The temperature dependence of the Raman T2g lattice mode in K2S crystals

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The temperature dependence of the Raman T2g lattice mode in K2S crystals

BERTHEVILLE, B., BILL, Hans

Abstract

The first-order Raman spectrum of K[2]S was measured over the temperature range from 10 to 742 K. The temperature dependence of the linewidth can be explained using results from the anharmonic lattice dynamics approach. Both the cubic and the quartic anharmonic interactions are of importance for this system. At 293 K, the Raman line is at ω[T2g]=128 cm[−1] with a full width at half maximum Γ[T2g]=2.9 cm[−1].

BERTHEVILLE, B., BILL, Hans. The temperature dependence of the Raman T2g lattice mode in K2S crystals. Solid State Ionics , 2001, vol. 139, no. 1-2, p. 159-162

DOI : 10.1016/S0167-2738(00)00823-7

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The temperature dependence of the Raman T

_2g

lattice mode in K S

₂

crystals

a b ,

*

B. Bertheville , H. Bill

aLaboratoire de Cristallographie, Universite de Geneve, 24 Quai Ernest Ansermet, CH-1211 Geneve 4, Switzerland´ ` `

bDepartement de Chimie-Physique, Sciences II, Universite de Geneve, 30 Quai Ernest Ansermet, CH-1211 Geneve 4, Switzerland´ ´ ` ` Received 14 February 2000; received in revised form 20 October 2000; accepted 7 November 2000

Abstract

The first-order Raman spectrum of K S was measured over the temperature range from 10 to 742 K. The temperature₂ dependence of the linewidth can be explained using results from the anharmonic lattice dynamics approach. Both the cubic

21

and the quartic anharmonic interactions are of importance for this system. At 293 K, the Raman line is atv_T 5128 cm

21 2g

2g

Keywords: Potassium sulfide; Ionic conductor; Raman effect; Thermal anharmonicity PACS: 78.30.Hv; 66.70; 72.80.Ng

1. Introduction [2] for a general survey). Potassium sulfide is

probably the least studied member of this group and Potassium sulfide, K S, is an ionic material crys-₂ information about its thermal and optical properties tallizing in the antifluorite structure. Compounds is still largely absent. A diffuse transition was having this structure (e.g. Li O, Li S, Na S) or the₂ ₂ ₂ observed by Dworkin and Breding [3] with the aid of antimorphous fluorite structure (e.g. CaF , SrF ,₂ ₂ calorimetric measurements as a function of tempera- BaF ) are known to present a high temperature₂ ture. It begins at approximately 820 K and continues superionic phase with a characteristic temperature up to the melting point at 1221 K after showing a (T ) often hundreds of degrees below their melting_c sharp specific heat maximum at 1050 K. This result point (T_c#0.8T ) [1]. This transition, initially iden-_m was confirmed theoretically by Voronin [4], who tified through heat capacity measurements versus analyzed several phenomenological thermodynamic temperature, where a broad peak was observed models of superionic disorder using potassium sul- around T , has been confirmed by further numerous_c fide and strontium chloride as examples. It was recent investigations using NMR, neutron diffraction, thereby confirmed that the temperature-dependent Brillouin and Raman scattering experiments (see Ref. lattice disorder is related to the anharmonic ion–ion

interaction potential.

Both the cubic antifluorite and fluorite structures

*Corresponding author.

E-mail address: hans.bill@chiphy.unige.ch (H. Bill). have one Raman-active phonon mode of T_2g symme-

P I I : S 0 1 6 7 - 2 7 3 8 ( 0 0 ) 0 0 8 2 3 - 7

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160 B. Bertheville, H. Bill / Solid State Ionics 139 (2001) 159 –162

try [the Brillouin-zone center representation is G 5 cally, the Raman experiments were made in the 1808 T (acoustic)_1u 1T (optic,IR)_1u 1T (optic,Raman)]._2g scattering geometry with a laser output power of 20 Experimental and theoretical studies (see, e.g. Ref. mW at 488 nm and slits set to 100 mm. Low- [5]) of the temperature dependence of the Raman temperature Raman spectra were recorded using an spectrum of alkaline-earth fluorides have shown that Oxford Instruments helium flow-through cryostat, the quasi-harmonic approximation is often suitable to whereas the high-temperature spectra were obtained explain the temperature dependence of the Raman with the aid of a home-built furnace (see Ref. [6], frequency and linewidth. Recent Raman scattering where experimental details are reported) under a 5N experiments performed in our laboratory on Li S [6]₂ Ar atmosphere. The pressure was stabilized during were interpreted by using this model [5]. This the experiments with the aid of a cold finger allowed us to show that, above 850 K [well below immersed in liquid nitrogen. At high temperatures, the melting point (T_c#0.55T )], a contribution due_m slight depositions on the inner side of the quartz to lattice disorder was distinctly present, in addition envelope of the Raman furnace were observed, to that arising from the anharmonic effects. K S has₂ probably due to the decomposition of the poly- crystallochemical properties which are quite different sulfides present. Further, crystal surface changes from those of Li S. This should influence, among₂ were noted.

other things, the temperature dependence of the zone center optical vibrations. For these reasons a Raman

study of the K S compound was performed as a₂ 3. Results and discussion function of temperature. This paper gives the results

obtained from crystals and analyzes them with the First-order Raman spectra were obtained in the aid of a model [7–10]. temperature range between 10 and 742 K. Fig. 1 shows typical spectra recorded at different temperatures. The Raman signal intensity decreased with 2. Experimental increasing temperature, and sizeable broadening was observed. Over the whole range the Raman line was

2.1. Synthesis found to be Lorentzian. The position and width of

the Raman line were accurately obtained by fitting Crystalline samples of K S were grown in a₂ the spectra with this function. The resulting ex- Bridgman furnace. They all exhibited an orange perimental temperature-dependent line width, G_T , coloration indicative of the presence of several 2g

and center frequency, v_T , are depicted in Fig. 2.

polysulfides with known low melting points 2g

This latter quantity decreased linearly by approxi- (T (K S )m 2 2 5793 K, T (K S )m 2 3 5565 K). Samples mately 15–20 cm21between room temperature (RT)

of about 3 to 4 mm in diameter were used for the 21

and 700 K with slope dv/ dT5 20.0175 cm / K, Raman experiments. Since K S is a very hygro-₂

while GT_2g increased almost exponentially. The RT scopic compound, preparation and crystal growth

values of the center frequency and the line width

were realized under an ultrapure argon atmosphere in 21

26 were: v_T (293 K)5128 cm and G_T (293 K)5

2g 2g

a glove box (residual oxygen partial pressure,10

2.9 cm21. Note that the Li S zone center Raman line

mmHg). 2

at RT has parameters: v_T 5372.6 cm21, G_T 5

2g 2g

2.2. Raman scattering 10.8 cm21 [6]. The temperature dependence of the Raman line width must be accounted for by includ- The Raman setup consisted of a 5 W argon ion ing cubic as well as quartic anharmonic contributions laser, a 1403 SPEX double monochromator and a to the harmonic crystal potential (see, e.g. Ref. [8]

cooled 31034-A20 Burle photomultiplier in conjunc- for a general reference). K S (and Li S) has a rather₂ ₂ tion with Stanford Research dual channel photon low and consequently highly anharmonic potential counting equipment. The spectrometer is fully com- barrier between normal and interstitial cationic sites puter controlled through home-built interfaces. Typi- in the antifluorite-type structure, which favors the

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Fig. 2. Temperature dependence of the T2gphonon frequency (n) and of the line width (d).

where G₀ is the residual broadening due to static lattice imperfections, a / 2 and b / 3 are constants, and the phonon occupation numbers n 5n (v ), etc. are

Fig. 1. Unpolarized Raman spectra of the T2g phonon mode in a a a

K S as a function of temperature.² given by the Bose–Einstein statistics. The second

term on the right-hand side of Eq. (1) is due to the importance of these terms. Breakdown of the model cubic anharmonicity, while the third term arises from of the harmonic crystal indeed produces the mecha- the quartic terms. A Matlab program using the nisms which allow the optical phonon hv_T , formal- Nelder–Mead simplex method was written to obtain ly created by the light scattering process, to decay2g the best fit between the model and the experimental into several ones of lower energy. The following data. Close agreement was obtained (model: solid analytical expression forG(T ) is obtained by assum-_j line in Fig. 2) from 10 to 700 K. The values of the ing thermal equilibrium of the phonons and under the three parameters are given in Table 1, together with simplifying hypothesis that the processes considered the corresponding quantities for Li S [6]. A second₂ produce the decay of one optical phonon into two or fit of the model was further performed by treatingv_a three acoustical ones, respectively, of mutually the and v_b as additional free parameters. The result is

1 1

] ]

same frequency (i.e. v 5 v_a ₂ _T , v 5 v_b ₃ _T ). It is

2g 2g

Table 1

based on second- and third-order perturbation contri-

Least-square fitted parameters of Eq. (1)

butions in the vibrational part within the quasihar-

Compound G a b b /a

monic lattice dynamics model [7,8,10]: ⁰

21 21 21

(cm ) (cm ) (cm )

K S2 a 0.818 0.048 0.088 1.83

1 1 2 1 _{Li S}^b _4.21 _0.572 _1.862 _3.26

] ] ] 2

S D FS D G

Gj(T )5G 10 a na12 1b nb12 112 , a

This paper.

(1) bRef. [6].

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162 B. Bertheville, H. Bill / Solid State Ionics 139 (2001) 159 –162

that the values of the constants G₀, a and b are very the rather low S /N obtained at temperatures above similar to those given in Table 1 andv 5_a 68.8 cm21 700 K did not permit us to confirm unambiguously and v 5_b 44.2 cm21. This result is an additional the existence of a diffuse phase transition around 820 argument for the applicability of the model initially K. Experiments with a very good S /N would be developed by Wallis et al. [7]. The constants G₀, a required in this temperature domain.

and b (Table 1) relating to K S are significantly₂ smaller than those for Li S. This may be related to₂ the mass of the respective cations, but confirmation

Acknowledgements of this hypothesis has to await knowledge of the

dynamical matrix. Comparison of the ratio b /a (see

This work was supported by the Swiss National Table 1) for Li S and K S shows that the effect of₂ ₂

Science Foundation. One of the authors (BB) thanks the quartic anharmonicity is reduced by approxi-

Dr. H. Hagemann for help with Raman experiments mately a factor of 2 in the latter lattice. Possibly, this

and both authors thank F. Rouge and D. Frauchiger is related to the density of phonon states. The

for technical assistance at various stages (crystal experimental Raman spectra show, even at RT, a

growth and mechanical construction work).

broad low-frequency band due to slight breakdown of the k¢_result(0 selection rule of the Raman process by static defects and anharmonicity. The peak of this

feature is at around 64 cm21 for K S. Li S has a2 2 References maximum in the acoustic phonon part of the spec-

trum between 120 and 140 cm21. As these peaks [1] W. Hayes, Crystals With the Fluorite Structure, Clarendon Press, Oxford, 1974.

correspond quite closely to a maximum in the

[2] C.R.A. Catlow, in: L. Laskar, S. Chandra (Eds.), Superionic

density of acoustic phonon states the corresponding

Solids and Solid Electrolytes, Academic Press, New York,

decay channels are probably favored. It is difficult,

1989, p. 339.

however, to make any quantitative progress as long [3] A.S. Dworkin, M.A. Breding, J. Phys. Chem. 72 (1968)

as no experimental neutron scattering results are 1277.

[4] B.M. Voronin, J. Phys. Chem. Solids 56 (6) (1997) 839.

available for K S.₂

[5] R.J. Elliot, W. Hayes, W.G. Kleppmann, A.J. Rushworth, J.F.

Finally, the remarkably smaller T50 K residual

Ryan, Proc. R. Soc. A 360 (1978) 317.

line width in K S in comparison with that in Li S₂ ₂

[6] B. Bertheville, H. Bill, H. Hagemann, J. Phys. Condens.

may be due to the zero point energy of the host Matter 10 (1998) 2155.

cation. Note that the eigenvectors of the harmonic [7] R.F. Wallis, I.P. Ipatova, A.A. Maradudin, Fiz. Tverd. Tela (Leningrad) 8 (1966) 1064, Sov. Phys. Solid State 8 (1966)

zone center T_2g vibration are determined by the sole cation displacement coordinates. Lower zero point 850.

[8] I.P. Ipatova, A.A. Maradudin, R.F. Wallis, Phys. Rev. 155

energy corresponds to less influence of the anhar-

(1967) 882.

monic potential. Additionally, the crystal quality of [9] Ph. Choquard, The Anharmonic Crystal, Benjamin Press,

our Li S samples was always better than that of K S.2 2 New York, 1967.

The strong broadening of the T_2g line as well as [10] T. Sakurai, T. Sato, Phys. Rev. B 4 (1971) 583.