Lattice dynamical studies of ternary superionic conductors Ag 3 SX (X=I, Br)

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1 Indian Journal of Engineering & Materials Sciences Vol. 7, Octoer-Decemer 2, pp Lattice dynamical studies of ternary superionic conductors Ag 3 SX (X=I, Br) M M Sinha" & K Wakamura ' Department of Physics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur , India High Tech. Research Center, Okayama Universi ty of Science, 1-1 Ridai-cho, Okayama 7-5, Japan Received 25 Feruary 2; accepted 5 Septemer 2 A de Launey angu lar force model has een applied to study the phonon dispersion in three symmetric directions of ternary superionic conductor Ag 3 SX (X =1, Br) y assuming them to e ideal perovskite type structure. A lattice dynamical calculation reasonaly interprets the dominance of moile ions in highest frequency mode. The short-range ifs) and longrange ifl) forces in Ag 3 SX (X = I, Br) for a high frequency and are estimated near the transition temperature Tc and elow 3 K. The IL values in oth the conductors show an increase with T aove Tc whereas the values of Is decrease with T. The temperature dependence of IL and Is are explained satisfactorily from this calculation. Superionic conductors form a particular class of solid materials characterized y ionic conductivities of an order of magnitude as is usually found for molten salts. The high ionic conductivity is due to movement of one type of ions etween the sites provided y the ionic sulattice, which is oscillating aout fixed equilirium positions. Recently, considerale attention has een paid to the electronic susystem of these materials in order to elucidate the origin of superionic conduction' -6. Many anomalous properties have een oserved in the optical spectra 7. Aniya has suggested that the change of onding, which occurs locally and fluctuates in time, is the key mechanism responsile for superionic transport 2,3, There, the change of onding is considered to e driven y the lattice virations. In order to gain further insight into the microscopic mechanism of superionic transport, the study of lattice virations of these materials may give some useful information. Keeping this in view, de Launey angular force (OAF) models has een used in the present work to investigate the zone-center phonons and phonon dispersion relation of y-phase of Ag3SX (X=I,Br) for ideal cuic perovskite structure. The calculated results are compared with the experimental results. The temperature dependence of short-range forces (fs) and long-range force (fl) in Ag3SX are estimated and are interpreted. Crystal Structure Ag3SI exhiits three crystallographic structures, i.e., the a-phase (T?519 K), the 13-phase (157T519 K) and the y-phase (T157 K)9. Whereas Ag3SBr is an isostructural to Ag3SI and it appears in y-phase elow 118 K 1. y-ag3si is an ordered structure, which is closely related to the structure of 13-Ag3SI. The 13- Ag3SI is cuic with space group Pm3m where Ag ions are distriuted into four positions apart.5 A from the face centered positions toward [1], while in y-ag3si the positions of the anions are almost the same as in 13-Ag3SI and Ag ions are located at one of the four positions of the 13-phase oeying a threefold symmetry axis around [111] axis. Accordingly, the structure is no longer cuic ut elongs to the rhomohedral space group R3. In the present investigation, the y phase of Ag3SX (X=I, Br) assumed to have the ideal perovskite type structure as shown ill Fig.1. The unit cell of Ag3SX is one formula unit. This implies that there are 5 atoms per unit cell and will give rise to 15 phonon modes, 3 acoustic and 12 optical modes at the r-point. The symmetry of phonon modes at the r-point in the Oh representation is descried as: z Fi g.1 - Ox Ag V 1- /----- Ideal cuic perovskite structure... (1)

2 386 INDIAN J. ENG. MATER. SCI., OCTOBER-DECEMBER 2 where oth h i and T 211 modes are triply degenerate. One TIll mode is acoustic and the remaining are infrared active optical modes. The hi mode is inactive. Thus, the crystal has no Raman active mode in this phase. Theory Here we use de Launey angular force (OAF) model 8 to study the zone-center phonons and phonon dispersion of Ag 3 SX (X=I, Br). In OAF model, the relative di splacement of the reference atom and one of its neighor is considered. The restoring force on the reference atom is taken proportional to the component of the relative displacement perpendicular to the line joining the two atoms at their equilirium positions. The forces due to all neighors are calculated separately and summed up together. Different force constants are used for the various categories of neighors and the net force on the reference atom is otai ned y summing over the contriution from all the neighors. We employ four central force constants a i, a2, a3 and a4 and four angular force constants a ;, a, a and a etween S-Ag, X-Ag, X-S and Ag Ag (X=I, Br) atoms, respectively. The (l5x15) dynamical matrix is reduced to three (5x5) matrices at zone center ll. These interatomic force constants are then otained y fitting the experimental values of transverse infrared active phonon frequencies at zone center I The force constants thus calculated are listed in Tale 1. Taking these force constants as input parameters, we computed the dynamical matrix at the zone-center as well as along three symmetric directions [koo], [kko] and [kkk]. The zone-center phonons thus otained for Ag 3 SX (X=I, Br) are listed in Tale 2 alongwith their experimental values. A set of eigen vectors corresponding to each zone center frequencies are calculated and assigned as shown in Fig.2. Tale I - Val ues of force constants (1) dynes em-i) for Ag)SI and Ag)SBr Force constants Ag)SI Ag)SBr UI (S-Ag) al' (S- A g) U2 (X-Ag) U2' (X-Ag) u) (X-S) u/ (X-S) (Ag-Ag) (4' (Ag-Ag) The short range (fs) and long-range (fl ) forces in perovskite type superionic conductors (SIC) Ag 3 SX are estimated as a function of temperature (T) from the phonon frequencies of transverse (W TO ) and longitudinal (Ww ) modes l2. 14 under the point charge model IS. The relations for the forces are given in terms of effective charge ZOe, volume V and a reduced mass J..! as, 2 * 2 W TO = (fs/il) - 2n(Z e) /31lV... (2)... (3) The values of short range force (fs) and long range force (fl=n(z*e)2/3ilv) can e estimated from Eqs (2) and (3) with the measured values as f s/il= (2 W T 2 + WL 2 )/3 fdll= (WL 2 - Wro 2 )/6... (4)... (5) In Ag 3 SX, the values of fs and fl for highest frequency and (VI) and second highest and (V2) are estimated near the transition temperature Tc and elow 3K which are shown in Figs 5 and 6. Tale 2 - Assigned Mode VI V2 vj V4 Fig.2 - o X Zone center frequencies (em- I) for Ag)SI and Ag)SBr Exptl v, Ag,lSI Ag,lSBr Calculated Exptl Calculated The normal virat ional modes ofy-ag,lsx (X=I, Br) at zone center

3 SINHA & WAKAMURA: TERNARY SUPERIONIC CONDUCTORS Ag 3 SX (X=I,Br) 387 [koo] [kko] [kkk] 2SO , E ISO ISO i)- 14 c: Q) :::I 12 tt Q)... 1 U- 8 SO 4 2 K T r L M r!l Wave Vector A Fig.3 - Phonon dispersion curves of Ag 3 S1 [koo] [kko] [kkk] E ISO i)' 16 c: Q) 14 :::I tt U {O 2 K o.{ O.l.2 T.1. r. 1.2 L O.l Wave Vector.1.2 O.l /). O.{ A FigA - Phonon dispersion curves of Ag)SBr

4 388 INDIAN 1. ENG. MATER. SCI., OCTOBER-DECEMBER 2 6 " Tc=159K Short-range fo rce vi-and 1. ' '----' E.8 o Long-range forc e.6 vi-and O.4 L- -L :.68 '---"'-"".-.-."T"':'."':'."':'. -.'T".----, , ,.----, E: ' -;:; ".6 Short -range force vz-and '--_-'--_...l.- -'-_--L_--'.l.-----l.4.35 Long- range force Vj -and Tc=159K o a o '-- -'- -l.. --l.3 '-- -' "-..1..",--,- Fig.5 - o TEMPERATURE(K) Temperature dependence of short-range and long-range force in Ag)SI 6 ' Ag 3 SBr , Tc=1l8K short-range force VI -and < long-range force.6 VI-and... -'.4 L- I -L. -L ' --l -.J.9 r---, r-----, N '6.8 x short-range force v2 and Tc=118K..." O. 6 '-----l l- --,- " -1.J Fig.6 - :.6 r----'"r---r----,--..., , ---. '6 Long-range force 3 V2 -and S.4 o. 2 L- --l -L. ' --l TEMPERATURE(K) Temperature dependence of short-range and long-range force in Ag)SBr Results and Discussion It is ovious from Tale 1 that the force constant u) corresponding to interatomic interaction etween cage ions (S-X) is largest. This result is plausile since S and X-ions are the frame ions aove Te and therefore, the magnitude of the force constant for these must e larger than that involving the moile ions even elow Te. The agreement of experimental and the calculated res ults is visile in Tale 2. The normal viration modes at zone center in y-phase of Ag)SX are assigned with the help of calculated eigen vectors. The ass igned highest mode (VI) in the present investigation is different from that done y others for ideal perovskite compounds l6. The justification for this is given in our earlier paperl7. Figs 3 and 4 depict the calculated dispersion relations along symmetry directions for Ag)SI and Ag)SBr. The experimental results at the I-point are shown y solid circles for comparison. It is emphasized that the fit is very good and low-lying acoustical mode characteristics in superionic conductors l8 are well descried. The further comparison at other than zone center could not e done ecause of non-availaility of oserved values. It is seen from Figs 5 and 6 that the values of A for oth the conductors AgJSX (X=I, Br) are increasing with T aove Te for highest ands whereas fs decreasing with temperature. These results reveal the enhancement of ionic character of interionic forces etween cage ion since the highest and (VI) is due to virational modes which consist of dominantly the virations of cage ions. This is ascertained from the values of ratio (js/a), since it shows the increase with T for VI and ut decrease for the mode of moile ion viration. These temperature dependences are understood with respect to those of the volume thermal expansion and interionic distance etween cage and moile ions. Similar ehaviors appear in u phase of Ag)SI and more clearly in AgCrS2!9. These are consistent with the increase of ZOe with T, oserved in superionic conducting phase of several superionic conductors l References 1 Kleppmann W G & Weer W, Phys Rev B, 2 (1979) Aniya M, Solid State /onics, 5 (1992) 125.

5 SINHA & W AKAMURA: TERNARY SUPERIONIC CONDUCTORS Ag 3 SX (X=I,Br) Aniya M, J Phys Soc Japan, 61 (1992) Wakamura K, Solid State Comm, 86 (1993) Yamanishi T, Kanashira T, Michihira Y, Kishimoto Y & Ohno T, J Phys Soc Japan, 64 (1995) Tomoyose T, Solid State fonies, 79 (1995) Akopyan I Kh, Klochikhin A A, Bovikov B V, Valakh M Ya, Litvinchuk A P & Kosazkii I, Phys Status Solidi, 199 a (199) Launey J de, Solid State Physics, 2 (1956) Perenthaler E & Schulz H, Acta Crys!. B, 37 (1981) 117 and Didisheim J, Mcmullan R K & Wuensch B J, Solid State fonies, 18 & 19 (1986) Reuter Von B & Hardell K, Z Anorg Allg Chem, 34 (1965) 168. II Sinha M M & Wakamura K, Solid State fonies, (1999) (in press). 12 Wakamura K, Kojima A & Noda Y, 11,h fl1l Can! On Ternary and Muitinary Compounds, Salford (Ins!. Phys. Conf. Ser. No. 152), (1997) Wakamura K & Hirakawa K, Proe. 3 rd fnt Can! On Phonon Physics and 6,h 1nl Can! On Phonon Scattering in Can dens Matter (World Scientific, Singapore), I (199) Wakamura K, Miura F, Kojima A & Kanashira T, Phys Rev B, 41 (199) Mitra S S, Oplieal properties a! solids, edited y S Nudelman and S S Mitra (Plenum, New York), Hua G L, J Phys Condens Matter, 3 (1991) Sinha M M & Wakamura K, J Phys Chem Solids, (i 999) (sumitted). 18 Wakamura K, Phys Rev B, 59 (1999) Wakamura K & Hirakawa K & Orita K, J Phys Chem Solids, 57 (1996) Aniya M & Wakamura K, Solid Siale fonies, (1996) 183.