PHYSICAL REVIEW BVOLUME 46, NUMBER 22 1DECEMBER 1992-II
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Con inuous p essu e-induced s uc u al ansi ion in he noble-me al halide mel s
M. Silbe
School o Physics, Uni ue si y o Eas Anglia, No wich NR4 7TJ, Uni ed Kingdom
A. Gi o and J.T ullas
Depa amen de Fisica iEnginye ia Nuclea , Facul a d'In o ma ica de Ba celona, Uniue si a Poli 'ecnica de Ca alunya,
08028 Ba celona, Spain
(Recei ed 30 Ma ch 1992)
The educ ion o he cha ge o he species in mol en sal s, including he comple e emo al o he
Coulomb in e ac ion, appea s o ha e he same eFec as an inc ease in he p essu e on hese sys ems.
This obse a ion leads o he p edic ion ha acon inuous p essu e-induced s uc u al change is o be
ound in he noble-me al halide mel s a much lowe p essu es han hose used o induce asimila ansi-
ion in he alkali halide mel s.
Some yea s ago, Ma in Ross and co-wo ke s' ex-
amined he e idence o acon inuous p essu e-induced
ansi ion in he alkali halide mel s, namely, a ansi ion
om he s uc u e o asimple mol en sal o ha o a
a e gas-like equimola a omic liquid bina y mix u e.
Thei wo k ollowed ex ensi e expe imen al, and a ew
heo e ical, s udies o hese mel s when subjec ed o high
p essu es. In pa icula , Ross and Roge s ca ied ou
ex ensi e calcula ions o mol en CsI, o which he mel -
ing cu e was es ima ed by exploi ing he ac ha CsI is
isoelec onic wi h Xe. These calcula ions clea ly es ab-
lish how he s uc u al eo de ing o his mel akes
place. In spi e o di e ences o de ail be ween he s uc-
u e o mol en CsI and o he alkali halide mel s, he
s udy o Ross and Roge s inco po a ed all he impo an
ea u es ha cha ac e ize he changes expe ienced by all
he alkali halide mel s along he mel ing cu e.
Mo e ecen ly, we p esen ed he esul s o compu e
simula ions o mol en "NaC1" and "CuC1". The quo a-
ion ma ks indica e ha , besides he simula ion o he ac-
ual sys ems, we also conside ed he s uc u al and
dynamical changes p oduced by a ying he deg ee o
cha ge ans e ~Z~. Ou wo k add essed he ques ion o
he in e play be ween cha ge o de ing and size e ec s o
wo classes o mol en sal s o which he abo e may be e-
ga ded as a che ypes: NaC1 o he alkali halides, CuC1 o
he noble-me al halides. The molecula dynamics (MD)
simula ions s udied he e ec s on he s uc u e and ionic
anspo p ope ies o he wo sys ems esul ing om e-
ducing he cha ge on he species, including he comple e
emo al o he Coulomb in e ac ion. CuC1 mel s om
wha may be ega ded as asupe ionic phase, and i is
long known ha i exhibi s some homopola binding
which we model by aking apa ial cha ge ~Z~ =0.501.
Mo eo e , he e is ala ge size di e ence be ween he
ionic adii, c , in CuC1 han in NaC1 (oI/o~ =0.36 in
CuC1 and ATM/ x=0. 74 in NaC1; M=Na, Cu, X=Cl).
Ou esul s show ha he e a e ma ked di Fe ences in he
s uc u e and ionic anspo p ope ies no only be ween
he ac ual sys ems bu also when he Coulomb in e ac ion
is emo ed ( he case ~Z~ =0). We no ed ha he e appea
o be wo compe ing leng hs, he ionic adii and he mean
ion sphe e adius a=(3/4mp)'~, wi h pdeno ing he ion-
ic densi y. In he case o CuC1, O.c&)aand, as a esul ,
i s s uc u e is la gely insensi i e o he Coulomb in e ac-
ion; i appea s as i he Cl ions a e always a ec ed by he
epulsi e wall a he han he Coulomb epulsion in
de e mining hei pa ial s uc u e ac o . Hence he
changes esul ing om educing he cha ges in CuC1 a e
no ed in he pa ial s uc u e ac o o he Cu ions and in
he c oss co ela ion. In NaC1, o.c„o.N, (a, and all h ee
pa ials change signi ican ly as he cha ge is educed o
ze o.
In ap i a e communica ion Ross b ough o ou a en-
ion he possible connec ion be ween hei s udy, on he
e ec o comp ession on he alkali halide mel s, and
ou s, on he e ec s o educing he ion cha ge. Al-
hough ou wo k was ca ed ou a cons an densi y, he
simila i y be ween hei esul s o he pa ial pai dis i-
bu ion unc ions g,"( ) o mol en CsI unde comp ession,
and ou s, wi h pa ial o no cha ge o mol en NaC1, ap-
pea s o indica e ha he inc ease in p essu e along he
14 886 1992 The Ame ican Physical Socie y
46 BRIEFREPORTS 14 887
TABLE I. Resul s ob ained o "NaC1", "CuC1","CuB ", and "AgI" sys ems.
Sys em E(IZI )/E. P(IZI)/P. n++ (R++)
(A) n(A) n+ (R+ )
(A)
NaC1
CQC1
CuB
AgI
IZ.11
Izl 0.32
0.
iZ, iO.SO)
ized o.
IZ, lO.483
iZ[ O.
IZ, lo.6
Izl o.
0.012
—
0.12
1
—
0.44
1
—
0.5
1
—
0.66
30
1
8
1
7.5
1
1.5
14.1(6.3)
3.8(4.4)
5.3(4.4)
13.4(5.5)
43.5(7.7)
13.5(5.8)
40. (7.9)
14.8(6.4)
53. (8.8)
14.1(6.3)
6.6(5.0)
7.2(5.0)
13.5(5.5)
12. (5.2)
13.5(5.8)
12. (5.5)
13.7(6.2)
12.8(6.1)
4.8(4.2)
7(4.8)
5.8(4.7)
4.3(3.6)
6.1(4.4)
4(4.5)
6.3(4.6)
5(4.3)
2.3(4.1)
mel ing line has he e ec o educing he ion cha ge.
The pu pose o his pape is o epo he esul s o cal-
cula ions o he p essu e P, ob ained om ou MD si nu-
la ions, which show ha indeed he change om a ully
o apa ially ionized "NaC1" mel esul s in an inc ease
o Pin he sys em. Mo eo e , and assuming he abo e
connec ion holds o he noble-me al halides as well, we
sugges ha asimila p essu e-induced s uc u al ansi-
ion in he noble-me al halides should be expec ed o be
ound a lowe p essu es han in he alkali halides.
Fo easons discussed below, he esul s p esen ed in
his pape ha e meaning only in aquali a i e sense.
Howe e , we submi ha hey es ablish he co ec
ends o be expec ed om mo e exac ing calcula ions.
We ha e calcula ed he equa ion o s a e o "NaC1"
and he noble-me al halides "CuC1", "CuB ", and "AgI"
using he ela ion
P41 p gI~3~ij ()d
pK~ T6, o5
whe e he po en ials P;,( ) used in he calcula ions a e as
discussed in Re s. 6and 8.
The calcula ion o Eq. (1) is, in all cases, e y sensi i e
o e o s, gi en ha i sums o e a eas o simila magni-
ude and opposi e signs. The di icul y in ou case is com-
pounded by bo h he long- ange Coulomb in e ac ion,
and ha he in o ma ion we ha e o he g,"( ) is es ic -
ed o he size o he simula ion box. We ha e es ima ed
he p essu e by aking g; ( ) wi hin he simula i. on box in
such away ha he oscilla ion comple es a ull loop.
Beyond his, we ha e assumed g, ( )=1. This assump-
ion in oduces signi ican sys ema ic e o s in ou calcu-
la ions o which we canno gi e ap ecise es ima e.
Howe e , as aguide, i yields p essu es nea he iple
poin o he ac ual sys ems o a ew kba s ins ead o a ew
ba s. The e o e, he esul s a e p esen ed in he o m o
he a io P( ~Z~ )/Po, whe e Po is he p essu e o he ac u-
al sys em nea he iple poin , and P(~Z~ ) he alue o
he p essu e o agi en choice o he ion cha ge ~Z~. Fo
he same easons, we a e no including he alues o he
con igu a ional con ibu ion o he ee ene gies ( ypically
—
60 kcal/mo1 o he "supe ionic" mel s, and +30
kcal/mol o he ~Z~=0 cases). We include he esul s
o he ene gies as he a io E(~Z~ )/Eo, whe e Eo is he
con igu a ional ee ene gy o he ac ual sys em nea he
iple poin .
In he case o he pa ially ionized "NaC1" mel , we e-
po he esul s o ~Z~ =0.32 ins ead o he alue
~Z~ =0.5used in Re . 6. The eason is ha o (Z~ =0.5,
we could no ake a ull oscilla o y loop wi hin he simu-
la ion box o all h ee g;i( ), whe eas he unpublished e-
sul s o ~Z~=0. 32 made his possible. The esul s ob-
ained a e summa ized in Table I.
We no e ha he changes in p essu e o CuC1 and
CuB a e abou he same, bu much smalle han in
NaC1. This is o be expec ed as bo h he s uc u e and
ionic anspo p ope ies o CuC1 and CuB a e e y
simila . The esul s o mol en AgI con ain he la ges
e o s bu , i i s s uc u e and ionic anspo p ope ies
a e ause ul guide, we sugges i e lec s he co ec end.
The con igu a ional ee ene gy in "NaC1" goes down
as he cha ge is educed o ~Z~ =0.32, as a esul o shal-
lowe minima in he ca ion-anion in e ac ion. In all
cases, he ene gies change sign o he ~Z~ =0because he
"neu al" sys ems a e only p obing he epulsi e walls.
In Table I, we ha e also included he coo dina ion
numbe s n; (ij =+,—
). These we e e alua ed by es-
ima ing he a ea unde nea h he i s peak o g,"( ), om
he poin whe e g,"( =Ra)=0 o he es ima ed posi ion
o he i s minimum, i.e.,g; ( =R,"). The . alues o R;J
a e lis ed in b acke s nex o he coo dina ion numbe s.
The alues o n; o he ac ual NaC1 sys em a e in
good ag eemen wi h o he compu e simula ions and ex-
pe imen al esul s. As he cha ge is educed, he coo di-
na ion numbe s in "NaC1" go down in alue. This is a
consequence o wo king a cons an densi y, namely, he
he modynamic s a e o he sys em is unlikely o be along
he mel ing line.
The esul s o he noble-me al halide mel s a e e y
di e en . The anion-anion coo dina ion numbe s, n
do no change signi ican ly on wi hd awing he cha ges,
because he anions a e no a ec ed by he Coulomb epul-
sion. On he o he hand, he ca ion-ca ion coo dina ion
numbe s, n++, inc ease d ama ically, as aconsequence
o he size e ec . Ac ually, he i s peak o g++( ) sam-
ples he a e age size o he clus e enclosed in he cage
o med by he anions. The n+ coo dina ion numbe in
14 888 BRIEFREPORTS 46
"CuC1" and "CuB " inc eases o abou 6 o ~Z~ =O. We
belie e ha he dec ease o n+ "AgI" is aconsequence
o he la ge e o s in ol ed in i s es ima ion, and we ex-
pec ha acompu e simula ion wi h ala ge numbe o
pa icles will b ing his alue up in line wi h hose ob-
ained o he o he supe ionic mel s.
To ou knowledge, expe imen al esul s o he noble-
me al halide mel s unde p essu e ha e no been epo ed
in he li e a u e. This pape sugges s ha he p essu e-
induced s uc u al ansi ion in hese sys ems is likely o
ake place a p essu es ha a e mo e easily accessible
han hose needed o he alkali halide mel s.
I is apleasu e o hank D . Ma in Ross o b inging
o ou a en ion he possible ela ion be ween his wo k
and ou s and o D . Phil Salmon o use ul discussions.
One o us (M.S.) hanks he hospi ali y o he Depa men
de Fisica iEnginye ia Nuclea o he Uni e si a
Poli ecnica de Ca alunya, du ing a esea ch isi when
his wo k was s a ed. Financial suppo by DGICYT,
P ojec PB90-0613-C03,is acknowledged.
'M. Ross and F.J.Roge s, J.Phys. (Pa is) 45, C8-229 (1984).
M. Ross and F.J.Roge s, Phys. Re . B31, 1463 (1985).
3M. Ross and G. Wol , Phys. Re . Le . 57, 214 (1986).
4Also see B. Rodousky, M. Ross, A. C. Mi chell, and W. J.
Nellis, Phys. Re . B31, 1457 (1985),and e e ences he ein.
5A. Ba anyai, I. Ru , and R. L. McG ee y, J. Phys. C19, 453
(1986).
J.T ullas, A. Gi o, J.A. Pad o, and M. Silbe , Physica A171,
384 (1991).
7J. E.Maye and R.B.Le y, J.Chem. Phys. 1,647 (1933).
A. J.S a o d, M. Silbe , J.T ullas, and A. Gi o, J.Phys. Con-
dens. Ma e . 2, 6631 (1990);J. T ullas, A. Gi o, and M. Sil-
be , ibid. 2, 6643 (1990). Fo u he de ails see J. T ullas,
Ph.D. hesis, Uni e si a de Ba celona, 1990(unpublished).
J.E.Ende by and G. W. Neilson, Ad . Phys. 29, 323 (1980).