Purely dynamical signature of the orientational glass transition

VOLUME 83, NUMBER 14 PHYSICAL REVIEW LETTERS 4OCTOBER 1999 Pu ely Dynamical Signa u e o he O ien a ional Glass T ansi ion M. Jiménez-Ruiz,1A. C iado,1F.J. Be mejo,1G.J. Cuello,1F.R. T ouw,2R. Fe nández-Pe ea,2H. Löwen,3 C. Cab illo,1and H.E. Fische 4 1Consejo Supe io de In es igaciones Cien ´ icas, Se ano 121-123, E-28006 Mad id, Spain and Depa amen o de Fı ´sica de la Ma e ia Condensada, Uni e sidad de Se illa, P.O. Box 1065, E-41080 Se ille, Spain 2A gonne Na ional Labo a o y, A gonne, Illinois 60439 3Ins i u ü Theo e ische Physik II, Hein ich-Heine-Uni e si ä , Uni e si ä ss asse 1, D-40225 Düsseldo , Ge many 4Ins i u Laue Lange in, BP 156x, F-38042 G enoble Cedex 9, F ance (Recei ed 16 Ma ch 1999) The dynamics o he eezing ansi ion o he o a o phase c ys al o e hanol in o i s o ien a ional glass phase is moni o ed by measu emen s o molecula o a ional componen s in he quasielas ic neu on sca e ing spec um. We demons a e ha phenomena obse ed a pico- and nanosecond scales can be mapped on o hose shown by a model o in ini ely hin ha d needles o a ing a ound body- cen e ed-cubic la ice posi ions. As he model glass ansi ion is o pu ely dynamical o igin, ou indings suppo he idea ha he glass ansi ion is pu ely dynamical and no associa ed wi h any he modynamic phase ansi ion. PACS numbe s: 64.70.P , 61.20.Lc, 61.43.–j The na u e o he nonequilib ium ansi ion which oc- cu s by apid cooling o a liquid, he canonical liquid-glass ansi ion, emains an elusi e ques ion [1]. In a nu shell, he ansi ion may be iewed ei he as a pu ely dynami- cal phenomenon wi hou any associa ed changes in s a ic quan i ies [2] o as a emnan o an unde lying he mo- dynamic phase change [3,4] which is pa ially hidden by kine ic easons. A gumen s in a o o bo h poin s o iew a e pa ially suppo ed by expe imen al da a. On he o he hand, bo h al e na i es a e g ounded on ai ly well elabo- a ed heo e ical amewo ks such as kine ic heo ies o he mode-coupling amily [2] and hose o he dynamics o c i ical phenomena [3]. The main di icul ies in e alua ing he me i s o bo h ap- p oaches conce n he wide ange o complex phenomena in ol ed wi hin he glass ansi ion o a eal ma e ial which hides some o he beha io s expec ed o appea as cha ac- e is ic signa u es o he ansi ion. In ac , mos sys ems whe e de ailed s udies can be ca ied ou wi hin he deeply supe cooled liquid do show a ich a ie y o phenomena such as molecula o a ions and/o low-ene gy ib a ions, which a e s ongly coupled o he ansla ional dynamics due o he huge iscosi y cha ac e is ic o empe a u es nea he glass- ansi ion poin Tg. While some p og ess on he unde s anding o he e ec o such mo ions on quan i- ies usually employed o s udy he dynamic co ela ions a empe a u es close o Tghas been achie ed [5], he ques- ion emains as o whe he he s uc u al liquid-glass an- si ion is pu ely dynamical in o igin. The aim o his Le e is o es whe he he glass ansi ion leading om o a o phase c ys als (RP) o he o ien a ionally diso de ed [o ien a ional glass (OG)] s a e can be unde s ood as a pu ely dynamical c osso e . In o de o do so, we compa e neu on sca e ing da a o e hanol ac oss he abo e men ioned ansi ion wi h ha esul ing om a simple, albei non i ial model [6] which exhibi s a pu ely dynamical c osso e . We ind e y simila signa u es o he RP !OG ansi ion in bo h cases which suppo s he idea ha such a ansi ion is a pu ely dynamic phenomenon. Ou mo i a ion o moni o he RP !OG ansi ion on e hanol is h ee old: Fi s , while he eezing o RP c ys- als has been s udied in a ai numbe o sys ems [7], many de ails o he RP !OG ansi ion ha e been cla i ied e- cen ly o e hanol [8,9]. Second, he p esence o long- ange posi ional pe iodici y a bo h sides o he RP !OG ansi ion implies ha he mel ing p ocess is pu ely o- a ional ( o a ion- ansla ion coupling e ec s a e eason- ably small [10]), and can hus be ollowed by moni o ing he neu on quasielas ic sca e ing ac oss he ansi ion, in con as wi h he canonical glass ansi ion whe e he o- a ional mel ing is pa ially hidden by he eme gence o quasielas ic in ensi ies om o he sou ces. Thi d, e hyl alcohol has he unique ea u e ha i can be p epa ed in wo di e en phases showing glassy beha io a he same empe a u e, one o hese phases ha ing s uc u al diso - de (liquid and glass) and he o he ha ing only o ien a- ional diso de (RP and OG). In he diso de ed c ys als he molecula cen e s o mass si a he nodes o a bcc la ice [10,11], and mel ing in o he RP is signaled by jumps in speci ic hea [9] and he mal expansi i y. The close p ox- imi y o bo h ansi ions was also e ealed by dielec ic spec oscopy [12] whe e bo h a2 and sub2Tg elaxa ions appea as oundingly nea in equency and empe a u e de- pendence. Hence he canonical glass ansi ion seems o be domina ed by he eezing o he o ien a ional deg ees o eedom. I he e is e idence ha he RP !OG is pu ely dynamic, he same conclusion should apply o he canoni- cal glass ansi ion. Hence ou s udy e en sheds new ligh on he na u e o he s uc u al liquid-glass ansi ion. Two se s o neu on sca e ing expe imen s we e ca ied ou . Explo a ion o he mic oscopic dynamics wi hin a 0031-9007兾99兾83(14)兾2757(4)$15.00 © 1999 The Ame ican Physical Socie y 2757 VOLUME 83, NUMBER 14 PHYSICAL REVIEW LETTERS 4OCTOBER 1999 scale o abou 1 meV (艐1.5 ps21) was pu sued using he in e ed-geome y ime-o - ligh spec ome e QENS a he In ense Pulsed Neu on Sou ce, whe eas ha aking place a meV scales was moni o ed using he IN16 backsca e ing spec ome e a he Ins i u Laue Lange in (G enoble). The o me ins umen ope a es wi h a ixed inal ene gy o 3.65 meV enabling an ene gy esolu ion o DE⬃90 meV (HWHM), whe eas he la e was se up wi hin a con igu a ion which deli e ed a esolu ion o 1 meV and an ene gy- ans e ange up o 615 meV. P epa a ion o glass and RP c ys al samples ollowed ou es desc ibed p e iously [8,11,12]. Bo h liquid!glass and he RP !OG ansi ions occu in a empe a u e in e al cen e ed a abou 97 K. Pa ially (C2D5OH) deu e a ed samples we e employed o moni o i s s a e (glass, liquid, o cubic c ys al) by inspec ion o he di ac ion pa e ns. The shape o all measu ed spec a con o ms o ha shown in Fig. 1. Bo h a meV and meV scales i shows a s ong elas ic ( esolu ion-limi ed) componen plus a quasielas ic con ibu ion which can be seen by he naked eye. A sample o he empe a u e dependence o he quasielas ic linewid hs o wo ep esen a i e alues o he momen um ans e Qis shown in Fig. 2. No signi i- can dependences we e ound o o he explo ed Q alues. Apa om de ails a ising om he a he di e en e- quency windows and sca e ing powe o he wo spec o- me e s, he same dependence is obse ed, showing ha he b oadening o he quasielas ic spec um inc eases h ough he o a ional mel ing ansi ion. FIG. 1. Spec a as measu ed on bo h QENS (a) and IN16 (b) spec ome e s. Model i s a e shown by hin solid lines. Dashed and hick solid lines co espond o he elas ic and quasielas ic componen s, espec i ely. The assignmen o he obse ed b oadenings o unde - lying mic oscopic mo ions equi es he use o a model o ep esen he dynamics [13]. On symme y g ounds, one expec s ha i s basic ea u es a e encompassed wi hin he o malism desc ibing molecula eo ien a ions abou [100], [110], and [111] axes o a cubic la ice [14]. I p edic s a neu on sca e ing law gi en in e ms o ou classes o molecula o a ions wi h jump a es 21 j,j苷 14. The ime scales o wo o hese a es a e se om he spec al linewid hs measu ed wi h bo h ins umen s. Howe e , hei assignmen o speci ic mo ions equi es addi ional in o ma ion om some o he sou ces. To such an e ec , we ha e ca ied ou molecula dynamics simula ions on he N-P-Tensemble ( he cell shape is al- lowed o luc ua e) using a ealis ic model po en ial o he mic oscopic in e ac ions [15]. The esul s o such an endea o we e g a i ying since (a) he equilib ium la - ice s uc u e is ep oduced, (b) eezing o o a ional mo- ions occu s below 100 K, and (c) he c ys al s uc u e becomes uns able abo e 120 K ha is qui e close o ex- pe imen . F om he analysis o he compu ed ajec o ies, i was ound ha molecules will eo ien be ween some 24 p e e ed o ien a ions wi h as ly di e en a es. Re- o ien a ions lea ing una ec ed he mos p e e ed o ien- a ions (C—O bond along he [001] di ec ion and C—C bond close o 关11¯ 1兴, and hose ela ed by symme y) we e ound o ake place wi hin he picosecond scale, whe eas a mo e in equen jumps occu ing wi hin scales o hun- d eds o picoseconds we e also moni o ed. The calcula ed in e media e dynamic s uc u e ac o FMD共Q, 兲showed FIG. 2. (a) Tempe a u e dependence o he quasielas ic linewid h as measu ed on QENS ( illed) and IN16 (open symbols) spec ome e s. (b) Va ia ion o he wid h o F共 兲as calcula ed om he esul s o he sys em o ha d needles. The inse shows da a in he meV scale on a semiloga i hmic plo . 2758 VOLUME 83, NUMBER 14 PHYSICAL REVIEW LETTERS 4OCTOBER 1999 s ong de ia ions om exponen ial beha io and, in ac , ou di e en exponen ial decays we e needed o ully ac- coun o hei shapes. The jump a es 21 jes ima ed in such a way we e ound o be well sepa a ed in ime. Two o hose decays we e ound o be wi hin he equency windows co e ed by he expe imen s and he e o e we iden i y he obse ed elaxa ions wi h mo ions o he wo classes desc ibed abo e. Apa om he a ia ion wi h empe a u e o he linewid h, he RP !OG ansi ion is also ollowed by he aise wi h empe a u e o he quasielas ic in ensi y and he concomi an dec ease o he elas ic peak, as shown in Fig. 3. As seen he e, he ansi ion is e y nicely moni o ed ollowing he ans e o spec al in ensi y om elas ic o quasi- (o inelas ic) sca e ing and his shows e y simila cha ac e is ics o bo h equency windows. F om da a gi en abo e i is seen ha molecula o- a ions occu in he o a o -phase c ys al on pico- and nanosecond scales a empe a u es whe e he main a e- laxa ion explo ed by dielec ic spec oscopy [12] al eady eaches mac oscopic elaxa ion imes. Well below 80 K o a ional eezing seems comple e, and all he molecula deg ees o eedom which a e he mally exci ed will con- ibu e o he spec um as inelas ic (i.e., ini e- equency) signals [9]. This is in e y good ag eemen wi h speci ic hea da a [9] which also show ha he ex en in empe a- u es o he ansi ion is qui e compa able o ha e i- denced by he p esen da a (i.e., abou 18 K). In he ques o physically simple models which exhibi a pu ely dynamical glass ansi ion, a model o ha d in ini ely hin needles on a la ice as de eloped by Renne e al. [6] seems mos appealing. The sys em is cons i u ed by a se o ha d needles ha a e execu ing ee o a ions be ween elas ic collisions ha ing hei cen e s o mass loca ed a he nodes o a cubic la ice. The only con ol pa ame e is he a io ᐉ苷L兾ao he needle leng h L o he la ice cons an a[16]. Since he excluded olume o he needles is ze o, all he s a ic p ope ies o he model a e i ial (i.e., he e a e no s a ic co ela ions). Howe e , i s anspo and dynamical p ope ies exhibi a s ong dependence on ᐉ. The dynamics o he needle model is in es iga ed by compu e simula ions. We conside a sys em o N苷432 in ini ely hin needles wi h a homogeneous line mass den- si y m兾Lwhose cen e -o -mass coo dina es a e ixed on o a bcc la ice in a pe iodically epea ed cubic simula ion box. We ook a bcc c ys al in o de o inco po a e he e hanol la ice s uc u e in he RP. Calcula ing he ajec- o ies o he needles we ob ained he ime-au oco ela ion unc ion o he needle o ien a ions de ined as F1共 兲苷 具1 NPN i苷1 ៬ ui共0兲?៬ ui共 兲典, whe e he angula b acke s deno e he canonical a e age and ៬ ui共 兲is he ime-dependen a- jec o y o he uni ec o desc ibing he o ien a ion o he i h needle. We explo ed he ange 1.0 #ᐉ#5.0. The sys em was le o e ol e o e a long ime co esponding o 106collisions. As a esul , as ᐉinc eases he elax- FIG. 3. (a) Tempe a u e dependence o he elas ic (solid) and quasielas ic (open symbols) in ensi ies ac oss he RP ! OG ansi ion measu ed on he QENS spec ome e . (b) Same da a measu ed on IN16. (c) Con ibu ions om he F共 兲 o he elas ic (solid) and quasielas ic (open symbols) equency win- dows e sus he equi alen empe a u e Tⴱ o he esolu ion wid h D R苷90 meV. The inse shows da a o he esolu- ion wid h D R苷1meV. a ion o F1共 兲becomes mo e and mo e sluggish, and o ᐉ⬃3.4 he au oco ela ion is almos blocked on he ime scale explo ed in he simula ion. Fo ᐉ苷4.5 he o ien- a ional au oco ela ion is almos equal o uni y, ha is o ien a ions becoming ozen wi hin a e y na ow solid angle. Le us now discuss how o es ablish a link be- ween he needle model and ou expe imen al da a. The ime scale can be mapped di ec ly. In he needle model i is se by he ime ⬅pmL2兾24kBT. I we iden i y he momen o ine ia o he needles J苷mL2兾12 wi h ha o one e hanol molecule (J苷0.741 310245 Kgm2), we ob ain he ac ha he ime scale is o he o de o 1 ps a T苷100 K which se s he ime scale. Consequen ly we can ansla e expe imen al equencies in o simula- ion da a and ice e sa. Finally, in he a he mal needle model, only ᐉen e s, whe eas empe a u e is he c ucial pa ame e o ou measu emen s. In o de o es ablish a mapping be ween ᐉand T, we w i e an in e se e ec i e 2759 VOLUME 83, NUMBER 14 PHYSICAL REVIEW LETTERS 4OCTOBER 1999 a io 1兾ᐉas a Bol zmann ac o 1兾ᐉ苷Aexp共2E兾kBT兲 [17]. Clea ly he limi ᐉ!`co esponds o ze o em- pe a u e. The wo ee cons an s, namely, he ampli ude Aand he ene gy scale E, a e de e mined as ollows: Fi s we ecall ha i he needle leng h is smalle han he nea es neighbo dis ance p3a兾2 he needles a e non- in e ac ing ee o a o s, which co esponds o in ini e empe a u e and ixes he ampli ude A苷2兾p3苷1兾ᐉ0. Second, he ac i a ion ene gy Eshould co espond o he expe imen al glass ansi ion empe a u e such ha E苷kBTg. Hence, he ansla ion o empe a u es in he expe imen in o e ec i e a ios ᐉo ou model is gi en by ᐉ苷ᐉ0exp共Tg兾Tⴱ兲. To compa e expe imen and model esul s he Fou ie ans o m o F1共 兲in o he equency domain was e alua ed. Ou simula ion da a o F1共 兲we e con olu ed wi h he ins umen al esolu ion unc ions in o de o mimic he measu emen s. The esul ing unc ion F共 兲 was spli in o elas ic and quasielas ic pa s depending upon he wid h D R. The wid h and he ampli ude o he quasielas ic pa we e de e mined a e wa ds. The esul s o he wid hs a e gi en in Fig. 2 and hose o he in ensi y a ios in Fig. 3. No e ha he simula ion da a we e always exp essed in empe a u e ia he ansla ion gi en abo e. One clea ly sees a kink in he Lo en zian in ensi y bo h in he expe imen al da a and in he ans o med needle model da a a empe a u es abou 97 and 75 K, espec i ely. This is a clea cu inge p in o he o ien a ional glass ansi ion. On he o he hand, he elas ic in ensi y also exhibi s a simila kink. The di e ences be ween expe imen and model conce n he ela i e magni udes o changes in elas ic and quasielas ic in ensi ies as well as in he absolu e alues o he linewid hs. Whe eas expe imen con ains a s ong elas ic sca e ing componen a ising om he p esence o a well-de ined c ys al s uc u e ha ing ansla ional deg ees o eedom, such a con ibu ion is ob iously absen in he model which, by cons uc ion, shows no s ic ly elas ic componen . The ela i e wid h o he c osso e s a e abou 30 K in expe imen and 艐70 K o he needle model, a di e ence expec ed om he absence in he la e case o a ue in e ac ion po en ial. The e ec i e wid hs o he quasielas ic spec a o bo h model and expe imen shown in Fig. 2 exhibi c osso e s a he same empe a u es as do he kinks in he in ensi ies o Fig. 3. This gi es compelling e idence ha he essen ial signa u es o he o ien a ional glass ansi ion can be unde s ood om a pu ely dynamical model. In conclusion, we ha e shown ha he essen ial ea u es o he neu on sca e ing da a ac oss he o ien a ional glass ansi ion can be unde s ood in e ms o a pu ely dynami- cal model. The inge p in o he ansi ion as e ealed by a cusp in he inelas ic sca e ing is e y simila in he expe imen and in he model. The implica ions o such an analogy in dynamical beha io can, in he ligh o p e ious da a, o a la ge ex en be applied o he canonical glass-liquid ansi ion inasmuch as he la e mus ca y a la ge o a ional componen (in ac , he jump in speci ic hea a he glass and OG !RP ansi ions co esponds o an ac i a ion o 艐2.8 deg ees o eedom in he la e and abou 3.7 in he o me , he ex a deg ee su ely assignable o ansla ional mo ions). In consequence, he scena io o a ansi ion o pu ely dynamical o igin accoun s o mos o he obse ed signa u es o he glass ansi ion which, pu in o eal numbe s, amoun s o a di e ence o abou 20% o he jump in speci ic hea , an e en smalle di e ence in he low- equency spec a and low- empe a u e p ope ies, and a close p oximi y in he case o mac oscopic elaxa ions. This wo k was suppo ed in pa by he U.S. De- pa men o Ene gy, Basic Ene gy Sciences-Ma e ials Sciences, unde Con ac No. W-31-109-ENG-38 and DGICYT (Spain) G an No. PB95-0075-C03-01. [1] I. Gu zow and J. Schmelze , The Vi eous S a e (Sp inge - Ve lag, Be lin, 1995), p. 287. [2] W. Gö ze, in Liquids, F eezing and Glass T ansi ion, edi ed by J.P. Hansen e al. (No h Holland, Ams e dam, 1991). [3] J.P. Se hna e al., Phys. Re . B 44, 4943 (1991). [4] J. Ble y, Z. Na u o sch. A 51, 87 (1996). [5] R. Schilling e al., Phys. Re . E 56, 2932 (1997). [6] C. Renne e al., Phys. Re . E 52, 5091 (1995); S. Obuko e al. J. Phys. I (F ance) 7, 563 (1997). [7] M. Descamps e al., in Quasielas ic Neu on Sca e ing, edi ed by J. Colmene o e al. (Wo ld Scien i ic, Singapo e, 1994), p. 107. [8] M.A. Ramos e al., Phys. Re . Le . 78, 82 (1997). [9] C. Talóne al., Phys. Re . B 58, 745 (1998). [10] F.J. Be mejo e al., Phys. Re . B 56, 11536 (1997). [11] R. Fayos e al., Phys. Re . Le . 77, 3823 (1996). [12] M. Mille e al., Phys. Re . B 57, R13977 (1998); M. Jiménez-Ruiz e al., Phys. Re . B 59, 9155 (1999). [13] S.W. Lo esey, Theo y on Neu on Sca e ing om Con- densed Ma e (Ox o d Science Publica ions, New Yo k, 1984), Vol. I, p. 244. [14] M. Bée, Quasielas ic Neu on Sca e ing (Adam Hilge , B is ol, 1988), p. 228. [15] A. C iado e al. ( o be published). [16] D. F enkel and J.F. Magui e, Phys. Re . Le . 47, 1025 (1981); Mol. Phys. 49, 503 (1983). [17] A mo e elabo a e mapping is known o ha d sphe es whe e he e ec i e diame e is also aken as an a e aged Bol zmann ac o in o de o ma ch he second i ial coe icien , see, e.g., J.A. Ba ke e al., Re . Mod. Phys. 48, 587 (1976). 2760