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Submitted on 1 Jan 1978
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LOW-TEMPERATURE SPECIFIC-HEATS OF SOME
GexS1-x GLASSES
N. Thomas, W. Phillips
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-980
LOW-TEMPERATURE SPECIFIC-HEATS OF SOME G exS , _x GLASSES
N. Thomas and W.A. Phillips
Cavendish Laboratory, Cambridge, U.K.
Résumé.- On a mesuré la chaleur spécifique de plusieurs verres du type Ge S, entre 2 K et 18 K. On trouve pour chaque verre un maximum en C/T3, qui s'aggrandit et qui se trouve à une température de
plus en plus basse à mesure que la quantité de soufre s'accroît.
Abstract.- We have measured the low-temperature specific-heats of several glasses in the system Ge„S._ . Each glass shows a peak in C/T , which grows larger and moves to a lower temperature as the sulphur content increases.
In order to investigate the influence of structure on the low-temperature specific-heat C of glasses, we have measured C from 2 K to 18 K for various glasses in the system Ge -S. . Some results
° x 1-x
of this investigation have been reported previously
l \ l . The structures of the glasses in this system have been determined by Lucovsky and co-workers /2/. The glass-forming region extends from about x = 0.1 to about x = 0.45. Within this range the germanium atoms are four-fold coordinated and the sulphur atoms are two-fold coordinated. The compound GeS„(x=l/3) forms a glass consisting of GeSi, tetrahedra linked by shared sulphur atoms, analogous to the SiO te-trahedra of vitreous silica. On the sulphur-rich side of GeS2(x<l/3), the additional sulphur is used to link the GeS, tetrahedra so that Ge-S-S-Ge se-quences occur, with no Ge-Ge bonds. This "chain-crossing-model" description is valid for 1/3>X>1/5 for x<l/5 the extra sulphur forms S„ rings rather than long sulphur chains cross-linked by germanium. On the germanium-rich side of GeS2(x>l/3), 5e-Ge bonds appear and S-S bonds are absent.
Samples were prepared by reacting a few grams of high-purity germanium and sulphur inside evacua-ted silica ampoules and then quenching from the melt. The heat capacity of small samples (typical-ly 100-500 mg) was measured using the pulse techni-que with a silicon bolometer developed at Stanford /3/. The specific heats for various Ge S, glasses are plotted in figure I as C/T3 against T for
x = 0.16, 0.26, 0.33 and 0.40. The curves labelled (a), (b) and (c) are interpolation fits for x = 0.16 0.33 and 0.40 respectively. Also shown are the ex-perimental points for x =0.16, which showed the
largest random error, about 1 %, of these three samples. Results for x = 0.25 reported previously /!/ are also shown ; these have the largest scatter of all data and were taken using less sophisticated equipment than the recent results ; nonetheless they fit in quite well with the other data.
Fig. 1 : C/T3 v T for various GexSi-x glasses : (a) x = 0.16, (b) x = 0.33, (c) x = 0.40 ; circles and crosses are the experimental points for x=0.16 and x = 0.25 respectively. The arrow marks the cu-bic term for x = 0.40 /l/
Also marked in figure 1 is the coefficient of the cubic term for the very low temperature specific-heat of Ge S reported previously /I/.
The general trend apparent from figure 1 is that with increasing sulphur content the peak in C/T3 becomes larger and moves to a lower tempera-ture. In amorphous germanium /4/ and vitreous sili-ca /5/ the peak in C/T3 has been attributed to a
peak in g(o))> the vibrational density of states, analogous to the TA peaks observed in crystalline
germanium and cristobalite respectively. The peak in g(w) for these crystals is due to the flatness of the TA dispersion relation, which Weber /6/ has explained for crystalline germanium using a model based on short-range interactions between ions and bond charges. It seems probable that the modes res- ponsible for the peak in c/T3 in the glass involve the same sort of bond-bending motion as the crys- talline TA modes, but these modes are not presuma- bly plane waves. For the Ge S glasses the tempe-
x I-x
ratures of the c/T3 peaks suggest that the "peak" in g(w) occurs at lower frequencies as the sulphur content increases.
The c/T3 plots in figure 1 all have a similar shape if the peak heights and temperatures are nor- malised to unity : for each curve c/T3 falls to about half its peak value at three times the peak temperature and to about 0.8 times its peak value at half the -peak temperature. This suggest that g(w) appropriately scaled is similar for each of the glasses. In figure 2 we compare c/T3 plots for two different g(w) with the results for Geo.bSo.6
,
which are shown as curve (a).I
5 lo TIK l5 20
Fig. 2 : c/T3 vaT for Ge0,~S0,6: (a) experiment ;
(b) fit with a rectangular peak at 490 GHz ; (c) fit with a delta function at 700 GHz
Curve (b) uses a quadratic low-frequency g(w) cho- sen to give the correct intercept at 0 K. The qua- dratic term is cut off at 490 GHz (24.5 K or 16.3 cm-l) and replaced above this by a broad rectangu- lar peak of height 5.44 times the quadratic term at 490 GHz. Curve (c) uses a similar quadratic term, but cut off at 700 GHz with a delta function at this frequency with 5.1 times the weight of the low-f requency modes. The experimental peak in c/T3 is much broader than that produced by either of these models for g(w). Both models yield a peak which falls off much too rapidly at low temperatu- res, and curve (c) falls off much too rapidly at high temperatures as well. This suggests that the
real g(w) probably makes a smooth transition from the quadratic behaviour at very low frequencies to
-1
a broad peak above about 16 cm
.
Such a peak has been seen using neutron scattering /7/ on amorphous arsenic, which shows a c/T3 peak similar to the ones observed here /8/.In the absence of sound velocities or very low temperature specific-heats for most of the GexSlex glasses it is difficult to interpret the variation of the c/T3 peak heights. Since the sha- pes of g(~) seem to be broadly similar, this sug- gests that the increase in c/T3 with increasing sulphur content is due to a decrease in the elastic constants : this would imply that the cubic term in C should scale with the c/T3 peak height. Such a softening of the lattice with increasing sulphur content is perhaps supported by the shift of the c/T3 peak to lower temperatures, although in Weber' s bond-charge model for germanium /6/ the elastic constants and the TA-peak frequency have different microscopic origins. Further, the situation may be complicated by the contribution of two-level sys- tems to the quadratic density of states 191.
References
/ I / Phillips, W.A., and Thomas, N., Structure of Non-Crystalline Materials (Edited by P.H. Gas- kell) p 143, Taylor and Francis, London (1977) /2/ Lucovsky, G., Galeener, F.L., Keezer, R.C.,
Geils,
and
Six H~A., phys. ~ e v ; B 10- (1974) 5134131 Bachmann, R. and co-workers Rev. Sci. Instr. 43 (1972) 205
/ 4 / King, C.N., Phillips, W.A., and de Neufville, J.P., Phys. Rev. Lett. 32 (1974) 538
/5/ Bilir, N. and Phillips, W.A., Phil. Mag. 32 (1975) 113
161 Weber, W. Phys. Rev. Lett 33 (1974) 371 /7/ Leadbetter, A.J., Smith, P.M. and Seyfert, P.,
Phil. Mag. 33 (1976) 441
