Continuous pressure-induced structural transition in the noble-metal halide melts

PHYSICAL REVIEW BVOLUME 46, NUMBER 22 1DECEMBER 1992-II B ie Repo s B ie Repo s a e accoun s o comple ed esea ch which, while mee ing he usual Physical Re iew s anda ds o scien i ic quali y, do no wa an egula a icles A .B ie Repo may be no longe han ou p in ed pages and mus be accompanied by an abs ac T.he same publica ion schedule as o egula a icles is ollowed, and page p oo s a e sen o au ho s 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).