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 .
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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
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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).
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[7] M. Descamps e al., in Quasielas ic Neu on Sca e ing,
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1994), p. 107.
[8] M.A. Ramos e al., Phys. Re . Le . 78, 82 (1997).
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[13] S.W. Lo esey, Theo y on Neu on Sca e ing om Con-
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[14] M. Bée, Quasielas ic Neu on Sca e ing (Adam Hilge ,
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[15] A. C iado e al. ( o be published).
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(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).
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