005) showed ha bo h s udies could be econciled wi h each o he , i he oxygen dependence o Fe-Mg in e di usion was aken in o accoun , since bo h s udies we e conduc ed using a di e en oxygen bu e . Bo h s udies howe e also epo ed a di e en ac i a ion ene gy o di usion, which would mean ha 10 he ac i a ion ene gy o Fe-Mg in e di usion is also dependen on he oxygen ugaci y. Hin s o his we e gi en by Sa a and Go o (1982), who ound ha he dec ease o appa en ac i a ion ene gy o Fe-Mg in e di usion as unc ion o i on con en is dependen on he oxygen ugaci y. Oishi e al. (1983) de e mined he oxygen sel -di usi i y in pu e end-membe MgO. Thei esul s showed ha he e was a change in ac i a ion ene gy a ound 1500 °C. The ac i a ion ene gy in he high empe a u e egime appea ed o be independen o he impu i y concen a ion. This b eak has he e o e been in e p e ed as being a ansi ion om an ex insic egime below 1500 °C, cha ac e ized by an ac i a ion ene gy o ~ 213 kJ mol-1, o an in insic egime, cha ac e ized by an ac i a ion ene gy o ~ 536 kJ mol-1. Ando e al. (1983) showed ha in con as o Fe-Mg in e di usion, he oxygen di usi i y is independen on he i on concen a ion. Van O man e al. (2003) con i med ha he oxygen di usi i y in MgO is also independen on i alen impu i y con en a high p essu es. As hei s udy was a ace di usion s udy, hey we e able o de e mine he ac i a ion olume o magnesium ace di usion in MgO, and de e mined i o be ~ 3.0 cm3 mol-1., which is in good ag eemen wi h he magnesium sel -di usion coe icien s ob ained om a omis ic simula ions (I a and Cohen 1997). The la e p edic also a dec easing ac i a ion olume o magnesium sel -di usion wi h inc easing p essu e. 1.2.5 Ga ne s Though ga ne s cons i u e an impo an pa o Ea h's uppe man le and ansi ion zone, in he la e hey cons i u e up o ~40 ol.%, only a ew expe imen s ha e been conduc ed a condi ions p e alen in he ansi ion zone. Mos o he di usion s udies we e conduc ed a p essu e below 4 GPa. Though di usion models in ga ne based on zoning in na u al ga ne s ha e been o mula ed ea lie (Ande son and Buckley 1973, Loomis 1978), he i s epo om di usion expe imen s on ga ne is by F ee (1979). In his s udy Fe-Mn in e di usion was obse ed in almandine ga ne – sin e ed spessa ine ga ne di usion couples a 1 ba and be ween 822 °C and 1200 °C. A concen a ion dependen manganese di usi i y was obse ed, which was i ed agains an exponen ial unc ion, simila o as wha has been done in he case o magnesiowüs i e and oli ine. The manganese di usi i y inc eases abou hal an o de o magni ude om a ga ne con aining 5 w .% o Mn o a ga ne con aining 20 w .% Mn a a empe a u e o 1002 °C. F om he cons an p essu e expe imen s also an ac i a ion ene gy o Fe – Mn/Mg in e di usion o 132 ± 45 kJ mol-1, which as will be discussed la e , is signi ican ly lowe han he o he s udies on Fe-Mg in e di usion in ga ne . The ea ly heo e ical models (Ande son and Buckley 1973, Loomis 1978, Lasaga 1979) o in e di usion in ga ne no e ha du ing di usion he luxes o ca ions canno be conside ed o be independen , bu a e co ela ed by c oss e ms in he ma ix o di usion coe icien s. This hus in oduces a composi ional dependence in he di usi i y o he componen . This occu s, howe e , h ough a di e en mechanism as Fe-Mg in e di usion men ioned in he abo e mine als, whe e he i on concen a ion modi ies he bo h acancy concen a ion and he ac i a ion en halphy o di usion and he eby makes Fe-Mg in e di usion concen a ion dependen . In he expe imen s conduc ed on Fe-Mg-Mn in e di usion on spessa ine – almandine couples by Elphick e al. 11 (1985) i was no ed ha hei di usion p o iles could no be i ed by a single composi ion independen di usion coe icien . Subsequen ly hey i ed hei p o iles by wo di usion coe icien s, one o bo h ends o he di usion couple. Loomis e al. (1985) e-analysed he da a o Elphick e al. (1985) and i ed he di usion models o Lasaga (1979) and Manning (1968) o he da a. Doing so, he de e mined ha he ace di usi i y o manganese is oughly 3 – 5 imes la ge han he ace di usi i y o i on and magnesium. The ace di usi i y o he la e wo was de e mined o be e y simila in magni ude in he almandine – spessa ine di usion couples. Using hei me hod, Elphick e al. (1985) de e mined a di e ence up o a ac o wo in in e di usi i ies be ween bo h sides. Loomis e al. (1985) also de e mined ha he ac i a ion en halpy o ( ace ) di usion a 40 kba o magnesium is (251 ± 33 kJ mol-1) and i on (257 ± 36 kJ mol-1) is signi ican ly g ea e han ha o manganese (202 ± 33 kJ mol-1). The ac i a ion olume o ace di usion in ga ne hey de e mined o be ~4.7 cm3 mol-1 in he wo s udies. The da ase o Loomis e al. (1985) has been ex ended by Chak abo y and Ganguly (1992) o co e a g ea e p essu e and empe a u e ange. The de e mined ac i a ion ene gies o ace di usion we e sligh ly highe ( Fe: 276 ± 36 kJ mol-1, Mg: 285 ± 38 kJ mol-1, Mn: 254 ± 37 kJ mol-1). The ac i a ion olumes o di usion was also a bi highe han in he s udy by Loomis e al. (1985), bu wi hin expe imen al e o o he la e (5 – 6 cm3 mol-1 wi h a ~ 3 cm3 mol-1 e o ). Ganguly e al. (1998) ex ended he da ase u he wi h da a om in e di usion expe imen s conduc ed a he almandine – py ope join and also include calcium and manganese di usion da a. These di usion expe imen s showed a s ong con as in ela i e di usi i ies o magnesium, i on and manganese in almandine – py ope couples as compa ed o almandine – spessa ine couples by Loomis (1985). The ela i e ace di usi i ies in he Ganguly e al. (1998) s udy a e app oxima ely DMg = 10 DFe = 3 DCa and manganese ace di usi i y is simila o ha o i on, whe eas a he almandine – spessa ine join i on sel - di usion is simila o magnesium ace di usion. The ac i a ion ene gies and olume o di usion along he C- O bu e in he spessa ine – almandine couples and almandine – py ope couples a e equal wi hin each o he s e o s, indica ing ha he change in ela i e di usi i ies in no e y likely caused by a change in di usion mechanism. Ganguly e al. (1998) also showed ha he oxygen ugaci y has a p o ound e ec on he de e mined appa en ac i a ion olume o di usion. Schwand e al. (1996) pe o med calcium ace di usion expe imen s on ga ne be ween 800 – 1000 °C and a 1 ba . They ob ained ex emely sho di usion p o iles (~ 20 nm) which indica ed ha calcium sel -di usion is a leas one o de o magni ude slowe han magnesium sel -di usion a he same condi ions in hei ea lie expe imen s (Schwand e al. 1995). Thei ac i a ion ene gy o sel -di usion is signi ican ly lowe han ha de e mined in o he s udies (F ee and Edwa ds 1999, Pe chuk e al. 2008), which migh be a esul o he ex emely sho p o iles. The Ca sel -di usion coe icien s om F ee and Edwa ds (1999) a e howe e 3 – 4 o de s o magni ude as e han ob ained by o he wo ke s (Schwand e al. 1996, Ganguly e al. 1998, Vielzeu e al. 2007, Pe chuk e al. 2008). Al hough he e is some disc epancy in calcium di usion da a om he abo e men ioned wo ke s, hey gene ally ag ee ha calcium is he slowes di using di alen ca ion in ga ne . 12 i may be expec ed ha he dissolu ion o py oxene is hinde ed and hus py oxene may be p esen o dep hs g ea e han expec ed o an equilib ium assemblage. As he e is a signi ican densi y con as be ween ga ne and py oxenes, his may ha e impo an implica ions o he dynamics o subduc ion zones. The esul s o Sha p and Rubie (1995) ha e shown ha HP high clinoens a i e ca alyses he nuclea ion o ingwoodi e du ing he ans o ma ion o oli ine o wadsleyi e and/o ingwoodi e. Though eac ion kine ics o he oli ine o wadsleyi e and ingwoodi e ans o ma ion a e con olled by he g ow h kine ics, and he e o e he me as able p ese a ion o HP clinoens a i e is unlikely o in luence he ans o ma ion kine ics, i may esul in a educed g ain size o wadsleyi e and ingwoodi e a e ans o ma ion. This in u n may enhance supe plas ici y, which is hough o cause deep- ocus ea hquakes in subduc ion zones, as explained. Fu he mo e, py oxene exsolu ion needles ha e been ound in se e al UHP p o inces (Song e al. 2004, an Roe mund 2009, Pandey e al. 2010). The a e o dissolu ion o py oxene in o ga ne and he a e exsolu ion o py oxene om ga ne in hese cases will also be con olled by he di usi i y o he majo i e componen . The lack o exsolu ion needles in p e-Scandian ga ne s om No way in combina ion wi h di usion da a on he majo i e componen in ga ne may be used o cons ain he du a ion o UHP me amo phism in hese p o inces. I is hus clea ou unde s anding o impo an geological p ocess occu ing in he in e io o he Ea h will bene i om cons ain s on he majo elemen di usi i y in ga ne a dep h. A p esen un o una ely, he e is nei he da a on majo elemen di usion in ga ne a ailable a he condi ions p e alen in he Ea h's ansi ion zone, no da a on he majo i e di usi i y in ga ne . Du ing his PhD expe imen s i has been a emp ed o, a leas pa ially, ill his gap in ga ne di usion da a. Addi ionally, he e is no da a a ailable on he aluminium di usi i y in HP high clinoens a i e. As e iewed in he eac ion kine ics chap e he mic os uc u e o phases in he ansi ion zone con ols among o he s he s eng h o he subduc ing slab. I is expec ed ha he aluminium componen will be exsol ed as majo i ic ga ne . This equi es long- ange anspo o aluminium in ens a i e and he exsolu ion o ga ne om HP high clinoens a i e will he e o e be con olled by he aluminium di usi i y in HP high clinoens a i e. In his PhD s udy i has been a emp ed o s udy he mic os uc u e o he majo i ic ga ne exsolu ion p oduc s om high clinoens a i e and o de e mine he di usi i y o aluminium in HP high clinoens a i e o gain a be e unde s anding o he p ope ies o me as able HP high clinoens a i e a ansi ion zone condi ions. This disse a ion he e o e epo s on wo di e en s udies pe omed du ing his PhD. The i s pa epo s (chap e 5) on he esul s o an expe imen al s udy on he majo elemen di usi i y in ga ne a ansi ion zone condi ions. The second s udy (chap e 6) was an expe imen al high p essu e s udy pe o med on aluminous ens a i e o ge mo e insigh in o he e olu ion o HP clinoens a i e as i is p ese ed as a me as able phase du ing subduc ion and o de e mine he aluminium di usi i y in HP clinoens a i e a high p essu e and empe a u e. 19 1.5 Re e ences Akaogi, M., Akimo o, S. (1977), Py oxene-ga ne solid-solu ion equilib ia in he sys ems Mg4Si4O12 – Mg3Al2Si3O12 and Fe4Si4O12 – Fe3Al2Si3O12 a high p essu es and empe a u es. Phys Ea h Plane In e 15:90- 106. doi: 10.1016/0031-9201(77)90013-9 Akaogi, M., I o, E., Na o sky, A. (1989), Oli ine-modi ied spinel-spinel ansi ions in he sys em Mg2SiO4 - Fe2SiO4: Calo ime ic measu emen s, he mochemical calcula ion, and geophysical applica ion. J Geophys Res 94:15671-15685 Akimo o, S., Fujisawa, H. (1966), Oli ine-spinel ansi ion in he sys em Mg2SiO4-Fe2SiO4 a 800°C. Ea h Plane Sci Le 1:237-240. doi: 16/0012-821X(66)90076-8 Ammann, M., B odhol , J., Dobson, D.P. (2009), DFT s udy o mig a ion en halpies in MgSiO3 pe o ski e. Phys Chem Mine 36:151-158. doi: 10.1007/s00269-008-0265-z Ande son, D.E., Buckley, G.R. (1973), Zoning in ga ne s-Di usion models. Con Mine al Pe ol 40:87-104. doi: 10.1007/BF00378168 Ando, K., Ku okawa, Y., Oishi, Y. (1983), Oxygen sel -di usion in Fe-doped MgO single c ys als. J Chem Phys 78:6890. doi: 10.1063/1.444635 Angel, R.J., Chopelas, A., Ross, N.L. (1992), S abili y o high-densi y clinoens a i e a uppe -man le p essu es. Na u e 358:322-324. doi: 10.1038/358322a0 Angel, R.J., Hugh-Jones, D.A. (1994), Equa ions o s a e and he modynamic p ope ies o ens a i e py oxenes. J Geophys Res 99:19777-19783. doi: 199410.1029/94JB01750 A l , T., Angel, R.J., Mile ich, R., A mb us e , T., Pe e s, T. (1998), High-p essu e P21 /c – C2/c phase ansi ions in clinopy oxenes; in luence o ca ion size and elec onic s uc u e. Am Mine al 83:1176-1181 Béjina, F., Blancha d, M., W igh , K., P ice, G.D. (2009), A compu e simula ion s udy o he e ec o p essu e on Mg di usion in o s e i e. Phys Ea h Plane In e 172:13-19. doi: 10.1016/j.pepi.2008.04.008 Béjina, F., Jaoul, O. (1996), Silicon sel -di usion in qua z and diopside measu ed by nuclea mic o-analysis me hods. Phys Ea h Plane In e 97:145-162. doi: 10.1016/0031-9201(96)03137-8 Béjina, F., Jaoul, O., Liebe mann, R.C. (1999), Ac i a ion olume o Si di usion in San Ca los oli ine: Implica ions o uppe man le heology. J Geophys Res 104:PP. 25,529-25,542. doi: 199910.1029/1999JB900270 Béjina, F., Ra e on, P., Zhang, J., Jaoul, O., Liebe mann, R.C. (1997), Ac i a ion olume o silicon di usion in San Ca los oli ine. Geophys Res Le 24:2597-2600 Be an-Al a ez, Y., Jaoul, O., Liebe mann, R.C. (1992), Fe-Mg in e di usion in single c ys al oli ine a e y high p essu e and con olled oxygen ugaci y: echnological ad ances and ini ial da a a 7 GPa. Phys Ea h Plane In e 70:102-118. doi: 10.1016/0031-9201(92)90165-R Blank, S.L., Pask, J.A. (1969), Di usion o I on and Nickel in Magnesium Oxide Single C ys als. J Am Ce am Soc 52:669-675. doi: 10.1111/j.1151-2916.1969. b16074.x B ady, J.B., McCallis e , R.H. (1983), Di usion da a o clinopy oxenes om homogeniza ion and sel -di usion expe imen s. Am Mine al 68:95 -105 B idgman, P.W. (1945), Polymo phic ansi ions and geological phenomena. Am J Sci 243A:90-97 Buening, D.K., Buseck, P.R. (1973), Fe-Mg La ice Di usion in Oli ine. J Geophys Res 78:6852-6862. doi: 197310.1029/JB078i029p06852 Bu nley, P.C. (1990), The e ec o nonhyd os a ic s ess on he oli ine-spinel ans o ma ion in magnesium ge mana e. Uni e si y o Cali o nia, Da is 20 Bu nley, P.C., G een, H.W. (1989), S ess dependence o he mechanism o he oli ine-spinel ans o ma ion. Na u e 338:753-756. doi: 10.1038/338753a0 Bu nley, P.C., G een, H.W., P io , D.J. (1991), Faul ing Associa ed wi h he Oli ine o Spinel T ans o ma ion in Mg2GeO4 and i s Implica ions o Deep- ocus Ea hquakes. J Geophys Res 96:425-443. doi: 199110.1029/90JB01937 Canil, D. (1994), S abili y o clinopy oxene a p essu e- empe a u e condi ions o he ansi ion egion. Phys Ea h Plane In e 86:25-34. doi: 16/0031-9201(94)05059-7 Ca pen e , M.A. (1982), Time- empe a u e- ans o ma ion (TTT) analysis o ca ion diso de ing in omphaci e. Con ib Mine al Pe ol 78:433-440. doi: 10.1007/BF00375205 Chak abo y, S. (1997), Ra es and mechanisms o Fe-Mg in e di usion in oli ine a 980°–1300°C. J Geophys Res 102:12,317-12,331. doi: 199710.1029/97JB00208 Chak abo y, S., Ganguly, J. (1992), Ca ion di usion in aluminosilica e ga ne s: expe imen al de e mina ion in spessa ine-almandine di usion couples, e alua ion o e ec i e bina y di usion coe icien s, and applica ions. Con ib Mine al Pe ol 111:74-86. doi: 10.1007/BF00296579 Chak abo y, S., Knoche, R., Schulze, H., Rubie, D.C., Dobson, D.P., Ross, N.L., Angel, R.J. (1999), Enhancemen o Ca ion Di usion Ra es Ac oss he 410-Kilome e Discon inui y in Ea h’s Man le. Science 283:362-365. doi: 10.1126/science.283.5400.362 Chak abo y, S., Rubie, D.C. (1996), Mg ace di usion in aluminosilica e ga ne s a 750-850° C, 1 a m. and 1300° C, 8.5 GPa. Con ib Mine al Pe ol 122:406-414. doi: 10.1007/s004100050136 Chen, W.-K., Pe e son, N.L. (1980), I on di usion and elec ical conduc i i y in magnesio-wüs i e solid solu ions (Mg, Fe)O. J Phys Chem Solids 41:335-339. doi: 10.1016/0022-3697(80)90206-1 Cygan, R.T., Lasaga, A.C. (1985), Sel -di usion o magnesium in ga ne a 750 deg ees o 900 deg ees C. Am J Sci 285:328 -350. doi: 10.2475/ajs.285.4.328 Däßle , R., Yuen, D.A., Ka a o, S., Riedel, M.R. (1996), Two-dimensional he mo-kine ic model o he oli ine- spinel phase ansi ion in subduc ing slabs. Phys Ea h Plane In e 94:217-239. doi: 10.1016/0031- 9201(95)03103-0 Dimano , A., Ing in, J. (1995), P emel ing and high- empe a u e di usion o Ca in syn he ic diopside: An inc ease o he ca ion mobili y. Phys Chem Mine 22: doi: 10.1007/BF00200321 Dimano , A., Jaoul, O. (1998), Calcium sel -di usion in diopside a high empe a u e: implica ions o anspo p ope ies. Phys Chem Mine 26:116-127. doi: 10.1007/s002690050168 Dimano , A., Jaoul, O., Sau e , V. (1996), Calcium sel -di usion in na u al diopside single c ys als. Geochem Cosmochem Ac a 60:4095-4106. doi: 10.1016/S0016-7037(96)00250-5 Dobson, D.P. (2003), Oxygen ionic conduc ion in MgSiO3 pe o ski e. Phys Ea h Plane In e 139:55-64. doi: 10.1016/S0031-9201(03)00144-4 Dobson, D.P., Dohmen, R., Wiedenbeck, M. (2008), Sel -di usion o oxygen and silicon in MgSiO3 pe o ski e. Ea h Plane Sci Le 270:125-129. doi: 10.1016/j.epsl.2008.03.029 Dodson, M.H. (1973), Closu e empe a u e in cooling geoch onological and pe ological sys ems. Con Mine al and Pe ol 40:259-274. doi: 10.1007/BF00373790 Dohmen, R., Becke , H.-W., Chak abo y, S. (2007), Fe–Mg di usion in oli ine I: expe imen al de e mina ion be ween 700 and 1,200 ° C as a unc ion o composi ion, c ys al o ien a ion and oxygen ugaci y. Phys Chem Mine 34:389-407. doi: 10.1007/s00269-007-0157-7 Dohmen, R., Becke , H.-W., Meißne , E., E zel, T., Chak abo y, S. (2002a), P oduc ion o silica e hin ilms using 21 pulsed lase deposi ion (PLD) and applica ions o s udies in mine al kine ics. Eu J Mine al 14:1155 -1168. doi: 10.1127/0935-1221/2002/0014-1155 Dohmen, R., Chak abo y, S. (2007), Fe–Mg di usion in oli ine II: poin de ec chemis y, change o di usion mechanisms and a model o calcula ion o di usion coe icien s in na u al oli ine. Phys Chem Mine 34:409- 430. doi: 10.1007/s00269-007-0158-6 Dohmen, R., Chak abo y, S., Becke , H.-W. (2002b), Si and O di usion in oli ine and implica ions o cha ac e izing plas ic low in he man le. Geophys Res Le 29:4 PP. doi: 200210.1029/2002GL015480 Elphick, S.C., Ganguly, J., Loomis, T.P. (1985), Expe imen al de e mina ion o ca ion di usi i ies in aluminosilica e ga ne s. Con ib Mine al Pe ol 90:36-44. doi: 10.1007/BF00373039 E ison, F.F. (1967), On he occu ence o olume change a he ea hquake sou ce. Bulle in o he Seismological Socie y o Ame ica 57:9 -25 Fa be , D.L., Williams, Q., Rye son, F.J. (1994), Di usion in Mg2SiO4 polymo phs and chemical he e ogenei y in he man le ansi ion zone. Na u e 371:693-695. doi: 10.1038/371693a0 Fa be , D.L., Williams, Q., Rye son, F.J. (2000), Di alen ca ion di usion in Mg2SiO4 spinel ( ingwoodi e), β phase (wadsleyi e), and oli ine: Implica ions o he elec ical conduc i i y o he man le. J Geophys Res 105(B1):513-529 Fique , G. (2001), Mine al phases o he Ea h´s man le. Zei sch i ü K is allog aphie 216:248-271. doi: 10.1524/zk i.216.5.248.20374 F ee , R. (1979), An expe imen al measu emen o ca ion di usion in almandine ga ne . Na u e 280:220-222. doi: 10.1038/280220a0 F ee , R., Edwa ds, A. (1999), An expe imen al s udy o Ca-(Fe,Mg) in e di usion in silica e ga ne s. Con ib Mine al Pe ol 134:370-379. doi: 10.1007/s004100050491 F ohlich, C. (1989), The Na u e o Deep-Focus Ea hquakes. Annu Re Ea h Plane Sci 17:227-254. doi: 10.1146/annu e .ea.17.050189.001303 F os , D.J. (2003), The s uc u e and sha pness o (Mg,Fe)2SiO4 phase ans o ma ions in he ansi ion zone. Ea h Plane Sci Le 216:313-328. doi: 16/S0012-821X(03)00533-8 F os , D.J. (2008), The Uppe Man le and T ansi ion Zone. Elemen s 4:171-176 Ganguly, J., Bha acha ya, R.N., Chak abo y, S. (1988), Con olu ion e ec in he de e mina ion o composi ion p o iles and di usion coe icien s by mic op obe s ep scans. Am Mine al 73:901-909 Ganguly, J., Cheng, W., Chak abo y, S. (1998), Ca ion di usion in aluminosilica e ga ne s: expe imen al de e mina ion in py ope-almandine di usion couples. Con ib Mine al Pe ol 131:171-180. doi: 10.1007/s004100050386 Gaspa ik, T. (1989), T ans o ma ion o ens a i e - diopside - jadei e py oxenes o ga ne . Con Mine al and Pe ol 102:389-405. doi: 10.1007/BF00371083 Gaspa ik, T. (1990), Phase Rela ions in he T ansi ion Zone. J Geophys Res 95:769 Gaspa ik, T. (2003), Phase diag ams o geoscien is s: an a las o he ea h’s in e io . Sp inge , Heidelbe g-Be lin Gé a d, O., Jaoul, O. (1989), Oxygen di usion in san ca los oli ine. J Geophys Res 94(B4):4119-4128 G een II, H.W., Bu nley, P.C. (1989), A new sel -o ganizing mechanism o deep- ocus ea hquakes. Na u e 341:733-737. doi: 10.1038/341733a0 Gu ney, J.J., Ha e, B. (1980), Chemical Va ia ions in Uppe Man le Nodules om Sou he n A ican Kimbe li es. Phil T ans R Soc A A297:273 -293. doi: 10.1098/ s a.1980.0215 22 Heidelbach, F., S e on, I., Langenho s , F., Mackwell, S. (2003), Fab ic e olu ion du ing high shea s ain de o ma ion o magnesiowüs i e (Mg0.8Fe0.2O). J Geophys Res 108:2154 Hi ose, K., Fei, Y., Ma, Y., Mao, H.-K. (1999), The a e o subduc ed basal ic c us in he Ea h’s lowe man le. Na u e 397:53-56. doi: 10.1038/16225 Hog e e, A., Rubie, D.C., Sha p, T.G., Sei e , F. (1994), Me as abili y o ens a i e in deep subduc ing li hosphe e. Na u e 372:351-353. doi: 10.1038/372351a0 Holzap el, C., Chak abo y, S., Rubie, D.C., F os , D.J. (2007), E ec o p essu e on Fe–Mg, Ni and Mn di usion in (FexMg1−x)2SiO4 oli ine. Phys Ea h Plane In e 162:186-198. doi: 10.1016/j.pepi.2007.04.009 Holzap el, C., Chak abo y, S., Rubie, D.C., F os , D.J. (2009), Fe–Mg in e di usion in wadsleyi e: The ole o p essu e, empe a u e and composi ion and he magni ude o jump in di usion a es a he 410km discon inui y. Phys Ea h Plane In e 172:28-33. doi: 10.1016/j.pepi.2008.09.005 Holzap el, C., Rubie, D.C., Elphick, S.C., F os , D.J. (2003), E ec o p essu e on Fe–Mg in e di usion in (FexMg1−x)O, e ope iclase. Phys Ea h Plane In e 139:21-34. doi: 10.1016/S0031-9201(03)00142-0 Holzap el, C., Rubie, D.C., F os , D.J., Langenho s , F. (2005), Fe-Mg In e di usion in (Mg,Fe)SiO3 Pe o ski e and Lowe Man le Reequilib a ion. Science 309:1707 -1710. doi: 10.1126/science.1111895 Houlie , B., Che aghmakani, M., Jaoul, O. (1990), Silicon di usion in San Ca los oli ine. Phys Ea h Plane In e 62:329-340. doi: 10.1016/0031-9201(90)90177-Y Houlie , B., Jaoul, O., Abel, F., Liebe mann, R.C. (1988), Oxygen and silicon sel -di usion in na u al oli ine a T = 1300°C. Phys Ea h Plane In e 50:240-250. doi: 10.1016/0031-9201(88)90105-7 Inoue, T., Yu imo o, H., Kudoh, Y. (1995), Hyd ous modi ied spinel, Mg1.75SiH0.5O4: A new wa e ese oi in he man le ansi ion egion. Geophys Res Le 22:117-120 I i une, T. (1987), An expe imen al in es iga ion o he py oxene-ga ne ans o ma ion in a py oli e composi ion and i s bea ing on he cons i u ion o he man le. Phys Ea h Plane In e 45:324-336. doi: 10.1016/0031-9201(87)90040-9 I i une, T., Ringwood, A.E. (1993), Phase ans o ma ions in subduc ed oceanic c us and buoyancy ela ionships a dep hs o 600-800 km in he man le. Ea h Plane Sci Le 117:101-110. doi: 10.1016/0012-821X(93)90120-X I i une, T., Sekine, T., Ringwood, A.E., Hibbe son, W.O. (1986), The eclogi e-ga ne i e ans o ma ion a high p essu e and some geophysical implica ions. Ea h Plane Sci Le 77:245-256. doi: 10.1016/0012- 821X(86)90165-2 I a, J., Cohen, R.E. (1997), E ec s o P essu e on Di usion and Vacancy Fo ma ion in MgO om Nonempi ical F ee-Ene gy In eg a ions. Phys Re Le 79:3198-3201. doi: 10.1103/PhysRe Le .79.3198 I o, E., Sa o, H. (1991), Aseismici y in he lowe man le by supe plas ici y o he descending slab. Na u e 351:140-141. doi: 10.1038/351140a0 I o, Y., To iumi, M. (2010), Silicon sel -di usion o MgSiO3 pe o ski e by molecula dynamics and i s implica ion o lowe man le heology. J Geophys Res 115:B12205 Jaoul, O., Be an-Al a ez, Y., Liebe mann, R.C., P ice, G.D. (1995), Fe-Mg in e di usion in oli ine up o 9 GPa a T = 600–900°C; expe imen al da a and compa ison wi h de ec calcula ions. Phys Ea h Plane In e 89:199-218. doi: 10.1016/0031-9201(94)03008-7 Jaoul, O., F oide aux, C., Du ham, W.B., Michau , M. (1980), Oxygen sel -di usion in o s e i e: Implica ions o he high- empe a u e c eep mechanism. Ea h Plane Sci Le 47:391-397. doi: 10.1016/0012-821X(80)90026-6 Jaoul, O., Houlie , B., Abel, F. (1983), S udy o 18O di usion in magnesium o hosilica e by nuclea mic oanalysis. J Geophys Res 613-624 23 Kanzaki, M. (1991), O ho/clinoens a i e ansi ion. Phys Chem Mine als 17:726-730. doi: 10.1007/BF00202244 Ka a o, S.-I., Jung, H. (2003), E ec s o p essu e on high- empe a u e disloca ion c eep in oli ine. Phil Mag 83:401-414. doi: 10.1080/0141861021000025829 Ka ki, B.B., Khanduja, G. (2007), A compu a ional s udy o ionic acancies and di usion in MgSiO3 pe o ski e and pos -pe o ski e. Ea h Plane Sci Le 260:201-211. doi: 10.1016/j.epsl.2007.05.031 Ka o, T., Kumazawa, M. (1985), Ga ne phase o MgSiO3 illing he py oxene-ilmeni e gap a e y high empe a u e. Na u e 316:803-805. doi: 10.1038/316803a0 Ka su a, T., I o, E. (1989), The Sys em Mg2SiO4 – Fe2SiO4 a High P essu es and Tempe a u es: P ecise De e mina ion o S abili ies o Oli ine, Modi ied Spinel, and Spinel. J Geophys Res 94:670 Ke schho e , L., Dupas, C., Sha p, T.G., Du ham, W.B., Rubie, D.C. (1998), Polymo phic ans o ma ions be ween oli ine, wadsleyi e and ingwoodi e: mechanisms o in ac ys alline nuclea ion and he ole o elas ic s ain. Mine al Mag Ke schho e , L., Rubie, D.C., Sha p, T.G., McConnell, J.D.C., Dupas-B uzek, C. (2000), Kine ics o in ac ys alline oli ine- ingwoodi e ans o ma ion. Phys Ea h Plane In e 121:59-76. doi: 10.1016/S0031-9201(00)00160-6 Ke schho e , L., Sha p, T.G., Rubie, D.C. (1996), In ac ys alline T ans o ma ion o Oli ine o Wadsleyi e and Ringwoodi e Unde Subduc ion Zone Condi ions. Science 274:79 -81. doi: 10.1126/science.274.5284.79 Ki by, S.H., Du ham, W.B., S e n, L.A. (1991), Man le Phase Changes and Deep-Ea hquake Faul ing in Subduc ing Li hosphe e. Science 252:216 -225. doi: 10.1126/science.252.5003.216 Ki by, S.H., S ein, S., Okal, E.A., Rubie, D.C. (1996), Me as able man le phase ans o ma ions and deep ea hquakes in subduc ing oceanic li hosphe e. Re Geophys 34:261-306. doi: 199610.1029/96RG01050 Kohls ed , D.L., Kepple , H., Rubie, D.C. (1996), Solubili y o wa e in he α, β and γ phases o (Mg,Fe)2SiO4. Con ib Mine al Pe ol 123:345-357. doi: 10.1007/s004100050161 Kubo, T., Shimojuku, A., Oh ani, E. (2004), Mg–Fe in e di usion a es in wadsleyi e and he di usi i y jump a he 410-km discon inui y. Phys Chem Mine 31:456-464. doi: 10.1007/s00269-004-0412-0 Lasaga, A.C. (1979), Mul icomponen exchange and di usion in silica es. Geochem Cosmochem Ac a 43:455- 469. doi: 10.1016/0016-7037(79)90158-3 Lasaga, A.C. (1983), Geospeedome y: An Ex ension o Geo he mome y. in: Saxena S.K.(ed.) Kine ics and Equilib ium in Mine al Reac ions, Ad ances in Physical Geochemis y pp. 81-114 Lasaga, A.C., Jiang, J. (1995), The mal his o y o ocks; P-T- pa hs o geospeedome y, pe ologic da a, and in e se heo y echniques. Am J Sci 295:697-741. doi: 10.2475/ajs.295.6.697 Liu, L. (1983), Phase ans o ma ions, ea hquakes and he descending li hosphe e. Phys Ea h Plane In e 32:226-240. doi: 10.1016/0031-9201(83)90128-0 Liu, L.-G. (1978), High-p essu e phase ans o ma ions o albi e, jadei e and nepheline. Ea h Plane Sci Le 37:438-444. doi: 10.1016/0012-821X(78)90059-6 Loomis, T.P. (1978), Mul icomponen di usion in ga ne ; I, Fo mula ion o iso he mal models. Am J Sci 278:1099-1118 Loomis, T.P., Ganguly, J., Elphick, S.C. (1985), Expe imen al de e mina ion o ca ion di usi i ies in aluminosilica e ga ne s. Con ib Mine al Pe ol 90:45-51. doi: 10.1007/BF00373040 Mackwell, S., Bys icky, M., Sp oni, C. (2005), Fe–Mg In e di usion in (Mg,Fe)O. Phys Chem Mine 32:418-425. doi: 10.1007/s00269-005-0013-6 Manning, J.R. (1968), Di usion kine ics o a oms in c ys als. Van Nos and, P ince on 24 Mei, S., Kohls ed , D.L. (2000), In luence o wa e on plas ic de o ma ion o oli ine agg ega es 2. Disloca ion c eep egime. J Geophys Res 105(B9):21471-21481 Misene , D.J. (1974), Ca ionic di usion in oli ine o 1400 °C and 35 kba . in: Geochemical T anspo and Kine ics, Ca negie Ins i u ion o Washing on, Washing on, pp. 117-129 Mo ioka, M. (1980), Ca ion di usion in oli ine—I. Cobal and magnesium. Geochim Cosmochem Ac a 44:759- 762. doi: 10.1016/0016-7037(80)90165-9 Mosen elde , J.L., Ma on, F.C., Ross, C.R., Ke schho e , L., Rubie, D.C. (2001), Expe imen al cons ain s on he dep h o oli ine me as abili y in subduc ing li hosphe e. Phys Ea h Plane In e 127:165-180. doi: 10.1016/S0031-9201(01)00226-6 Nakamu a, A., Schmalz ied, H. (1983), On he nons oichiome y and poin de ec s o oli ine. Phys Chem Mine 10:27-37. doi: 10.1007/BF01204323 Nixon, P.H., Roge s, N.W., Gibson, I.L., G ey, A. (1981), Deple ed and Fe ile Man le Xenoli hs om Sou he n A ican Kimbe li es. Annu Re Ea h Plane Sci 9:285-309. doi: 10.1146/annu e .ea.09.050181.001441 Ogu i, K., Funamo i, N., Sakai, F., Kondo, T., Uchida, T., Yagi, T. (1997), High-p essu e and high- empe a u e phase ela ions in diopside CaMgSi2O6. Phys Ea h Plane In e 104:363-370. doi: 16/S0031-9201(97)00029-0 Oishi, Y., Ando, K., Ku okawa, H., Hi sco, Y. (1983), Oxygen Sel -Di usion in MgO Single C ys als. J Am Ce am Soc 66:C-60-C-62. doi: 10.1111/j.1151-2916.1983. b15695.x Ono, S., I o, E., Ka su a, T. (2001), Mine alogy o subduc ed basal ic c us (MORB) om 25 o 37 GPa, and chemical he e ogenei y o he lowe man le. Ea h and Plane a y Science Le e s 190:57-63. doi: 10.1016/S0012- 821X(01)00375-2 O man, J.A.V., Fei, Y., Hau i, E.H., Wang, J. (2003), Di usion in MgO a high p essu es: Cons ain s on de o ma ion mechanisms and chemical anspo a he co e-man le bounda y. Geophys Res Le 30:4 PP. doi: 200310.1029/2002GL016343 Pandey, A., Leech, M., Mil on, A., Singh, P., Ve ma, P.K. (2010), E idence o o me majo i ic ga ne in Himalayan eclogi e poin s o 200-km-deep subduc ion o Indian con inen al c us . Geology 38:399 -402. doi: 10.1130/G30584.1 Pe chuk, A.L., Bu cha d, M., Sche l, H.-P., Ma esch, W.V., Ge ya, T.V., Be nha d , H.-J., Vidal, O. (2008), Di usion o di alen ca ions in ga ne : mul i-couple expe imen s. Con ib Mine al Pe ol 157:573-592. doi: 10.1007/s00410-008-0353-6 Poi ie , J.-P. (1985), C eep o C ys als: High-Tempe a u e De o ma ion P ocesses in Me als, Ce amics and Mine als. Camb idge Uni e si y P ess, Camb idge Poi ie , J.P. (1981), On he kine ics o oli ine-spinel ansi ion. Phys Ea h Plane In e 26:179-187. doi: 10.1016/0031-9201(81)90006-6 Pu nis, A. (1992), An In oduc ion o Mine al Sciences. Camb idge Uni e si y P ess, Camb idge Ranalli, G. (2001), Man le heology: adial and la e al iscosi y a ia ions in e ed om mic ophysical c eep laws. J Geodyn 32:425-444. doi: 10.1016/S0264-3707(01)00042-4 Ranalli, G., Fische , B. (1984), Di usion c eep, disloca ion c eep, and man le heology. Phys Ea h Plane In e 34:77-84. doi: 10.1016/0031-9201(84)90086-4 Rigby, E.B., Cu le , I.B. (1965), In e di usion S udies o he Sys em FexO-MgO. J Am Ce am Soc 48:95-99. doi: 10.1111/j.1151-2916.1965. b11806.x Ringwood, A.E. (1956), The Oli ine-Spinel T ansi ion in he Ea h’s Man le. Na u e 178:1303-1304. doi: 10.1038/1781303a0 25 Ringwood, A.E. (1962), A Model o he Uppe Man le. J Geophys Res 67:PP. 857-867. doi: 196210.1029/JZ067i002p00857 Ringwood, A.E., Majo , A. (1966), Syn hesis o Mg2SiO4 – Fe2SiO4 spinel solid solu ions. Ea h Plane Sci Le 1:241-245. doi: 16/0012-821X(66)90077-X Ringwood, A.E., Majo , A. (1970), The sys em Mg2SiO4 – Fe2SiO4 a high p essu es and empe a u es. Phys Ea h Plane In e 3:89-108. doi: 16/0031-9201(70)90046-4 Ringwood, A.E., Majo , A. (1971), Syn hesis o majo i e and o he high p essu e ga ne s and pe o ski es. Ea h Plane Sci Le 12:411-418. doi: 10.1016/0012-821X(71)90026-4 Roe mund, H. an (2009), Man le-wedge ga ne pe ido i es om he no he nmos ul a-high p essu e domain o he Wes e n Gneiss Region, SW No way. Eu J Mine al 21:1085-1096. doi: 10.1127/0935-1221/2009/0021-1976 Rubie, D.C. (1984), The oli ine --> spinel ans o ma ion and he heology o subduc ing li hosphe e. Na u e 308:505-508. doi: 10.1038/308505a0 Rubie, D.C. (1990), Mechanisms o eac ion-enhanced de o mabili y in mine als and ocks. in: Ba be D.J., Me edi h P.G.(eds.) De o ma ion P ocesses in Mine als, Ce amics and Rocks, Unwin Hyman, London, pp. 262- 295 Rubie, D.C., Ross, C.R. (1994), Kine ics o he oli ine-spinel ans o ma ion in subduc ing li hosphe e: expe imen al cons ain s and implica ions o deep slab p ocesses. Phys Ea h Plane In e 86:223-243. doi: 10.1016/0031-9201(94)05070-8 Rye son, F.J., Du ham, W.B., Che niak, D.J., Lan o d, W.A. (1989), Oxygen Di usion in Oli ine: E ec o Oxygen Fugaci y and Implica ions o C eep. J Geophys Res 94(B4):4105-4118 Sa a, N., Go o, K.S. (1982), Oxygen-P essu e Dependence o Ca ion In e di usi i y in Magnesiowus i e Solid Solu ions. J Am Ce am Soc 65:158-162. doi: 10.1111/j.1151-2916.1982. b10386.x Sau e , V., Jaoul, O., Abel, F. (1988), Aluminum di usion in diopside using he 27Al(p,γ)28Si nuclea eac ion: p elimina y esul s. Ea h Plane Sci Le 89:109-114. doi: 10.1016/0012-821X(88)90036-2 Schmeling, H., Monz, R., Rubie, D.C. (1999), The in luence o oli ine me as abili y on he dynamics o subduc ion. Ea h Plane Sci Le 165:55-66. doi: 10.1016/S0012-821X(98)00249-0 Schwand , C.S., Cygan, R.T., Wes ich, H.R. (1995), Mg sel -di usion in py ope ga ne . Am Mine al 80:483 -490 Schwand , C.S., Cygan, R.T., Wes ich, H.R. (1996), Ca sel -di usion in g ossula ga ne . Am Mine al 81:448 -451 Schwand , C.S., Cygan, R.T., Wes ich, H.R. (1998), Magnesium sel -di usion in o hoens a i e. Con ib Mine al Pe ol 130:390-396. doi: 10.1007/s004100050373 Sha p, T.G., Rubie, D.C. (1995), Ca alysis o he Oli ine o Spinel T ans o ma ion by High Clinoens a i e. Science 269:1095 -1098. doi: 10.1126/science.269.5227.1095 Shimojuku, A., Kubo, T., Oh ani, E., Nakamu a, T., Okazaki, R., Dohmen, R., Chak abo y, S. (2009), Si and O di usion in (Mg,Fe)2SiO4 wadsleyi e and ingwoodi e and i s implica ions o he heology o he man le ansi ion zone. Ea h Plane Sci Le 284:103-112. doi: 10.1016/j.epsl.2009.04.014 Shimojuku, A., Kubo, T., Oh ani, E., Yu imo o, H. (2004), Silicon sel -di usion in wadsleyi e: Implica ions o heology o he man le ansi ion zone and subduc ing pla es. Geophys Res Le L13606 Sil e , P.G., Beck, S.L., Wallace, T.C., Meade, C., Mye s, S.C., James, D.E., Kuehnel, R. (1995), Rup u e Cha ac e is ics o he Deep Boli ian Ea hquake o 9 June 1994 and he Mechanism o Deep-Focus Ea hquakes. Science 268:69 -73. doi: 10.1126/science.268.5207.69 Sipling, P.J., Yund, R.A. (1973), Kine ics o Al/Si diso de ing in alkali eldspa s. 185-193 26 Song, S., zhang, L., Niu, Y. (2004), Ul a-deep o igin o ga ne pe ido i e om he No h Qaidam ul ahigh- p essu e bel , No he n Tibe an Pla eau, NW China. Am Mine al 89:1330-1336 S e on, I., Heidelbach, F., Mackwell, S., Langenho s , F. (2001), Disloca ion c eep o magnesiowüs i e (Mg0.8Fe0.2O). Ea h Plane Sci Le 194:229-240. doi: 10.1016/S0012-821X(01)00533-7 Sung, C.-M., Bu ns, R.G. (1976), Kine ics o high-p essu e phase ans o ma ions: Implica ions o he e olu ion o he oli ine spinel ansi ion in he downgoing li hosphe e and i s consequences on he dynamics o he→ man le. Tec onophysics 31:1-32. doi: 10.1016/0040-1951(76)90165-7 Tsai, T.-L., Dieckmann, R. (2002), Va ia ion o he oxygen con en and poin de ec s in oli ines, (FexMg1−x)2SiO4, 0.2 ≤ x ≤ 1.0. Phys Chem Mine 29:680-694. doi: 10.1007/s00269-002-0283-1 Vaughan, P.J., Coe, R.S. (1981), C eep mechanism in Mg2GeO4: E ec s o a phase ansi ion. J Geophys Res 86:389-404. doi: 198110.1029/JB086iB01p00389 Vielzeu , D., Ba onne , A., Pe chuk, A.L., Lapo e, D., Bake , M.B. (2007), Calcium di usi i y in alumino-silica e ga ne s: an expe imen al and ATEM s udy. Con ib Mine al Pe ol 154:153-170. doi: 10.1007/s00410-007-0184-x Wa son, E.B., Dohmen, R. (2010), Non- adi ional and Eme ging Me hods o Cha ac e izing Di usion in Mine als and Mine al Agg ega es. Re Mine al Geochem 72:61 -105. doi: 10.2138/ mg.2010.72.3 Wee man, J., Whi e, S., Cook, A.H. (1978), C eep Laws o he Man le o he Ea h [and Discussion]. Phil T ans R Soc A 288:9 -26. doi: 10.1098/ s a.1978.0003 Wiens, D.A., McGui e, J.J., Sho e, P.J. (1993), E idence o ans o ma ional aul ing om a deep double seismic zone in Tonga. Na u e 364:790-793. doi: 10.1038/364790a0 Wiens, D.A., McGui e, J.J., Sho e, P.J., Be is, M.G., D aunidalo, K., P asad, G., Helu, S.P. (1994), A deep ea hquake a e shock sequence and implica ions o he up u e mechanism o deep ea hquakes. Na u e 372:540-543. doi: 10.1038/372540a0 Wiens, D.A., Snide , N.O. (2001), Repea ing Deep Ea hquakes: E idence o Faul Reac i a ion a G ea Dep h. Science 293:1463 -1466. doi: 10.1126/science.1063042 Wilson, B.M. (2007), Igneous Pe ogenesis A Global Tec onic App oach. Sp inge W igh , K., P ice, G.D. (1993), Compu e Simula ion o De ec s and Di usion in Pe o ski es. J Geophys Res 98:22 Yamazaki, D., I i une, T. (2003), Fe–Mg in e di usion in magnesiowüs i e up o 35 GPa. Ea h Plane Sci Le 216:301-311. doi: 10.1016/S0012-821X(03)00534-X Yamazaki, D., Ka o, T., Yu imo o, H., Oh ani, E., To iumi, M. (2000), Silicon sel -di usion in MgSiO3 pe o ski e a 25 GPa. Phys Ea h Plane In e 119:299-309. doi: 10.1016/S0031-9201(00)00135-7 Zhang, X., Ganguly, J., I o, M. (2009), Ca–Mg di usion in diopside: ace and chemical in e -di usion coe icien s. Con ib Mine al Pe ol 159:175-186. doi: 10.1007/s00410-009-0422-5 27 Chap e 2: Ga ne s and di usion kine ics 2.1 Ga ne s and majo i e, a high p essu e polymo ph o ens a i e 2.1.1 Ga ne Ga ne mine als o m an impo an g oup o ock o ming mine als. Since na u al ga ne s a e me as able a ambien condi ions, hey a e only ound a he Ea h's su ace in me amo phic e anes o amphiboli e acies and highe g ade. This pa ag aph summa izes he mos impo an p ope ies o na u al ga ne s, o a mo e comp ehensi e discussion he eade is e e ed o Gelle (1967), Rickwood (1968) and No ak and Gibbs (1971). Mos o he in o ma ion in his pa ag aph can be ound in hese e e ences, unless s a ed o he wise. Na u al ga ne s a e o en desc ibed in e ms o end-membe componen s, which a e lis ed in able 2.1 . The space g oup o na u al ga ne is Ia3d, which is one o he cubic B a ais la ices, and he uni cell con ains 8 o mula uni s (160 a oms). I s la ice pa ame e s depend on composi ion (and physical condi ions), bu ange a ambien condi ions be ween a = 11.4 Å o py ope o a = 12.7 Å o he (hypo he ical) end-membe hyd og ossula . The 96 oxygen a oms in ga ne occupy he h-posi ion in his uni cell, and he me al ca ions ei he occupy he 16 a- posi ions (oc ahed al si es), 24 c-posi ions (dodecahed al si es) o 24 d-posi ions ( e ahed al si es). Though na u al ga ne s ha e 96 oxygen a oms and 64 me al ca ions in i s uni cell, i can con enien ly be desc ibed by he gene al chemical o mula X3Y2Z3O12. The X me al ca ions (Mg, Fe2+, Ca and Mn) occupy he dis o ed cubic c si es o ga ne s, he Y me allic ca ions (Al3+, Fe3+, C 3+) occupy he oc ahed al si es, and he Z me allic ca ions (mos ly Si4+) occupy he e ahed al si es. The e ahed a sha e wo edges wi h he neighbou ing dodecahed a, he oc ahed a sha e six edges wi h neighbou ing dodecahed a and he dodecahed a sha e wo edges wi h neighbou ing e ahed a, ou wi h neighbou ing and ou wi h o he neighbou ing dodecahed a ( igu e 2.1). Since ga ne is a common mine al in high p essu e me amo phic e anes and i s end-membe s o m a comple e solid-solu ion wi h each o he , hey a e o en used when in equilib ium wi h o he phases as geo he mome e s. O'Neill and Wood (1979) calib a ed a he mome e o he Mg-Fe exchange be ween ga ne and oli ine, and geo he mome e we e de eloped o Fe-Mg exchange be ween ga ne and bio i e (Holdaway 2000), be ween clinopy oxene and ga ne (Ellis and G een 1979, Powell 1985)., and be ween o hopy oxene and ga ne (Ha ley 1984). Nex o i s use as a geo he mome e , ga ne is also o en used as a geoch onome e da ing me amo phic e en , using he Lu-H , Sm-Nd and U-Pb sys ems. The e o e, ga ne cons i u e an 28 Table 2.1: Chemical composi ion o he mos impo an ga ne end-membe s. End-membe name Chemical o mula Py ope Mg3Al2Si3O12 Almandine Fe2+3Al2Si3O12 G ossula Ca3Al2Si3O12 Spessa ine Mn3Al2Si3O12 And adi e Ca3Fe3+2Si3O12 U a o i e Ca3C 2Si3O12 Skiagi e Fe2+3Fe3+2Si3O12 Hyd og ossula Ca3Al2H12O12 Hyd oand adi e Ca3Fe3+2H12O12 3FeFe+½O2(gas)⇋2FeFe +VFe '' +FeO (2.8) o which he equilib ium cons an can be w i en as: K=[FeFe ]2[VFe ' ' ]aFeO O2 ½ (2.9) Whe e [ ] deno es he concen a ions o he eac an s. Subsc ip s in he wo abo e equa ions deno e he si e ha is occupied by he ion (V o acancy) and he supe sc ip deno es he elec ical cha ge o he si e. A solid ci cle deno es ha he si e is posi i ely cha ged (e e y solid ci cle co esponds o an elec on hole), a p ime deno es a nega i ely cha ged si e (e e y p ime co esponds o a su plus elec on). F om equa ion 2.8 i can be seen ha [Fe•Fe] = 2 [V''Fe] and assuming ha ac i i y o FeO does no change signi ican ly wi h oxygen ugaci y O2 hey w i e he concen a ion o i on o me al acancies as unc ion o oxygen ugaci y as: [VFe ' ' ]∝ O2 1/6 (2.10) This mechanism equi es ha Fe3+ can be accommoda ed on an Fe2+ si e, which migh be ques ionable o no mal ga ne s, since as o ye , he e is no con incing e idence ha Fe3+ can occupy he dodecahed al si e in ga ne (C. McCammon, pe s. comm.). Howe e , o majo i ic ga ne i has been ound ha he e is cha ge ans e be ween adjacen docecahed ally coo dina ed Fe2+ and oc ahed al coo dina ed Fe3+ (Kepple and McCammon 1996), so he dodecahed ally coo dina ed Fe3+ ion (di ec ly a e oxida ion) migh ecei e an elec on om i s neighbou ing oc ahed ally coo dina ed Fe2+ ion, e ec i ely exchanging i s 3+ cha ge wi h he 2+ cha ge o i s oc ahed al neighbou . Howe e he s ong pa i ioning be ween Mg and Fe on he oc ahed al si e in majo i e, wi h Mg p e e en ially on he oc ahed al si e (O’Neill e al. 1993), migh inhibi his mechanism. Also he p esence o oc ahed ally coo dina ed e ous i on in majo i e migh enable he abo e men ioned mechanism a highe p essu e. Mackwell e al. (2005) de eloped he ollowing gene al exp ession based upon poin de ec chemis y:  D=DV 0e−Qm/RT  k1 0k2 0 O2 mxpe−Q  x/ RT  (2.11) whe e k01 and k02 a e equilib ium cons an s o he in insic and ex insic acancy mechanisms espec i ely, m and p a e cons an s depending on he acancy mechanism (1/6 o equa ion 2.8), Qm is he mig a ion en halpy o a me al acancy, Q he o ma ion en halpy o me al acancies a low i on concen a ions, x is he i on concen a ion and he e m -α·x in he exponen ial co ec s o change in o ma ion en halpy a highe i on and acancy le els. 2.2.5 Mul i-componen models When mo e han one componen o elemen is di using a he same ime, as a esul o mass conse a ion and om he Gibbs-Duhem equa ion, hei luxes ha e o be coupled. I e e sible he modynamics shows ha luxes can o en be linea ly ela ed o hei d i ing o ces (G oo and Mazu 1984). In he absence o empe a u e g adien s and ex e nal o ces he d i ing o ce o di usion in an n-componen sys em becomes 35 he g adien in chemical po en ial μi o he componen s (G oo and Mazu 1984, Ganguly 2002): Ji=−∑ k n−1 Lik  ∇k−n T  (2.12) Whe e L is a ma ix o phenomenological coe icien s. The las lux is calcula ed conside ing conse a ion o mass. In he case ha he o diagonal elemen s in L can be neglec ed he equa ion leads o he ollowing exp ession o he di usion coe icien Di: Di=Di +  1∂ln i ∂ln Ci  (2.13a) whe e γi is he ac i i y coe icien and Di +=RLi Ci (2.13b) whe e R is he gas cons an . Equa ion (2.13a) spli s he chemical di usion coe icien in wo pa s, an ideal pa and a he modynamic pa , he pa wi hin b acke s is usually e e ed o he he modynamic ac o . No e ha al hough o diagonal e ms in L a e negligible, he di usion coe icien s and luxes s ill coupled h ough he ac i i y coe icien s. In he case ha he o diagonal e ms in L a e no negligible one needs o ew i e (2.1) as: Ji=−∑ j Dij ∇Cj (2.14) Loomis (1978) de i ed an exp ession o he di usion coe icien ma ix D om i e e sible he modynamics: Dij=ij Di 0Di 0Xi [ ∂ln i ∂Xj −∂ln i ∂Xn ] −Xi∑ k=1 n−1 XkDk 0−Dn 0 [ jk Xk ∂ln k ∂Xj −∂ln k ∂Xn ] (2.15a) δij is k onecke 's del a (δij = 0 o i ≠ j, δij = 1 o i = j) and Di0 deno es he ace di usion coe icien o componen i. In he case o ideal solu ions his educes o: Dij=ij Di 0XiDn 0−Dj 0 (2.15b) Lasaga (1979) de i ed, also om i e e sible he modynamics, a di e en exp ession o he D ma ix in he case o ionic di usion, which is mo e app op ia e o mine als: Dij=Di 0ijDi 0ci [ ∂ln i ∂cj −∂ln i ∂cn ⋅zj zn ] −  Di 0zici ∑ k=1 n zk 2ckDk 0  × { zjDj 0−Dn 0∑ k=1 n zkckDk 0 [ ∂ln k ∂cj −∂ln k ∂cn ⋅zi zn ] } (2.16a) which educes o (nea ) ideal solu ions o negligible ac i i y coe icien g adien s o a mo e comp ehensible o m: 36 Dij=Di 0ij−Di 0zizj ∑ k=1 n zk 2ckDk 0 ⋅ Dj 0−Dn 0 (2.16b) In he equa ions zi is he cha ge o ion i and he size o he di usion ma ix D is (n – 1)x(n – 1), he las p o ile is calcula ed by cha ge balance. In he case ha he e a e only wo ions di using, bo h wi h an equal cha ge, equa ion 2.10b becomes he well known exp ession o bina y in e di usion o cha ged species (Manning 1968): D11=Dbina y ionic =D1 0D2 0 X1D1 0X2D2 0 (2.17) whe e Xi is he ca ion mole ac ion o ca ion i, i.e. X1 = c1 / (c1 + c2). Chak abo y and Ganguly (1992) used he ideal Lasaga model success ully o model Fe – Mg – Mn di usion p o iles in ga ne and o ob ain ace di usion coe icien s o Fe, Mg and Mn. The alidi y o he model o ga ne s was con i med by a Mg ace di usion s udy on ga ne by Chak abo y and Rubie (1996). 2.3 Re e ences Akaogi, M., Akimo o, S. (1977), Py oxene-ga ne solid-solu ion equilib ia in he sys ems Mg4Si4O12 – Mg3Al2Si3O12 and Fe4Si4O12 – Fe3Al2Si3O12 a high p essu es and empe a u es. Phys Ea h Plane In e 15:90- 106. doi: 10.1016/0031-9201(77)90013-9 Ande sen, T.B. (2010), Excu sion Guide, Wes e n No way 3-4 June 2010. Bu ial and exhuma ion o High and Ul a-High-P essu e Rocks. Angel, R.J., Finge , L.W., Hazen, R.M., Kanzaki, M., Weidne , D.J., Liebe mann, R.C., Veblen, D.R. (1989), S uc u e and winning o single-c ys al MgSiO3 ga ne syn hesized a 17 GPa and 1800 °C. Am Mine al 74:509- 512 Chak abo y, S., Ganguly, J. (1992), Ca ion di usion in aluminosilica e ga ne s: expe imen al de e mina ion in spessa ine-almandine di usion couples, e alua ion o e ec i e bina y di usion coe icien s, and applica ions. Con ib Mine al Pe ol 111:74-86. doi: 10.1007/BF00296579 Chak abo y, S., Rubie, D.C. (1996), Mg ace di usion in aluminosilica e ga ne s a 750-850° C, 1 a m. and 1300° C, 8.5 GPa. Con ib Mine al Pe ol 122:406-414. doi: 10.1007/s004100050136 Ellis, D.J., G een, D.H. (1979), An expe imen al s udy o he e ec o Ca upon ga ne -clinopy oxene Fe-Mg exchange equilib ia. Con Mine al Pe ol 71:13-22. doi: 10.1007/BF00371878 F os , D.J. (2008), The Uppe Man le and T ansi ion Zone. Elemen s 4:171-176 Ganguly, J. (2002), Di usion kine ics in mine als: P inciples and applica ions o ec ono-me amo phic p ocesses. in: G amaccioli C.M.(ed.) Ene gy Modelling in Mine als, EMU no es in mine alogy 4, Eu opean Mine alogical Union, Vienna 37 Gaspa ik, T. (2003), Phase diag ams o geoscien is s: an a las o he ea h’s in e io . Sp inge , Heidelbe g- Be lin Gelle , S. (1967), C ys al chemis y o he ga ne s. Z K is allog 125:1-47 G oo , S.R.D., Mazu , P. (1984), Non-Equilib ium The modynamics. Do e Publica ions Hacke , B.R., Ande sen, T.B., Johns on, S., Kylande -Cla k, A.R.C., Pe e man, E.M., Walsh, E.O., Young, D. (2010), High- empe a u e de o ma ion du ing con inen al-ma gin subduc ion & exhuma ion: The ul ahigh- p essu e Wes e n Gneiss Region o No way. Tec onophysics 480:149-171. doi: 10.1016/j. ec o.2009.08.012 Hacke , B.R., Ande sen, T.B., Roo , D.B., Mehl, L., Ma inson, J.M., Wooden, J.L. (2003), Exhuma ion o high- p essu e ocks benea h he Solund Basin, Wes e n Gneiss Region o No way. J Me amo ph Geol 21:613-629. doi: 10.1046/j.1525-1314.2003.00468.x Ha ley, S.L. (1984), An expe imen al s udy o he pa i ioning o Fe and Mg be ween ga ne and o hopy oxene. Con ib Mine al Pe ol 86:359-373. doi: 10.1007/BF01187140 Heinemann, S. (1996), De Phasenüne gang kubisch - e agonal im Sys em de G ana e Majo i (Mg4Si4O12) - Py op (Mg3Al2Si3O12). Bay eu h Heinemann, S., Sha p, T.G., Sei e , F., Rubie, D.C. (1997), The cubic- e agonal phase ansi ion in he sys em majo i e (Mg4Si4O12) – py ope (Mg3Al2Si3O12), and ga ne symme y in he Ea h’s ansi ion zone. Phys Chem Mine 24:206-221. doi: 10.1007/s002690050034 Holdaway, M.J. (2000), Applica ion o new expe imen al and ga ne Ma gules da a o he ga ne -bio i e geo he mome e . Am Mine al 85:881-892 I i une, T. (1987), An expe imen al in es iga ion o he py oxene-ga ne ans o ma ion in a py oli e composi ion and i s bea ing on he cons i u ion o he man le. Phys Ea h Plane In e 45:324-336. doi: 10.1016/0031-9201(87)90040-9 Ka o, T., Kumazawa, M. (1985), Ga ne phase o MgSiO3 illing he py oxene-ilmeni e gap a e y high empe a u e. Na u e 316:803-805. doi: 10.1038/316803a0 Kepple , H., McCammon, C.A. (1996), C ys al ield and cha ge ans e spec um o (Mg, Fe)SiO3 majo i e. Phys Chem Mine 23: doi: 10.1007/BF00202304 Ki el, C. (2005), In oduc ion o solid s a e physics. Wiley, New Yo k Lasaga, A.C. (1979), Mul icomponen exchange and di usion in silica es. Geochem Cosmochem Ac a 43:455- 469. doi: 10.1016/0016-7037(79)90158-3 Lasaga, A.C. (1983), Geospeedome y: An Ex ension o Geo he mome y. in: Saxena S.K.(ed.) Kine ics and Equilib ium in Mine al Reac ions, Ad ances in Physical Geochemis y pp. 81-114 Lasaga, A.C., Jiang, J. (1995), The mal his o y o ocks; P-T- pa hs o geospeedome y, pe ologic da a, and 38 in e se heo y echniques. Am J Sci 295:697-741. doi: 10.2475/ajs.295.6.697 Loomis, T.P. (1978), Mul icomponen di usion in ga ne ; I, Fo mula ion o iso he mal models. Am J Sci 278:1099-1118 Mackwell, S., Bys icky, M., Sp oni, C. (2005), Fe–Mg In e di usion in (Mg,Fe)O. Phys Chem Mine 32:418-425. doi: 10.1007/s00269-005-0013-6 Manning, J.R. (1968), Di usion kine ics o a oms in c ys als. Van Nos and, P ince on Mason, B., Nelen, J., Whi e, J.S. (1968), Oli ine-Ga ne T ans o ma ion in a Me eo i e. Science 160:66 -67. doi: 10.1126/science.160.3823.66 Meh e , H. (2005), Di usion: In oduc ion and Case S udies in Me als and Bina y Alloys. in: Hei jans P., Kä ge J. (eds.) Di usion in Condensed Ma e : me hods, ma e ials, models, Sp inge , pp. 3-65 Mo ioka, M., Nagasawa, H. (1991), Ionic Di usion in Oli ine. in: Ganguly J.(ed.) Di usion, A omic O de ing and Mass T anspo , Ad ances in Physical Geochemis y 8, Sp inge -Ve lag, New Yo k, p. No ak, G.A., Gibbs, G.V. (1971), The c ys al chemis y o he silica e ga ne s. Am Mine al 56:791-825 O’Neill, H.S.C., McCammon, C.A., Canil, D., Rubie, D.C., Ross, C.R., Sei e , F. (1993), Mössbaue spec oscopy o man le ansi ion zone phases and de e mina ion o minimum Fe3+ con en . Am Mine al 78:456-461 O’Neill, H.S.C., Wood, B.J. (1979), An expe imen al s udy o Fe-Mg pa i ioning be ween ga ne and oli ine and i s calib a ion as a geo he mome e . Con ib Mine al Pe ol 70:59-70. doi: 10.1007/BF00371872 Pandey, A., Leech, M., Mil on, A., Singh, P., Ve ma, P.K. (2010), E idence o o me majo i ic ga ne in Himalayan eclogi e poin s o 200-km-deep subduc ion o Indian con inen al c us . Geology 38:399 -402. doi: 10.1130/G30584.1 Powell, R. (1985), Reg ession diagnos ics and obus eg ession in geo he mome e /geoba ome e calib a ion: he ga ne -clinopy oxene geo he mome e e isi ed. J Me amo ph Geol 3:231-243. doi: 10.1111/j.1525- 1314.1985. b00319.x Rich e , F.M., Da is, A.M., DePaolo, D.J., Wa son, E.B. (2003), Iso ope ac iona ion by chemical di usion be ween mol en basal and hyoli e. Geochem Cosmochem Ac a 67:3905-3923. doi: 10.1016/S0016- 7037(03)00174-1 Rickwood, P.C. (1968), On ecas ing analyses o ga ne in o end-membe molecules. Con ib Mine al Pe ol 18:175-198. doi: 10.1007/BF00371808 Ringwood, A.E., Majo , A. (1966), High-p essu e ans o ma ions in py oxenes. Ea h Plane Sci Le 1:351-357. doi: doi: DOI: 10.1016/0012-821X(66)90023-9 Roe mund, H. an (2009), Man le-wedge ga ne pe ido i es om he no he nmos ul a-high p essu e domain o he Wes e n Gneiss Region, SW No way. Eu J Mine al 21:1085-1096. doi: 10.1127/0935-1221/2009/0021-1976 39 Roe mund, Van, D u y (1998), Ul a-high p essu e (P > 6 GPa) ga ne pe ido i es in Wes e n No way: exhuma ion o man le ocks om > 185 km dep h. Te a No a 10:295-301. doi: 10.1046/j.1365- 3121.1998.00213.x Roe mund, Van, D u y, Ba nhoo n, Ronde, De (2000), Supe -silicic ga ne mic os uc u es om an o ogenic ga ne pe ido i e, e idence o an ul a-deep (>6 GPa) o igin. J Me amo ph Geol 18:135-147. doi: 10.1046/j.1525- 1314.2000.00251.x Sau e , V., Ha e, B. (1990), Di usion g adien s in an eclogi e xenoli h om he Robe s Vic o kimbe li e pipe: (2) kine ics and implica ions o pe ogenesis. Con ib Mine al Pe ol 105:637-649. doi: 10.1007/BF00306530 Scambellu i, M., Pe ke, T., Roe mund, H.L.M. an (2008), Majo i ic ga ne s moni o deep subduc ion luid low and man le dynamics. Geology 36:59-62. doi: 10.1130/G24056A.1 Schmalz ied, H. (1981), Solid s a e eac ions. Ve lag Chemie, Weinheim/Be gs . [Wes Ge many] Smi h, J.V., Mason, B. (1970), Py oxene-Ga ne T ans o ma ion in Coo a a Me eo i e. Science 168:832 -833. doi: 10.1126/science.168.3933.832 Song, S.G., Yang, J.S., Xu, Z.Q., Liou, J.G., Shi, R.D. (2003), Me amo phic e olu ion o he coesi e-bea ing ul ahigh-p essu e e ane in he No h Qaidam, No he n Tibe , NW China. J Me amo ph Geol 21:631-644. doi: 10.1046/j.1525-1314.2003.00469.x Song, S., zhang, L., Niu, Y. (2004), Ul a-deep o igin o ga ne pe ido i e om he No h Qaidam ul ahigh- p essu e bel , No he n Tibe an Pla eau, NW China. Am Mine al 89:1330-1336 Spengle , D. (2006), O igin and E olu ion o Deep Uppe Man le Rocks om Wes e n No way. PhD Thesis, U ech Spengle , D., B ueckne , H.K., Roe mund, H.L.M. an, D u y, M.R., Mason, P.R.D. (2009), Long-li ed, cold bu ial o Bal ica o 200 km dep h. Ea h Plane Sci Le 281:27-35. doi: doi: DOI: 10.1016/j.epsl.2009.02.001 Spengle , D., Roe mund, H.L.M. an, D u y, M.R., O olini, L., Mason, P.R.D., Da ies, G.R. (2006), Deep o igin and ho mel ing o an A chaean o ogenic pe ido i e massi in No way. Na u e 440:913-917. doi: 10.1038/na u e04644 Teng, F.-Z., McDonough, W.F., Rudnick, R.L., Walke , R.J. (2006), Di usion-d i en ex eme li hium iso opic ac iona ion in coun y ocks o he Tin Moun ain pegma i e. Ea h Plane Sci Le 243:701-710. doi: 10.1016/j.epsl.2006.01.036 V ijmoed, J.C., Roe mund, H.L.M. Van, Da ies, G.R. (2006), E idence o diamond-g ade ul a-high p essu e me amo phism and luid in e ac ion in he S a be ge Fe–Ti ga ne pe ido i e–webs e i e body, Wes e n Gneiss Region, No way. Mine al Pe ol 88:381-405. doi: 10.1007/s00710-006-0160-6 Ye, K., Cong, B., Ye, D. (2000), The possible subduc ion o con inen al ma e ial o dep hs g ea e han 200 km. Na u e 407:734-736. doi: 10.1038/35037566 40 Chap e 3: Expe imen al and analy ical echniques 3.1 High p essu e – high empe a u e expe imen s To simula e ac ual geological p ocesses ha a e occu ing in he Ea h's uppe man le and ansi ion zone one needs o ep oduce he condi ions p e alen he e. I is usually assumed ha hea anspo due o he mal conduc ion is negligible in he Ea h's man le (Fowle 2005). The empe a u e p o ile in he man le can hus be well app oxima ed by an adiaba ic empe a u e p o ile o which he empe a u e g adien as a unc ion o dep h is gi en by (Fowle 2005):  ∂T ∂  S =−Tg Cp (3.1) whe e T is empe a u e, α is he coe icien o he mal expansion o he bulk man le, g accele a ion due o g a i y and Cp he hea capaci y a cons an p essu e. The igu e below shows h ee di e en man le adiaba s o di e en po en ial empe a u es, i.e. he empe a u e o he adiaba ex apola ed o he su ace, hough o be ep esen a i e o he Ea h's p esen man le (McKenzie and Bickle 1988, Ande son 2000, Fowle 2005, Ka su a e al. 2010). To simula e he condi ions p e alen in he man le ansi ion zone one hus needs a de ice o gene a e p essu es in he ange o 15 – 24 GPa (ca. 410 – 670 km) and empe a u es in he ange o 1450 – 1800 °C. Two di e en de ices a e gene ally used o each hese condi ions, i.e. he diamond an il cell and he mul i-an il appa a us. The las de ice has been used o his disse a ion and is he e o e explained in mo e de ail below. 41 Figu e 3.1:The man le adiaba calcula ed o h ee di e en po en ial empe a u es ( empe a u es ex apola ed o he Ea h's su ace). The he mal expansion coe icien is aken om Ka su a e al. (2010) and app oxima ed by an exponen ially decaying unc ion as unc ion o dep h. 3.1.1 The Mul i-an il appa a us High p essu e de ices can gene a e high p essu es ollowing wo di e en app oaches which can be unde s ood om he gene al equa ion o p essu e: p=F A (3.2) whe e p is p essu e, F is o ce and A is he su ace a ea o e which he o ce is applied. The i s app oach would be o apply a easonable o ce o e a e y small su ace a ea, an example o such a de ice is he diamond an il cell (DAC). The down side o his ype o de ices is ha he sample olume is also e y small, which migh pose a p oblem wi h analy ical echniques, and la ge p essu e and empe a u e g adien s exis in a DAC. The second app oach is o gene a e a la ge o ce and apply his on a ( easonable) small su ace a ea. Such a de ice is he mul i – an il p ess, which was used in his di usion s udy. The sample olume ha can be used in he mul i-an il appa a us is conside ably la ge han ha o he DAC, and in addi ion i gene a es mo e hyd os a ic condi ions and empe a u e g adien s wi hin he assembly a e smalle (I o 2007).The down side o he mul i-an il appa a us is ha in-si u measu emen s a e mo e complica ed han in he DAC, and gene ally equi e a high b illiance x- ay sou ce like a synch o on in he case o a s udy equi ing x- ays (Kepple and F os 2005). The i s mode n mul i-an il de ice used in mos labo a o ies now, was designed by Kawai and Endo (1970). I consis ed o a 6 / 8 ype spli -sphe e mul i-an il de ice. This means ha a se o six ha dened s eel ou e an ils ha o m a sphe e when assembled we e used as i s s age an ils. The six ou e an ils a e unca ed in such a way, ha in he cen e o he sphe e hey c ea e a cubic ca i y. In his cubic ca i y a se o eigh second s age ungs en ca bide an ils a e pu . Each o he eigh WC cubes has (a leas ) one o i s co ne s unca ed. Assembled, hese WC cubes o m an oc ahed al ca i y in i s cen e in which he p essu e medium wi h he 42 Figu e 3.2: ske ch o he 6 / 8 spli -sphe e design inco po a ed in a me al guide block. The op and lowe pa o he i s s age an ils a e unca ed o inhibi o a ion o he an ils. The MgO p essu e cell has been pu in he cen e o he 8 WC cube second s age an ils, wi h unca ed co ne s. expe imen al load is placed. In he o iginal design o Kawai and Endo he sphe ical assembly was con ained in a ubbe shell and hen subme ged in an oil ese oi . This oil ese oi was p essu ized and he p essu e exe ed by he oil ese oi is hen ansmi ed and concen a ed by he an ils on he oc ahed al p essu e medium con ained wi hin he oc ahed al ca i y c ea ed by he WC an ils. In la e designs he oil ese oi was eplaced by guide blocks in which he lowe and uppe hal o he sphe ical an il assembly was placed, g ea ly educing he cumbe some p epa a ion o he expe imen s (Kawai e al. 1973). The uppe and lowe guide blocks a e d i en oge he by a uni-axial hyd aulic p ess. The hyd os a ic condi ions in his case mus be p o ided by using app op ia e p essu e media. In la e designs he op and lowe pa s o he i s s age an ils we e unca ed in o de o inhibi he o a ion o he an ils (Kepple and F os 2005). Using adi ional WC an ils he maximum a ainable p essu es a e a ound 28 – 30 GPa, which is su icien o he uppe man le, ansi ion zone and op pa o he lowe man le. Highe p essu es howe e , can be ob ained by using sin e ed diamond an ils, which a e also mo e cos ly. Recen ly, p essu es up o 90 GPa ha e been eached using a mul i-an il appa a us equipped wi h sin e ed diamond second s age an ils (I o e al. 2010). The ca i y in he second s age an ils is illed wi h a (usually) MgO p essu e cell, which needs o be longe han he unca ion leng hs o he WC an ils o gene a e he high p essu e condi ions. The maximum a ainable p essu e is dependen on he a io o oc ahed al edge leng h o unca ion edge leng h and hei absolu e sizes, he comp essibili y o he p essu e medium, he esis ance o plas ic de o ma ion o he an ils, he sealing ac ion o he gaske ma e ial, and he maximum load o he p ess. As he p essu e medium will ge comp essed du ing loading, he p essu e medium will be ex uded ou o he oc ahed al ca i y, o ming a gaske . Usually an addi ional se o py ophylli e gaske s ips a e placed a ound he oc ahed al ca i y, o gi e be e la e al suppo o he second s age an il assembly and o p e en blow-ou s (I o 2007). A high loads mos o he applied o ce by he p ess will be pu in ex uding he gaske ma e ial, and hus educing he p essu e gene a ing e iciency o he p ess and he de o ma ion p ope ies o he gaske is hus an impo an ac o in de e mining he maximum a ainable p essu e (I o 2007). In he ea ly designs o Kawai and Endo (1970) and Kawai e al.(1973) he used p essu e medium was py ophylli e (Al2Si4O10(OH)2), which is a phyllosilica e mine al. Howe e , py ophylli e b eaks down abo e 600 °C and 10 GPa successi ely in o s isho i e + an unknown hyd ous aluminosilica e and s isho i e + Al5Si5O17(OH) and abo e 20 GPa in o s isho i e + co undum, which esul ed in a educ ion o p essu e du ing high p essu e uns (I o 2007). Nowadays, semi-sin e ed MgO (wi h a po osi y o ~ 35%) is being used as p essu e media. Unde high empe a u es MgO has a e y low shea s eng h and hus gene a es a good hyd os a ic p essu e egime (Kepple and F os 2005). Th ough he cen e o one o he aces o he oc ahed on a cylind ical hole is d illed in which a hollow cylinde o Z O2 is pu su ounding he hea e . The ole o he Z O2 cylinde is o he mally isola e he esis ance hea e , since he he mal conduc i i y o MgO is high, making i e y di icul o hea he expe imen abo e 1000 °C wi hou he he mal insula o . Di e en ma e ials can unc ion as hea e , he mos common being a me al oil (e.g. pla inum o henium), LaC O3, TiC3 / diamond mix u e o g aphi e hea e . A he Baye isches Geoins i u usually LaC O3 hea e s we e used. LaC O3 also educes empe a u e g adien s wi hin 43 he u nace because o i s nega i e esis ance dependence on empe a u e, especially o smalle p essu e cells (Kawashima and Yagi 1988). Fu he educ ion o empe a u e g adien s inside he u nace can be achie ed by using a s epped hea e , whe e he hea e consis s o h ee cylinde s o which he hickness o he wall o he middle one is g ea e han he ou e ones (Kawashima e al. 1990). The empe a u e is measu ed by he mocouples in he mul i-an il appa a us. The mocouples wo k because he mal g adien s in (semi-)conduc o s induce an elec os a ic po en ial di e ence be ween he ho and cold end, also known as he Seebeck e ec . I wo conduc o s (o me al) wi h di e en Seebeck coe icien s a e used o c ea e a ci cui , an elec ical cu en will s a o low, o which he magni ude is dependen on he ac ual empe a u e g adien along he he mocouple wi e. The mocouples used in he mul i-an il usually consis o W3%Re – W25%Re he mocouple wi es o W5%Re – W26%Re he mocouple wi es because o hei high mel ing poin s and he small p essu e e ec o he mocouple ol age on p essu e, which is unknown quan i a i ely (Kepple and F os 2005). The he mocouple can be inco po a ed in wo ways in he oc ahed al p essu e cell. The i s way, and as used in he di usion s udy in his disse a ion, he he mocouple is pu close o he capsule 44 Figu e 3.3: Two ske ches o he MgO p essu e cell used in he mul i-an il appa a us. a) P essu e cell wi h whe e he he mocouple is b ough in adially. b) P essu e cell whe e he he mocouple is b ough in axially. The o me one is used a he Baye isches Geoins i u o smalle assemblies. a b 200 kV ( hough high ol age TEMs go up o 3 MeV), which would hus co espond o a wa eleng h o 4.2 pm and 2.5 pm espec i ely. To compa e, he adius o a silicon a om is 111 pm (1.1 Å). Since high ene gy elec ons canno be ocused by glass lenses ( hey would be abso bed and backsca e ed like in he case o bulk samples), magne ic lenses a e used in a TEM. Those lenses consis o a hollow cylind ically symme ic so magne ic co e, i.e. he co e is easily magne ized and demagne ized, su ounded by a coppe coil which gene a es a adially symme ic magne ic ield when a cu en lows h ough i . The objec i e lens is he mos impo an and complica ed lens in he TEM since i p oduces he image and di ac ion pa e n, which he o he image o ming lenses me ely magni y (Williams and Ca e 2009). 3.2.3 Elas ic sca e ing wi hin he specimen As he elec ons en e he specimen hey will in e ac wi h he elec os a ic po en ial o he specimen la ice, esul ing in elas ic sca e ing o he inciden elec ons. This kind o sca e ing is associa ed wi h only a negligible loss o ene gy o he inciden elec on beam. The o he kind o sca e ing, inelas ic sca e ing, whe e he e is a signi ican ans e o ene gy be ween he in ol ed pa icles is gi ing ano he kind o in o ma ion, and is ea ed la e . The TEM has ou di e en modes o imaging: •Di ac ion mode •Ampli ude con as imaging (BD/DF mode) •High esolu ion mode (HRTEM) •STEM mode In di ac ion mode an image o he back- ocal plane o he objec i e lens is p oduced on he imaging plane. In he case ha he inciden elec on beam is illumina ing he specimen pa allel, he image p oduced will consis o a pa e n o spo s. Each such a spo co esponds o a beam ha is e ac ed om a plane ha (nea ly) sa is ies he B agg condi ion: n=2dsinB (3.5) whe e n is an in ege , d is he spacing o he e ac ing la ice planes and θB is he e ac ion angle (know as B agg's angle). The di ac ion pa e n is de ined by he in e sec ion o he ecip ocal la ice and he Ewald sphe e, which can be shown o be a geome ical econs uc ion o he B agg condi ions. Ampli ude con as imaging can be done by ei he selec ing he di ec beam o one o he di ac ed beams by he use o an objec i e ape u e. In he o me case i is called b igh ield (BF) imaging, in he la e case da k ield (DF) imaging. The names o igina e om he ac ha in DF imaging, holes in he oil appea black and he pic u e is gene ally da ke han o BF imaging. These wo imaging echniques can be used o image s ain ields wi hin c ys als. S ain is de ined by he displacemen o an a om om i s posi ion ha would be expec ed om he o dina y pe iodici y o he c ys al. Causes o such a s ain ield can be disloca ions, plana de ec s o o he impe ec ions in he c ys al la ice. 51 The dis o ion o he la ice a ound a disloca ion co e may al e he la ice in such a way ha di ac ed beams ha a e in he undis o ed la ice no exci ed, become exi ed in he dis o ed la ice. The displacemen ield a ound a disloca ion co e o an iso opic solid is gi en by (Williams and Ca e 2009): R=1 2  b 1 41− {beb×u21−2ln cos2}  (3.6) whe e be is he edge componen o he bu ge s ec o , ν Poisson's a io and and φ a e he sphe ical coo dina es along he disloca ion line. The Howie-Whelan (HW) equa ions, he equa ions ha desc ibe he in ensi y o he di ec and di ac ed beam and hus he con as in ampli ude con as images, can be modi ied o include a la ice dis o ion (Williams and Ca e 2009): dg dz =i 0 gi g exp [ −2iszg⋅R ] (3.7) whe e g is he di ac ed beam used o image. The only di e ence o he HW-equa ions o an undis o ed la ice is he addi ional g∙R e m, and hus only a change in con as will be obse ed when he scala p oduc o he di ac ion ec o and displacemen ield will be non-ze o. I he displacemen ield is he one co esponding o a pu e sc ew disloca ion R educes o R = bφ / 2π. The disloca ion o a sc ew disloca ion will hus no be isible is he Bu ge s ec o is pe pendicula o he di ac ed beam. In he case o a pu e edge disloca ion we need he comple e o m o 3.6, so he in isibili y c i e ia become g∙b = 0 and g∙(b x u) = 0. The las e m can be asc ibed o he buckling o la ice planes pe pendicula o bo h he Bu ge s ec o and disloca ion line (Williams and Ca e 2009). Using da k ield imaging, one can hus de e mine he Bu ge s ec o and slip sys em o he s udied phase. Ano he ype o de ec s a e plana de ec s. Examples a e s acking aul s, an i-phase domain bounda ies and g ain bounda ies. Again one can use a displacemen ec o R o desc ibe he ansla ion o he la ice o e he plana de ec , a poin n co esponds on he o he side o he plana aul o he poin n' = n + R. Since R on ei he side o he plana de ec is independen o z, equa ion 3.7 comes down o adding a phase e m o Howie- Whelan equa ions o he di ac ed beam, which can be w i en as eiα; whe e α = 2πg∙R. Again, no change will be isible when α = 0. When α ≠ 0, he e will be a change in con as depending on he dep h o he plana de ec . In he case o an inclined plana de ec , ligh and da k inges will be isible, since one needs o in eg a e 3.7 o e he amoun o oil unde he plana de ec . Simila ly o disloca ions, one can de e mine he displacemen ec o by a mo e de ailed in es iga ion o he inges wi h di e en g∙R condi ions. B igh ield, da k ield and weak beam da k ield imaging a e all ampli ude con as imaging echniques, which is one o he wo main imaging modes o he TEM, as al eady explained. The o he imaging mode is phase con as imaging, whe e he con as in he image is caused by in e e ence o mul iple beams. To do so, one uses an ape u e i he back ocal plane o he objec i e lens o le some o he di ac ed beams pass h ough and block he o he s. When one selec s a 2D a ay o di ac ed beams in he objec i e ape u e, a phase con as image will be o med wi h a wo dimensional s uc u e. The image o med in HRTEM images can be 52 exp essed as he p oduc o se e al con ibu ions. The i s one being he specimen unc ion desc ibing how he specimen in e ac s wi h he inciden elec on beam and wha wa e unc ion o he elec on beam is a e hey eme ge om he specimen. The o he con ibu ions a ise because o he elec on op ical sys em and i s main componen s a e hose om he ape u es, a enua ion o he wa e in he lens and abe a ion o he lens om a pe ec lens (Williams and Ca e 2009). The image one obse es in he end can be w i en as a con olu ion o hese con ibu ions: g =∫  'h − 'd '=  ∗h  (3.8) whe e is he specimen unc ion and h is he unc ion desc ibing he elec on op ical sys em, he * deno es he con olu ion wi h h. The con olu ion can be w i en as he p oduc o he Fou ie ans o m o he unc ions ha a e con ol ed oge he . I we b eak down h in o he con ibu ions men ioned abo e one can w i e: Gu= AuEuBuFu (3.9) whe e A is he Fou ie ans o m o he ape u e unc ion, E he Fou ie ans o m o he en elope (a enua ion) unc ion, B he ou ie ans o m o he abe a ion unc ion, F he Fou ie ans o m o he specimen unc ion an u a ecip ocal la ice ec o . Equa ion 3.9 dec ibes how he de ail on a ce ain scale (u) is a ec ed by he elec on op ical sys em. The specimen unc ion can be w i en in he phase objec app oxima ion (POA), which holds o hin specimens and when abso p ion can be neglec ed (Spence 2009, Williams and Ca e 2009):  =exp  −iVp   (3.10) whe e Vp is he p ojec ed elec os a ic po en ial o he la ice pa allel o he x-y plane (pe pendicula o he inciden elec on beam) and σ = π/λE he in e ac ion cons an . The specimen unc ion is hus di ec ly ela ed o he (p ojec ed) elec os a ic po en ial inside he specimen i sel . 53 Figu e 3.7 :La ice inges in ens a i e. The dominan s uc u e isible a e la ice inges ela ed o he 18.2 Å la ice epea ((1 0 0) plane spacings). S acking aul s un om he op le o he bo om igh . The inal mode is he scanning ansmission elec on mic oscope (STEM) mode. In his mode he elec on op ical sys em c ea es a condensed p obe which scans he specimen, simila o in an SEM. Fo e e y pixel he in ensi y o ei he he di ec beam (b igh ield STEM) o di ac ed beams (da k ield STEM) a e measu ed using an angula de ec o . In his way he image is build by scanning o e he specimen wi h he condensed beam. This mode has been used o measu e he di usion p o iles p esen ed in chap e 4. 3.2.4 Inelas ic sca e ing – Ene gy dispe si e spec oscopy Al al eady s a ed, he o he ype o in e ac ion be ween high ene gy inciden elec ons and he a oms o he specimen is inelas ic sca e ing. The main di e ence be ween elas ic sca e ing and inelas ic sca e ing is ha he la e one in ol es a signi ican amoun o ene gy ans e om he inciden elec on o he pa icle wi h which i in e ac s. To ge an imp ession o he impo ance o he di e en ypes o sca e ing, one can ha e a look a he p obabili y ha a pa icula p ocess will occu and sca e s an inciden high ene gy elec on, which is gi en by he sca e ing c oss sec ion. An o e iew o he impo ance o he di e en sca e ing p ocesses is gi en in igu e 3.8. Inelas ic sca e ing can occu due o ene gy ans e du ing elec on – a om in e ac ions, elec on – elec on in e ac ions, and in e ac ions wi h mul iple a oms o elec ons simul aneously. The i s kind o in e ac ion is also he cause o elas ic sca e ing, and in a c ys al la ice i will esul in a sha ply peaked dis ibu ion o sca e ing di ec ions, called di ac ion as desc ibed in he p e ious sec ion. Du ing high angle sca e ing, enough ene gy can be ans e ed o he a oms such ha he a om is knocked ou o i s posi ion in he specimen la ice, esul ing in knock-on o displacemen damage wi hin he specimen. (Ege on 1996), a p ocess ha can lead o complica ions du ing he chemical analyses o specimens. In appendix 5.1 a me hod is desc ibed o co ec o his kind and o he kinds o adia ion damage. The second kind o in e ac ions, elec on – elec on in e ac ions, esul s in he ans e o ene gy om he inciden elec on o elec ons o he sca e ing a om in 54 Figu e 3.8: Sca e ing c oss sec ions in Al in he case o o wa d sca e ing (θ = 0°) o di e en ypes o elec on - specimen in e ac ions. P = plasmon sca e ing, E = elas ic sca e ing, K and L a e K and L shell ioniza ion and SE is seconda y elec on gene a ion. Plasmon gene a ion and elas ic sca e ing a e he dominan sca e ing p ocesses in he TEM. Rep oduced om Williams and Ca e (2009). he specimen. The ene gy ans e ed in his p ocess can be he esul o wo kinds o in e ac ions wi h he elec ons o an a om: •I he ene gy ans e is small, i can be used o in a- and in e band elec onic ansi ions in he a om being exci ed, o in he ejec ion o an ou e ( alance) elec on om he a om (seconda y elec on). I can also lead o he collec i e oscilla ion o ou e shell elec ons o many a oms, a p ocess which is called plasmon esonance. •A highe amoun s o ans e ed ene gies, i.e. ew hund ed eV o ens o kE , inne shell elec ons (K, L o M) can be exci ed o a highe unoccupied bound s a e o o he con inuum le el, he la e one esul ing in ioniza ion o he a om. The las ype o in e ac ion o m he basis o wo widely used spec oscopic echniques in he TEM, i.e. Elec on Ene gy Loss Spec oscopy (EELS) and Ene gy Dispe si e Spec oscopy (EDS), whe eby he name o he la e e e s o he de ice used o measu e he spec a and will be handled in mo e de ail in his sec ion. Figu e 3.9 shows he physical p ocess which o ms he basis o EDS. A high ene gy elec on in he inciden elec on beam passes h ough he elec on cloud o an a om. Due o Coulombic in e ac ion wi h o he elec ons in he elec on cloud, he inciden elec on ge s de lec ed and ans e s a pa o i s ene gy o an elec on in he elec on cloud. The la e elec on hen can ge ejec ed om he a om i he ans e ed ene gy is g ea e han he ioniza ion ene gy o he pa icula shell. The c ea ion o a hole in he shell ep esen s an exci ed s a e o an a om, i.e. i is in an ene gy s a e highe han i s g ound s a e. The a om can ge back o i s g ound s a e by 55 Figu e 3.9: Gene a ion o x- ays by inne shell ioniza ion o a specimen a om. a) A high ene gy inciden elec on pene a es he elec on clouds and passes close o he inne shell elec on. b) Coulombic in e ac ion wi h inne shell elec ons causes a change o inciden elec on di ec ion and ans e o ene gy om he inciden elec on o he inne shell elec on, ejec ing he la e one om he specimen. c) An elec on om a highe shell alls back o ill he elec on hole in he inne shell and he eby eleasing he po en ial ene gy as an x- ay. ac b mo ing an elec on om one o i s highe shells o ill he elec on hole, which was c ea ed by he in e ac ion wi h he inciden high ene gy elec on. Mo ing an elec on om a highe shell o a lowe shell esul s in he lowe ing o he po en ial ene gy o he a om. This ene gy can be eleased om he a om by ei he he emission o a pho on o a cha ac e is ic ene gy o ano he elec on om a highe shell, he eleased elec on is called an Auge elec on and he ansi ion is called a non- adia i e ansi ion. The p obabili y o a adia i e (one du ing which a pho on is emi ed) s. non- adia i e ansi ion is gi en by he luo escence yield ω, and o he ollowing app oxima ion can be used (Williams and Ca e 2009): = Z4 aZ4 (3.11) whe e a is a cons an dependen on he shell and Z is he a omic numbe . The luo escence yield is hus a s ong unc ion o a omic numbe and he in ensi y o he CKα line is he e o e much less in ense han ha o he FeKα. The low p obabili y o a adia i e ansi ion o ligh elemen s in combina ion wi h s ong abso p ion in he specimen and de ec o window o x- ays wi h low ene gies makes EDS no he ideal echnique o measu e ligh elemen s. In such case, he complimen a y echnique o analyse ligh elemen s is EELS. Nex o cha ac e is ic x- ay lines h ough which elemen s in he specimen can be uniquely de e mined, ano he kind o adia ion is emi ed by he inciden high ene gy elec on when i in e ac s wi h he specimen, called B emss ahlung (Ge man o b eaking- adia ion). In e ac ion o he inciden elec on wi h he elec ic ield o he nucleus esul s in a change o p opaga ion di ec ion o he inciden elec on. The cen ipe al accele a ion ha is associa ed wi h his change in di ec ion o momen um esul s in he loss o ene gy o he inciden elec on, which is emi ed as elec omagne ic adia ion (Ege on 1996). The gene a ed in ensi y I as unc ion o pho on ene gy is gi en by K ame s (Williams and Ca e 2009): 56 Figu e 3.10: Top-ha il e applied o a measu ed EDS spec um o almandine, applying he op-ha il e emo es he backg ound bu changes he shape o he x- ay peaks. Quan i ica ion o he x- ay peak in ensi y is hen done by compa ing he il e ed spec um o o he il e ed (elemen al) e e ence spec a. IE= KZ E0−E E (3.12) whe e E0 is he ene gy o he inciden elec on, E he ene gy o he emi ed B emss ahlung, Z he a e age a omic numbe and K is K ame s' cons an , which may i sel also be a unc ion o he a e age a omic numbe (Small e al. 1987). The o al spec um is a sum o he cha ac e is ic x- ay lines and he B emss ahlung o backg ound adia ion. The b emss ahlung can be emo ed om he spec um by ei he i ing an equa ion ela ed o 3.12 o o emo e he backg ound om he spec um by a digi al il e me hod. The la e one uses a op-ha il e which emo es any linea componen om he spec um including he B emss ahlung componen since he la e one is nea ly a linea unc ion o ene gy wi h mino de ia ions only a low ene gies (Reed 1993). I he B emsss ahlung backg ound was s ipped using a modi ied o m o 3.12, Gaussian peaks a e i ed o he cha ac e is ic x- ay lines and he a ea unde he peaks gi es he in ensi y o each line. I he il e - i me hod is used, op-ha il e ed e e ence spec a a e used o i he il e ed measu ed spec a and om his he in ensi y o each cha ac e is ic x- ay is de e mined. Fo he esul s p esen ed in his disse a ion he backg ound modelling in combina ion wi h i ing o Gaussian peaks ha e been used, since he il e - i me hods equi es good elemen al e e ence spec a ha we e no a ailable. Unless he specimen is e y hin, abso p ion o x- ays in he specimen mus be conside ed, which can be exp essed by ollowing he equa ion: I=I0 Acosec  [ 1−e− A cosec  ] (3.13) whe e I0 is he gene a ed x- ay in ensi y, μA he mass abso p ion coe icien o elemen A in he specimen, ρ he mass densi y, he hickness o he hin oil and α he ake-o angle o he x- ays om he oil o he x- ay de ec o (see igu e 3.11). Since oils in he TEM a e gene ally hin and he e o e ene gy loss o he elec on beam wi hin he oil can be neglec ed one can w i e o he concen a ion o an elemen : CA CR =kAR ⋅ AR ⋅IA IR wi h (3.14) 57 Figu e 3.11: Ske ch o he sample – de ec o geome y du ing an EDS measu emen s. The inciden elec on beam ionizes and exci es a olume in he TEM oil (da k g ay a ea), which emi s x- ays when a oms again e u n o hei lowes ene gy s a e. The angle be ween he x- ays eaching he de ec o and he sample su ace is called he ake-o angle (TOA). No e ha ion-milled oils don´ ha e pa allel su ace bu a e wedge shaped. AR=A spec R spec [ 1−exp R spec  cosec 1−exp A spec  cosec ] kAR is he Cli -Lo ime ac o o elemen A using R as a io elemen , AR ep esen s an abso p ion co ec ion ac o , IA and IR a e he ne coun s o elemen A and elemen R and μspeci is he mass abso p ion coe icien o elemen i in he specimen, which can be calcula ed om he mass abso p ion coe icien s in a pu e s anda d j (μij): i spec=∑ j Cji j (3.15) Using as addi ional cons ain ha he o al concen a ion should add up o 100%, one can calcula e he composi ion o an unknown specimen, i he hickness is known. Though i is possible o de e mine he hickness by EELS, hickness inges o con e gen beam elec on di ac ion (Williams and Ca e 2009), hese me hods a e o en cumbe some and imp ac ical when i comes down o measu ing many poin s. Van Cappellen and Doukhan (1994) p oposed o use he ne cha ge o all elemen s as an al e na i e cons ain o de e mine he hickness o he specimen, o x- ay abso p ion hickness o he specimen. Using an app oxima ion o 3.14 hey exp essed he o al cha ge as unc ion o specimen hickness as a second o de polynomial and om his hey de e mined he hickness and composi ion o he specimen a he place o analyses. A p og am was de eloped du ing he wo k on he di usion s udy ha employs a modi ied e sion o hei me hod (see appendix 5.2) A majo issue wi h high p essu e phases is hei ins abili y unde he in ense elec on beam, which can lead o p e e en ial loss o some elemen s. In his disse a ion a me hod is de eloped o co ec o a change in composi ion due o adia ion damage du ing EDS analyses, and which is desc ibed in mo e de ail in appendix 5.1. 3.2.5 Elec on ene gy loss spec oscopy A complemen a y analy ical echnique o EDS is EELS, whe e no he p oduced x- ay in ensi y is measu ed, bu he ene gy loss o he ansmi ed elec ons. The physical p ocess unde lying EELS is he same as he one unde lying EDS, i.e. inelas ic sca e ing o he inciden beam. Since EELS is independen o he luo escence yield o a ce ain elec onic ansi ion, EELS can also be used o ligh elemen s, which ha e a low luo escence yield and whe e abso p ion by he specimen and he window in on o he EDS de ec o may cause p oblems. The ac ha low ene gy losses o he high ene gy inciden beam a e mo e likely han high ene gy losses, also makes EELS a a ou able me hod o de e mine he concen a ion o ligh elemen s. The EELS spec um is usually di ided in wo pa s, a low loss pa below ± 50 eV and a co e loss spec um, he measu ed ene gy loss egion abo e ± 50 eV. The low loss spec um con ains he ze o-loss peak, which ep esen he ansmi ed elec ons ha did no loose any ene gy, and is by a he mos in ense peak in he spec um. The wid h o he ZLP gi es he ul ima e esolu ion o he analyses. The peak a e he ZLP and usually loca ed somewhe e be ween 5 and 35 eV ene gy loss is he plasmon peak. High ene gy elec ons pene a ing he 58 specimen induce collec i e oscilla ions o he ou e shell elec ons o he specimen, so called plasmons, which gi e ise o he plasmon peak. The shape o he plasmon peak is con olled among o he s by he ype o bonding and can be used o phase iden i ica ion (Ege on 2009, Williams and Ca e 2009). Figu e 3.12 shows he ea u es o a ypical co e-loss spec um. The shape o an edge when wi hou any con ibu ions o bonding, un illed highe s a es and backg ound o p e ious edges would look like (A), a sha p inc ease a he ioniza ion edge ene gy ollowed by a long ail which can be app oxima ed by a powe -law decay in in ensi y a e he ioniza ion edge. In (B) he backg ound is added o his ioniza ion edge, which is he sum o he ails o p e ious edges and he plasmon peak, and can hus also be app oxima ed by a powe -law unc ion (Ege on 1996). I he co e-le el elec on is ejec ed om i s shell, bu did no gain enough ene gy o ge in o he acuum le el, i will end up in some un illed s a e abo e he Fe mi le el, bu s ill bound o he nucleus by Coulomb o ces. The p obabili y ha an elec on will go o a ce ain s a e wi hin an associa ed ene gy ange is dependen on he numbe o s a es in his ene gy ange, and is hus gi en by he Densi y O S a es (DOS) o he sys em. This will gi e ise o addi ional spec al s uc u e upon he backg ound and ioniza ion edge (C), he Ene gy-Loss Nea -Edge S uc u e (ELNES) up o 30-50 eV a e he onse o he ioniza ion edge and Ex ended Ene gy-Loss Fine s uc u e (EXELFS) beyond he e (D). In he case ha hese emp y s a es a e well de ined emp y s a es (in he sense o hei ene gy), hey will gi e ise o peaks, o whi e lines, on op o he ioniza ion 59 Figu e 3.12:The s uc u e o co e loss spec a. a) The shape o hyd ogene ic abso p ion edge. b) The hyd ogene ic is supe imposed on he ail o o he abso p ion edges and he plasmon peak, due o plu al-sca e ing. c) When elec ons can be exi ed o bound unoccupied s a es, his leads o he supe posi ion o whi e lines on op o he abso p ion edge, he ELNES s uc u e. d) Beyond he ELNES s uc u e is he EXELFS s uc u e. Modi ied a e Williams and Ca e (2009). d b a c edge, which can gi e aluable in o ma ion on o example he bond ype o oxida ion s a e (Ege on 1996, Williams and Ca e 2009). In his disse a ion EELS has been used o de e mine he oxida ion s a e o i on in ga ne . Van Aken e al. (1998) and Van Aken and Liebsche (2002) used he shape o he FeL2,3 edge o de e mine he e ic / e ous in di e en mine als o known e ic/ e ous i on a io, and p oduced a uni e sal cu e o de e mine he e ic/ e ous i on a io in unknown mine als. The FeL3 edge a 707.8 eV consis s o se e al whi e lines, o which he mos p ominen a e one a 707.8 eV and one a 709.5 eV. The la e one becomes mo e in ense wi h inc easing Fe3+ con en . A simila beha iou is seen o he FeL2 edge, which also consis o mul iple peaks, o which he ones a 720 eV and 721.5 eV eac mos s ongly o he Fe3+ con en , he la e one becoming mo e in ense wi h inc easing Fe3+ con en . Van Aken e al. (1998) used he in eg a ed in ensi y a io in wo ene gy windows a 708.5 – 710.5 eV and 719.7 – 721.7 eV o p oduce a uni e sal cu e om which one can de e mine he Fe3+ / Fe2+ a io using he same me hod. To co ec o ansi ions o he con inuum s a e, hey i a double a c an unc ion o he egions ou side o he edge a e he powe -law backg ound has been emo ed:  E= h1 ⋅ [ a c an   w1  E−E1   2 ] h2 ⋅ [ a c an   w2  E−E2   2 ] (3.16) whe e h1 and h2 a e he heigh s o he peaks, w1 and w2 he wid hs o he con inuum ansi ion, ΔE he ene gy los and E1 = 708.65 eV and E2 = 721.65 eV he posi ions o he con inuum ansi ions. In specimens ha a e no e y hin, mul iple sca e ing plays an impo an ole, and he e o e he measu ed co e-loss spec a a e a con olu ion o he single sca e ing co e-loss spec a, i.e. he de ec ed elec on only los ene gy by a single inne shell sca e ing e en , and he low-loss spec a since he low ene gy loss sca e ing e en s a e mos likely o occu . Fo good quan i ica ion o he Fe3+/Fe2+ a io in he specimen he mul iple sca e ing e ec needs o be emo ed, o decon ol ed. This can be achie ed by using he Fou ie - a io echnique (Ege on 1996): k1=I0jk / jl  (3.17) whe e k1(ν) is he Fou ie ans o m o he single-sca e ing co e-loss spec um, I0 he in ensi y o he ze o-loss peak, jk(ν) he Fou ie ans o m o he measu ed co e-loss spec um and jl(ν) he Fou ie ans o m o he low- loss spec um. Doing his, howe e , is no s aigh o wa d and equi es addi ional ea men o he spec a which is beyond he scope o his disse a ion bu can be ound in mo e de ail in Ege on (1996). 3.3 The elec on mic op obe Chemical cha ac e iza ion on he sample scale o he eco e ed samples was done by elec on mic op obe analysis (EMPA) using wa eleng h dispe si e spec oscopy (WDS). The elec on mic op obe is an elec on mic oscope like he TEM. The main di e ences a e ha i wo ks on bulk samples, i.e. he sample is no anspa en o elec ons, and he elec on op ical sys em he e o e consis s only o a se o condense and objec i e lenses ha ocus he elec on beam on he sample. The ope a ing ol age o an elec on mic op obe is 60 The nume ical scheme has been es ed agains an analy ical solu ion o a semi-in ini e hal space p oblem wi h a cons an bounda y concen a ion C0 and an ini ial concen a ion p o ile o C( =0) = 0 (C ank 1980): C=C0e c  x 2  D  (4.4) whe e x is he spa ial coo dina e, D is he di usion coe icien , ime and e c is he complemen a y e o unc ion e c x = 1 – e x. As igu e 4.1 shows, he e o is smalle han 0.0015 on a o al ange o 1.0, which co esponds o an e o o less han 0.15%. The e o can be u he educed by aking a ine g id o ake smalle ime s eps. The p og am allows o di e en di usion models o be used, by calcula ing he ma ix o di usion coe icien s using he ela ions co esponding o each di usion model. Cu en ly ou models a e suppo ed:(1) he mos simple di usion model wi h cons an di usion coe icien s independen o composi ion and all o -diagonal elemen s o D equal o ze o, (2) he di usion model o Lasaga (1979) o ideal solu ions, (3) he di usion model o Lasaga (1979) using a symme ic non-ideal solu ion desc ibed by Ma gules pa ame e s and (4) he di usion model by Loomis (1978) o an ideal solu ion. The p og am also has op ions o modi y he ace di usion coe icien s used in he di e en di usion models o model he di usi i y dependence o elemen s on o he elemen s ha can ha e mul iple alence s a es, o example i on. Following Mackwell e al. (2005) he ollowing equa ion is used o model his:  Di 0=Di 0k1Cm k2e−k3Cm (4.5) whe e k1, k2 and k3 a e adjus able pa ame e s o he model and Cm is he concen a ion o he mul i- alen ion. Nex o his a di e en kind o composi ional dependence can also be modelled, acco ding o he ollowing equa ion: 67 Figu e 4.1: The esul s o he nume ical s. analy ical solu ion o he mul i- componen di usion p og am mcdi . The analy ical solu ion is no isible since i o e laps wi h he nume ical solu ion a he scale o he igu e. The di e ence be ween he wo is plo ed on he igh y-axis. The di e ence be ween he analy ical and nume ical solu ion is less han 0.15%. Simula ion condi ions: g id spacing dx = 0.005, ime s ep 0.01, ime in e al 0 – 1, di usion coe icien 0.01.  Di 0=Di 0  1∑ j=1 n kijCj  (4.6) whe e kij a e adjus able pa ame e s. A second p og am (mc i e ) was de eloped o i he measu ed di usion p o iles o calcula ed p o iles. The p og am uses he ou ines in he mcdi p og am o calcula e a p o ile and hen o i his p o ile o measu ed p o iles. I allows o i ing he ace di usi i ies used in he di usion models, ini ial composi ions and he adjus able pa ame e s in equa ion 4.5. A gap in he di usion p o ile can also be i ed, as well as a shi in he p o ile o i he ini ial in e ace. The p o iles a e simul aneously i ed by minimizing he χ2 alue de ined by: 2=∑ i=1 k∑ i=1 l  Oij−Mij  eij  2 (4.7) whe e k is he numbe o componen s, l he numbe o measu emen s, Oij is he measu ed concen a ion o componen i in measu emen j, Mij is he modelled concen a ion o componen i in measu emen j and eij is he e o in he measu emen o componen i in measu emen j. The minimiza ion is done using he Le enbe g – Ma qua d me hod con ained in he MINPACK o an so wa e ou ine package1. The e o s on he i ed pa ame e s a e calcula ed using he boo s ap me hod (E on and Tibshi ani 1994) which is a esampling me hod o calcula e e o s on i ed pa ame e s. A e he p o iles ha e been i ed, he esiduals a e calcula ed and scaled o hei measu emen e o . New 'pseudo-p o iles' a e hen calcula ed using he i ed p o ile and he esiduals by andom sampling he scaled esiduals and adding his o i ed alues o he measu ed p o iles. The 'pseudo-p o iles' a e hen again i ed o ob ain he 'pseudo-pa ame e s'. This was epea ed o 5000 'pseudo-p o iles' and he e o s in he i ed pa ame e s a e hen de e mined by inding he symme ic in e al a ound he o iginally i ed pa ame e s ha encompasses 90% ( o he 90% con idence in e al) o he i ed 'pseudo-pa ame e s'. 1 h p://www.ne lib.o g/minpack/ 68 Figu e 4.2: The esul s o he nume ical s. analy ical solu ion o he 3D sphe ical adially symme ic di usion p og am addi . The analy ical solu ion is no isible since i o e laps wi h he nume ical solu ion a he scale o he igu e. The di e ence be ween he wo is plo ed on he igh y-axis. The absolu e e o (di e ence be ween nume ical and analy ical solu ion) is less han 0.0002% o he s eady s a e solu ion. Simula ion condi ions: g id spacing d = 0.005, ime s ep 0.01, ime in e al 0 – 100, di usion coe icien 0.01. 4.2 Di usion in a sphe ical o cylind ical geome y To model di usion in a g ain and di usion con olled g ow h o a g ain o needle a ini e di e ence model was used. The basic equa ion ha go e ns di usion in a sphe ical and cylind ical geome y assuming a cons an di usion coe icien D is gi en by (C ank 1980): ∂C ∂ =D  n ∂C ∂ ∂2C ∂ 2  (4.8) whe e C is he concen a ion, he adius om he cen e, ime, D he di usion coe icien , and n = 1 o a cylind ical geome y and n = 2 o a sphe ical geome y. Equa ion 4.8 has been disc e ized using a ully implici scheme: Ci k=−  1  n 2 i  Ci1 k1  1−2   Ci k1−  1  −n 2 i  Ci−1 k1 Wi h = D  (4.9) whe e k is he ime index, i he spa ial index, Δ he dis ance be ween wo nodes, and Δ he ime s ep o empo al disc e iza ion. Equa ion 4.9 desc ibes a idiagonal linea sys em and can be sol ed using s anda d me hods included in he LAPACK so wa e lib a y o example. The code has been es ed agains a s eady s a e analy ical solu ion o a hollow sphe e and hollow cylinde , which a e espec i ely gi en by (C ank 1980): C=aC1b− bC2 −a b−a (4.10) and C=C1lnb/ C2ln /a lnb/a (4.11) whe e is he adial dis ance om he cen e o he sphe e/cylinde , C1 is he concen a ion on he inside su ace, C2 he concen a ion on he ou side su ace, a he adial dis ance om he cen e o he sphe e o cylinde o he inside su ace and b he adial dis ance om he cen e o he sphe e/cylinde o he ou e su ace. Figu e 4.2 shows he esul o he sphe ical geome y, he e o is less han 0.0002% o he s eady s a e solu ion. Fo he cylind ical solu ion he e o is less han 0.002% in he case o he s eady s a e solu ion (see igu e 4.3). G ain g ow h (o sh inkage) was modelled by di iding he domain in o h ee pa s; he in e nal pa , he bounda y and he ex e nal pa ( igu e 4.4). The in e nal pa co esponds o he g ain and o his pa equa ion 4.9 is sol ed o e e y ime s ep. The bounda y has a cons an concen a ion, co esponding o he composi ion o he in e nal phase when in equilib ium wi h he ex e nal phase, and i s posi ion de e mines he size o he ex e nal and in e nal pa s. The ex e nal pa co esponds o he ex e nal phase and also has a cons an concen a ion, no necessa ily equal o he bounda y concen a ion. Since he bounda y concen a ion is 69 di e en om he concen a ion o he in e nal pa , ma e ial will low in o ou o he g ain. The o al lux o ma e ial ha has lown in/ou o he g ain is de e mined a e e e y ime s ep by in eg a ion o he concen a ion p o ile o e he comple e g ain, aking in o accoun he p ope geome y. The bounda y posi ion is hen upda ed o he nex ime s ep based on he o al lux o ma e ial ha has lown in/ou o he g ain (Min ) and he concen a ion o densi y o ma e ial in he ex e nal pa (ρex ): Vg ain=Min −M0 ex (4.12) M0 is he s a ing concen a ion o ma e ial in he g ain. In he case o g ain g ow h, he composi ion o he new nodal poin s in he in e nal pa is se o he bounda y composi ion. The g ow h o he g ain can be s opped a e a ce ain amoun o ma e ial has lown in o he g ain. The bounda y posi ion is kep cons an a e his poin has eached. To s op ma e ial om lowing in o ou o he 70 Figu e 4.3 : The esul s o he nume ical s. analy ical solu ion o he 3D cylindi ical adially symme ic di usion p og am addi . The analy ical solu ion is no isible since i o e laps wi h he nume ical solu ion a he scale o he igu e. The di e ence be ween he wo is plo ed on he igh y-axis. The absolu e e o is less han 0.002% o he s eady s a e solu ion. Simula ion condi ions: g id spacing d = 0.005, ime s ep 0.01, ime in e al 0 – 100, di usion coe icien 0.01. Figu e 4.4 : Ske ch o he se up o he domain. Solid black ci cles deno e nodal poin s a which he solu ion is calcula ed. In he in e nal pa he ele an desc e ized di e en ial equa ion is sol ed, whe eas he ex e nal pa unc ions as a kind o ese oi o accommoda e g ain g ow h o sh inkage. The posi ion o he bounda y is calcula ed by de e mining he amoun o ma e ial a lowed in o he in e nal pa . g ain, he bounda y lux is o ced o be ze o using a Neumann bounda y condi ion: Cb k1−Cb−1 k1=0 (4.13) whe e b is he bounda y node. In he case ha he in e nal pa con ains he i s node, also a Neumann ype bounda y condi ion was used o he i s node. 4.3 Re e ences Ande son, E., Bai, Z., Bischo , C., Black o d, S., Demmel, J., Donga a, J., C oz, J. Du, G eenbaum, A., Hamma ling, S., McKenney, A., So ensen, D. (1999), LAPACK Use s’ Guide. Socie y o Indus ial and Applied Ma hema ics, Philadelphia, PA C ank, J. (1980), The Ma hema ics o Di usion. Ox o d Uni e si y P ess, USA E on, B., Tibshi ani, R.J. (1994), An In oduc ion o he Boo s ap. Chapman and Hall/CRC, London Lasaga, A.C. (1979), Mul icomponen exchange and di usion in silica es. Geochem Cosmochem Ac a 43:455- 469. doi: 10.1016/0016-7037(79)90158-3 Loomis, T.P. (1978), Mul icomponen di usion in ga ne ; I, Fo mula ion o iso he mal models. Am J Sci 278:1099-1118 Mackwell, S., Bys icky, M., Sp oni, C. (2005), Fe–Mg In e di usion in (Mg,Fe)O. Phys Chem Mine 32:418-425. doi: 10.1007/s00269-005-0013-6 71 Chap e 5: Di usion o he majo i e componen in ga ne 5.1 In oduc ion Majo i e is a high p essu e polymo ph o ens a i e (Mg2Si2O6) and o ms a solid solu ion wi h he o he ga ne s in Ea h's man le. Ga ne wi h a la ge majo i e componen , so called majo i ic ga ne , is hough o cons i u e up o 40 - 60 olume % o he Ea h's ansi ion zone (Bass and Pa ise 2008, F os 2008), whe eas subduc ed oceanic c us migh con ain up o 80 olume % majo i ic ga ne in he ansi ion zone (I i une and Ringwood 1993). Also, he ecogni ion o py oxene lamellae and needles wi hin ga ne wi h a clea opo axial ela ionship as being he p oduc s o exsolu ion om majo i ic ga ne s (Song e al. 2004, Scambellu i e al. 2008, an Roe mund 2009), e ocused he in e es o he scien i ic communi y o he solubili y o he majo i e componen in ga ne . Di e en s udies ha e shown ha he solubili y o he majo i e componen in ga ne inc eases wi h inc easing p essu e (Akaogi and Akimo o 1977, Gaspa ik 2003), which is he eason why majo i ic ga ne is an impo an phase in Ea h's ansi ion zone. A subduc ing (oceanic) slab should hus dissol e i s (clino)py oxene in o ga ne , by a mechanism which unde d y condi ions is p obably di usion con olled. The p ese a ion o exsol ed py oxene lamellae om ea lie e en s as well as lack o new p ecipi a es a e a UHP me amo phic e en , as in he case o he Wes e n Gneiss Region (Scambellu i e al. 2008, an Roe mund 2009), migh hus gi e impo an in o ma ion on he du a ion o his UHP me amo phic e en , p o ided ha he di usi i y and solubili y o he majo i e componen in ga ne a he ele an condi ions is known. As he subduc ing slab descends deepe in o he man le, di usion o he majo i e componen in o ga ne will also be an impo an ac o in he he modynamic equilib a ion o he slab. Howe e , he mass anspo p ope ies o majo i ic ga ne and especially di usion p ope ies o he majo i e componen in ga ne a high p essu e a e no well cons ained. The e o e di usion expe imen s ha e been conduc ed a ansi ion zone condi ions o de e mine he di usi i y o he majo i e componen in ga ne as unc ion o empe a u e, p essu e and also composi ion. 5.1.1 Di usion in mine als In he absence o a luid phase, olume di usion is he main mechanism o educe concen a ion g adien s and o equilib a e mine al assemblages in he solid ea h. The di usi i y o componen s in mine als is hus an impo an ac o con olling he a e a which mine al assemblages equilib a e and di usion p o iles ha e he e o e been used o place cons ain s on he a e a which geological p ocesses occu in he Ea h (Lasaga and Jiang 1995, Chak abo y 2008). Ga ne s, as one o he impo an mine als ound on he su ace o he Ea h, has been in he ocus o se e al di usion s udies (Elphick e al. 1985, Loomis e al. 1985, Chak abo y and Ganguly 1992, Chak abo y and Rubie 1996). Howe e , he applica ion o hese da a was di ec ed owa ds he in e p e a ion o di usion p o iles ha de eloped in ga ne du ing a me amo phic e en , and he e o e he p essu e ange a which hese s udies we e done was limi ed o below 4 GPa, wi h one poin a 8.5 GPa by Chak abo y and Rubie (1996). Fo he same eason, he abo e men ioned s udies only ocused on he di usi i y o di alen ca ions, ha occupy he dodecahed al si e in ga ne . The s udy p esen ed he e 72 in es iga es he di usion a highe p essu e condi ions, as well as he di usi i y o he majo i e componen , which in ol es di usion o di alen , i alen and e a alen ions occupying bo h he dodecahed al and oc ahed al si es. Since he expe imen s p esen ed he e in ol e di usion o mo e han one componen , he p o iles a e ea ed as mul i-componen di usion p o iles. The gene al one dimensional o m o a n-componen sys em is: ∂Ci ∂ =∑ i n−1∂ ∂x  Dij ∂Cj ∂x  (5.1) whe e Ci is he concen a ion o componen i, ime, x he spa ial coo dina e and D is a (n – 1) x (n – 1) ma ix o di usion coe icien s, which makes i a sys em o coupled pa ial di e en ial equa ions. The o -diagonal elemen s in D ep esen he in luence o one di using componen on he o he . The las componen (Cn) is calcula ed om cha ge balance. The ma ix D is calcula ed using ei he he ideal mul i-componen model o Lasaga (1979) o , i om isual inspec ion he e was no eason o hink ha he e is a composi ional dependence o he di usion coe icien , cons an di usion coe icien s we e used, whe e he o -diagonal elemen s o D we e se o ze o, e ec i ely educing 5.1 o: ∂Ci ∂ =∂ ∂x  Di ∂Ci ∂x  (5.2) In he case ha he di usion model wi h cons an pa ame e s did no gi e a sa is ac o y i , he model o Lasaga (1979) o ideal ionic (solid) solu ions was used: Dij=Di 0ij−Di 0zizj ∑ k=1 n zk 2ckDk 0 ⋅ Dj 0−Dn 0 (5.3) whe e D0i is he ace di usi i y o componen i, i.e. when componen i would di use independen ly om all o he componen s, δij is K onecke 's del a ( δij = 1 i i = j, o he wise ze o) and zi he cha ge o componen i. In he case o a bina y sys em, equa ion 5.1 educes o 5.2 wi h D1 gi en by: D1=D0 0D1 0 X0D0 0X1D1 0 (5.4) whe e X0 and X1 a e he ca ionic mole ac ions (X0 = C0 / (C0 + C1)). This model was al eady success ully used by Chak abo y and Ganguly (1992) o model mul i-componen di usion p o iles in ga ne s. The modelling and i ing o he di usion p o iles was done by wo p og ams ha we e de eloped, mcdi and mc i e , ha sol e equa ion 4.1 and allows o di e en models o he calcula ions o he D ma ix. A mo e de ailed explana ion o he p og ams was gi en in chap e 4. One o he objec i es o his s udy is, nex o de e mining he ac ual di usion coe icien s hemsel es, o de e mine he ac i a ion en halpy o di usion ΔH, which is a measu e o he empe a u e dependence o he di usi i y o he componen s. The empe a u e dependence can be exp essed by an A henius s yle ela ion: 73 ln Di 0T=ln D 'i 0−H RT (5.5) The ac i a ion en halpy o di usion is de e mined om he slope in a log D – 1/T plo , which gi es a s aigh line. The p essu e dependence, exp essed h ough he ac i a ion olume ΔV, can be ob ained h ough he s anda d ela ion o he modynamic po en ials and leads o: ln Di 0=ln D 'i 0−ΔE+(P−1)ΔV RT (5.6) whe e ΔE is he ac i a ion ene gy and P p essu e in ba s, and which also de ines a s aigh line in a log D – (P - 1) plo a cons an empe a u e. 5.2 Expe imen al me hods 5.2.1 S a ing ma e ials Th ee di e en se s o expe imen s we e conduc ed wi h a ious s a ing ma e ials, all expe imen s we e conduc ed using he di usion couple me hod, i.e. wo cylinde s o ga ne we e placed oge he wi h hei polished aces acing each o he in a capsule and hen annealed a ansi ion zone condi ions. The i s se o expe imen s was conduc ed wi h polished cylinde s o syn he ic majo i ic ga ne (composi ion Py55Mj45) and na u al py ope ga ne (Py93Alm5G 2) om he Do a Mai a Massi in I aly (Sche l e al. 1991) o de e mine he py ope – majo i e in e di usi i y. Na u al almandine ga ne (Alm70Py15G 15) om he Ö z al in Aus ia oge he wi h he same majo i ic ga ne we e used in he second se o expe imen s o de e mine almandine – majo i e in e di usi i y. The las se o expe imen s was a single expe imen o de e mine he py ope – majo i e in e di usi i y, he s a ing ma e ials o his expe imen we e Do a Mai a py ope ga ne and Ö z al almandine ga ne also used in he o he se s o expe imen s. The cylinde s we e mi o -polished on he sides whe e hey con ac each o he . Be o e he expe imen he e ic i on con en s ha e been de e mined by Mössbaue spec oscopy. The Do a Mai a ga ne con ains no de ec able 74 Table 5.1: Composi ion de e mined by elec on mic op obe o he s a ing ma e ials used in he di usion expe imen s Elemen Do a Mai a ga ne Ö z al almandine Majo i ic ga ne W . % pe 12 O W . % pe 12 O W . % pe 12 O MgO 27.88 2.83 3.32 0.39 35.43 3.52 FeO 1.93 0.11 43.37 2.14 0.01 0.00 CaO 0.62 0.05 5.20 0.44 0.00 0.00 MnO 0.04 0.00 0.21 0.01 0.00 0.00 Al2O3 25.04 2.01 21.56 2.01 12.61 0.99 TiO2 0.02 0.00 0.08 0.00 0.04 0.00 SiO2 44.05 3.00 37.83 2.99 52.54 3.50 To al 99.58 8.00 100.57 8.00 100.63 8.01 amoun o e ic i on (de ec ion limi 0.5 %) whe eas he almandine ga ne om Ö z al con ains 2 ± 1 % o e ic i on. The wa e con en s o Do a Mai a py ope was de e mined by Lu & Kepple (1997) o be 58 ppm, which co esponds o a p o ona ion o 0.02% o he e ahed al si es assuming ha he hyd oga ne subs i u ion is he dominan subs i u ion mechanism. Since majo i ic ga ne is no commonly ound in na u e, i was necessa y o syn hesize i using he mul i-an il appa a us. Fi s eagen g ade MgO, Al2O3 and SiO2 oxide powde s we e mixed in a mo a oge he wi h e hanol o c ea e a suspension. Subsequen ly he e hanol was e apo a ed using an in a- ed lamp and a e his he mixed powde s we e used in a u nace a 1650 °C. The glass ob ained was hen c ushed and g ounded o a ine powde unde e hanol, a e which he e hanol was again e apo a ed. The powde was hen again used in a 1650°C u nace, a e which i was c ushed again and g ound o a ine powde . This powde was hen loaded in o a P capsule (inne diame e 0.8 mm, ou e diame e 1.2 mm, leng h 2.2 mm) o syn hesizing majo i ic ga ne . Jus be o e he syn hesis expe imen s, he ube wi h powde was pu o 5 minu es in a 1000 °C u nace o d y he powde , a e wa ds i was sealed by pu ing he P ube in a capsule die and p essing i in a bench ice. Majo i ic ga ne was hen syn hesized in a mul i-an il appa a us using a 10/5 assembly (numbe s deno e oc ahed on edge leng h and WC cube unca ion edge leng h, espec i ely) a 1800 °C and 16 GPa o 8 hou s. A e eco e y o he pla inum capsule, i was cu in o discs o 0.5 mm hickness and a single side was polished. The g ain size o he syn he ic majo i ic ga ne was 5 – 10 μm and he g ains we e, as a as could be de e mined by TEM, andomly o ien a ed. The cylinde s o na u al ga ne we e single c ys al, hough some o he c ys als we e c acked. The c ys al size o he na u al ga ne s was gene ally bigge han 200 μm. The Do a Mai a py ope ga ne con ained a mino amoun o hyd ous mine als, which we e des oyed be o e he expe imen s by 75 Table 5.2: Run condi ions o he di usion expe imen s. 1Type o di usion couple: Py – Mj = Do a Mai a py ope – majo i ic ga ne di usion couple, Py – Alm = Do a Mai a py ope – Ö z al almandine di usion couple, Alm – Mj = Ö z al almandine – majo i ic ga ne di usion couple. 2Oc ahed on edge size / inne an il unca ion size no a ion Run numbe Di usion couple1 P essu e cell2P essu e Tempe a u e Run du a ion H2986 Py - Mj 14/8 15 GPa 1600 °C 4 h H3050 Py - Mj 14/8 15 GPa 1800 °C 2 h H3076 Py - Mj 14/8 15 GPa 1500 °C 24 h H3084 Py - Mj 10/5 20 GPa 1800 °C 20 h H3086 Py – Alm 14/8 15 GPa 1500 °C 12 h H3088 Alm - Mj 14/8 15 GPa 1600 °C 7 h H3106 Py – Mj 14/8 15 GPa 1900 °C 2 h H3119 Alm - Mj 14/8 15 GPa 1600 °C 4 h H3201 Py - Mj 14/8 12 GPa 1800 °C 4 h H3244 Alm - Mj 10/5 15 GPa 1400 °C 24 h H3257 Py - Mj 10/5 15 GPa 1400 °C 24 h pu ing he cylinde s in a u nace a 1000 °C o 5 minu es. A e his ea men no peaks o hyd ous mine als could be ound by x- ay di ac ion and also inspec ion by SEM could no iden i y any hyd ous mine als. 5.2.2 Appa a us and p essu e cell The di usion expe imen s we e ca ied ou in a 1000 on mul i-an il appa a us a he Baye isches Geoins i u in Bay eu h. The mul i-an il appa a us used was o he 6/8 spli -sphe e ype (Kawai e al. 1973, Kepple and F os 2005), e e ing o he numbe o ou e and inne an ils and guidie block geome y. The inne an ils consis ed o 8 ungs en ca bide cubes wi h hei co ne s unca ed, o o m an oc ahed al shaped p essu e chambe in which he p essu e cell esided. The leng h o he he mocouple was inc eased such ha he he mocouple junc ion was inside he cen al hea e , he capsule was he e o e made smalle han in he s anda d assembly. The di usion couple was con ained wi hin a pla inum capsule in he case o he py ope – majo i ic ga ne di usion couples and wi hin an i on capsule in case o he almandine – majo i ic ga ne di usion couples, he leng h o he capsules was 1.7 mm, he diame e 1.6 mm, and he wall hickness was 0.2 mm. The i on capsule in he expe imen s wi h almandine should ha e bu e ed he oxygen ugaci y nea he i on-wüs i e (IW) bu e . A ungs en 3% henium - ungs en 25% henium he mocouple was used o measu e he empe a u e, he p essu e e ec on he EMF is unknown and has he e o e no been co ec ed o . To p e en he pla inum capsule om en e ing in o he he mocouple ube o om eac ing wi h he i on capsule he he mocouple has been sepa a ed om he capsule wi h a 25 μm hick henium disc in he o me case and a 200 μm hick densi ied Al2O3 disc in he la e case. Be o e he expe imen s, he samples we e d ied in a acuum o en a 175 °C o 24 hou s, a e which he capsules we e p essu e sealed as as as possible in a bench ice. Since he i on capsules oxidized e en in a acuum o en, hey we e no d ied bu s o ed in a desicca o wi h silica gel. A e he p essu e cell was loaded in he mul i-an il appa a us and was p essu ized o he desi ed p essu e, inc easing he empe a u e was done a a a e o 100 °C / minu e, wi h he las 200 °C in one minu e. Quenching was done by cu ing o he powe , he sample was quenched in his way o ~ 100 °C in oughly 10 seconds. Tempe a u e was con olled au oma ically wi h a Eu o he m con olle . Fo a mo e de ailed accoun o he calib a ion o he mul i-an il appa a us he eade is e e ed o chap e 3 o Kepple & F os (2005). 5.3 Analy ical me hods A e eco e y o he sample he capsule was cu pe pendicula o he con ac in e ace be ween he wo hal es o he di usion couple (he ea e e e ed o as he di usion in e ace) and p epa ed as a 30 µm hick hin sec ion. These hin sec ions we e subsequen ly analysed by a JEOL JXA-8200 elec on mic op obe o gain insigh in o he leng h o he di usion p o iles. Since in all cases he di usion p o iles we e oo sho o be measu ed by elec on mic op obe, he samples we e u he p epa ed o TEM. Molybdenum meshes wi h a mesh size o 135 µm we e glued wi h epoxy glue on he hin sec ion a e which he sample wi h mesh was sepa a ed om he slide by dissol ing he c ys albond glue in ace one. The sample was hen u he milled down in an A ion-mille a 4.5 keV and 1.0 mA o elec on anspa ency. F om expe imen s H3201 abou 250- 76 The esul s o he o he py ope – majo i ic ga ne expe imen s a 15 GPa a e gi en in able 5.3. As expec ed, he e is clea ly a empe a u e dependence o he di usion coe icien o bo h majo i e and py ope in ga ne . The ac i a ion en halpy ob ained by i ing he measu ed 'bina y' di usion coe icien o equa ion (4.5) was 291± 51 kJ mol-1 wi h he p e-expon ial being 2.3 x 10-7 cm2 s-1 when using he di usion coe icien s o he majo i e componen . Fo he py ope componen he alues a e 302 ± 61 kJ mol-1 o he ac i a ion en halpy and 4.3 x 10-7 cm2 s-1 o he p e-exponen ial. 5.4.3 P essu e dependence In o de o de e mine he e ec o p essu e on he di usi i y o he majo i e and py ope componen s di usion expe imen s we e conduc ed a 12 and 20 GPa, bo h a 1800 °C using he same py ope – majo i ic ga ne di usion couples as in he expe imen s desc ibed abo e. The measu ed p o iles o expe imen H3201 a e shown in igu e 5.7, un a 12 GPa and 1800 °C o 4 hou s, and can be compa ed o he p o ile shown in igu e 5.5 o un H3050, which was an expe imen a 15 GPa and 1800 °C o 2 hou s. The di usion p o iles o expe imen H3050, un a 15 GPa, a e abou hal he leng h o he di usion p o iles ob ained om expe imen 83 Figu e 5.7: Di usion p o iles o un H3201, an a 12 GPa and 1800 °C. a) Shows he measu ed di usion p o ile exp essed as ga ne end-membe ac ion. b) The loca ion (black line) o he measu ed di usion p o ile. The whi e spo s a e con amina ion ma ks o o he analyses. b a Py ope Majo i e H3201, which was un a 12 GPa. Since he di usion dis ance is p opo ional o √(D ), whe e D is he di usion coe icien and he un leng h o he expe imen , one can es ima e ha a 3 GPa inc ease in p essu e leads o a ac o ~1.4 dec ease in di usi i y. Figu e 5.8 shows he i ed di usion coe icien s o he majo i e componen in ga ne in a Log10 D – P plo o he expe imen s conduc ed a 1800 °C be ween 12 – 20 GPa. F om his plo , using equa ion 5.6, he ac i a ion olume o di usion o he majo i e componen in ga ne was de e mined o be 3.3 (1) cm3 mol-1. Combining his wi h he al eady p e iously de e mined ac i a ion en halpy a 15 GPa, one can deduce an ac i a ion ene gy o di usion o he majo i e componen in ga ne o 241 ± 54 kJ mol-1 and a p e-exponen ial ac o o 1.4 x 10-7 cm2 s-1. 5.4.4 Magnesium – i on in e di usion To de e mine he magni ude o he di usi i y o he majo i e componen ela i e o ha o magnesium – i on in e di usion in ga ne , an expe imen (H3086) on a py ope – almandine di usion couple was conduc ed a 15 GPa and 1500 °C. Since he di usion p o iles ob ained om he eco e ed sample o his expe imen we e much longe han hose ob ained om he Do a Mai a py ope – majo i ic ga ne uns, i was possible o measu e p o iles wi h a la ge scanning pa e n and adia ion damage co ec ion was no necessa y. Since bo h hal es o he di usion couple sepa a ed du ing decomp ession he e was a gap in he di usion p o ile o unknown wid h. The posi ion o he gap is deno ed in igu e 5.9 by he dashed e ical line. The mc i e p og am was modi ied o his, o i he wid h o he gap along wi h he o he a iables. Fo his sample he ideal model o Lasaga (1979) was used, since i ga e a signi ican ly be e esul han he simple cons an di usion coe icien model (a dec ease o 49% in he χ2 alue). The ace di usion coe icien ob ained by i ing he p o iles a e DMg = 2.1 x 10-13 cm2 s-1, DFe = 4.8 x 10-13 cm2 s-1 and DCa = 3.6 x 10-14 cm2 s-1, i.e. he di usi i y o dodecahed ally coo dina ed Mg and Fe in ga ne is 2 – 3 o de s o magni ude as e han he di usi i y o he majo i e componen a he same condi ions ( un H3076) and he di usi i y o Ca is 1 – 2 o de s o magni ude as e han ha o he majo i e componen . 84 Figu e 5.8: P essu e dependence o he di usi i y o he majo i e componen in ga ne . The ob ained ac i a ion olume o di usion is 3.3(1) cm2 mol-1. 5.4.5 Almandine – (Mg) majo i e di usion Expe imen s H3088 (15 GPa, 1600 °C), H3119 (15 GPa, 1600 °C) and H3244 (15 GPa, 1400 °C) we e conduc ed wi h almandine – majo i e di usion couples, o in es iga e he e ec o i on on di usion. The di usion p o ile o expe imen H3244 is shown in igu e 5.10, and is dis inc ly di e en om he di usion p o iles wi h he py ope – majo i e couples and he almandine – py ope couples. The asymme y in he p o iles is clea , wi h he g adien s in Fe and Mg (and o al lesse ex en Ca oo) ex ending much a he in o he majo i ic ga ne hal han in o he almandine pa . Due o he complexi y o he di usion p o ile he i ing was adjus ed manually done, since he mc i e p og am did no p oduce ealis ic i s nea he di usion in e ace and on he almandine side o he di usion couple. The alues o he di usion coe icien s o Mg, Fe and Ca we e chosen by keeping in mind he ela i e magni udes o he di usion coe icien s o Mg, Fe and Ca ob ained om he py ope – almandine di usion expe imen (H3086). The asymme y o he di usion p o ile could only be modelled when a s ong dependence o he di usion coe icien o he di alen ca ions on majo i e composi ion was assumed. The concen a ion dependence o he di usion coe icien was exp essed in he ollowing o m: D=D0  1∑ i=1 N iCi  (5.9) whe e N is he numbe o componen s in he sys em, αi is a coe icien de e mined by i ing and Ci is he concen a ion o componen i. Though he i is no pe ec , he main cha ac e is ics a e well ep oduced and i is s ill possible o make some quali a i e in e ences. The i ed ace di usi i ies o Mg, Fe and Ca a e 3.5 x 10- 14 cm2 s-1, 9.3 x10 -14 cm2 s-1 and 9.3 x 10-15 cm2 s-1 espec i ely. Fo Al and Si hese a e 2.3 x 10-15 cm2 s-1 and 4.6 x 10 -15 cm2 s-1, espec i ely. The absolu e magni ude o he di usion coe icien s may howe e no be 85 Figu e 5.9 : a) he measu ed di usion p o iles o he di alen ca ions in expe imen H3086 a 15 GPa and 1500 °C. The ca ion ac ions a e calcula ed as XMg = XMg / (XMg + XFe + XCa). The i ed ace di usion coe icien s a e DMg = 2.1 x 10-13 cm2 s-1, DFe = 4.8 x 10-13 cm2 s-1 and DCa = 3.6 x 10-14 cm2 s-1. The e ical dashed line indica es he posi ion o he gap in he p o ile. b) A da k- ield STEM image o he loca ion o he di usion p o ile (black line) in expe imen H3086. The ho izon al lines a e due o he pic u e being a mosaic o se e al pic u es. b aPy ope Almandine ep esen a i e o he bulk di usion coe icien , since bo h sides con ain a ela i ely high densi y o disloca ions. The ' shoulde ' in Fe and Mg ex ending in o he majo i ic ga ne side could only be modelled i he di usi i y in majo i ic ga ne o Mg was a leas a ac o 15 as e han in he almandine side (αMg = 30 -50) and he di usi i y o Fe a ac o 5 highe . (αFe = 10-15). The composi ions we e also exp essed in e ms o py ope, almandine, g ossula and Mg-majo i e componen s ( ugu e 5.11). The addi ion o an and adi e componen did no change he p o iles ( he and adi e componen was nea ly equal o ze o), which is also suppo ed by he EELS measu emen s in he o he almandine – py ope and almandine – majo i ic ga ne di usion couples ha we e un in Fe capsules which showed a Fe3+ / (Fe2+ + Fe3+) a io o nea ly ze o. The addi ion o an Fe-majo i e componen p oduced a la ge nega i e Mg-majo i e componen a he almandine side o he di usion p o ile, and was hus conside ed un ealis ic. Exp essing he 86 Figu e 5.10:The measu ed di usion p o ile (a) and loca ion (black line) (b) o expe imen H3244, un a 1400 °C and 15 GPa o 24 hou s. No e he shoulde o Fe in he di usion p o ile ex ending in o he majo i ic ga ne pa o he di usion couple. b a Almandine Mj ga ne Majo i e Almandine composi ion in e ms o ga ne componen s esul ed in a py ope peak nea he poin whe e he Mg-majo i e componen d ops o ze o. In p inciple his could be he esul o p esence o a miscibili y gap be ween almandine ich ga ne and Mg-majo i e ich ga ne . Howe e , he e is no e idence o a miscibili y gap be ween majo i e ich ga ne and almandine ich ga ne , Ringwood and Majo (1971) syn hesized majo i ic ga ne s nea he almandine – majo i e join a 1000 °C. Because miscibili y gaps end o close a highe empe a u es i is hus unlikely ha one exis s a he condi ions o he di usion anneals. Mo eo e , he exis ence o a miscibili y gap would also equi e nex o he p ecipi a ion o a py ope ich phase, he p ecipi a ion o a Fe-majo i e ich phase which is no obse ed and is no e y likely conside ing ha end-membe Fe-majo i e is no s able (Oh ani e al. 1991). Di usion in he almandine – majo i ic ga ne expe imen s has he e o e no been in e p e ed in e ms o di usion o ga ne componen s, as in he expe imen s desc ibed abo e, bu in e ms o he di usion o ca ions. The i ing has been done wi hou ega d o end-membe componen s, i.e. magnesium in he Mg-majo i e and py ope componen has been ea ed as a single di using componen . Expe imen H3119 (see igu e 5.12) shows a simila ly shaped p o ile, wi h again a shoulde o Mg, Fe and Ca 87 Figu e 5.12: Di usion p o ile ob ained om expe imen H3119, an a 1600 °C and 15 GPa o 4 hou s. The shape o he di usion p o iles show g ea simila i y wi h hose om expe imen H3244. Again, he di usion p o iles could only be modelled by assuming a s ong dependency o he di usi i y o Mg, Fe and Ca on he majo i e con en . Figu e 5.11: P o ile H3244 exp essed in e ms o py ope, almandine, g ossula and Mg-majo i e componen s. No e he spike in he py ope componen a he loca ion whe e he Mg- majo i e componen dec eases o ze o. Majo i e Almandine pene a ing deepe in o he majo i ic ga ne side han in o he almandine side. The di usion p o ile has again been i ed by hand using he abo e men ioned me hod. The ob ained ace di usion coe icien s a e o Mg, Fe and Ca 2.1 x 10-13 cm2 s-1, 5.6 x 10-13 cm2 s-1 and 3.1 x 10-14 cm2 s-1, espec i ely. Fo Al and Si 2.8 x 10-14 cm2 s-1 and 2.4 x 10-14 cm2 s-1, espec i ely. The alues o Mg, Fe and Ca a e e y simila o hose ob ained in he almandine – py ope di usion expe imen , howe e his un was pe o med a a empe a u e 100 °C highe . Howe e i mus again be s essed ha he i o he model o he measu ed di usion p o iles o his un is no op imal which migh be caused by he used minimiza ion ou ine o negligence o he e ec o i on on he di usi i y o he elemen s. The o he almandine – majo i ic ga ne un shows a simila di usion p o ile. 5.5 Discussion Al hough he di usion expe imen s we e conduc ed a ela i ely high empe a u es, he di usion p o iles we e s ill oo sho o be measu ed by elec on mic op obe, indica ing ha di usion o he majo i e componen is much slowe han he in e di usion o he di alen ca ions in ga ne (Mg, Ca, Fe and Mn, which di use as enough such ha hey can be measu ed a e expe imen s on a mic op obe a hese condi ions). This is also con i med by he py ope – almandine di usion couple (H3086), which p oduced p o iles ha a e conside ably longe and o which he i ed di usion coe icien s o he dodecahed ally coo dina ed ca ions a e 2 – 3 o de s o magni ude as e o Mg and Fe, and 1 – 2 o de s o magni ude as e o Ca, as compa ed o he di usi i y o he majo i e componen in ga ne . The ac ual alues a 1600 °C and 15 GPa, DMj = 1.4 x 10-15 cm2 s-1, a e 88 Figu e 5.13: The di usion dis ance o he majo i e componen as unc ion empe a u e and ime. The numbe s on he lines a e in me e s. See ex o mo e explana ion. compa able o he ( ace ) di usi i y o Si in wadsleyi e a 1600 °C and 16 GPa, which was also de e mined o be 1.4 x 10-15 cm2 s-1 (Shimojuku e al. 2009). This again s esses ha di usion o he majo i e componen in ga ne is slow. 5.5.1 Homogeniza ion o he uppe man le Because o i s highe alumina con en , he oceanic c us will consis o 80 – 90 ol. % ga ne in he ansi ion zone (I i une e al. 1986). The e o e, when he oceanic c us is subduc ed, i will o m a majo i e inhomogenei y in he Ea h's man le. Fo he unde s anding o he di e en ia ion o he man le, i is impo an o know whe he he oceanic c us will pe sis as an inhomogenei y in he man le o no o e geological ime scales. The di usion dis ance o he majo i e componen has been calcula ed as unc ion o empe a u e and ime a 18 GPa using he di usion da a p esen ed in his chap e . When di usion occu s o e a leng h scale ha is signi ican ly longe hen he g ain size, g ain bounda y di usion is he dominan di usion mechanism a condi ions whe e g ain bounda y di usion is signi ican ly as e (Ha ison 1961). The g ain bounda y coe icien has been aken as 104 x he bulk di usion coe icien , based on g ain bounda y di usion expe imen s on YAG- ga ne c ys als a 1500 °C (Ma qua d (née Ha mann) e al. 2011). The di usion dis ance was calcula ed as: x=  Dgb (5.10) whe e Dgb is he g ain bounda y coe icien and di usion ime. The esul s a e plo ed in igu e 5.13. Es ima es o he empe a u e on he man le adiaba a 18 GPa ange om 1500 °C o 1800 °C (chap e 3). The igu e shows ha a hese condi ions, he majo i e componen will only be able o di use o e a dis ance o 5 – 15 me e s on he ime scale o he age o he Ea h. I is clea ly no possible o homogenize he man le by solid s a e di usion and he oceanic c us will pe sis as a majo i e homogenei y in he Ea h's man le. 5.5.2 Rheology o ga ne in he ansi ion zone In de o ma ion p ocesses con olled by disloca ion c eep ( h ough disloca ion climb) and di usion c eep mechanisms, he olume di usi i y o he slowes di using ion is an impo an a e con olling ac o (Wee man 1957, Poi ie 1985). As will be explained below, he e a e a gumen s o assume ha oc ahed al and e ahed al Si do no di use as independen componen s, bu di use as one componen , which migh be e en as e han he di usion o Al in ga ne . I can hus be assumed ha he di usi i y o he majo i e componen is ep esen a i e o he di usi i y o he slowes componen . The c eep a es o disloca ion c eep (by he Wee man model) and di usion c eep a e gi en by espec i ely: ˙=disl Dsd b3.5 M0.5     4.5  kT and ˙=di Dsd   d2k T (5.11) whe e α is a geome ic ac o , Dsd he sel -di usi i y o he a e con olling ion, b he bu ge s ec o o he disloca ion, M he densi y o disloca ion sou ces, σ he applied s ess, μ he shea modulus, k Bol zmann's 89 cons an , T empe a u e, d g ain size, Ω olume o he acancy. Using a shea modulus a 16 GPa and 1600 °C o 85 GPa o majo i ic ga ne and 104 GPa o wadsleyi e (Nishiha a e al. 2008, Hun e al. 2010), and he <1 1 1> o <1 0 0> Bu ge s ec o s o he ac i a ed slip sys ems in (majo i ic) ga ne (Co die e al. 1996) and <1 1 1> o [1 0 0] o wadsleyi e (Demouchy e al. no da e), and assuming simila disloca ion sou ce densi ies, g ain size and olume o acancies o ga ne and wadsleyi e one inds ha i he di usi i y o e ahed ally coo dina ed Si in ga ne is less han in wadsleyi e, majo i ic ga ne will be mo e esis an o low han wadsleyi e (i.e. 's onge '). The ela i e de o ma ion a es a e hen gi en by he ollowing equa ion: ˙ ϵg ˙ ϵwads ≈0.2 Dsd g Dsd wads (5.12) 90 Figu e 5.14: Composi ion o a g owing ga ne g ain as unc ion o he adial dis ance and o se e al imes. a) G aphical ep esen a ion o he model. The sphe ical ga ne g ain (ligh ed) is su ounded by py oxene (g een). Dissolu ion o py oxene in o ga ne (hea y a ows) leads o he g ow h o he ga ne g ain (da k ed ci cle and ligh a ows). The g aph in he igh side o he g ain shows how o in e p e he concen a ion p o iles in b) and c). b) A 1 cm g ain ep esen a i e o he lowe pa o he subduc ing li hosphe ic man le, condi ions a e 18 GPa and 1400 °C, and c) is ep esen a i e o he subduc ed oceanic c us , condi ions a e 18 GPa and 1000 °C. G ain g ow h is s opped a e an amoun o majo i e componen co esponding o a homegonous composi ion o Py60Mj40 has luxed in o he g ain. A e his he g ain is le o homogenize. The g ain size can be de e mined by inding he posi ion whe e he p o iles cu he uppe 70% majo i e line (b) o he 55% majo i e (c) line. b c a o disloca ion c eep, and ˙ ϵg ˙ ϵwads ≈Dsd g Dsd wads o di usion c eep. I he di usi i y o he majo i e componen in ga ne is o he same o de as ha o he di usi i y o Si in wadsleyi e, he e will be no g ea con as be ween majo i ic ga ne and wadsleyi e. Howe e , i due o he low di usi i y o he majo i e componen he ga ne phase did no equilib a e, one migh expec a lowe di usi i y o Si, since i will be con ined o he e ahed al si e. The s eng h o ga ne in subduc ion zones, he loca ion whe e mos likely he e will be lack o equilib a ion due o lowe empe a u es and i s dynamic cha ac e , in his case will be con olled by he deg ee o equilib a ion and hus he di usi i y and g ain size o ga ne . To model his, a p og am has been de eloped ha simul aneously models di usion in a (sphe ical) g ain, and di usion con olled g ow h o he same g ain. A mo e de ailed explana ion o he code is gi en in chap e 4.2. Figu e 5.14 shows how long i will ake o ens a i e o dissol e in o a ga ne g ain and hen homogenize he g ain o wo di e en scena ios. Scena io A ( igu e 5.14b) co espond o a g ain in he middle o lowe pa o he subduc ing li hosphe ic man le. Condi ions he e a e assumed o be 1400 °C and 18 GPa, which co espond o condi ions on an a e age subduc ion geo he m (Emme son and McKenzie 2007). The composi ion o he newly g own majo i ic ga ne (Py30Mj70) was in e ed om phase diag ams by Gaspa ik (2003) and Akaogi and Akimo o (1977). The maximum in lux o majo i e componen was chosen such ha he inal composi ion a e homogeniza ion was Py60Mj40, co esponding o high-p essu e expe imen s on py oli ic composi ions (I i une 1987). The ini ial g ain size is 1 cm. The esul s o he modelling show ha i akes abou 4 My o he g ain o g ow o i s inal size. Howe e , a e his i s ill has a la ge co e o almos pu e py ope composi ion. I akes abou 20 My be o e he g ain is homogenized. Assuming an a e age a e o bu ial due o subduc ion o 20 mm y-1, i would ake 12.5 My o pass he ansi ion zone. Fo he subduc ed li hosphe ic man le homogeniza ion is hus oughly a he same imescale as he subduc ion p ocess. Things, howe e , a e di e en o he subduc ed oceanic c us (scena io B, igu e 5.14c ). Condi ions in his case a e 1000 °C and 18 GPa, again om he compu ed subduc ion geo he m o Emme son and McKenzie (2007). The composi ion o he newly g own majo i ic ga ne was Py45Mj55, om Akaogi and Akimo o (1977) and he maximum in lux was again chosen such ha he inal composi ion would be Py60Mj40, co esponding o expe imen s conduc ed on e ac o y MORB ma e ial a e pa ial mel ing and ans o ma ion o an eclogi e assemblage, ep esen a i e o he subduc ed oceanic c us (I i une e al. 1986). The ini ial g ain size was aken as 1 mm, which is also a ypical g ain size o eclogi es. The plo in igu e 5.14b shows ha i akes o e 300 My s o comple e equilib a ion. A e 12.5 My only abou 38% o he py oxene would ha e dissol ed in o ga ne . I migh hus be mo e likely ha he basal ic c us will p ese e a me as able assemblage o ga ne + clinopy oxene + o hopy oxene du ing i s subduc ion ins ead o he ga ne i e assemblage o , since ens a i e b eaks down o s isho i e + wadsleyi e o ingwoodi e abo e 17 GPa a hese condi ions (Akaogi and Akimo o 1977), ga ne + clinopy oxene + wadsleyi e/ ingwoodi e + s isho i e. The sluggish eac ion kine ics o ens a i e 91 b eakdown may hen also esul in he o ma ion akimo oi e a g ea e dep hs (Hog e e e al. 1994). The middle o lowe pa o he subduc ing slab is hus expec ed o be able o dissol e all i s ens a i e in o ga ne du ing he ime ha , hough wi h a signi ican delay. This would mean ha he e would be no signi ican con as in s eng h be ween ga ne and wadsleyi e in he ansi ion zone, excep pe haps o he uppe ~80 km o he ansi ion zone. Di usion o he majo i e componen in ga ne is oo slow o dissol e al he py oxene in o ga ne in he oceanic c us du ing subduc ion. I migh he e o e be expec ed ha a signi ican amoun o py oxene we be p ese ed as me as able phase. This would make ga ne ela i ely s ong, howe e since py oxenes a e ela i ely weak (Ohuchi e al. 2010), he p ese a ion o py oxene may make he oceanic c us weake han expec ed in he ansi ion zone. Ex apola ion o he di usion da a in his s udy o he highe p essu es p e ailing in he ingwoodi e s abili y ield shows ha he di usi i y o he majo i e componen a hese condi ions is again simila o he di usi i y o silicon sel -di usion in ingwoodi e, i.e. 3.5 x 10-17 cm2 s-1 o majo i ic ga ne s. 8.5 x 10-17 cm2 s-1 a 22 GPa and 1500 °C (Shimojuku e al. 2009). The conclusions in he p e ious pa ag aph hus also hold o ingwoodi e s abili y ield. 5.5.3 Compa ison wi h p e ious expe imen al da a Chak abo y and Ganguly (1992) de e mined he alue o he ac i a ion olume o di usion o Mg in ga ne o be 5.3 ± 3.0 cm3 mol-1. Chak abo y and Rubie (1996) ex ended hei da a wi h hei own o include Mg ace di usi i y da a done o e a b oade ange o p essu es o educe he e o in ac i a ion olume de e mined by Chak abo y and Ganguly (1992). They de e mined om he combined da a se an ac i a ion olume o Mg ace di usion in ga ne o 8 ± 1 cm3 mol-1. The p essu e dependence o he majo i e componen , 3.3 ± 0.1 cm3 mol-1, de e mined in his s udy is hus signi ican ly lowe . Chak abo y and Ganguly (1992) also de e mined he ac i a ion en halpy o Mg di usion in ga ne o be 285 ± 38 kJ mol-1 om a mul i-componen di usion s udy, Chak abo y and Rubie (1996), in hei ace di usion s udy, de e mined a lowe alue o he ac i a ion en halpy o Mg di usion o 226 ± 21 kJ mol-1. Compa ing hese o he alues de e mined in his s udy show ha hey a e e y simila , i.e. 241 ± 54 kJ mol o he di usion o he majo i e componen in ga ne . The ac ha di usion o he majo i e componen in ol es di usion o bo h dodecahed ally and oc ahed ally coo dina ed ca ions does no seem o in luence he ac i a ion ene gy p o oundly. The di e ence in ac i a ion olumes be ween di usion o he majo i e componen and di usion o he eigh - old coo dina ed Mg, as de e mined by Chak abo y and Rubie (1996), sugges a di e en di usion mechanism in ol ing a less comp essible si e. Hazen and Finge (1978) indeed epo ha he oc ahed al si e o ga ne is less comp essible han he dodecahed al si e, which migh explain he di e ence in ac i a ion olumes. 5.5.4 E ec o majo i e con en on di usi i y o he elemen s Though he di usion p o iles ob ained om he almandine – majo i ic ga ne di usion couples we e oo complex o model well enough o de e mine absolu e di usion coe icien s om, i is s ill possible o each some quali a i e conclusions. One o he p ominen ea u es o all di usion p o iles in he almandine – majo i ic 92 by: Ico =IsI0 u (5.18) Fi ing o 5.17 o he da a has been done by minimizing he χ2 – alue, which is de ined as: 2=∑ i nOi−Ei2 Oi (5.19) Whe e Oi is he obse ed in ensi y o he cha ac e is ic x- ay line and Ei is he expec ed o i ed in ensi y o he cha ac e is ic x- ay line. The minimiza ion is done by using he non-linea Le enbe g – Ma quand minimiza ion algo i hm a ailable in he Ma lab so wa e package. The e a e now wo scena ios. In he i s scena io, he s anda d case, beam damage is no signi ican and we can use he s anda d me hod, i.e. using he simple a i hme ic mean o all measu emen , o calcula e he in ensi y o he measu ed x- ay peak. In he second one, whe e adia ion damage is signi ican , equa ion 5.17 should be used o de e mine he adia ion co ec ed in ensi y o he measu ed x- ay peak. To do his, we can use he a io o he χ2 – alue o bo h models co ec ed o he deg ees o eedom in bo h models in an F- es wi h he ollowing F s a is ic: F=n 2 c 2⋅n−3 n−1 (5.20) Whe e χn2 is he χ2 alue o he no mal case and χc2 is he χ2 alue o he adia ion damage co ec ed case. The expec ed alue o F when using 8 measu emen s pe spo is 1 2/3 when he e is no di e ence be ween he 99 Figu e 5.15 :The in ensi y o he MgKα peak in majo i ic ga ne as unc ion o he ime elapsed since he s a o he measu emen . Solid do s co espond o he ac ual measu emen s, each do co espond o he cumula i e coun s o e a 15 second in e al. The solid line is he i ed in ensi y using he model p oposed he e. models. The adia ion damage co ec ed model is used when he F alue exceeds a ce ain minimum alue, which can be ob ained om s anda d ables o he F-dis ibu ion (in his hesis 4.88, which co esponds o a 95% con idence le el when using 8 measu emen s pe spo ). Appendix 5.2: Quan i ica ion o he EDS analyses The ac ual elemen al concen a ion can be calcula ed om he in ensi ies o he cha ac e is ic x- ay peaks using Cli -Lo ime k- ac o s when abso p ion can be neglec ed: CA CR =kAR IA IR (5.21) whe e A and R deno es elemen A and he a io-elemen R espec i ely, C a e he concen a ions, I he cha ac e is ic x- ay in ensi ies and kAR is he Cli -Lo ime k- ac o o elemen A using R as a io-elemen . The Cli -Lo ime k- ac o s a e de e mined by measu ing specimens wi h a known composi ion. As addi ional cons ain o calcula e he ac ual concen a ions can be used ha he concen a ions o all elemen s should add up o 100%. Usually abso p ion can no be comple ely neglec ed and one should co ec he k- ac o s o abso p ion: kAR *=kAR A spec R spec 1−exp −R spec  cosec  1−exp −A spec  cosec  (5.22) whe e k*AR is he co ec ed k- ac o , μspeci is he mass abso p ion coe icien (MAC) o cha ac e is ic line i in he specimen, ρ he mass hickness o he oil and α he ake-o angle o he x- ays ha hi he de ec o . The MAC is calcula ed as ollows: i spec=∑ j Cji j (5.23) whe e Cj is he concen a ion o elemen j and μij is he MAC o he cha ac e is ic line o elemen I by pu e elemen j. As can be seen in hese equa ions, one needs o know he hickness o he specimen. Because measu ing he exac hickness o he oil is o en di icul , Van Cappellen and Doukhan (1994) used ne neu al cha ge as an addi ional c i e ion o de e mine he hickness. Fo easie calcula ion, hey app oxima ed equa ion 5.22 wi h a i s o de Taylo expansion, which makes he ne cha ge as unc ion o hickness quad a ic in na u e and easily sol able. In his hesis he B en oo inding algo i hm (P ess e al. 1992) in combina ion wi h he ull exp ession o 5.22 is used o quan i y he elemen al concen a ions. The sou ce code o he p og am (TemQuan ) is a ailable upon eques . Appendix 5.3:P ecision o TEM EDS measu emen s The di usion p o iles o he majo i ic ga ne – py ope di usion expe imen s we e modelled wi h a cons an composi ion independen di usion coe icien . Though bina y di usion p o iles can be modelled by a single di usion coe icien , i should s ill be composi ion dependen h ough equa ion 5.0, unless he di usion 100 coe icien s o he majo i e componen and py ope componen a e equal. Chak abo y and Ganguly (1992), o example, modelled hei di usion p o iles o di usion in he almandine – spessa ine di usion couples wi h wo di e en di usion coe icien o each side o he couple, poin ing ou he composi ional dependence o he di usion coe icien s. Howe e , he p ecision o he analyses on he TEM may le i appea as i he bina y di usion coe icien is composi ion independen , since only sligh ly asymme ic p o iles a e no dis inguishable om pe ec ly symme ic p o iles. To de e mine wha he sensi i i y is o he p o iles measu ed by he TEM o he composi ion dependence o he bina y di usion coe icien , se e al p o iles ha e been modelled wi h a di e en composi ion dependence wi h he use o he Lasaga model. F om he calcula ed p o ile a se o 25 poin s has been aken as 'measu emen da a' and his da a has been i ed by he composi ion independen di usion model. The i o mis i is plo ed in igu e 5.16. The g ay a ea line gi es he ypical e o o he analy ical TEM using EDS, which is 1.5 % unde op imal condi ions. The bes elemen o check o his would be Al, since o e e y 1 % o majo i e componen inco po a ed, he Al ac ion will be educed by 0.02 pe o mula uni . Figu e 5.16 shows ha he a io o DPy o DMj should be below 10, o he wise asymme y o he di usion p o iles would be oo s ong o emain unde ec ed by he TEM. Howe e he e o in he de e mined di usion coe icien would be smalle , as is poin ed ou in able 4.4, since he de e mined di usion coe icien using he composi ion independen di usion 101 Figu e 5.16: A plo o he mis i by i ing a composi ion independen di usion model o da a gene a ed om a composi ion dependen model. The alue is he a io o DPy o DMj and he g ay a ea deno es he p ecision o he TEM o Al in majo i ic ga ne . Table 5.4 : The ob ained alues when using he cons an di usion coe icien model when i ing da a o he Lasaga mul i-componen model. On he le side he DMj – DPy a io used o model he 'measu ed' da a wi h he use o he ideal mul i-componen model by Lasaga, on he igh side he di usion coe icien ob ained by i ing he measu ed da a o a cons an composi ion independen di usion coe icien ela i e o he DPy alue used as inpu o he Lasaga model. DMj – DPy a io Fi ed coe icien 0.01 0.013 0.1 0.13 0.5 0.56 1 1.0 2 1.63 5 2.67 10 3.32 coe icien model would lie be ween he ac ual alues o DPy and Dmj. Appendix 5.4: Majo i ic ga ne – Do a Mai a py ope di usion couple p o iles H2986 P = 15 GPa T = 1600 °C = 4h DPy = 1.4(2) x 10-15 cm2 s-1 DMj = 1.4(2) x 10-15 cm2 s-1 H3076 P = 15 GPa T = 1500 °C = 24 h DPy = 4(2) x 10-16 cm2 s-1 DMj = 3(1) x 10-16 cm2 s-1 H3106 P = 15 GPa T = 1900 °C = 2h DPy = 3.7(7) x 10-14 cm2 s-1 DMj = 4(1) x 10-14 cm2 s-1 102 H3257 P = 15 GPa T = 1400 °C = 24 h DPy = 2.5(8) x 10-16 cm2 s-1 DMj = 3.4(8) x 10-16 cm2 s-1 H3084 P = 20 GPa T = 1800 °C = 20 h DPy = 2.2(7) x 10-15 cm2 s-1 DMj = 2(1) x 10-15 cm2 s-1 103 Chap e 6: Exsolu ion o ga ne om o hopy oxene 6.1 In oduc ion O hopy oxene, wi h spaceg oup Pbca and composi ion anging om end-membe s ens a i e Mg2Si2O6 o e osili e Fe2Si2O6 can inco po a e aluminium by wo di e en subs i u ion mechanisms. The i s mechanism is he calcium o magnesium Tsche mak subs i u ion mechanism (end-membe s CaAl2SiO6 and MgAl2SiO6). Bo h Ca/Mg and Si a oms a e subs i u ed o wo Al a oms in he py oxene s uc u e. The Al inco po a ed in he e ahed al chains s ongly p e e s he Si(B) si e, in acco dance wi h he Al-a oidance p inciple (Okamu a e al. 1974). The aluminium in he oc ahed al laye s has a p e e ence o he M1 si e, howe e he M2 si es accommoda e Al oo (Okamu a e al. 1974, Ganguly and Ghose 1979). In he p esence o excess silica, aluminium can also be inco po a ed (by he second mechanism) by a calcium Eskola componen (Ca0.5AlSi2O6), whe e disc epancy in cha ge on he M si es be ween Al3+ and Ca2+ is balanced by a acancy on he M2 si e (Gaspa ik and Lindsley 1980). The ens a i e end-membe o he py oxene se ies has di e en polymo phs depending on he p essu e and empe a u e condi ions. Figu e 6.1 shows he phase diag am o MgSiO3 a uppe -man le p essu e. Up o ± 15 GPa he di e en py oxene polymo phs a e s able, a e which i b eaks down o ei he majo i e o wadsleyi e/ ingwoodi e + s isho i e. The di e en polymo phs ha a e s able a e o hoens a i e (space g oup Pbca), p o oens a i e (space g oup Pbcn), low clinoens a i e (space g oup P21/c), high empe a u e high clinoens a i e (space g oup C2/c) and high p essu e high clinoens a i e (space g oup C2/c). Though he las wo polymo phs ha e he same space g oup, hei oxygen packing sequence is di e en , i.e. he high p essu e polymo ph has a cubic close packing sequence and he high empe a u e o m has a hexagonal close packing sequence (Thompson and Downs 2003). Though he pu e end-membe HT clinoens a i e MgSiO3 has only a 104 Figu e 6.1: The phase diag am o MgSiO3 a he condi ion o Ea h's uppe man le showing he s abili y o he di e en ens a i e polymo phs, a e Gaspa ik 2003. e y limi ed s abili y ield, he subs i u ion o Mg by Fe expands he s abili y ield o HT high clinoens a i e signi ican ly (A l e al. 1998). P e ious s udies ha e shown ha bo h high clinoens a i e polymo phs a e no quenchable and ans o m back o he P21/c low ens a i e polymo ph upon e u n o oom condi ions (Kanzaki 1991, A l e al. 1998). Fo he sake o simplici y in he es o his chap e , when high clinoens a i e is men ioned, he high p essu e o m o high clinoens a i e is mean . As a gued in chap e 5, slow di usion kine ics o he majo i e componen in ga ne hampe s he dissolu ion o py oxene in ga ne in he cold subduc ed slab. The e o e he py oxene componen in he subduc ed slab can be iewed as a (semi-)isola ed sys em. Expe imen al s udies (I i une e al. 1986; I i une 1987) ha e shown ha he amoun o aluminium ha can be dissol ed in py oxene dec eases wi h inc easing p essu e. As a esul o his, ga ne will be exsol ed om py oxene while he slab is subduc ed in o he man le. The a e a which his will occu in py oxene will be con olled by he di usi i y o aluminium in high clinoens a i e a enhanced p essu es, o which he e a e cu en ly no da a a ailable. Fo py oxene exsolu ions in ga ne i has been shown ha he e is a opo ac ic ela ionship be ween he ga ne hos and he py oxene exsolu ions (Spengle 2006). Howe e , he opo ac ic ela ion be ween py oxene and exsol ed ga ne a high p essu e, i.e. in he Ea h's ansi ion zone, whe e py oxene has a monoclinic s uc u e (high clinoens a i e C2/c) is unknown a p esen . The e o e, expe imen s on na u al aluminous ens a i e ha e been conduc ed o in es iga e wha happens o o hopy oxene ha is p esen in he subduc ed slab when i is anspo ed in o he man le. Expe imen s we e conduc ed in he p esence o ga ne , o close simula e wha occu s in he Ea h du ing subduc ion. 6.2 Expe imen al se up Expe imen s ha e been conduc ed in a 1000- on mul i-an il de ice a he Baye isches Geoins i u , using a 14 / 8 p essu e cell, indica ing he oc ahed on edge leng h and he unca ion edge leng h o he ungs en-ca bide an ils in millime es, espec i ely. The p essu e cells we e MgO oc ahed a wi h a cen al hole in o which sample and a LaC O3 s epped u nace was placed, o a mo e de ailed desc ip ion see chap e 3 on expe imen al me hods. The leng h o he pla inum capsules was 2.4 mm, he diame e 1.6 mm and he wall hickness 0.2 mm. Tempe a u e was measu ed by W3%Re – W25%Re he mocouples wi h a junc ion jus on op o he capsule. The he mocouple wi es we e isola ed om he capsules by a 25 μm henium disc o p e en pla inum om in uding in o he he mocouple ubes. The s a ing ma e ials we e couples o single c ys al mi o polished Do a Mai a py ope and Tanzania ens a i e cylinde s. The Do a Mai a py ope c ys als we e he same as used in he di usion expe imen s desc ibed in chap e 5. The chemical composi ion (see able 6.1) o he Tanzania ens a i e c ys als we e de e mined by elec on mic op obe and co espond o hose de e mined by 105 Table 6.1 : Chemical composi ion o he Tanzania ens a i e, a e Rauch (2000) Oxide W . % SiO258.10 FeO 2.00 MgO 38.50 Al2O31.50 MnO 0.10 CaO 0.15 Na2O 0.01 To al 100.35 Fe3+/Fe o 23% Rauch (2000). The expe imen s we e conduc ed a 1700 °C and 15 GPa, wi h un du a ions be ween 1 hou and 19 hou s, he condi ions a e lis ed in able 6.2. A e he end o he un he sample was quenched by cu ing o he powe , esul ing in a empe a u e d op in 10 seconds o oughly 100 °C. 6.3 Analy ical se up A e eco e y o he samples he capsule we e cu by a diamond wi e saw along he leng h o he capsule and moun ed in an epoxy block, polished and u he p epa ed o analyses by elec on mic op obe and SEM. The chemical composi ions o he samples we e measu ed by means o an elec on mic op obe, using 20 s coun ing ime o he peak posi ion and 10 s coun ing ime o he backg ound posi ion, 15 kV accele a ion ol age and 15 nA beam cu en . The s anda ds and cha ac e is ic x- ay peaks used o de e mine he chemical composi ion a e lis ed in able 6.3. Two expe imen s, H2975 and S4378, we e also p epa ed o u he examina ion by TEM. The TEM samples we e i s polished down o a hickness o 30 μm, a e which a molybdenum mesh wi h a squa e size o 135 μm was glued upon hem using A aldi e epoxy glue. The c ys albond glue be ween he sample and he glass slide which was used o polishing down he sample o 30 μm was hen dissol ed by ace one. The sample was hen A -ion milled o elec on anspa ency in a Ga an Duomill 600, unde an angle o 14 ° a 4.5 kV and 1.0 A. Mic os uc u al cha ac e iza ion and de e mina ion o opo ac ic ela ions be ween he (clino-)ens a i e hos and he ga ne exsolu ions we e pe o med using a Philips CM20 FEG TEM ope a ing a an accele a ion ol age o 200 kV. 106 Table 6.2: Run condi ions o he expe imen s Run numbe P essu e Tempe a u e Du a ion H2975 15 GPa 1700 °C 19 h S4378 15 GPa 1700 °C 19 h S4391 15 GPa 1700 °C 1h Table 6.3 : Elec on mic op obe s anda ds & peaks Elemen S anda d Cha ac e is ic peak Mg Fo s e i e MgKα Fe Me allic i on FeKα Ca Diopside CaKα Al Py ope AlKα Mn MnTiO3 MnKα Si Fo s e i e SiKα Ti Ru ile TiKα 6.4 Resul s 6.4.1 De e mina ion o he ens a i e polymo ph As explained, ens a i e has se e al polymo phs and he e o e is impo an o de e mine o which polymo ph he opo ac ic ela ionship be ween he ens a i e hos and majo i ic ga ne was de e mined. The polymo phs ha we e conside ed a e o hoens a i e (Pbca), p o oens a i e (Pbcn), low clinoens a i e (P21/c), and high clinoens a i e (C2/c). The sys ema ic p esence ( ig. 6.2a) o 100 e lec ions in he [001] zone axis pa e n indica e ha i canno be ei he he p o oens a i e o high clinoens a i e polymo ph. F om he geome y o he zone axis pa e n i can also be excluded ha he h00 e lec ions a e caused by double di ac ion. Figu e 6.2b shows he di ac ion pa e n aken down he <013> zone axis. The spacing o he h31 e lec ions indica es ha he d- spacing o he 100 planes is ± 9.2 Å. This d-spacing excludes he possibili y ha he in es iga ed ens a i e c ys al is he o hoens a i e polymo ph (whe e he d-spacing is 18.2 Å) and hus needs o be he low clinoens a i e polymo ph. 6.4.2 Mic os uc u e Figu e 6.3 shows a backsca e ed elec on (BSE) image o he ens a i e pa o he sample o expe imen H2975. The ens a i e pa con ains a high densi y o ga ne p ecipa es wi h a The exsol ed g ains o majo i ic ga ne show a clea a angemen ela i e o he hos py oxene, he long axis o he p ecipi a es a e pa allel o he (100) planes o he py oxene hos . The le side o he pic u e shows ec ys allized g ains o clinoens a i e ha 107 Figu e 6.2: Di ac ion pa e ns o he eco e ed low clinoens a i e sample ha show i is he low clinoens a i e polymo ph (see ex ). a) Di ac ion pa e n down he [001] di ec ion in low clinoens a i e and b) down he <013> di ec ion. a b Figu e 6.3: BSE image o he low clinoens a i e pa o expe imen H2975. The shape p e e ed o ien a ion o he ga ne p ecipi a es in he unde o med single c ys al pa (cen e ) is clea ly isible. On he le he de o med pa is isible. The middle g ay phase is low clinoens a i e, he ligh g ay phase majo i ic ga ne and he da k g ay phase is s isho i e. p obably o med due o he inden a ion o he he mocouple. The composi ion o he majo i ic ga ne p ecipi a es a e lis ed in able 6.4. The componen ac ions a e calcula ed using he me hod explained in chap e 5. The p ecipi a es ha e a high majo i e componen (± 61 %), which is sligh ly highe han he equilib ium composi ion in he Mg3Al2Si3O12 – Mg4Si4O12 sys em a he expe imen al condi ions (chap e 2), based on da a om Gaspa ik (2003). The hickness o he majo i ic ga ne laye ha o med a he ga ne – ens a i e in e ace was gene ally hin (< 3 µm o he 19 hou expe imen s and absen wi hin he esolu ion o he mic op obe o he 1 hou expe imen ). This ag ees well wi h he low majo i e di usi i y in ga ne ha was de e mined om majo i ic ga ne – py ope di usion couples and o which he esul s a e p esen ed in chap e 5. The eco e ed sample o un H2975 has been in es iga ed in de ail by TEM. Figu e 6.4 shows a da k ield (DF) image ob ained using g = 6 13 as di ac ion ec o . Twinning on he (100) mi o planes is pe asi e in he sample, and is indica ed by he sho whi e a ows. Nex o winning, one can also obse e s acking aul s pa allel o he win plane h oughou he sample ( igu e 6.4 and 6.5). Figu e 6.5a shows a DF image using g = 021 as di ac ion ec o , demons a ing again he pe asi e na u e o he s acking aul s in his sample. The co esponding HRTEM image in an a*-b p ojec ion (* deno ing he ecip ocal di ec ion) o clinoens a i e shows a single s acking aul ( ig. 6.5b). F om his HRTEM image one can deduce ha he displacemen ec o ac oss he s acking aul is R = <½ ½ w>, he exac componen s can be 108 Figu e 6.4: DF TEM image o wins (and s acking aul s) pa allel o (100) in clinoens a i e in expe imen H2975. Two win planes a e indica ed by he whi e a ows. The di ac ion ec o (g = 6 1 3) is indica ed by he ligh g ay a ow. The ga ne p ecipi a es a e indica ed by G . As can be seen, he la ge p ecipi a e on he igh has i s long axis (semi-)pa allel o he win planes and s acking aul s in low clinoens a i e. Table 6.4:Composi ion o he exsol ed majo i ic ga ne p ecipi a es. Oxide W % MgO 34.80 CaO 0.24 FeO 1.65 Al2O39.83 SiO253.66 To al 100.18 Componen F ac ion Majo i e 0.610 Py ope 0.352 Almandine 0.032 G ossula 0.007 comple e c ys al is pa allel o {211} since e e y ubula column is shi ed ela i e o a neighbou ing ubula column by 1/3 o he e ahed a plus oc ahed a laye hickness. In he iew down he <111> di ec ion he space be ween he ubula columns o ms channels pa allel o {110}. Though he s uc u es o py oxene and ga ne a e as ly di e en , silica e ahed a also o m a linea s uc u e in ga ne s uc u e down he <111> di ec ion. Fo he ans o ma ion om py oxene o ga ne , he chains o silica e ahed a down he c-axis in py oxene need o be b oken in o isola ed silica e ahed a. The dis ance o e which he silica e ahed a need o be di used (o ansla ed and o a ed) may hus be minimal when he new ga ne c ys al o ms wi h i s <111> di ec ion down he o iginal c-axis o high clinoens a i e. The opo ac ic ela ionship would in his case hus no be con olled by minimiza ion o he s ain ene gy on he in e ace be ween bo h phases, bu by he di usion kine ics o silicon, because silicon is usually he slowes di using species. 6.5.3 Aluminium di usi i y in clinoens a i e The di usion in high clinoens a i e down he [101]*di ec ion was de e mined o be 6 x 10-11 cm2 s-1 a 15 GPa and 1700 °C, which is 3 – 4 o de s o magni ude as e han he di usion o he majo i e componen in ga ne . The epo ed di usi i y is a lowe limi , since he exac ime equi ed be o e a majo i ic nucleus o med is unknown. Howe e , he measu ed p o ile used in he i model was he longes ha was ound in he sample and hus p obably also co esponds o one o he nucleus ha o med i s du ing he expe imen . The egion a ound he measu ed p ecipi a e is ela i ely de oid o o he p ecipi a es, which also indica es ha he p ecipi a e om which he p o ile was measu ed nuclea ed du ing an ea ly s age o he expe imen . Expe imen S4391 ( igu e 6.6) was un a he same condi ions, bu only o 1 hou . The p esence o ga ne p ecipi a es in his expe imen indica e he i s p ecipi a es nuclea e wi hin he i s hou . Since he un du a ion o expe imen S4378 was 19 hou s, i is hough ha he e o due o he unce ain y abou he exac ime o nuclea ion o he p ecipi a es is no signi ican . To p ojec he di usion coe icien s o subduc ion zone condi ions one needs he ac i a ion ene gy o di usion o aluminium in py oxene (o ideally high clinoens a i e). The e is, howe e , a gene al lack o di usion da a on aluminium in mine als in he li e a u e, he only da a on aluminium di usion in diopside is by Sau e e al. (1988) and Jaoul e al. (1991) o e a limi ed empe a u e ange be ween 1000 – 1180 °C a 1 ba . They ob ain an ac i a ion ene gy o 273 kJ mol-1. The ac i a ion en halpy, desc ibing he empe a u e dependence, o di usion o aluminium in high clinoens a i e will p obably be highe , since he expe imen s in his s udy we e conduc ed a a p essu e o 15 GPa. The e o e a ypical ange o ac i a ion en halpies ha e been assumed, i.e. be ween 275 kJ mol-1 and 350 kJ mol-1, co esponding o an ac i a ion olume o he di usion o aluminium in clinoens a i e be ween 0 – 5 cm3 mol-1. Fo he uppe pa o he subduc ing slab a a empe a u e o 1000 °C (Emme son and McKenzie 2007), co esponding o he subduc ed oceanic c us , i gi es an aluminium di usion coe icien in he ange o 5 x 10-16 cm2 s-1 o 6 x 10-15 cm2 s-1. Fo he middle o lowe pa o he subduc ing slab a 1400 °C (Emme son and McKenzie 2007), co esponding o he subduc ed man le li hosphe e, he ange is smalle due o a smalle empe a u e di e ence be ween he ex apola ed empe a u e and he expe imen al condi ion, and is in he ange be ween 3 x 10-12 cm2 s-1 and 4 x 10-12 cm2 s-1. Again his shows ha di usion o aluminium in 115 high clinoens a i e (in he [101]* di ec ion) is signi ican ly as e han he di usion o he majo i e componen in ga ne , i.e. 3 – 4 o de s o magni ude slowe . Since he dis ance o e which a componen can di use can be app oxima ed by x = √(D ), wi h he ime o which he componen is allowed o di use, one can calcula e he dis ance o e which aluminium can di use in py oxene. A 1000 °C and 10 My , which is a ypical ime scale o subduc ion (see chap e 5), his is be ween 0.5 – 1.5 cm and a 1400 °C be ween 20 – 30 cm. I g ain bounda y di usion plays a signi ican ole, he alues will be a ac o 100 la ge , i.e. a he me e scale a 1000 °C and a he decame e scale a 1400 °C. Compa ing he absolu e alues o he di usion s udy by Jaoul e al. (1991) o he da a p esen ed in his s udy shows ha ou da a is signi ican ly as e , Jaoul e al. ob ained a di usi i y o 3.7 x 10-17 cm2 s-1 a 1180 °C a 1 ba and ou s udy 6 x 10-11 cm2 s-1 a 1700 °C. This would co espond o an ac i a ion ene gy o di usion o aluminium in clinopy oxene o 655 kJ mol-1 (when he e ec o p essu e is neglec ed), which is anomalously high, o when using hei ac i a ion ene gy o Al di usion his co esponds o an ac i a ion olume o di usion o aluminium in clinopy oxene o -25 cm3 mol-1, which would mean ha wi h inc easing p essu e di usion would become as e . F om his i can be concluded ha he e is a la ge di e ence in di usi i y be ween ha o aluminium in HP clinoens a i e a high p essu e and ha o aluminium di usion in diopside a low p essu e, which possibly can be a ibu ed o di e en di usion mechanism in bo h clinopy oxene phases a he di e en condi ions o a s ong dependence o he di usi i y o aluminium in clinopy oxene on he calcium con en . 6.6 Conclusions •Twins and s acking aul s on (100) a e pe asi e h oughou he ens a i e sample a e quenching and decomp ession om 15 GPa and 1700 °C. The displacemen ec o ac oss he s acking aul bounda y was de e mined o be <½ ½ w>, mos likely being ½ <111>. This displacemen ec o can be explained be he ans o ma ion o high clinoens a i e o low clinoens a i e. •The win bounda ies and s acking aul s ha o med in high clinoens a i e pa allel o he (100) planes du ing he ansi ion om Pbca o ho ombic o he C2/c high p essu e phase seem o ha e ac ed as nuclea ion si es o majo i ic ga ne p ecipi a es. •In he case ha he e was a well de ined long axis o he ga ne p ecipi a e in he obse ed TEM sec ion, his long axis was p edominan ly o ien ed pa allel o (100) and he win planes / s acking aul s in low clinoens a i e. •The e is no unique opo ac ic ela ionship be ween he low clinoens a i e hos and he majo i ic ga ne p ecipi a es. Howe e , a dominan linea ela ionship was ound wi h he <111> di ec ion in ga ne being pa allel o he [001] di ec ion in low clinoens a i e. This di ec ion is p obably con olled by he di usi i y o silicon in py oxene and no by minimiza ion o s ain ene gy a he in e ace be ween he clinoens a i e hos and majo i ic ga ne p ecipi a es. The la e is p obably due o he absence o a well de ined oxygen close packing di ec ion in ga ne . 116 •The di usi i y o aluminium in C2/c HP-clinoens a i e in he [101]* di ec ion a 15 GPa and 1700 °C was de e mined o be a leas 6 x 10-11 cm2 s-1, which is 3 – 4 o de s o magni ude as e han he di usi i y o he majo i e componen in ga ne a he same condi ions. •The e is a la ge di e ence in he di usi i y o aluminium in clinopy oxene a high p essu e and he di usi i y o aluminium in clinopy oxene a oom p essu e, which e en ually indica es a change in di usion mechanism wi h p essu e o a s ong dependence o he di usi i y o aluminium on calcium con en in clinopy oxene. 117 6.7 Re e ences Angel, R.J., Chopelas, A., Ross, N.L. (1992), S abili y o high-densi y clinoens a i e a uppe -man le p essu es. Na u e 358:322-324. doi: 10.1038/358322a0 A l , T., Angel, R.J., Mile ich, R., A mb us e , T., Pe e s, T. (1998), High-p essu e P21/c-C2/c phase ansi ions in clinopy oxenes; in luence o ca ion size and elec onic s uc u e. Am Mine al 83:1176-1181 Coe, R.S., Ki by, S.H. (1975), The o hoens a i e o clinoens a i e ans o ma ion by shea ing and e e sion by annealing: Mechanism and po en ial applica ions. Con ib Mine al Pe ol 52:29-55. doi: 10.1007/BF00378000 Duysen, J.C. Van, Doukhan, N., Doukhan, J.C. (1985), T ansmission elec on mic oscope s udy o disloca ions in o hopy oxene (Mg, Fe)2Si2O6. Phys Chem Mine 12:39-44 Emme son, B., McKenzie, D. (2007), The mal s uc u e and seismici y o subduc ing li hosphe e. Phys Ea h Plane In e 163:191-208. doi: 10.1016/j.pepi.2007.05.007 Ganguly, J., Ghose, S. (1979), Aluminous o hopy oxene: O de -diso de , he modynamic p ope ies, and pe ologic implica ions. Con ib Mine al Pe ol 69:375-385. doi: 10.1007/BF00372263 Gaspa ik, T. (2003), Phase diag ams o geoscien is s: an a las o he ea h’s in e io . Sp inge , Heidelbe g-Be lin Gaspa ik, T., Lindsley, D.H. (1980), Phase equilib ia a high p essu e o py oxenes con aining mono alen and i alen ions. in: P ewi C.T.(ed.) Re iews in Mine alogy and Geochemis y, pp. 309-339 Iijima, S., Buseck, P.R. (1975), High Resolu ion Mic oscopy o Ens a i e I: Twinning, Polymo phism, and Poly ypism. Am Mine al 60:758 - 771 I i une, T. (1987), An expe imen al in es iga ion o he py oxene-ga ne ans o ma ion in a py oli e composi ion and i s bea ing on he cons i u ion o he man le. Phys Ea h Plane In e 45:324-336. doi: 10.1016/0031- 9201(87)90040-9 I i une, T., Sekine, T., Ringwood, A.E., Hibbe son, W.O. (1986), The eclogi e-ga ne i e ans o ma ion a high p essu e and some geophysical implica ions. Ea h Plane Sci Le 77:245-256. doi: 10.1016/0012- 821X(86)90165-2 Jaoul, O., Sau e , V., Abel, F. (1991), Nuclea Mic oanalyses: A Tool o Measu ing Low A omic Di usi i y. in: Ganguly J.(ed.) Di usion, A omic O de ing and Mass T anspo , Ad ances in Physical Geochemis y 8, Sp inge - Ve lag, Heidelbe g-Be lin, pp. 198-220 Kanzaki, M. (1991), O ho/clinoens a i e ansi ion. Phys Chem Mine als 17:726-730. doi: 10.1007/BF00202244 Ke schho e , L., Rubie, D.C., Sha p, T.G., McConnell, J.D.C., Dupas-B uzek, C. (2000), Kine ics o in ac ys alline oli ine- ingwoodi e ans o ma ion. Phys Ea h Plane In e 121:59-76. doi: 10.1016/S0031-9201(00)00160-6 Okamu a, F.P., Ghose, S., Ohashi, H. (1974), S uc u e and C ys al Chemis y o Calcium Tsche mak’s Py oxene, 118 CaAlAlSiO6. Am Mine al 59:549 - 557 Pu nis, A. (1992), An In oduc ion o Mine al Sciences. Camb idge Uni e si y P ess, Camb idge Rauch, M. (2000), De Einbau on Wasse in Py oxene. Sau e , V., Jaoul, O., Abel, F. (1988), Aluminum di usion in diopside using he 27Al(p,γ)28Si nuclea eac ion: p elimina y esul s. Ea h Plane Sci Le 89:109-114. doi: 10.1016/0012-821X(88)90036-2 Sk o zki, W. (1994), De ec s uc u e and de o ma ion mechanisms in na u ally de o med augi e and ens a i e. Tec onophysics 229:43-68. doi: 10.1016/0040-1951(94)90005-1 Spengle , D. (2006), O igin and E olu ion o Deep Uppe Man le Rocks om Wes e n No way. U ech S eu en, J.M., Roe mund, H.L.M. Van (1989), An op ical and elec on mic oscopy s udy o de ec s uc u es in na u ally de o med o hopy oxene. Tec onophysics 157:331-338. doi: 10.1016/0040-1951(89)90148-0 Thompson, R.M., Downs, R.T. (2003), Model py oxenes I: Ideal py oxene opologies. Am Mine al 88:653-666 119 Ich e klä e hie mi , dass ich die o liegende A bei ohne unzulässige Hil e D i e und ohne Benu zung ande e als de angegebenen Hil mi el ange e ig habe. Die aus emden Quellen di ek ode indi ek übe nommenen Gedanken sind als solch kenn lich gemach . Die A bei wu de bishe wede im Inland noch im Ausland in gleiche ode ähnliche Fo m als Disse a ion einge eich und is als Ganzes auch noch nich e ö en lich . Fe ne e klä e ich hie mi , dass ich nich be ei s ande wei ig mi ode ohne E olg e such habe, eine Disse a ion einzu eichen ode mich de Dok o p ü ung zu un e ziehen. Ulm, 29. Mä z 2012 Willem Louis an Mie lo