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Phase transitions and optical absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals
Accepted Manuscript Phase transitions and optical absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals I.P. Studenyak, V. Yu Izai, V.I. Studenyak, S.O. Rybak, A.I. Pogodin, O.P. Kokhan, M. Kranjčec PII:
S0925-8388(17)33901-4
DOI:
10.1016/j.jallcom.2017.11.144
Reference:
JALCOM 43837
To appear in:
Journal of Alloys and Compounds
Received Date: 9 August 2017 Revised Date:
8 November 2017
Accepted Date: 10 November 2017
Please cite this article as: I.P. Studenyak, V.Y. Izai, V.I. Studenyak, S.O. Rybak, A.I. Pogodin, O.P. Kokhan, M. Kranjčec, Phase transitions and optical absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2017.11.144. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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ACCEPTED MANUSCRIPT Phase transitions and optical absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x
mixed crystals I.P. Studenyak1,*, V.Yu Izai1, V.I. Studenyak1, S.O. Rybak1, A.I. Pogodin1,
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O.P. Kokhan1, M. Kranjčec2
Uzhhorod National University, 46 Pidhirna Str., 88000, Uzhhorod, Ukraine 2
University North, 33 J. Križanića St., 642000 Varaždin, Croatia
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Abstract. (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals were grown by chemical vapour transport. Low-temperature isoabsorption and polarisation studies of phase transitions (PT) were performed. A second-order PT characterised by appearance of light transmission in the polariser-crystal-analyser system and a typical knee at the isoabsorption dependence, is clearly revealed. With increasing Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals, the second-order PT shifts down in temperature range and becomes smeared. Temperature behaviour of the optical absorption edge is studied in the temperature interval 77–320 K. In the superionic phase the absorption edge has an exponential shape and a characteristic Urbach bundle is observed. In the vicinity of the second-order PT, a variation of the Urbach absorption edge parameters and exciton-phonon interaction is revealed. Influence of compositional disordering on the parameters of the Urbach absorption edge, exciton-phonon interaction parameters, and the PT temperatures is studied.
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Key words: A. Inorganic compounds; B. Crystal growth; D. Phase transitions; D. Optical properties
1.Introduction
Cu6PS5Br crystal belongs to argyrodite-structure compounds [1, 2]. Due to high ionic
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conductivity, they are promising materials for new effective sources of energy, electrochemical sensors and supercapacitors [3, 4]. At room temperature Cu6PS5Br crystal belongs to the cubic crystal system ( F 4 3m space group) while at low temperatures two phase transitions (PTs) occur: a ferroelastic one at TII =(268±2) K and a superionic one at TI=(166–180) K [3, 4]. Below the ferroelastic PT temperature Cu6PS5Br crystal belongs to the monoclynic crystal system (Cc space group); the superionic PT reveals the features of an isostructural transformation [5]. Dielectric, calorimetric, and acoustic properties and their anomalous behaviour in the range of the PTs are studies in Refs. [3, 6–8]. Optical polarisation studies have shown that domain structure and birefringence appear in the ferroelastic phase of the Cu6PS5Br crystal [9, 10]. Cu7PS6 compound is formed with a large excess of S2- anions and in the simplified case its structure can be viewed as a Cu2S matrix containing isolated [PS4]3- ions [11]. Its high-temperature
modification contains a disordered subsystem of metal ions that are characterized by high ionic
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conductivity due to a considerable mobility of monovalent cations while with cooling an ordered phase is formed. In Cu7PS6, a PT from the high-temperature phase with F 43m symmetry to the low-temperature phase with P213 symmetry is observed at 515 K. Calorimetric studies of Cu7PS6 showed no phase transitions in the temperature range of 100–400 K, the linear temperature dependence of specific heat capacity being an evidence for strong anharmonicity [12]. The present paper is aimed at isoabsorption, polarisation and spectrometric studies of optical
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absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals, its temperature behaviour in the PT range as well as the influence of Cu7PS6 content increase on the Urbach parameters of the absorption edge and disordering processes. The investigation of (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals is restricted by the range of concentration х≤0.2, for which the solid solutions, similarly to
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Cu6PS5Br, possess cubic symmetry.
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2.Material and methods
(Cu6PS5Br)1-x(Cu7PS6)x mixed crystals were grown by chemical vapour transport. Synthesis
was carried out from elemental copper (M-000, 99.9 95% wt), phosphorous (Aldrich, 99.999+% wt), sulphur (Aldrich, 99.997% wt) additionally purified by vacuum distillation as well as CuBr (99.8% wt) additionally purified by double vacuum distillation. It should be noted that the synthesis of (Cu6PS5Br)1-x(Cu7PS6)x was performed by the
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following procedure: heating at a rate of 50 K/h to 673 K, ageing at this temperature for 24 h, then heating to 923–963 K and ageing at this temperature for 72 h. The temperature of the free end of ampoules was maintained by 50 K above the temperature of the synthesis zone. Then the temperature of the synthesis zone (vapour zone) was increased to 1023 K for Cu6PS5Br, to 1043 K
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for (Cu6PS5Br)0.95(Cu7PS6)0.05, and to 1063 K for (Cu6PS5Br)0.9(Cu7PS6)0.1, while the temperature of the crystallization zone (growth zone) was kept by 35–40 K lower. The growth duration was 144–
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192 h. As a result, (Cu6PS5I)1-x(Cu7PS6)x mixed crystals of 45–50 mm length and 10–12 mm in diameter were obtained.
X-ray diffraction studies were carried out with powder method using diffraction
patterns obtained on a DRON 4-07 diffractometer (conventional θ-2θ scanning method, Bragg angle 2θ ≅10-600, Ni-filtered CuKα radiation). It is shown that for х≤0.2 (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals with F 4 3m symmetry and Z=4 are obtained. The lattice parameters were a=9.725(4) Å for Cu6PS5Br, a=9.723(9) Å for (Cu6PS5Br)0.95(Cu7PS6)0.05, and a=9.722(4) Å for (Cu6PS5Br)0.9(Cu7PS6)0.1. Since the lattice parameter for Cu6PS5Br exceeds that for Cu7PS6, for
the Cu6PS5Br–Cu7PS6 solid solutions the lattice parameter linearly decreases with Cu7PS6 content according to the Vegard's law.
Isoabsorption and spectrometric studies of optical absorption edge were carried out in the
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temperature range 77–320 K using a LOMO MDR-3 grating monochromator. For low temperature studies, a UTREX cryostat was used, the stability and accuracy of the temperature measurements was ± 0.5 K. The absorption coefficient value α was calculated based on the experimental values of transmission coefficient Ttr and reflectivity r using the known formula
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2 4 2 2 1 (1 − r ) + (1 − r ) + 4Ttr r α = ln d 2Ttr
(1)
where d is the sample thickness. The relative error in the absorption coefficient determination ∆α/α did not exceed 10% at 0.3 ≤ αd ≤ 3. The isoabsorption studies of the optical absorption edge
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consisted in determination of the energy position of the optical absorption edge Egα(Т) at fixed values of the absorption coefficient α and temperature T [13]. Polarisation studies consisted in
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measuring of light intensity that passes through the crystal placed between crossed polariser and analyser.
3.Results and discussion
In order to study the compositional behaviour of PTs in (Cu6PS5Br)1-x(Cu7PS6)x mixed
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crystals, optical isoabsorption and polarisation measurements were performed (Figs.1 and 2). For the isoabsorption curves, a characteristic knee is revealed in the range of the second-order ferroelastic PT at T=TII, which becomes significantly smeared with increasing Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals (Fig. 1). This is the evidence of the influence of
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compositional disordering. Polarisation studies have shown that at the PT at T=TII the onset of light transmission in the polariser-crystal-analyser system is observed (Fig.2). This confirms the results of isoabsorption studies and shows that the PT is accompanied by a transition from an isotropic
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paraelastic phase to an anisotropic ferroelastic phase. It should be noted that first-order PT at T=TI in the mixed crystals under investigation is strongly smeared and is observed as a variation of the slope of the isoabsorption temperature dependences. Based on the isoabsorption and polarisation measurements the, a dependence of the ferroelastic PT temperature at T=TII on the Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals was obtained (see the inset in Fig. 2). It is shown that the Cu7PS6 content increase leads to a decrease of the PT temperature TIІ from 265.6 K in Cu6PS5Br to 255 K in the mixed (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal. Spectral
dependences
of
the
absorption
coefficient
at
300 K
for
Cu6PS5Br,
(Cu6PS5Br)0.95(Cu7PS6)0.05 and (Cu6PS5Br)0.9(Cu7PS6)0.1 crystals are presented in Fig.3. It is shown that the optical pseudogap E g* ( E g* is the energy position of the absorption edge at the fixed value of the absorption coefficient α=103 cm-1) nonlinearly decreases from 2.280 eV to 2.249 eV with increasing
Cu7PS6 content in (Cu6PS5Br)1-x (Cu7PS6)x mixed crystals, while the Urbach energy EU ( EU is the ACCEPTED MANUSCRIPT energy width of the exponential absorption edge) nonlinearly increases from 56.0 meV to 87.5 meV (see the inset in Fig. 3). The latter is the evidence for compositional disordering in (Cu6PS5Br)1x(Cu7PS6)x
mixed crystals which increases with Cu7PS6 content.
Temperature studies of the optical properties of the (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystal have shown that at Т>ТІ, exponential segments appear at the absorption edge (Fig.4), their
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temperature behavior is described by the Urbach rule [14]:
hν − E 0 σ (hν − E 0 ) = α o ⋅ exp kT EU (T )
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α (hν ,T ) = α o ⋅ exp
where EU is the Urbach energy (a reciprocal of the absorption edge slope EU
−1
(2)
= ∆(ln α ) / ∆(hν ) ),
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σ is the absorption edge steepness parameter, α 0 and E 0 are the convergence point coordinates of the Urbach bundle, k is the Boltzmann constant, T is temperature, hν is photon energy. The typical Urbach absorption edge is shown in Fig.4 for mixed (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal. The analysis of absorption edge has shown that the temperature dependence of the
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absorption edge steepness parameter is well described by the Mahr formula [15] 2kT ℏω p ⋅ th ℏ ω p 2kT
σ (T ) = σ 0 ⋅
(3)
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where ℏω p is the effective phonon energy in a one-oscillator model describing the exciton-phonon interaction (EPI) and σ 0 is a parameter related to the EPI constant g as σ 0 = (2 / 3) g −1 (the
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parameters ℏω p and σ0 are given in Table 1). It should be noted that for mixed (Cu6PS5Br)1x(Cu7PS6)x
crystals the value σ0 < 1 (Table 1) that indicates a strong EPI [16]. With increasing
Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x an enhancement of the EPI is observed (the
σ 0 parameter
decrease by 36% in (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal). It should be noted that at the transition from ferroelastic phase to paraelastic phase increase of ℏω p and σ0 parameters is observed (Table 1). Figure 5 presents the temperature dependences of such Urbach absorption edge parameters as the optical pseudogap E g* and the Urbach energy EU for (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal. Temperature variation of E g* due to the EPI for (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals (Fig. 5) is well described within the Einstein model by the relationship [17]
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g
g
E
1 exp(θ E / T ) − 1
(4)
where E g* (0) is the optical pseudogap at zero temperature, S g* is a dimensionless constant of interaction, θ E is the Einstein temperature, corresponding to the average frequency of phonon excitations of a system of non-interacting oscillators. The obtained E g* (0) , S g* та θ E parameters for
EU can be described in the Einstein model by the relation [18]
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(Cu6PS5Br)1-x(Cu7PS6)x mixed crystals are listed in Table 1. It is well known that the Urbach energy
(5)
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1 ( EU ) = ( EU ) 0 + ( EU )1 exp(θ E / T ) − 1
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where ( EU ) 0 and ( EU )1 are constant values. The above mentioned parameters for the mixed (Cu6PS5Br)1-x(Cu7PS6)x crystals are listed in Table 1.
It is shown that in the paraelastic phase (Т>ТІI) and partly in the ferroelastic phase (ТІ<Т<ТІI) the temperature dependences of E g* and EU are described by Eqs. (4) and (5) with different E g* (0) ,
S g* , θ E ( EU ) 0 , and ( EU )1 parameters which are changed at the second-order PT (Table 1). The
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temperature dependences of E g* and EU for (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal calculated from Eqs. (4) and (5), are shown in Fig. 5 for different phases by different line style. It should be noted that the Urbach behaviour and the absorption edge shape are determined
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by the influence of temperature-related, structural and compositional disordering, i.e. the Urbach
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energy EU is described by equation [19] EU = ( EU ) T + ( EU ) S + ( EU ) C = ( EU ) T + ( EU ) S + C
(6)
where ( EU ) T , ( EU ) S and ( EU ) C are the contributions of temperature-related, structural and compositional disordering to EU , respectively. The first term in the right-hand side of Eq. (5) represents the sum of structural and compositional disordering, and the second one represents temperature-related disordering. From Eqs. (5) and (6) one can estimate the relative contributions of different types of disordering into EU for mixed (Cu6PS5Br)1-x(Cu7PS6)x crystals. It should be
noted that the contribution of structural disordering to the Urbach energy of Cu6PS5Br crystal is predominant and comprises 95.6% of EU (Table 1). With increasing Cu7PS6 content both the contribution of temperature-related disordering and the total contribution of
structural and compositional disordering of (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals increase
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(Fig.6), besides the total contribution grows up due to the contribution of the compositional disordering which is typical for a number of substitutive solid solutions. 4.Conclusions Isoabsorption and polarisation measurements carried out in the temperature interval 77–320 K have shown that the ferroelastic second-order PT is accompanied by an onset of light
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transmission in the polariser-crystal-analyser system and a typical knee at the isoabsorption plot. The increasing Cu7PS6 content leads to a decrease of the ferroelastic PT temperature at Т=TIІ from 265.6 K in Cu6PS5Br to 255 K in (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystal. It should be noted that the superionic first-order PT at T=TI in the crystals under investigation is highly smeared and is
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observed as a variation of slope in the isoabsorption temperature dependences.
The spectroscopic studies of the absorption edge in (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystals
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have shown that in the superionic phase at Т>ТІ its temperature behaviour is described by the Urbach rule. The Urbach behavior of the absorption edge is caused by exciton-phonon interaction which is strong in (Cu6PS5Br)0.9(Cu7PS6)0.1. The parameters of Urbach absorption edge and the parameters of exciton-phonon interaction are changed at the second-order PT. The temperature variations of the optical pseudogap and the Urbach energy in (Cu6PS5Br)1-x(Cu7PS6)x are well described within the Einstein model for different phases.
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The performed studies of (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals have shown that with increasing Cu7PS6 content: (i) the optical pseudogap nonlinearly decreases while the Urbach energy nonlinear increases, (ii) the exciton-phonon interaction is enhanced, (iii) both the total contribution of structural and compositional disordering and the contribution of temperature-related disordering
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increase. Finally, it is shown that the compositional variation of the parameters of the Urbach absorption edge, the exciton-phonon interaction parameters, and the PT temperatures are caused by
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the compositional disordering in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals.
References
[1] W.F. Kuhs, R. Nitsche, K. Scheunemann, Vapour growth and lattice data of new compounds with icosahedral structure of the type Cu6PS5Hal (Hal=Cl, Br, I), Mat. Res. Bull. 11 (1976) 11151124. [2] V.V. Panko, I.P. Studenyak, V.S. Dyordyai, Gy.S. Kovacs, A.N. Borets, Yu.V. Voroshilov, Influence of technological conditions on properties of Cu6PS5Hal crystals, Neorg. Mat. 24 (1988) 120-123 [in Russian]. [3] R.B. Beeken, J.J. Garbe, N.R. Petersen, Cation mobility in the Cu6PS5X (X=Cl, Br, I) argyrodites, J. Phys. Chem. Solids 64 (2003) 1261-1264.
[4] I.P. Studenyak, R.Vaitkus, V.S. Dyordyai, A. Kezenis, V. Mikucenis, V.V. Panko, Gy.S.
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Kovacs, V.A. Stefanovich, A. Orliukas, A.N. Borets, V.Yu. Slivka, Phase transitions in Cu6PS5I single crystals, Fiz. Tverd. Tela 28 (1986) 2555-2557 [in Russian]. [5] I.P. Studenyak, V.O. Stefanovich, M. Kranjčec, D.I. Desnica, Yu.M. Azhnyuk, Gy.S. Kovacs, V.V. Panko, Raman scattering studies of Cu6PS5Hal (Hal= Cl, Br and I) fast-ion conductors, Solid State Ionics 95 (1997) 221-225. [6] A.Gagor, A.Pietraszko, D.Kaynts, Diffusion paths formation for Cu+ ions in superionic Cu6PS5I 3375.
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single crystals studied in terms of structural phase transition, J. Solid State Chem. 178 (2005) 3366-
[7] S.Fiechter, E.Gmelin, Thermochemical data of argyrodite-type ionic conductors: Cu6PS5Hal (Hal= Cl, Br, I), Thermochimica Acta 85 (1985) 155-158.
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[8] I.P. Studenyak, Gy.S. Kovacs, A.F.Orliukas, E.T. Kovacs, Temperature variations of dielectric and optical properties in Cu6PS(Sе)5Hal superionics and ferroelastics at phase transitions, Izv. AN:
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Ser. Phys. 56 (1992) 86-93 [in Russian].
[9] V. Samulionis, V. Valevičius, I.P. Studeniak, D.S. Kovač, Acoustic properties of superionic ferroelastic Cu6PS5I and Cu6PS5Br crystals, Ultragarsas 25 (1993) 129-136. [10] V. Samulionis, J. Banys, Y. Vysochanskii, I. Studenyak, Investigation of ultrasonic and acoustoelectric properties of ferroelectric-semiconductor crystals, Ferroelectrics 336 (2006) 29-38. [11] H. Andrae, R. Blachnik, Metal sulphide-tetraphosphorusdecasulphide phase diagrams, J.
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Alloys and Compounds 189 (1992) 209-215.
[12] S. Fiechter, E. Gmelin, Thermochemical data and phase transition of argyrodite-type ionic conductors Me6PS5Hal and Me7PS6 (Me = Cu, Ag; Hal = Cl, Br, I), Thermochimica Acta 87 (1985) 319-334.
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[13] I.P. Studenyak, M. Kranjčec, Gy.Sh. Kovacs, V.V. Panko, I.D. Desnica, A.G. Slivka, P.P. Guranich, The effect of temperature and pressure on the optical absorption edge in Cu6PS5X (X=
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Cl, Br, I) crystals, J. Phys. Chem. Solids 60 (1999) 1897-1904. [14] F. Urbach, The Long-Wavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids, Phys. Rev. 92 (1953) 1324-1326. [15] H. Sumi, A. Sumi, The Urbach-Martienssen rule revisited, J. Phys. Soc. Japan 56 (1987) 22112220.
[16] M.V. Kurik, Urbach rule (Review), Phys. Stat. Sol. (a) 8 (1971) 9-30. [17] M. Beaudoin, A.J.G. DeVries, S.R. Johnson, H. Laman, T. Tiedje, Optical absorption edge of semi-insulating GaAs and InP at high temperatures, Appl. Phys. Lett. 70 (1997) 3540-3542. [18] Z. Yang, K.P. Homewood, M.S. Finney, M.A. Harry, K.J. Reeson, Optical absorption study of ion beam synthesized polycrystalline semiconducting FeSi2, J. Appl. Phys.78 (1995) 1958-1963.
[19] G.D. Cody, T. Tiedje, B. Abeles, B. Brooks, Y. Goldstein, Disorder and the optical-absorption
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edge of hydrogenated amorphous silicon, Phys. Rev. Lett. 47 (1981) 1480-1483.
Figure captions
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Fig.1. Temperature dependences of E gα for Cu6PS5Br crystal (1) taken at α=350 cm-1, for (Cu6PS5Br)0.95(Cu7PS6)0.05 crystal (2) taken at α=250 cm-1, and (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal (3) taken at α=380 cm-1.
Fig.2. Temperature dependences of light intensity in the polariser-crystal-analyser system for
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Cu6PS5Br (1), (Cu6PS5Br)0.95(Cu7PS6)0.05 (2), and (Cu6PS5Br)0.9(Cu7PS6)0.1 (3) crystals. The inset shows the dependence of the PT temperature TII on the Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x
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mixed crystals.
Fig. 3. Spectral dependences of absorption coefficient at 300 K for Cu6PS5Br (1), (Cu6PS5Br)0.95(Cu7PS6)0.05 (2), and (Cu6PS5Br)0.9(Cu7PS6)0.1 (3) crystals. The inset shows the dependences of the optical pseudogap E g* (1) and the Urbach energy EU (2) on the Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals.
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Fig. 4. Absorption edge spectra for (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystals at different temperatures
Т: 320 K (1), 310 K (2), 300 K (3), 290 K (4), 280 K (5), 270 K (6), 260 (7). The inset shows the temperature dependence of the σ parameter.
Fig. 5. Temperature dependences of the optical pseudogap E g* (1) and the Urbach energy EU (2) for
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(Cu6PS5Br)0.9(Cu7PS6)0.1 crystal.
Fig. 6. Compositional dependences of the total contribution of structural and compositional
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disordering ( EU ) S +C (1) as well as the contribution of temperature-related disordering ( EU ) T (2) to the Urbach energy EU for (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals.
ACCEPTED MANUSCRIPT Table 1 Parameters of Urbach absorption edge and EPI for (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals Cu6PS5Br
(Cu6PS5Br)0.95(Cu7PS6)0.05
(Cu6PS5Br)0.9(Cu7PS6)0.1
Crystal T
T>TII
E g* (300K), eV
2.280
2.256
EU (300K), meV
58.5
81.8
α 0 , cm-1
1.1×107
2.8×104
E0 , eV
2.800
2.515
0.743
0.895
0.502
ℏω p , meV
81.0
100.1
74.1
θE , К
996
1162
( EU ) 0 , meV
54.6
55.9
( EU )1 , meV
135
121
E g* (0) , eV
2.329
2.318
S g*
16.2
18.4
87.5
2.1×104 2.524
0.536
0.362
0.514
80.8
49.9
84.3
860
938
579.5
975
73.6
75.2
67.6
77.6
156
144
142
250
2.310
2.339
2.283
2.301
7.71
22.4
2.12
15.00
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T>TII 2.249
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ACCEPTED MANUSCRIPT • Phase transitions in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals are investigated. • Optical absorption edge is measured in the temperature interval 77–320 K.
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• Influence of compositional disordering on the optical parameters is studied.
S0925-8388(17)33901-4
DOI:
10.1016/j.jallcom.2017.11.144
Reference:
JALCOM 43837
To appear in:
Journal of Alloys and Compounds
Received Date: 9 August 2017 Revised Date:
8 November 2017
Accepted Date: 10 November 2017
Please cite this article as: I.P. Studenyak, V.Y. Izai, V.I. Studenyak, S.O. Rybak, A.I. Pogodin, O.P. Kokhan, M. Kranjčec, Phase transitions and optical absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2017.11.144. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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ACCEPTED MANUSCRIPT Phase transitions and optical absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x
mixed crystals I.P. Studenyak1,*, V.Yu Izai1, V.I. Studenyak1, S.O. Rybak1, A.I. Pogodin1,
1
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O.P. Kokhan1, M. Kranjčec2
Uzhhorod National University, 46 Pidhirna Str., 88000, Uzhhorod, Ukraine 2
University North, 33 J. Križanića St., 642000 Varaždin, Croatia
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Abstract. (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals were grown by chemical vapour transport. Low-temperature isoabsorption and polarisation studies of phase transitions (PT) were performed. A second-order PT characterised by appearance of light transmission in the polariser-crystal-analyser system and a typical knee at the isoabsorption dependence, is clearly revealed. With increasing Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals, the second-order PT shifts down in temperature range and becomes smeared. Temperature behaviour of the optical absorption edge is studied in the temperature interval 77–320 K. In the superionic phase the absorption edge has an exponential shape and a characteristic Urbach bundle is observed. In the vicinity of the second-order PT, a variation of the Urbach absorption edge parameters and exciton-phonon interaction is revealed. Influence of compositional disordering on the parameters of the Urbach absorption edge, exciton-phonon interaction parameters, and the PT temperatures is studied.
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Key words: A. Inorganic compounds; B. Crystal growth; D. Phase transitions; D. Optical properties
1.Introduction
Cu6PS5Br crystal belongs to argyrodite-structure compounds [1, 2]. Due to high ionic
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conductivity, they are promising materials for new effective sources of energy, electrochemical sensors and supercapacitors [3, 4]. At room temperature Cu6PS5Br crystal belongs to the cubic crystal system ( F 4 3m space group) while at low temperatures two phase transitions (PTs) occur: a ferroelastic one at TII =(268±2) K and a superionic one at TI=(166–180) K [3, 4]. Below the ferroelastic PT temperature Cu6PS5Br crystal belongs to the monoclynic crystal system (Cc space group); the superionic PT reveals the features of an isostructural transformation [5]. Dielectric, calorimetric, and acoustic properties and their anomalous behaviour in the range of the PTs are studies in Refs. [3, 6–8]. Optical polarisation studies have shown that domain structure and birefringence appear in the ferroelastic phase of the Cu6PS5Br crystal [9, 10]. Cu7PS6 compound is formed with a large excess of S2- anions and in the simplified case its structure can be viewed as a Cu2S matrix containing isolated [PS4]3- ions [11]. Its high-temperature
modification contains a disordered subsystem of metal ions that are characterized by high ionic
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conductivity due to a considerable mobility of monovalent cations while with cooling an ordered phase is formed. In Cu7PS6, a PT from the high-temperature phase with F 43m symmetry to the low-temperature phase with P213 symmetry is observed at 515 K. Calorimetric studies of Cu7PS6 showed no phase transitions in the temperature range of 100–400 K, the linear temperature dependence of specific heat capacity being an evidence for strong anharmonicity [12]. The present paper is aimed at isoabsorption, polarisation and spectrometric studies of optical
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absorption edge in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals, its temperature behaviour in the PT range as well as the influence of Cu7PS6 content increase on the Urbach parameters of the absorption edge and disordering processes. The investigation of (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals is restricted by the range of concentration х≤0.2, for which the solid solutions, similarly to
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Cu6PS5Br, possess cubic symmetry.
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2.Material and methods
(Cu6PS5Br)1-x(Cu7PS6)x mixed crystals were grown by chemical vapour transport. Synthesis
was carried out from elemental copper (M-000, 99.9 95% wt), phosphorous (Aldrich, 99.999+% wt), sulphur (Aldrich, 99.997% wt) additionally purified by vacuum distillation as well as CuBr (99.8% wt) additionally purified by double vacuum distillation. It should be noted that the synthesis of (Cu6PS5Br)1-x(Cu7PS6)x was performed by the
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following procedure: heating at a rate of 50 K/h to 673 K, ageing at this temperature for 24 h, then heating to 923–963 K and ageing at this temperature for 72 h. The temperature of the free end of ampoules was maintained by 50 K above the temperature of the synthesis zone. Then the temperature of the synthesis zone (vapour zone) was increased to 1023 K for Cu6PS5Br, to 1043 K
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for (Cu6PS5Br)0.95(Cu7PS6)0.05, and to 1063 K for (Cu6PS5Br)0.9(Cu7PS6)0.1, while the temperature of the crystallization zone (growth zone) was kept by 35–40 K lower. The growth duration was 144–
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192 h. As a result, (Cu6PS5I)1-x(Cu7PS6)x mixed crystals of 45–50 mm length and 10–12 mm in diameter were obtained.
X-ray diffraction studies were carried out with powder method using diffraction
patterns obtained on a DRON 4-07 diffractometer (conventional θ-2θ scanning method, Bragg angle 2θ ≅10-600, Ni-filtered CuKα radiation). It is shown that for х≤0.2 (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals with F 4 3m symmetry and Z=4 are obtained. The lattice parameters were a=9.725(4) Å for Cu6PS5Br, a=9.723(9) Å for (Cu6PS5Br)0.95(Cu7PS6)0.05, and a=9.722(4) Å for (Cu6PS5Br)0.9(Cu7PS6)0.1. Since the lattice parameter for Cu6PS5Br exceeds that for Cu7PS6, for
the Cu6PS5Br–Cu7PS6 solid solutions the lattice parameter linearly decreases with Cu7PS6 content according to the Vegard's law.
Isoabsorption and spectrometric studies of optical absorption edge were carried out in the
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temperature range 77–320 K using a LOMO MDR-3 grating monochromator. For low temperature studies, a UTREX cryostat was used, the stability and accuracy of the temperature measurements was ± 0.5 K. The absorption coefficient value α was calculated based on the experimental values of transmission coefficient Ttr and reflectivity r using the known formula
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2 4 2 2 1 (1 − r ) + (1 − r ) + 4Ttr r α = ln d 2Ttr
(1)
where d is the sample thickness. The relative error in the absorption coefficient determination ∆α/α did not exceed 10% at 0.3 ≤ αd ≤ 3. The isoabsorption studies of the optical absorption edge
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consisted in determination of the energy position of the optical absorption edge Egα(Т) at fixed values of the absorption coefficient α and temperature T [13]. Polarisation studies consisted in
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measuring of light intensity that passes through the crystal placed between crossed polariser and analyser.
3.Results and discussion
In order to study the compositional behaviour of PTs in (Cu6PS5Br)1-x(Cu7PS6)x mixed
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crystals, optical isoabsorption and polarisation measurements were performed (Figs.1 and 2). For the isoabsorption curves, a characteristic knee is revealed in the range of the second-order ferroelastic PT at T=TII, which becomes significantly smeared with increasing Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals (Fig. 1). This is the evidence of the influence of
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compositional disordering. Polarisation studies have shown that at the PT at T=TII the onset of light transmission in the polariser-crystal-analyser system is observed (Fig.2). This confirms the results of isoabsorption studies and shows that the PT is accompanied by a transition from an isotropic
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paraelastic phase to an anisotropic ferroelastic phase. It should be noted that first-order PT at T=TI in the mixed crystals under investigation is strongly smeared and is observed as a variation of the slope of the isoabsorption temperature dependences. Based on the isoabsorption and polarisation measurements the, a dependence of the ferroelastic PT temperature at T=TII on the Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals was obtained (see the inset in Fig. 2). It is shown that the Cu7PS6 content increase leads to a decrease of the PT temperature TIІ from 265.6 K in Cu6PS5Br to 255 K in the mixed (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal. Spectral
dependences
of
the
absorption
coefficient
at
300 K
for
Cu6PS5Br,
(Cu6PS5Br)0.95(Cu7PS6)0.05 and (Cu6PS5Br)0.9(Cu7PS6)0.1 crystals are presented in Fig.3. It is shown that the optical pseudogap E g* ( E g* is the energy position of the absorption edge at the fixed value of the absorption coefficient α=103 cm-1) nonlinearly decreases from 2.280 eV to 2.249 eV with increasing
Cu7PS6 content in (Cu6PS5Br)1-x (Cu7PS6)x mixed crystals, while the Urbach energy EU ( EU is the ACCEPTED MANUSCRIPT energy width of the exponential absorption edge) nonlinearly increases from 56.0 meV to 87.5 meV (see the inset in Fig. 3). The latter is the evidence for compositional disordering in (Cu6PS5Br)1x(Cu7PS6)x
mixed crystals which increases with Cu7PS6 content.
Temperature studies of the optical properties of the (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystal have shown that at Т>ТІ, exponential segments appear at the absorption edge (Fig.4), their
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temperature behavior is described by the Urbach rule [14]:
hν − E 0 σ (hν − E 0 ) = α o ⋅ exp kT EU (T )
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α (hν ,T ) = α o ⋅ exp
where EU is the Urbach energy (a reciprocal of the absorption edge slope EU
−1
(2)
= ∆(ln α ) / ∆(hν ) ),
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σ is the absorption edge steepness parameter, α 0 and E 0 are the convergence point coordinates of the Urbach bundle, k is the Boltzmann constant, T is temperature, hν is photon energy. The typical Urbach absorption edge is shown in Fig.4 for mixed (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal. The analysis of absorption edge has shown that the temperature dependence of the
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absorption edge steepness parameter is well described by the Mahr formula [15] 2kT ℏω p ⋅ th ℏ ω p 2kT
σ (T ) = σ 0 ⋅
(3)
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where ℏω p is the effective phonon energy in a one-oscillator model describing the exciton-phonon interaction (EPI) and σ 0 is a parameter related to the EPI constant g as σ 0 = (2 / 3) g −1 (the
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parameters ℏω p and σ0 are given in Table 1). It should be noted that for mixed (Cu6PS5Br)1x(Cu7PS6)x
crystals the value σ0 < 1 (Table 1) that indicates a strong EPI [16]. With increasing
Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x an enhancement of the EPI is observed (the
σ 0 parameter
decrease by 36% in (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal). It should be noted that at the transition from ferroelastic phase to paraelastic phase increase of ℏω p and σ0 parameters is observed (Table 1). Figure 5 presents the temperature dependences of such Urbach absorption edge parameters as the optical pseudogap E g* and the Urbach energy EU for (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal. Temperature variation of E g* due to the EPI for (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals (Fig. 5) is well described within the Einstein model by the relationship [17]
ACCEPTED E * (TMANUSCRIPT ) = E * (0) − S * kθ g
g
g
E
1 exp(θ E / T ) − 1
(4)
where E g* (0) is the optical pseudogap at zero temperature, S g* is a dimensionless constant of interaction, θ E is the Einstein temperature, corresponding to the average frequency of phonon excitations of a system of non-interacting oscillators. The obtained E g* (0) , S g* та θ E parameters for
EU can be described in the Einstein model by the relation [18]
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(Cu6PS5Br)1-x(Cu7PS6)x mixed crystals are listed in Table 1. It is well known that the Urbach energy
(5)
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1 ( EU ) = ( EU ) 0 + ( EU )1 exp(θ E / T ) − 1
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where ( EU ) 0 and ( EU )1 are constant values. The above mentioned parameters for the mixed (Cu6PS5Br)1-x(Cu7PS6)x crystals are listed in Table 1.
It is shown that in the paraelastic phase (Т>ТІI) and partly in the ferroelastic phase (ТІ<Т<ТІI) the temperature dependences of E g* and EU are described by Eqs. (4) and (5) with different E g* (0) ,
S g* , θ E ( EU ) 0 , and ( EU )1 parameters which are changed at the second-order PT (Table 1). The
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temperature dependences of E g* and EU for (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal calculated from Eqs. (4) and (5), are shown in Fig. 5 for different phases by different line style. It should be noted that the Urbach behaviour and the absorption edge shape are determined
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by the influence of temperature-related, structural and compositional disordering, i.e. the Urbach
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energy EU is described by equation [19] EU = ( EU ) T + ( EU ) S + ( EU ) C = ( EU ) T + ( EU ) S + C
(6)
where ( EU ) T , ( EU ) S and ( EU ) C are the contributions of temperature-related, structural and compositional disordering to EU , respectively. The first term in the right-hand side of Eq. (5) represents the sum of structural and compositional disordering, and the second one represents temperature-related disordering. From Eqs. (5) and (6) one can estimate the relative contributions of different types of disordering into EU for mixed (Cu6PS5Br)1-x(Cu7PS6)x crystals. It should be
noted that the contribution of structural disordering to the Urbach energy of Cu6PS5Br crystal is predominant and comprises 95.6% of EU (Table 1). With increasing Cu7PS6 content both the contribution of temperature-related disordering and the total contribution of
structural and compositional disordering of (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals increase
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(Fig.6), besides the total contribution grows up due to the contribution of the compositional disordering which is typical for a number of substitutive solid solutions. 4.Conclusions Isoabsorption and polarisation measurements carried out in the temperature interval 77–320 K have shown that the ferroelastic second-order PT is accompanied by an onset of light
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transmission in the polariser-crystal-analyser system and a typical knee at the isoabsorption plot. The increasing Cu7PS6 content leads to a decrease of the ferroelastic PT temperature at Т=TIІ from 265.6 K in Cu6PS5Br to 255 K in (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystal. It should be noted that the superionic first-order PT at T=TI in the crystals under investigation is highly smeared and is
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observed as a variation of slope in the isoabsorption temperature dependences.
The spectroscopic studies of the absorption edge in (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystals
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have shown that in the superionic phase at Т>ТІ its temperature behaviour is described by the Urbach rule. The Urbach behavior of the absorption edge is caused by exciton-phonon interaction which is strong in (Cu6PS5Br)0.9(Cu7PS6)0.1. The parameters of Urbach absorption edge and the parameters of exciton-phonon interaction are changed at the second-order PT. The temperature variations of the optical pseudogap and the Urbach energy in (Cu6PS5Br)1-x(Cu7PS6)x are well described within the Einstein model for different phases.
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The performed studies of (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals have shown that with increasing Cu7PS6 content: (i) the optical pseudogap nonlinearly decreases while the Urbach energy nonlinear increases, (ii) the exciton-phonon interaction is enhanced, (iii) both the total contribution of structural and compositional disordering and the contribution of temperature-related disordering
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increase. Finally, it is shown that the compositional variation of the parameters of the Urbach absorption edge, the exciton-phonon interaction parameters, and the PT temperatures are caused by
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the compositional disordering in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals.
References
[1] W.F. Kuhs, R. Nitsche, K. Scheunemann, Vapour growth and lattice data of new compounds with icosahedral structure of the type Cu6PS5Hal (Hal=Cl, Br, I), Mat. Res. Bull. 11 (1976) 11151124. [2] V.V. Panko, I.P. Studenyak, V.S. Dyordyai, Gy.S. Kovacs, A.N. Borets, Yu.V. Voroshilov, Influence of technological conditions on properties of Cu6PS5Hal crystals, Neorg. Mat. 24 (1988) 120-123 [in Russian]. [3] R.B. Beeken, J.J. Garbe, N.R. Petersen, Cation mobility in the Cu6PS5X (X=Cl, Br, I) argyrodites, J. Phys. Chem. Solids 64 (2003) 1261-1264.
[4] I.P. Studenyak, R.Vaitkus, V.S. Dyordyai, A. Kezenis, V. Mikucenis, V.V. Panko, Gy.S.
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Kovacs, V.A. Stefanovich, A. Orliukas, A.N. Borets, V.Yu. Slivka, Phase transitions in Cu6PS5I single crystals, Fiz. Tverd. Tela 28 (1986) 2555-2557 [in Russian]. [5] I.P. Studenyak, V.O. Stefanovich, M. Kranjčec, D.I. Desnica, Yu.M. Azhnyuk, Gy.S. Kovacs, V.V. Panko, Raman scattering studies of Cu6PS5Hal (Hal= Cl, Br and I) fast-ion conductors, Solid State Ionics 95 (1997) 221-225. [6] A.Gagor, A.Pietraszko, D.Kaynts, Diffusion paths formation for Cu+ ions in superionic Cu6PS5I 3375.
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single crystals studied in terms of structural phase transition, J. Solid State Chem. 178 (2005) 3366-
[7] S.Fiechter, E.Gmelin, Thermochemical data of argyrodite-type ionic conductors: Cu6PS5Hal (Hal= Cl, Br, I), Thermochimica Acta 85 (1985) 155-158.
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[8] I.P. Studenyak, Gy.S. Kovacs, A.F.Orliukas, E.T. Kovacs, Temperature variations of dielectric and optical properties in Cu6PS(Sе)5Hal superionics and ferroelastics at phase transitions, Izv. AN:
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Ser. Phys. 56 (1992) 86-93 [in Russian].
[9] V. Samulionis, V. Valevičius, I.P. Studeniak, D.S. Kovač, Acoustic properties of superionic ferroelastic Cu6PS5I and Cu6PS5Br crystals, Ultragarsas 25 (1993) 129-136. [10] V. Samulionis, J. Banys, Y. Vysochanskii, I. Studenyak, Investigation of ultrasonic and acoustoelectric properties of ferroelectric-semiconductor crystals, Ferroelectrics 336 (2006) 29-38. [11] H. Andrae, R. Blachnik, Metal sulphide-tetraphosphorusdecasulphide phase diagrams, J.
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Alloys and Compounds 189 (1992) 209-215.
[12] S. Fiechter, E. Gmelin, Thermochemical data and phase transition of argyrodite-type ionic conductors Me6PS5Hal and Me7PS6 (Me = Cu, Ag; Hal = Cl, Br, I), Thermochimica Acta 87 (1985) 319-334.
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[13] I.P. Studenyak, M. Kranjčec, Gy.Sh. Kovacs, V.V. Panko, I.D. Desnica, A.G. Slivka, P.P. Guranich, The effect of temperature and pressure on the optical absorption edge in Cu6PS5X (X=
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Cl, Br, I) crystals, J. Phys. Chem. Solids 60 (1999) 1897-1904. [14] F. Urbach, The Long-Wavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids, Phys. Rev. 92 (1953) 1324-1326. [15] H. Sumi, A. Sumi, The Urbach-Martienssen rule revisited, J. Phys. Soc. Japan 56 (1987) 22112220.
[16] M.V. Kurik, Urbach rule (Review), Phys. Stat. Sol. (a) 8 (1971) 9-30. [17] M. Beaudoin, A.J.G. DeVries, S.R. Johnson, H. Laman, T. Tiedje, Optical absorption edge of semi-insulating GaAs and InP at high temperatures, Appl. Phys. Lett. 70 (1997) 3540-3542. [18] Z. Yang, K.P. Homewood, M.S. Finney, M.A. Harry, K.J. Reeson, Optical absorption study of ion beam synthesized polycrystalline semiconducting FeSi2, J. Appl. Phys.78 (1995) 1958-1963.
[19] G.D. Cody, T. Tiedje, B. Abeles, B. Brooks, Y. Goldstein, Disorder and the optical-absorption
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edge of hydrogenated amorphous silicon, Phys. Rev. Lett. 47 (1981) 1480-1483.
Figure captions
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Fig.1. Temperature dependences of E gα for Cu6PS5Br crystal (1) taken at α=350 cm-1, for (Cu6PS5Br)0.95(Cu7PS6)0.05 crystal (2) taken at α=250 cm-1, and (Cu6PS5Br)0.9(Cu7PS6)0.1 crystal (3) taken at α=380 cm-1.
Fig.2. Temperature dependences of light intensity in the polariser-crystal-analyser system for
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Cu6PS5Br (1), (Cu6PS5Br)0.95(Cu7PS6)0.05 (2), and (Cu6PS5Br)0.9(Cu7PS6)0.1 (3) crystals. The inset shows the dependence of the PT temperature TII on the Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x
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mixed crystals.
Fig. 3. Spectral dependences of absorption coefficient at 300 K for Cu6PS5Br (1), (Cu6PS5Br)0.95(Cu7PS6)0.05 (2), and (Cu6PS5Br)0.9(Cu7PS6)0.1 (3) crystals. The inset shows the dependences of the optical pseudogap E g* (1) and the Urbach energy EU (2) on the Cu7PS6 content in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals.
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Fig. 4. Absorption edge spectra for (Cu6PS5Br)0.9(Cu7PS6)0.1 mixed crystals at different temperatures
Т: 320 K (1), 310 K (2), 300 K (3), 290 K (4), 280 K (5), 270 K (6), 260 (7). The inset shows the temperature dependence of the σ parameter.
Fig. 5. Temperature dependences of the optical pseudogap E g* (1) and the Urbach energy EU (2) for
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(Cu6PS5Br)0.9(Cu7PS6)0.1 crystal.
Fig. 6. Compositional dependences of the total contribution of structural and compositional
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disordering ( EU ) S +C (1) as well as the contribution of temperature-related disordering ( EU ) T (2) to the Urbach energy EU for (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals.
ACCEPTED MANUSCRIPT Table 1 Parameters of Urbach absorption edge and EPI for (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals Cu6PS5Br
(Cu6PS5Br)0.95(Cu7PS6)0.05
(Cu6PS5Br)0.9(Cu7PS6)0.1
Crystal T
T>TII
E g* (300K), eV
2.280
2.256
EU (300K), meV
58.5
81.8
α 0 , cm-1
1.1×107
2.8×104
E0 , eV
2.800
2.515
0.743
0.895
0.502
ℏω p , meV
81.0
100.1
74.1
θE , К
996
1162
( EU ) 0 , meV
54.6
55.9
( EU )1 , meV
135
121
E g* (0) , eV
2.329
2.318
S g*
16.2
18.4
87.5
2.1×104 2.524
0.536
0.362
0.514
80.8
49.9
84.3
860
938
579.5
975
73.6
75.2
67.6
77.6
156
144
142
250
2.310
2.339
2.283
2.301
7.71
22.4
2.12
15.00
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T>TII 2.249
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ACCEPTED MANUSCRIPT • Phase transitions in (Cu6PS5Br)1-x(Cu7PS6)x mixed crystals are investigated. • Optical absorption edge is measured in the temperature interval 77–320 K.
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• Influence of compositional disordering on the optical parameters is studied.