Phase transitions in lawsonite: a calorimetric study

This is he Au ho s’ accep ed manusc ip . ©2001 E. Schweize ba ’sche Ve lagsbuchhandlung. D-70176 S u ga The Ve sion o Reco d is a ailable a Eu opean Jou nal o Minea ology 13 5–14 (2001) unde doi:10.1127/0935-1221/01/0013-0005 Phase ansi ions in lawsoni e: a calo ime ic s udy J M Ma ´ın-Olalla,1, ∗S ua A. Haywa d,1Hin ich-Wilhem Meye ,2Sa u io Ramos,1Jaime del Ce o,1and Michael A. Ca pen e 2 1Depa amen o de F´ısica de la Ma e ia Condensada, ICMSE-CSIC, Uni e sidad de Se illa. Apa ado de Co eos 1065 E-41080 SEVILLA SPAIN 2Depa men o Ea h Sciences, Uni e si y o Camb idge, Downing S ee , Camb idge, CB2 3EQ, Uni ed Kingdom (Submi ed: 26 June 2002; Accep ed 12 No embe 2002; Published: 27 Decembe 2002) The speci ic hea o lawsoni e, CaAl2Si2O7(OH)2·H2O, has been measu ed in he empe a u e ange [125 K,325 K]. An anomaly is seen a 273 K, which is e- la ed o he Cmcm–Pmcn phase ansi ion. The magni ude o he o al excess en opy associa ed wi h his ansi ion is no ep oducible, a ying in he ange [5.93 J K−1mol−1,6.24 J K−1mol−1]. On hea ing, he speci ic hea anomaly is con- sis en wi h a ic i ical phase ansi ion. Howe e , on cooling, signi ican hys e esis is obse ed, and he o m o he Cpanomaly is qui e di e en . In all measu emen s ex ensi e p e- ansi ional e ec s a e obse ed abo e Tc. Analysis o exis ing speci ic hea da a in he empe a u e ange [75 K,175 K] shows an anomaly associa ed wi h he Pmcn–P21cn phase ansi ion. The excess en opy associa ed wi h his ansi ion is 6(1) J K−1mol−1. These da a a e in e p e ed as showing ha bo h ansi ions a e caused by he in e ac ion o p o on o de ing and displaci e changes in he aluminosilica e amewo k. The s anda d en opy o lawsoni e a 298 K is ecalcula ed, inco po a ing he e ec s o he wo ansi ions. Two me hods a e used o his ecalcula ion, gi ing alues o S0 298 = 233.27 J K−1mol−1and and S0 298 = 234.96 J K−1mol−1 espec i ely. I. INTRODUCTION In oduc ion Lawsoni e, CaAl2Si2O7(OH)2·H2O, is a common cons i uen o high-p, low-Tme amo phic ocks, such as blueschis s. As a ela i ely dense hyd ous min- e al, lawsoni e has equen ly been in es iga ed as p o- iding a po en ial mechanism o ca y wa e deep in o he Ea h’s in e io . These s udies (Cha e jee and Leis ne , 1984; Pawley, 1994; Schmid and Poli 1994) ha e indi- ca ed ha lawsoni e emains s able down o he p es- su e and empe a u e condi ions o he man le. Wa e in he lawsoni e s uc u e is signi ican o ano he ea- son. X- ay di ac ion and in a edspec oscopy expe - imen s (Libowi zky and A mb us e , 1995; Libowi zky and Rossman, 1996) ha e shown ha lawsoni e unde - goes phase ansi ions a low empe a u es, associa ed wi h he o ien a ion o he H2O molecules and hyd oxyl g oups wi hin he lawsoni e s uc u e. These ansi ions a e in e es ing since hey allow he in e ac ion be ween hyd ogen a oms and an aluminosilica e amewo k o be s udied. The oom- empe a u e s uc u e o lawsoni e has space g oup Cmcm. A 273 K, he H2O molecules o a e a ound [100], educing he symme y o Pmcn. The sec- ond phase ansi ion, a 120 K, educes he symme y o he s uc u e o P21cn. This ansi ion is associa ed ∗[email p o ec ed]; h ps://o cid.o g/0000-0002-3750-9113; h ps:// o .o g/03yxnpp24 wi h a u he o a ion o he H2O molecules a ound a di e en axis. Two dis inc mechanisms may be en isaged o his ansi ion. In a displaci e model o he ansi ion, hese o a ions occu as a unc ion o empe a u e below he ansi ion. In an o de -diso de ansi ion, he o ien- a ion o he wa e molecules hops be ween a numbe o almos ixed posi ions; he c ys al s uc u e obse ed expe imen ally is hen a dynamic a e age o he a - ious o ien a ions. Fo a pu ely o de -diso de ansi- ion, he excess en opy o he ansi ion may be cal- cula ed di ec ly using con igu a ional mixing models. In a displaci e ansi ion, he excess en opy comes om changes in phonon equencies associa ed wi h he s uc- u al changes, which a e a he less simple o calcula e. In o de o in es iga e hese e ec s u he , a single sample o lawsoni e has been cha ac e ised by a numbe o di e en me hods. The expe imen al quan i ies mea- su ed ha e been elas ic cons an s, dielec ic cons an s, bi e ingence, mac oscopic dila a ion (Sonde geld e al., 2000), la ice pa ame e s and in a ed spec a (Meye e al., 2000). In his a icle, we epo he esul s o calo ime ic measu emen s ac oss he 273 K ansi ion, and ela e hem o some o hese o he da a. A numbe o o he calo ime ic s udies o lawsoni e ha e been pe - o med (King and Welle , 1961; Pe kins e al., 1980) bu he pu pose o hese s udies was o unde s and he s a- bili y o lawsoni e in me amo phic eac ions. As a esul , he da a close o he ansi ions a e a he scan y. Typese by REVT EX 2 II. EXPERIMENTAL METHODS A. Sample desc ip ion The lawsoni e sample used in his s udy came om Valley Fo d, Sonoma Coun y, Cali o nia, and is no. 120943 o he Ha a d Uni e si y mine al collec ion. This sample was gene ously p o ided by D . C. F ancis (Ha - a d Uni e si y, USA). In handspecimen, he sample con- ained a ein se e al cm wide consis ing p edominan ly o in e locking lawsoni e g ains, along wi h a small p o- po ion o calci e. A small disc app oxima ely 10 mm in diame e and 3.9 mm hick was cu om his ein o he calo ime ic measu emen s. The mass o his sample was 0.9 g. A e he calo ime ic measu emen s we e comple ed he disc was cu in o ci cula slices and moun ed as hin sec ions. Poin coun ing o hese sec ions in a pe o- g aphic mic oscope ga e he olume ac ions o law- soni e and calci e as 97.95 % and 2.05 % espec i ely. Elec on-mic op obe analysis (EDS) showed he majo ca ion elemen s in lawsoni e o be Ca, Al, Fe, and Si only. Analyses o Ti, C , Mn, Ni, Mg, Na, K, Cl, P and S we e also ca ied ou , bu hese elemen s we e only p esen a le els less han 1σon coun ing s a is ics. Wa e con en o his ma e ial was de e mined using he mog a ime y (S. Ma ion, pe s. comm.); wi hin expe imen al e o he sample is ully hyd a ed. P e ious analyses (Dee e al. 1992, and e e ences he ein) indica e ha he wa e con en does no a y subs an ially be ween na u al lawsoni es; he quo ed wa e con en s a e in he ange 10.61 o 11.70 (w %). Using he a e age o ou p obe analyses, he composi ion o he lawsoni e phase in his sample is Ca1.00Al1.95Fe0.05Si2.00O7(OH)2·H2O. B. Calo ime ic expe imen s The sample was placed in a conduc ion calo ime e o a ype desc ibed p e iously (del Ce o, 1987; del Ce o e al., 1987). The calo ime e consis s o a la ge block o alu- minium, which ac s as a he mal ese oi . Two luxme- e s, each consis ing o 48 he mocouples, a e placed elec- ically in se ies and he mally in pa allel. The ou e junc ion o each luxme e is ixed o he calo ime ic block, and he sample is p essed be ween he inne junc- ions. The con ac s be ween he luxme e s and he sam- ple a e sil e pla es, o ensu e good he mal con ac and homogenisa ion. The en i e assembly is e acua ed o 10−5mba , and placed in an alcohol ba h. This ba h may be cooled om oom empe a u e o liquid-ni ogen empe a u e. The sample empe a u e may be adjus ed by hea ing o cooling he alcohol ba h. By cooling he sys em slowly, equilib ium may be main ained be ween he sample and he hea ba h. FIG. 1 Expe imen al measu emen s o speci ic hea as a unc- ion o empe a u e in lawsoni e. Pa a) shows he da a o e he whole empe a u e ange o he expe imen s, and pa b) is a magni ca ion o he da a in he icini y o he Cmcm–Pmcn ansi ion. The ou solid lines show he da a o he wo hea ing and wo cooling uns pe o med in his s udy, and he ci cles show he da a ob ained by Pe kins e al. (1980) o hea ing a di e en lawsoni e sample. The Cpmeasu emen s a e pe o med using a small hea e a ached o he luxme e s. The sample is hea ed un il a s eady s a e is a ained, a which poin he hea e powe is cu o . The elaxa ion o he sample back o equilib ium wi h he hea sink depends on he hea capac- i y o he sample, and so CP may be measu ed as a unc- ion o empe a u e. In his expe imen , ou measu e- men uns we e ca ied ou . The sample was quenched om oom empe a u e o 125 K. Measu emen s o he speci ic hea we e ca ied ou as he sample was hea ed slowly (ca. 0.6 K h−1) o 320 K ( un 1). Fo he second un, he sample was cooled a he same a e o 200 K. The sample was hen hea ed back o oom empe a u e, again a he same a e ( un 3). Finally, he sample was cooled o 260 K, again a he same empe a u e a e ( un 4). In each case, he e was a minimal ime in e al be- ween he a ious measu emen uns. 3 III. EXPERIMENTAL RESULTS FOR THE Cmcm −Pmcn TRANSITION A. Speci ic hea as a unci on o empe a u e Fig. 1 shows he speci ic hea as a unc ion o em- pe a u e o each o he ou expe imen al uns. These da a a e no co ec ed o he sample pu i y. The da a o Pe kins e al. (1980), which we e measu ed using a di e en 95 % pu e lawsoni e sample om Valley Fo d, Cali o nia, a e also shown o compa ison. Examina ion o he da a close o Tc(Fig. 1b) indica es ha he speci ic hea anomaly in lawsoni e has wo pa s. The e is a dis inc change in he Cp(T) slope a ca. 295 K, which is e idence o a p onounced ail in he hea capac- i y anomaly abo e Tc. Simila e ec s ha e been seen in o he ypes o expe imen s; Sonde geld e al. (2000) no e p e- ansi ional e ec s in bi e ingence measu emen s up o ∼200 K abo e he ansi ion empe a u e. The ail is qui e ep oducible be ween he di e en expe imen al uns, o bo h hea ing and cooling he sample. A he ansi ion empe a u e, a dis inc peak is ex- pec ed, bu he magni ude o his peak a ies g ea ly be ween he expe imen al uns. In pa icula , he peak is a mo e p onounced when he sample is being hea ed han when i is cooled. B. Excess en opy calcula ions Analyses o bi e ingence, dielec ic cons an , elas ic cons an and co-elas ic spon aneous s ain da a (Son- de geld e al., 2000), as well as in a ed spec oscopic da a (Meye e al., 2000) a e consis en wi h a Landau model o he Cmcm–Pmcn ansi ion, whe e he ansi- ion is close o he ic i ical poin . Addi ional accoun mus be aken o he ails seen abo e Tc. Calcula ion o he excess en opy as a unc ion o empe a u e p o- ides a u he es o his model. In addi ion, we may compa e he o al excess en opy wi h he en opy p e- dic ed o a dipole o de -diso de p ocess. In o de o eliably calcula e excess quan i ies associa ed wi h he phase ansi ion, i is necessa y o know accu a ely he “baseline” beha iou o he expe imen al da a ( ha is, in he absence o he phase ansi ion). This issue is pa - icula ly p oblema ic o calcula ions o excess en opy om Cpda a. Well below Tc, he speci ic hea anomaly is small, and so e en small e o s in he baseline spe- ci ic hea may ha e a la ge sys ema ic e ec on he inal en opy calcula ion. Fo his s udy, we ha e he e o e used a wos age p o- cess o de e mine he excess en opy associa ed wi h he ansi ion. Fi s , we ha e used a simple in e pola ion me hod o gene a e a “p elimina y” baseline. Because his p elimina y baseline is well-ancho ed by expe imen- al da a om jus abo e he ansi ion empe a u e, i FIG. 2 Tempe a u e dependence o (T/∆Cp)2 o lawsoni e. Fo a ansi ion obeying Landau heo y, his unc ion is ex- pec ed o be linea . The de ia ions om linea i y a low em- pe a u e a e likely o be due o small e o s in he p edic ion o he baseline Cp0. is expec ed o be easonably accu a e immedia ely be- low he ansi ion empe a a u e. In any case, he la ge- ness o ∆Cpnea Tcmeans ha he unce ain ies in he baseline a e p opo iona ely less signi ican he e han a low empe a u es. We hen use a heo e ical model o he ansi ion (pa ame e ised by hese ini ial esul s), o de e mine he beha iou o ∆Cpa lowe empe a u es. F om his, we de e mine a “back-calcula ed” Cpbaseline, whose o m may be in o mally checked o i s plausibil- i y. The excess en opy is hen calcula ed wi h espec o his back-calcula ed baseline. I can be shown (see, o example, Salje, 1990) ha , o any phase ansi ion desc ibed by a s anda d 2:4.6 Landau po en ial, whe he i s o de o second o de , he speci ic hea anomaly may be linea ised as T ∆Cp2 ∝(T–T2),(1) whe e he di e ence be ween Tcand T2is a measu e o he closeness o he ansi ion o he ic i ical poin ; o a ansi ion which is s ic ly Landau ic i ical (i.e. ∆S∝Q2;Q∝ |Tc−T|1/4), Tcand T2a e equal. In any case, we may es he alidi y o Equa ion (1) close o Tcusing he p elimina y baseline. I his p o es o be easonable, Equa ion (1) hen de ines he beha iou o ∆Cpa lowe empe a u es, whe e he de e mina ion o he baseline is mo e p oblema ic. A p elimina y em- pi ical baseline Cp0was easily de e mined by i ing a pa abola hough he da a o he i s expe imen al un o T > 315 K and T < 150 K. Since ∆Cpis expec ed o be non-ze o a low empe a u es, his p elimina y base- line is no o ally co ec . The e o will be mos sig- ni ican a lowe empe a u es, whe e he ue alue o ∆Cpwill be sys ema ically la ge han we ob ain wi h he p elimina y baseline. The main consequence will be 4 FIG. 3 Tempe a u e dependence o excess en opy in law- soni e. Abo e 260 K (solid line), his cu e is calcula ed by simple in eg a ion o (∆Cp/T). Below 260 K (b oken line), i is assumed ha he linea i y o (T/∆Cp)2seen in Fig. 2 may be ex apola ed. ha he o al excess en opy o he ansi ion will be unde es ima ed. Howe e , he e o close o Tcwill be smalle and we can use he p elimina y baseline o s udy he beha iou o ∆Cpin he icin iy o Tc. Fig. 2 shows he dependence o (T/∆Cp)2on empe a u e o he i s hea ing cycle ( his being he expe imen whe e he peak in ∆Cpwas mos p onounced). The igu e clea ly shows he linea beha iou close o he ansi ion poin and he in e cep ion o he s aigh line wi h empe a u e axis gi e us T2= 275.3(1) K. The la ges alue o ∆Cpis ob- se ed a T= 272.8(4) K. The posi ion o he ∆Cppeak p o ides one de ini ion o Tc, albei a somewha p oblem- a ic one in a ansi ion wi h a signi ican ∆Cp ail abo e he ansi ion empe a u e. I is clea , howe e , ha he ansi ion is e y close o he Landau ic i ical poin . This p elimina y baseline may hen be imp o ed by aking accoun o Fig. 2. I we assume ha he obse ed linea i y should con inue o lowe empe a u es, we may calcula e he expec ed alue o ∆Cpa any empe a u e. This, in conjunc ion wi h he expe imen al da a Cp(T) allows he baseline o be calcula ed om Cp0=Cp–∆Cp. The b oken line in Fig. 1 shows he esul ing baseline, a - e he back-calcula ed Cp0(T) has been smoo hed. Close o he ansi ion empe a u e, he p elimina y and back- calcula ed baselines ag ee well. A lowe empe a u es, he back-calcula ed baseline is lowe han he p elimina y baseline, bu i is mo e ealis ic as i akes accoun o he small (bu non-ze o) ∆Cpexpec ed o any heo y o he ansi ion. Gi en he empe a u e dependence o Cpand Cp0, he o al excess en opy as a unc ion o empe a u e is cal- cula ed in Fig. 3. In Fig. 3, he con e sion om mass uni s o mola uni s includes a co ec ion o he calci e impu i ies in he expe imen al sample. Fo he pu poses o his calcula ion, i has been assumed ha he linea FIG. 4 Tempe a u e dependence o excess en opy o wo hea ing and wo cooling uns in lawsoni e. beha iou o (T/∆Cp)2may be ex apola ed o 0 K. Two a gumen s indica e ha his is no wholly ealis ic. Fi s ly, i akes no accoun o he endency o he o - de pa ame e o app oach a cons an alue a absolu e ze o (Salje e al., 1991). Secondly, i igno es he e ec o he phase ansi ion a 120 K. The classical ex apola ion is s ill use ul, howe e , since i p o ides he bes es ima e o ∆Sbe ween he high- empe a u e phase and he s uc- u e a ze o kel in. As shown in Fig. 3, he ex apola ed alue o ∆Sa absolu e ze o is 5.93(1) J K−1mol−1. The andom e o in his quan i y is small (i depends only on he e o in he g adien o he s aigh line i in Fig. 2, which is o he o de o 1 %). The sys ema ic e o s, due o he wo ac o s gi en abo e, a e p obably la ge , bu di icul o quan i y. C. Analysis o subsequen expe imen al uns Fig. 4 shows he empe a u e dependence o he ex- cess en opy o all ou expe imen al uns pe o med in his s udy. The wo hea ing expe imen s show e y sim- ila , almos ic i ical beha iou ; he e ec o he di e - ence in he heigh be ween he wo ∆Cppeaks is a he small. I he excess en opy in he second hea ing ex- pe imen ( un 3) is ex apola ed o 0 K, he esul ing ∆S= 6.24(1) J K−1mol−1. This esul may simply be an a e ac o he i ing me hod used; he low empe - a u e ∆Cp alues a e sligh ly highe o un 3 han o un 1. Fi ing bo h da a se s o a single baseline has a signi ican e ec o he inal calcula ion o en opy. Howe e , compa ison be ween he wo hea ing cu es and he wo cooling cu es (which a e e y simila o each o he ) indica es a signi ican deg ee o hys e esis in he ansi ion. The o m o he cooling cu es is no consis en wi h ic i ical beha iou , and he magni udes o ∆Sa e also inconsis en . 5 FIG. 5 Tempe a u e dependence o en opy (solid line) and co-elas ic spon aneous s ains a) e1 and b) e2 (solid poin s) in lawsoni e. The b oken line shows he beha iou expec ed o bo h hese quan i ies o s ic ic i ical beha iou (Q4∝ |Tc−T|). The empe a u e scales in he wo expe imen s ha e been adjus ed such ha he ansi ion empe a u e Tcis he same in each case. D. Compa isons wi h o he expe imen al da a Fig. 5a and 5b compa e he empe a u e dependence o he en opy obse ed in un 1 wi h measu emen s o he co-elas ic spon aneous s ain (Meye e al., 2000). In o - de o compa e he a ious da a, i was necessa y o add a cons an o se o all he empe a u es o he spon a- neous s ain da a. This may be due o di e en empe - a u e calib a ions in sepa a e appa a us. This cons an was ixed by de e mining he empe a u e a which linea ex apola ions o bo h (∆S)2and e2 i(bo h o which a e p opo ional o Q4) wen o ze o. Fa om Tc, he expec ed Landau ela ionship (∆S∝ ei∝Q2) is obeyed o all h ee componen s o he s ain enso . Howe e , e1 de ia es om his ela ionship o e a ange o ca. 20 K below Tc. The mos p obable eason o his is ha he simple ela ionship be ween sho - ange o de and long- ange o de is no applicable o small FIG. 6 Speci ic hea da a o lawsoni e in he icini y o he Pmcn −P21cn ansi ion, aken om Pe kins e al. (1980). The da a shows a s ep anomaly, consis en wi h a second o de phase ansi ion. deg ees o long- ange o de . F om Fig. 5, i is appa - en ha e1 is a he mo e sensi i e o sho ange o de han e2. The ail in e1 abo e Tcis signi ican ly mo e p onounced, and co ela es well wi h he en opy in his empe a u e ange (which, since he long- ange o de pa- ame e is ze o, mus be om sho - ange o de ). E. Reanalysis o he Pe kins e al. (1980) da a o he Pmcn–P21cn ansi ion P e ious calo ime ic s udies o lawsoni e (King and Welle 1961; Pe kins e al., 1980) no ed wo anomalies in he Cp(T) cu e. As we ha e shown abo e, he e is a good co ela ion be ween he lambda peak a 273 K and o he da a o a phase ansi ion a his empe a u e. The empe a u e o he second anomaly no ed by Pe kins e al. (1980) is app oxima ely 130 K. This is close o he empe a u e o he Pmcn–P21cn ansi ion, de e mined as 120 K by Sonde geld e al. (2000). Fig. 6 shows he da a o Pe kins e al. (1980) in he icini y o his ansi ion. The ansi ion shows limi ing second-o de beha iou (based on X- ay di ac ion mea- su emen s, Sonde geld pe s. comm.); he expec ed o m o he Cpanomaly in his case is a s ep, a he han a lambda peak. F om Fig. 6, he magni ude o his s ep a he ansi ion empe a u e is 6(1) J K−1mol−1. Thus he es ima ed ∆S o he Pmcn–P21cn ansi ion a comple- ion is 6(1) J K−1mol−1. 6 IV. DISCUSSION A. Implica ions o s anda d en opy calcula ions In his s udy, we ha e shown ha he anomalies in he speci ic hea cu e o lawsoni e a e associa ed wi h wo phase ansi ions unde gone by his mine al. They a e hus an in insic pa o he beha iou o lawsoni e, and hei e ec should be included in calcula ions o he s anda d en opy a 298 K, S0 298. I was no possible o simply in eg a e ei he o he exis ing da a se s o de- e mine S0 298; he da a o Pe kins e al. (1980) do no con ain su icien poin s close o he 275 K ansi ion o p ope ly cha ac e ise he peak, whe eas ou expe imen did no measu e Cpbelow 125 K. We used wo me hods o deal wi h his di icul y; i s , combining he da a om he wo expe imen s, and second, using ou knowledge o he cha ac e o he ansi ion o p oduce an in e po- la ion h ough he Cpda a measu ed by Pe kins e al. (1980). Ou Cpda a ag ee well wi h hose o Pe kins e al. (1980) in he empe a u e ange [140 K,180 K] (e.g. Fig. 1(a)), and so we used ou da a in he empe a u e ange [160 K,298 K], and he da a o Pe kins e al. (1980) in he ange [0 K,160 K]. Nume ical in eg a ion o hese da a ga e a alue o S0 298 = 233.27(1) J K−1mol−1. The disad an age o his me hod is ha i is no clea ha he wo da a se ies may be combined in his way; di e - en samples we e used o he wo expe imen s, and he Cppeak is appa en ly highe in he Pe kins e al. (1980) sample han in he one used in his s udy (Fig. 1(b)). We he e o e also i ed he Cpda a o Pe kins e al. (1980) o a lambda peak cha ac e is ic o a Landau i- c i ical phase ansi ion. This was done by he same me hod used abo e, and he esul ing in e pola ion is shown in Fig. 7. In eg a ion o he cu e in Fig. 7 leads o a alue o he s anda d en opy, S0298 = 234.96(1) JK-1mol-1. Bo h me hods o calcula ion lead o a highe alue o S0298 han p e iously published (S0298 = 230.19 JK-1mol-1, Pe kins e al., 1980). B. Signi icance o he magni ude o he excess en opy Bo h obse ed phase ansi ions in lawsoni e a e as- socia ed wi h appa en o a ion o he H2O molecules b eaking a symme y plane; he (001) plane a ca. 275 K, and (100) a 120 K. As a esul , each H si e in he Cmcm s uc u e becomes wo si es in he Pmcn s uc- u e, each o which unde goes a u he wo old spli ing in he P21cn s uc u e. The e is e idence om neu on di ac ion s udies (Lage e al., 1998) o u he H-si e spli ing a low empe a u es, bu his is no di ec ly im- plica ed in he phase ansi ions. The excess en opy associa ed wi h bo h o he phase FIG. 7 Speci ic hea da a o lawsoni e, de e mined by Pe kins e al. (1980), wi h an in e pola ion (solid line) con- sis en wi h a Landau ic i ical phase ansi ion. ansi ions has wo main possible sou ces. The i s is he con igu a ional en opy associa ed wi h mixing he wo possible s uc u al con igu a ions as wo dis inc si es in he high- empe a u e phase become indis inguishable in he low empe a u e phase. In a simple B agg-Williams model o hese wo phase ansi ions, we would expec he excess en opy associa ed wi h each ansi ion o be solely he con igu a ional en opy, which would imply ∆S= 5.76 J K−1mol−1 o each ansi ion. A con ibu ion o he en opy may also come om he e ec o he spon aneous s ain on he phonon equen- cies. This excess ib a ional en opy is expec ed o scale as he squa e o he o de pa ame e , bu i is no i - ial o calcula e i s magni ude. I is also unclea how much ib a ional en opy is equi ed o d i e a ansi ion om con igu a ional beha iou (e.g., B agg-Williams) o he Landau limi . In he case o albi e, he excess o he expe imen ally es ima ed en opy o e he calcula ed con igu a ional en opy is only abou 10 % (Ca pen e , 1988), and his appea s o be su icien . In bo h ansi ions, he obse ed excess en opy is ap- p oxima ely 6 J K−1mol−1. Thus he measu ed en opy in lawsoni e is no inconsis en wi h a model o he an- si ions whe e dipole o de ing is modi ied by s ain e ec s. C. Hy e esis in calo ime ic measu emen s The e is a signi ican deg ee o hys e esis in he calo i- me ic measu emen s o his phase ansi ion, which is no obse ed in o he expe imen s. One signi ican ac- o is ha he measu emen s o quan i ies such as he spon aneous s ain depend on bo h he o ien a ional o - de ing o H2O molecules, and he esponse o he es o he s uc u e o his o de ing. The absence o o - de on he leng h scale o he amewo k esponse may well mask signi ican sho - ange o de . One o he bes - 7 FIG. 8 Tempe a u e dependence o speci ic hea in lawsoni e, compa ed wi h a Landau model. Poin s show expe imen al da a ( i s hea ing un), he solid line is a Landau i , and he b oken line shows he baseline unc ion Cp0. documen ed examples o his is he s udy o co die i e by Pu nis e al. (1987), in which NMR measu emen s o (Al, Si) o de ing we e compa ed wi h spon aneous s ain da a. In co die i e, he expec ed ela ionship be ween he s ain and he deg ee o o de (Q∝ε) was only ound o Q > 0.9; less wello de ed samples showed no mac oscopic s ain. The e a e some pa allels be ween his beha iou and he obse a ion ha he s ain componen s e1and e2in lawsoni e beha e somewha di e en ly o small de- g ees o long- ange o de . The applica ion o his concep o he Cphys e e- sis in lawsoni e may be seen by s a ing wi h a ully o de ed s uc u e. On hea ing, he deg ee o o ien a- ional o de dec eases, and he emainde o he s uc u e elaxes owa ds he high- empe a u e s uc u e. The ag eemen be ween he calo ime ic da a and he spon- aneous s ains implies ha his p ocess is essen ially ho- mogeneous. On cooling, howe e , he si ua ion appea s o be di - e en . The elaxa ion o he s uc u e is e e sible, bu he speci ic hea measu emen s indica e ha he en opy does no scale wi h Q2 in he expec ed way. This im- plies ha he local aspec o he ansi ion ( he H2O o ien a ional o de ing) is no pe ec ly coupled wi h he long ange displaci e changes in he lawsoni e s uc u e o small deg ees o o de . Fu he expe imen s o s udy his hys e esis a e planned. D. Anomalies close o Tc As Fig. 2 shows, he hea capaci y anomaly de ia es om he p edic ions o Landau heo y some 2 K o 3 K below he ansi ion empe a u e. Fig. 8 shows he same e ec o he ac ual anomaly, a he han he linea ised unc ion in Equa ion (1). Fig. 8 emphasises ha he e a e wo de ia ions om he Landau model; immedia ely below Tc, he expe i- men al Cpda a a e lowe han Landau heo y p edic s, and abo e Tc, he Cpda a a e highe han he model. The con ibu ions o hese wo e ms o he excess en- opy associa ed wi h he ansi ion e y nea ly cancel each o he ou . E. H o de ing as a ic i ical Landau p ocess Calo ime ic da a o he ansi ion a e consis en wi h o he expe imen al da a in indica ing ha he Cmcm–Pmcn ansi ion in lawsoni e ollows a Landau model, close o he ic i ical poin . The excess en opy associa ed wi h he ansi ion appea s o be somewha a iable, which may indica e ha he ei he o bo h he deg ee o dipole o de a low empe a u es, and diso de a high empe a u es, a e incomple e. In any case, he ∆S o he ansi ion is sligh ly highe han we would p edic o a simple o de -diso de model. Quali a i ely simila esul s ha e been ob ained o o de -diso de ansi ions in a numbe o mine al sys- ems, including omphaci e (C2/c −P2/n, Ca pen e e al., 1990), calci e (R3m–R3c, Red e n e al., 1989), and albi e (C2/m −C1, Salje e al., 1985). As no ed abo e, he ac ha he he modynamics o hese ansi ions ap- pea o ollow a Landau model o he en opy, a he han a con igu a ional model, is ela ed o he ole o he i- b a ional en opy and i s dependence on he spon aneous s ain. 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