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.
ACKNOWLEDGMENTS
We would like o hank D . C. F ancis (Ha a d Uni-
e si y, USA) o he lawsoni e sample used in his s udy,
and D . S. Ma ion (Cen e o Ma e ials Science, Uni-
e si y o Oslo) o he mog a ime ic da a o his law-
soni e sample. We a e g a e ul o P o . A. Na o sky
and wo o he e iewe s o hei help ul commen s on
his manusc ip . This p ojec is suppo ed by he EU
TMR Ne wo k “Mine al T ans o ma ions” (ERBFMRX-
CT97-0108).
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