Temperature dependence of positions of the absorption edge Eα g (α = 550 cm−1) of Cu6PS5X (X=Br, I) crystals in the temperature range 77 to 323 K are studied by isoabsorption measurements. Temperature variation of the total electric conductivity in the range of the second-order ferroelastic phase transition are analyzed.Istražujem temperaturnu ovisnost položaja apsorpcijskog ruba Eα g (α = 550 cm−1) kristala Cu6PS5X (X=Br, I) u području temperature 77 do 323 K izoapsorpcijskim mjerenjima. Analiziram temperaturne promjene ukupne električne vodljivosti u području feroelastičnog faznog prijelaza drugog reda

Studenyak, I. P.

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ISSN1330–0008CODENFIZAE4ISOABSORPTION AND ELECTRICAL STUDIES OF Cu6PS5X (X=Br, I)CRYSTALS AT THE FERROELASTIC PHASE TRANSITIONI. P. STUDENYAKInstitute of Solid State Physics and Chemistry, Uzhhorod University, 46 Pidhirna St.,Uzhhorod 88000, UkraineReceived 15 March 2001; revised manuscript received 29 August 2001Accepted 10 September 2001 Online 25 May 2002Temperature dependence of positions of the absorption edge Eαg (α = 550 cm−1) ofCu6PS5X (X=Br, I) crystals in the temperature range 77 to 323 K are studied byisoabsorption measurements. Temperature variation of the total electric conductiv-ity in the range of the second-order ferroelastic phase transition are analyzed.PACS numbers: 77.80.Bh, 78.40.Pg UDC 621.315.61Keywords: ferroelastic phase transition, electric conductivity, optical absorption edge1. IntroductionCu6PS5X (X=Br, I) crystals are the most extensively investigated among theargyrodite family compounds, known as fast-ion conductors and ferroelastics, hav-ing a variety of important physical characteristics [1,2]. They undergo two phasetransitions (PT) below the room temperature, one of which being superionic (attemperature Ts), the other - ferroelastic (at temperature Tc) [2]. At room temper-ature, they are crystallized in cubic syngony (F 4̄3m space group) [3]. Below thetemperature of the ferroelastic PT Cu6PS5Br crystals belong to the monoclinicsyngony (Cc space group) and the superionic PT seems to be an isostructuraltransformation [3]. In the vicinity of the PT, anomalous behaviour of specific heat,dielectric constants, elastic and optical (Raman scattering, birefringence, opticalabsorption) properties is observed in Cu6PS5X (X=Br, I) crystals [2,4–7].Studies of absorption edge in Cu6PS5X (X=Br, I) crystals have shown excitonabsorption bands to be observed at T < Ts [2]. In the vicinity of the superionic PT,the bands undergo considerable changes which are caused by dynamic structuraldisordering of the copper cation sublattice. At T > Ts, at the absorption edge, theexponential parts appear, as described by the Urbach rule [2].FIZIKA A 11 (2002) 1, 43–50 43studenyak: isoabsorption and electrical studies of . . .The analysis of the temperature behaviour of the Urbach absorption edge hasshown a change of the character of the temperature dependence of optical pseudo-gap and absorption edge energy width to be observed at the ferroelastic PT. Besides,in the range of the ferroelastic PT, the parameters of the exciton(electron)-phononinteraction (EPI), namely the EPI constant and the energy of the effective phononparticipating in the absorption edge formation, are changed. The coordinates ofthe Urbach absorption edge convergency point in the crystals under investigationremain unchanged at the transition from the paraelastic to the ferroelastic phase.The present research is aimed at studying the temperature variation of opticalabsorption edge energy position and total electric conductivity of Cu6PS5X (X=Br,I) crystals in the vicinity of the second-order ferroelastic phase transition.2. ExperimentalCu6PS5X (X=Br, I) crystals were obtained by the chemical transport reactionsmethod. The isoabsorption studies of the optical absorption edge were carried outin the temperature range from 77 to 323 K. The studies consisted in investigationof the temperature behaviour of the absorption edge energy position Eαg at fixedabsorption levels α = const. The measurements were carried out for the samplesoriented at room temperature in cubic phase, with the light beam propagatingalong the [100] crystallographic direction. The experimental setup and techniqueare described in Ref. [2].3. Results and discussion3.1. Isoabsorption studies of Cu6PS5X (X=Br, I) crystalsThe isoabsorption mesurements have shown that in the range of the superionicPT, being of the first order, a step in Eαg (T ) behaviour is observed, while in therange of the ferroelastic PT, being of the second order, a typical change of theslope in the Eαg (T ) plot is revealed in Cu6PS5I crystals (Fig.1). The values ofEαg (T ) in paraelastic phase (T > Tc) can often be well described in a framework ofthe Einstein model by the relation [8]Eαg (T ) = Eαg (0) − Sgk θE[1exp(θE/T ) − 1], (1)Eαg (0) being the absorption edge energy position at T = 0 K, Sg a dimensionlessconstant, θE the Einstein temperature corresponding to the average frequency ofphonon excitations of a system of non-coupled oscillators. It should be noted that asharp anomaly, observed in the superionic PT range in Cu6PS5I crystal, is smearedwith the I→Br substitution (Fig. 1), what is explained by the increase of the effectof structural disordering [2].44 FIZIKA A 11 (2002) 1, 43–50studenyak: isoabsorption and electrical studies of . . .2,042,082,122,162,202,24  Egα (eV)T (K)50 100 150 200 250 300 350 4002,202,252,302,35Ts21TcTcTs  Egα (eV)Fig. 1. Temperature dependence of the absorption edge energy position Eαg (α =550 cm−1) for (1) Cu6PS5I and (2) Cu6PS5Br crystals.According to Ref. [9], the energy gap variation can be expanded into a series ofeven degrees of the PT order parameter η. Being restricted by the first term of theexpansion, it is given by∆Eαg = aη2 , (2)where a is the expansion coefficient. In the crystals under investigation, the natureof the PT order parameter, its dimensionality and number of components, unfortu-nately, have not been unambiguously determined yet. However, this PT is knownto be an improper ferroelastic transition [4], the spontaneous deformation is notthe order parameter, but arises due to the nonlinear relationship with the orderparameter, the role of the latter being played by some other physical quantity.In order to calculate the increment Eαg (T ), arising in the ferroelastic phase(T < Tc), the experimental dependence of Eαg (T ), in the paraelastic phase (T > Tc)was approximated by Eq. (1). Thus obtained curves are shown in Fig. 1 by solidlines. Then the experimental values Eαg (T ) were subtracted from the calculatedcurve. The ∆Eαg (T ) dependence for Cu6PS5X (X=Br, I) crystals is shown in Fig .2.Since [10]η ∼ τβ , (3)then∆Eαg ∼ τ2β , (4)FIZIKA A 11 (2002) 1, 43–50 45studenyak: isoabsorption and electrical studies of . . .where τ = (Tc − T )/Tc and β is a critical index. In accordance with the Landautheory β = 0.5. The tangent of the log(∆Eαg ) = f(log τ) plot permitted the deter-mination of the power index, and, accordingly, of the β value. The correspondingdependence is shown in the insert of Fig. 2 and the calculated values of βopt arelisted in Table 1.Fig. 2. Temperature dependence of variation of the absorption edge energy position∆Eαg for (a) Cu6PS5I and (b) Cu6PS5Br crystals. The inserts show the dependenceof log(∆Eαg ) = f(log τ).46 FIZIKA A 11 (2002) 1, 43–50studenyak: isoabsorption and electrical studies of . . .TABLE 1. The values of the pre-exponential factor A and conduction activationenthalpy Ha for paraelastic and ferroelastic phases, and critical indices βel and βoptof the order parameter in Cu6PS5X (X=Br, I) crystals.Crystal Temperature Ha A βel βoptrange (eV) ((Ωcm)−1)Cu6PS5Br T < Tc 0.5069 1.38 × 106 0.423 ± 0.003 0.428 ± 0.003T > Tc 0.4465 1.09 × 105 – –Cu6PS5I T < Tc 0.3001 5.33 × 104 0.437 ± 0.005 0.431 ± 0.003T > Tc 0.2352 3.45 × 103 – –3.2. Analysis of temperature dependence of conductivity of Cu6PS5X(X=Br, I) crystalsThe ln(σT ) = f(103/T ) plots, based on the experimental values of total elec-tric conductivity, obtained in Ref. [11] at the frequency of 100 Hz, are shown inFig. 3. In the ferroelastic PT range, knees are observed at the plots, what is typicalfor the second-order PT. The linear character of the temperature dependence ofconductivity indicates the thermoactivation character of the latter. To analyze thetemperature variation of the electric conductivity, a phenomenological approach isused, which had been earlier successfully applied for protonic and silver-containingsuperionic conductors [12].In the case of ionic conductivity, its temperature dependence is known [12] tobe described by the relations:σ = σ0 exp(−ΦakT)=ATexp(−HakT), (5)Φa = Ha − TSa, A = Tσ0 exp(Sak), σ0 =e2l2wniν0kT, (6)Φa being the thermodynamical activation potential, Ha the activation enthalpy, Sathe activation entropy, A a pre-exponential factor, e the elementary charge; l theion displacement due to an elementary hop, ni the number of mobile ions per unitvolume, ν0 the frequency of the ion vibrations in the equilibrium position and wthe probability of the ion to be located at a given site provided the adjacent site isfree.By fitting the measured temperature dependence by Eq. (5) enabled us to obtainthe Ha and A values for paraelastic (T > Tc) and ferroelastic (T < Tc) phases (Table1). The Ha and A values are seen to increase at the transition from the paraelasticto the ferroelastic phase. The temperature variation of the electric conductivity atthe paraelastic-to-ferroelastic phase transition can be determined from the relationσT = Ap exp(−Hpa + ∆ΦakT), (7)FIZIKA A 11 (2002) 1, 43–50 47studenyak: isoabsorption and electrical studies of . . .Fig. 3. Temperature dependence of ln(σT ) = f(103/T ) for (a) Cu6PS5I and (b)Cu6PS5Br crystals, derived from the experimental values of the total electricalconductivity, presented in Ref. [11]. The inserts show the dependence log(∆Φa) =f(log τ).48 FIZIKA A 11 (2002) 1, 43–50studenyak: isoabsorption and electrical studies of . . .Ap and Hpa being the values of the pre-exponential factor and the activation en-thalpy in the paraelastic phase. At temperatures T > Tc, the increment of thethermodynamic potential is given by ∆Φa = ∆Ha − T∆Sa, while at T < Tc, ∆Φaincreases following the relation∆Φa = λτ δ , (8)λ and δ being constants. Using the values of Hpa and Ap for the paraelastic phase,the thermodynamic activation potential increment in the ferroelectric phase ofCu6PS5X (X=Br,I) crystals was calculated. The plots of log(∆Φa) = f(log τ) (seethe insert in Fig. 3) show the temperature dependences of ∆Φa to be well approxi-mated by a power function (8). Besides, they allow the determination of the powerindex δ, which, according to Ref. [12], is related to the critical index β of the PTorder parameter (δ = 2β). The obtained values of βel and βopt for the crystalsunder investigation differ from the classical (? Landau) value β = 0.5 (See Table1). Finally, one should note that for the Cu6PS5Br crystal, the values of βel andβopt are in good agreement with the value β = 0.43, obtained from the analysis ofthe temperature dependence of birefringence [4].Finally, we note the importance of the correct choice of the fitting procedurefor the determination of the critical indices. To determine the critical index β,a group of log(∆Eαg ) = f(log τ) and log(∆Φa) = f(log τ) plots were made byscalling Tc around the most probable value. From the dependences with the bestlinearity up to Tc, the Tc values were selected and the critical indices, listed inTable 1, were determined. For the Cu6PS5Br crystal, the Tc value appeared to bethe same for the log(∆Eαg ) = f(log τ) and log(∆Φa) = f(log τ) plots and equalto 270 K. As to the Cu6PS5I crystal, the best fitting was obtained for Tc = 272.5K for the log(∆Φa) = f(log τ) plot and Tc = 269 K for the log(∆Eαg ) = f(log τ)plot. Such difference in the Tc values can be explained by the difference of thegrowth conditions of the Cu6PS5I samples, used for the isoabsorption studies andthe electric measurements, since, as known from Ref. [13], the ferroelectric PTtemperature can be varied within 10 K depending on the crystal growth procedures.4. ConclusionsThe results of the isoabsorption studies of Cu6PS5X (X=Br, I) crystal opticalabsorption edge have shown that in the vicinity of the ferroelastic PT (T = Tc),a typical change (for the second-order PT) of the slope of the temperature depen-dence of the absorption edge energy position Eαg is observed. A stepwise anomalyof the dependence of Eαg (T ), observed in the range of the first-order superionic PT,is smeared at the halogen substitution I→ Br. The analysis of the temperaturedependences of total electric conductivity and Eαg (T ) has shown that the incre-ments of ∆Eαg and of thermodynamical potential of conductivity activation ∆Φaare proportional to the square of the order parameter, and their variation at theferroelastic PT can be described by the Landau theory.FIZIKA A 11 (2002) 1, 43–50 49studenyak: isoabsorption and electrical studies of . . .References[1] W. F. Kuhs, R. Nitsche and K. Scheunemann, Mater. Res. Bull. 14 (1979) 241.[2] I. P. Studenyak, M. Kranjčec, Gy. Sh. Kovacs, V. V. Panko, D. I. Desnica, A. G. Slivkaand P. P. Guranich, J. Phys. Chem. Solids 60 (1999) 1897;[3] A. Haznar, A. Pietraszko and I. P. Studenyak, Solid State Ionics 119 (1999) 31;[4] I. P. Studenyak, Gy. Sh. Kovacs, A. S. Orliukas and Ye. T. Kovacs, Izv. AN: Ser. Fiz.(Moscow) 56 (1992) 86;[5] S. Fiechter and E. Gmelin, Thermochim. Acta 85 (1985) 155;[6] V. Samulionis, V. Valevičius, I. P. Studenyak and D. S. Kovač, Ultragarsas 25 (1993)129;[7] I. P. Studenyak, V. O. Stefanovich, M. Kranjčec et al., Solid State Ionics 95 (1997)221;[8] M. Beaudoin, A. J. G. DeVries, S. R. Johnson, H. Laman and T. Tiedje, Appl. Phys.Lett. 70 (1997) 3540;[9] V. I. Zametin, M. A. Yakubovsky and L. M. Rubkin, Fiz. Tverd. Tela 21 (1979) 491;[10] Light Scattering near Phase Transition Points, Ed. G. Cummings and A. P. Levanyuk,Nauka, Moscow (1990);[11] V. V. Panko, I. P .Studenyak, V. S. Djordyaj, Gy. Sh. Kovacs, O. M. Borets and Yu.V. Voroshilov, Neorg. Materialy (Moscow) 24 (1988) 120;[12] A. I. Baranov, Izv. AN SSSR: Ser. Fiz. (Moscow) 51 (1987) 2146.[13] I. P. Studenyak, M. Kranjčec, Gy. Sh. Kovacs, I. D. Desnica-Franković, V. V. Panko,V. V. Mitrovcij and O. A. Mikajlo, Mat. Res. Bull. (to be published).IZOAPSORPCIJSKA I ELEKTRIČNA ISTRAŽIVANJA KRISTALA Cu6PS5X(X=Br, I) OKO FEROELASTIČNOG FAZNOG PRIJELAZAIstražujem temperaturnu ovisnost položaja apsorpcijskog ruba Eαg (α = 550 cm−1)kristala Cu6PS5X (X=Br, I) u području temperature 77 do 323 K izoapsorpcijskimmjerenjima. Analiziram temperaturne promjene ukupne električne vodljivosti upodručju feroelastičnog faznog prijelaza drugog reda.50 FIZIKA A 11 (2002) 1, 43–50

Izoapsorpcijska i elektrićna istraživanja kristala Cu6PS5X (X=Br, I) oko feroelastičnog faznog prijelaza

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