Ultrasonic wave velocities and attenuation in IVb-Vb-VIb chalcogenide glasses: 2–300 K

Ultrasonic wave velocities and attenuation in IVb-Vb-VIb chalcogenide glasses: 2–300 K

Journal of Non-Crystalline Solids 18 (1975) 417-427 © North-Holland Publishing Company ULTRASONIC WAVE VELOCITIES AND ATTENUATION IN 1 V b - V b - V ...

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Journal of Non-Crystalline Solids 18 (1975) 417-427 © North-Holland Publishing Company

ULTRASONIC WAVE VELOCITIES AND ATTENUATION IN 1 V b - V b - V I b CHALCOGENIDE GLASSES: 2 - 3 0 0 K J.M. F A R L E Y * and G.A. SAUNDERS ** Department of Applied Physics and Electronics, University of Durham, South Road, Durham, UK Received 17 February 1975

The velocities and attenuation of longitudinal and shear ultrasonic (12 MHz) waves have been measured for several chalcogenide glasses (Gel oSi12As30Te48 , Ge20AsaoSeso, Si20Asa2Te48 , Ge10Si12As29Te49, Gel2 S14AsasTe49 ). The bulk, shear and Young's moduli and the Poisson ratio are found to be insensitive to the glass composition. The temperature dependences of the longitudinal and shear-wave velocities are negative at higher temperatures and approach 0 K with a zero slope. The ultrasonic attenuation does not exhibit either the broad loss peak or the smaller low-temperature peak found in many other glasses: the elastic and anelastic behaviour is quite different from that of oxide glasses - no evidence for the existence of two-level systems has been obtained from the ultrasonic measurements.

1. I n t r o d u c t i o n The thermal and acoustic properties of many non-crystalline dielectric solids differ not only in degree but also in kind from those of crystals [ 1 - 8 ] . An asymmetric two-well potential, tunnelling model with a broad distribution of the energy splitting has been developed [ 8 - 1 2 ] to explain the anomalous specific heat and thermal conductivity of glasses at low temperatures. The experimentally observed, short thermal phonon mean free path [3, 7] results from strong scattering of resonant phonons by these two-level systems; the anomalous ultrasonic attenuation and velocity observed in oxide glasses at low temperatures can be understood in terms of resonant and relaxation absorptions of phonons within the two-level systems [8]. Whether such two-level systems are a general feature of the glassy state remains to be settled by experiment. In the intermediate temperature range ( 4 . 2 - 4 0 0 K) a feature common to many glasses (including vitreous silica [ 1 3 - 1 5 ] , B20 3 [14, 16], A s 2 0 3 [14], GeO 2 [17], N a 2 0 - G e O 2 [17], N a 2 0 " B 2 0 3 - S i O 2 [18, 19] and B 2 0 3 - S i O 2 [19]) is a broad, frequency-dependent acoustic loss peak at megahertz frequencies together with an associated relaxation in the elastic moduli. Anderson and Bi3mmel [ 13] have shown * Present address: Babcock and Wilcock (Operations) Ltd., Research Station. Renfrew, Scotland. Present address: School of Physics, University of Bath, Claverton Down, Bath, UK.



J.M.Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - V b - Vlb glasses

that the characteristics of the loss peak in vitreous silica are consistent with a structural relaxation mechanism with a distribution of activation energies; they suggest for the mechanism a thermally activated transverse vibration of an oxygen atom, common to two adjacent SiO4 tetrahedra, between two wells of equal or nearly equal depth lying in the plane bisector of the vector joining the two silicon atoms of a non-linear Si-O-Si bond. A similar vibration can account for the occurrence of the broad loss peak in other glasses: for example, in B203 vibration of the oxygen atom in B - O - B . Another double-well potential mechanism which has been proposed [14, 15], involves the movement of the oxygen atom along the bond direction in a two-bond-length model. Although the behaviour of the loss peak intensity and temperature can be correlated with the number of bridging oxygen atoms - by studies [19] of different compositions of sodium borosilicate glasses in which the number of available bridging sites for the relaxation process is altered by the change in Na20 content - quantitative verification of the microscopic model is lacking. However, an alternative explanation [20] that the loss peak is the result of ultrasound phonon-thermal phonon interaction is not acceptable [ 18]. In vitreous silica [21, 22] and in other tetrahedrally coordinated glasses (GeO2, BeF 2 and Zn(PO3)2), but not in the triangular structure B203 glass [1 ], there is a small absorption peak near 4 K. This peak also occurs in the sodium borosilicate glasses [18]. It is frequency dependent in amplitude and has, on the basis of the Arrhenius model, an attempt frequency of 1011 Hz and an activation energy of 60 cal mo1-1 [22, 18]. Are the broad loss peak and its low-temperature satellite characteristic of the glassy state? With certain exceptions such as the investigations of low acoustic loss chalcogenide glasses [23] and that of amorphous As 2 S3 [24] (the attenuation data versus temperature of which have been interpreted on the basis of a double potential energy well model) most ultrasonic studies as a function of temperature in the vitreous state have been made on oxide glasses. This work comprises an experimental study of the velocity and attenuation of ultrasonic waves propagated in complex chalcogenide glasses. The major aims have been to characterize the elastic and anelastic properties of these materials and to find out (i) whether the broad loss peak and its associated elastic relaxation occur at intermediate temperatures, and (ii) if there is a low-temperature elastic anomaly due to the presence of two-level systems in these non-oxide amorphous solids.

2. Experimental The compositions of the specimens studied are listed in table 1. Glasses marked with an asterisk wereprepared at the Royal Radar Establishment, Malvern and were kindly supplied by Dr. C.B. Thomas. They were prepared from about 60 g of 99.999% purity elements sealed under vacuum in a silica glass ampoule. To ensure complete mixing of the silicon, the growth tube was kept at 900°C for about 57 h while being rocked and rotated. Specimens were then quenched in liquid nitrogen. These specimens

£M. Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - V b - VIb glasses


Table 1 Glass number a)

Glass composition

Measured density (kg m -3)

Longitudinal velocity (103 ms -1)

Transverse velocity (103 ms -1

1* 2* 3* 4t 5t

GeI oSil2 As3oTe48 Ge20As3oSeso

4940 4460 4900 5150 4920

2.31 2.26 2.26 2.32 2.42

1.30 1.24 1.29 1.37 1.41

Si2oAs32Te48 GeloSi12 As29Te49 Gea2Si14As35Te39

a) See text for explanation of * and t.

were in the form of cylinders approximately 1.3 cm in diameter and 0.7 cm long well suited for ultrasonic measurements. They were polished on solder metal laps using successively 10 vm and 1 vm diamond paste to yield end-faces flat and parallel to within 3 X 10 -5 rad. The specimens marked by a dagger symbol in table 1 were supplied by Dr. L. Rogers and had been prepared at Zenith Radio Research (UK) Limited from 99.999% purity elements melted in vacuo (< 10 -8 torr) and quenched in air. After being polished flat and parallel these specimens were rather thin and ultrasonic measurements were made on them only at room temperature. D e b y e Scherrer powder photographs of each glass yielded the diffuse halo patterns characteristic of amorphous materials, but no evidence of crystallinity. The ultrasonic measurements were made by the single-ended pulse echo technique using resonant quartz transducers (X-cut for longitudinal waves, Y-cut for shear waves) to generate the ultrasound. 'Nonaq' stopcock grease was a satisfactory bonding material and exponential echo trains were obtained at the frequencies investigated (10-100 MHz). Attenuation measurements were made by use of a calibrated exponential curve which was fitted to the echo pattern. Measurements of the temperature variation of velocity were made (at 12 MHz) by a pulse superposition technique [25] sensitive to transit time variations of 1 part in 105 . Specimen densities were measured at room temperature by Archimedes' method using methanol as a immersion liquid. The results obtained at room temperature are listed in table 1, and the temperature dependences of velocities given in fig. 1. Attenuation results are shown in fig. 2.

3. Elastic moduli at room temperature

The elastic moduli of the glasses have been computed at room temperature from the measured densities and the velocities of longitudinal vL and shear vs of ultrasound


J.M. Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - Vb- Vlb glasses 1



Gel 0 Si 12 As3o Te48




>- 2.31

_~ 2.35


~ 2.34


~2.33 g ~ 2.32

~ 2,28 J 2,27

2.31 1.28 >


"~ 1 . 2 7

_~ 1.32

~ 1.26



"•.... • ...., ,.

go i




100 200 Temperature (K)

2.32 _-,..


lOO 200 Temperature (K)



Si20 As32Te48

2.31 8 2.30 2.29 :5

.~ 2.28 2.27

1.32 "'..

.~ 1.31 •


"~ 1.29 0



100 200 Temperature (K)


Fig. 1. The temperature dependences of longitudinal and shear ultrasound velocities (in units of 10 3 ms -1 ) in several chalcogenide glasses•

J.M. Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - Vb- Vlb glasses






60 MHz








Temperature (K)

Fig. 2. Ultrasound attenuation versus temperature for the chalcogenide glass Ge2oAs3oSeso. Data are typical of those obtained in glasses 1 - 3 listed in table 1.


J.M. Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - Vb- Vlb glasses

Table 2 Glass humbet a)

Glass composition

Bulk modulus

Shear modulus

Young's modulus

109 N m -2

109 N m -2

109 N m -2

Poisson's Debye ratio temperature (o K)


GeloSi12 AsaoTe48






2* 3* 4t 5t


13.6 14.1 14.8 15.7

6.86 8.15 9.66 9.78

17.6 20.5 23.8 24.3

0.28 0.26 0.23 0.24

134 135 144 150

Si2oAs32 Te4s

GeloSil2As29Te49 Gel2 Sil4AS3s Te39

a) See text for explanation of * and t.

waves by means of the usual expressions: K = p(3o2L - 4o2)/3

(bulk modulus),

G = p o2

(shear modulus),

E = 002(302 - 4o2)/(o 2 - o2 ) (Young's modulus), v = (0 2 - 2o2)/(2(O2L - o 2 ) )

(Poisson's r a t i o ) .

Values obtained are listed in table 2; the glasses have elastic moduli which are very similar to those reported for four other glasses of the G e - A s - S e system [23, 26]. They are somewhat less stiff than vitreous silica SiO 2 (K = 36.3, G = 31.5, E = 7.32 GN m - 2 ) , the borosilicates or the sodium borosilicates (see for example table 2 of ref. [19]) but more resistant to elastic deformation than glassy boria B203(K = 12.0, G = 6.9, E = 17.4 GN m - 2 ) . A comparison of the values of Poisson's ratio is interesting. This parameter - which gives the ratio of the lateral and longitudinal strains which arise from a single tensile stress - has a comparatively small value in vitreous silica (0.164), lies between 0.20 and 0.26 in many binary and ternary oxide glasses and takes slightly larger values in the non-oxide chalcogenides (0.23-0.28) and in B203 (0.27). A striking result apparent from table 2 and the data of Reid [26] and Krause et al. [23] is that the elastic moduli of nine different, three- or four-component I V b - V b - V I b non-oxide glasses are very similar - almost equal within the bounds of experimental accuracy - despite some very great changes in composition. For example, compare glasses 1 and 2: a change in glass content from 50% Se to 48% Te and the replacement of 12% Si by Ge leads only to a small, hardly significant, decrease in the elastic constants. Similarly, a substantial change in arsenic concentration from 30% (glass 2) to 12% (glass composition Ge30As12Se55 [23]) has only a small effect on elastic constants. Equally large differences can be obtained as a result of differences in the

J.M. Farley, G.A. Saunders / Ultrasonic wave velocities in l V b - V b - V l b glasses


methods of preparation (compareglasses I and 4). The insensitivity of the elastic constants of the non-oxide chalcogenide glasses to composition is in complete contrast to the strong dependence on composition which is found in the derivatives of vitreous silica. Dembovsky [27] has studied the relationship between the softening temperatures Tg, the Young's and shear moduli and the structure of the vitreous chalcogenide semiconductors As2S3, As2Se3, GeSe2 and Se. He observed that each of these properties (P) depended on the main structural unit in the same way: P (chains, e.g. S, Se) < P (trigonal, e.g. As2 Se 3) < P (tetrahedral, e.g. GeSe2) . The glasses studied in this work are somewhat stiffer than those measured by Dembovsky. It is useful to compare the elastic properties of the glasses with those of the constituent elements in single crystal form. The bulk modulus K is the best single parameter to use for such a comparison, being a measure of the resistance of the medium to a pure volume dilation. The values of K for the glasses are nearly an order of magnitude less than those for the purely covalent single crystals germanium (K = 7.32 X 1010 N m -2) [281 and silicon (K = 9.78 X 1010 N m -2) [29], substantially less than that of arsenic (K = 5.81 × 1010 N m -2) [30], but similar to that of tellurium (K = 1.93 X 1010 N m -2) [31 ]. Some degree of van der Waals bonding i; recognized in the last two crystals. Certainly the interatomic binding forces are much weaker in the chalcogenide glasses than in covalently bound crystals. The elastic constants are not consistent with covalent binding being the only binding force. Plausibly, the glasses are comprised of covalently bound, multiply branched chains and rings held together by much weaker binding forces.

4. Debye temperatures The Debye temperatures of the glasses have been calculated from the room-temperature ultrasound velocities and densities. The Debye mean sound velocity Orn has been found using the expression om =


and then the Debye temperature 0 D obtained from 0 D = h / k (3N/47r) 1/3 Orn .

Here N is the volume density of the fundamental vibration units and is taken to be the number of individual atoms per unit volume (i.e. N = N o P / M , where M is the average molecular weight). The Debye temperature 0 D defined in this way characterizes the total vibrational spectrum, optical and acoustical modes not being


J.M. Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - Vb- Vlb glasses

separated [32]. The values obtained are listed in table 2. It is estimated that the error due to using room-temperature velocities and densities rather than the 0 K values is rather less than 5 K. The 0 D values of the chalcogenide glasses are small compared with those of vitreous silica (495 K) and many other oxide glasses (see table 2 of ref. [19]) and those of phosphate glasses [33].

5. Temperature dependence of ultrasound velocities and attenuation The temperature dependences of the longitudinal and shear ultrasound wave velocities of the glasses with compositions Ge loSil2 As30Te48, Ge20As30Se50 and Si20As32Te48 are shown in fig. 1. Actual data points are shown; no smoothing has been employed. In each glass for both the modes, the temperature coefficient of velocity (do/dT)/v; is negative and approximately constant between 100 and 300 K. Values at 0°C are -1.11 X 10 -4, -1.17 X 10 -4, -1.08 X 10-4K -1 for longitudinal modes, and -1.12 X 10 -4, -1.03 X 10 -4, -1.06 × 10 -4 K -1 for shear modes in the glasses listed above - they are relatively insensitive to composition. Negative coefficients of longitudinal velocity at room temperatures have been reported elsewhere for chalcogenide glasses of the G e - A s - S system [34], but for these glasses (du/dT)/u is strongly composition dependent and ranges between -0.5 and - 3 . 5 ) 104K -1. One of the well-established properties of the tetrahedrally coordinated glasses SiO 2, GeO2 and BeF2 is a positive temperature coefficient of velocity at high temperatures. At lower temperatures in many oxide glasses the ultrasound velocities exhibit minima which correspond to the relaxation of elastic moduli that accompanies the broad loss peak in the ultrasound attenuation. There is no such relaxation in the elastic moduli of the chalcogenide glasses and no temperature range in which the temperature coefficient of velocity is positive. Furthermore, the temperature dependence of ultrasonic attenuation in the chalcogenide glasses has been found to be different from that in the oxide glasses. There is no attenuation peak in the range 4.2-300 K for either longitudinal or transverse ultrasonic waves (10-100 MHz) in any of the chalcogenide glasses listed above. Attenuation was found to be rather dependent upon thermal history and preparation; samples of the same composition gave different attenuations and an increase in attenuation occurred after temperature cycling. Certain features were common to all the glasses and the results shown in fig. 2 are typical. At temperatures below about 200 K the attenuation remained constant and at higher temperatures increased with temperature - behaviour that has been associated with the softening of the glass as Tg is approached [34].

6. Velocity and attenuation of longitudinal waves at temperatures below 5 K A number of workers have reported the dependence of longitudinal ultrasound velocity and attenuation on temperature, frequency and acoustic intensity at low

J.M. Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - Vb- VIb glasses


temperatures (< 5K). The ultrasound velocity in vitreous silica [6] and in the borosilicate glasses [19] has been found to continue to increase on cooling right down to below 2 K - in distinct contrast to the behaviour in crystalline materials where velocities tend to a constant value below about 10 K. In vitreous silica, below 1.5 K the longitudinal ultrasound velocity then goes through a maximum and on further cooling decreases with decreasing tempeiature down to the present limit of the measurements 0.3 K [6]. In the region of temperature 0.4-2 K the ultrasonic attenuation has been found to be amplitude dependent and there is an increase of the unsaturated absorption with decreasing temperature for T < 0.6 K [5 ]. These anomalous acoustic properties have been attributed to the two-level systems with a broad distribution of energy splitting [5, 8, 9]. The two-level systems may be described as tunnelling states, but so far no direct evidence for the tunnelling nature has been given [9]. In view of the generality of the thermal anomalies it is important to establish which of the acoustic anomalies can be considered characteristic of the glassy state. The results of this work (fig. 1) indicate that the temperature dependence of velocity in the chalcogenide glasses differs from that of vitreous silica and sodium borosilicate glasses in the low-temperature region. To confirm this, further experiments at low temperature have been undertaken: the longitudinal wave ultrasound velocity has been measured in the glass of composition Ge10Si12As30Te48at intervals of ~ 0.2 K from 4.2 K down to 1.95 K. The ultrasonic wave transit times were measured by the pulse echo overlap method [35]. The oscilloscope repetition rate was derived from a frequen[




3 2


~-~ =--3








Temperature, K (logarithmicscale) Fig. 3. Comparison of the temperature dependence of the longitudinal wave ultrasound velocity in vitreous silica (solid line, data from [6]) and the cha]cogenJde glass GeloSil2As3oTe4s at temperatures below 4.2 K. Crosses (×): nonaq bond; solid circles (o): di(2-ethyl hexyl) sebacate bond.


J..M.Farley, G.A. Saunders / Ultrasonic wave velocities in I V b - Vb- Vlb glasses

cy synthesizer, and by overlapping echoes 1 and 5 a sensitivity of better than 1 part in 30 000 was achieved. Measurements were made at 12 MHz on an exponential echo train, first with a 'Nonaq' stopcock grease bond and then repeated using a different bond material, di(2-ethyl hexyl) sebacate, a low-viscosity liquid at room temperature which forms very thin bonds. The temperature was determined by measuring the vapour pressure over pumped helium; that the specimen temperature was in fact changing was monitored by means of a thermocouple bonded to the side of the specimen with GE 7031 low-temperature varnish. Results of the two runs are given in fig. 3 in comparison with the measurements reported for vitreous silica [6]. In the chalcogenide glas s over the temperature range studied there was no measurable change (i.e. less than I part in 30 000) in longitudinal wave velocity. This result is quite different to that for vitreous silica, and a need is apparent for measurements at temperatures below those obtainable in our laboratories. Furthermore, no change in attenuation was observable: the low-temperature absorption peak, which occurs in several oxide and tetrahedrally bonded glasses [21,22, 18], does not occur at 12 MHz in these chalcogenide glasses.

7. Conclusion The I V b - V b - V I b chalcogenide glasses studied here are relatively weakly bound materials, with particularly low ultrasonic velocities and low Debye temperatures; their elastic constants are rather insensitive to composition. The ultrasonic properties are quite different from those of the oxide glasses. At 12 MHz there is no broad acoustic loss peak or its associated elastic relaxation at intermediate temperatures; nor there is a satellite loss peak at 4 K. The temperature coefficients of longitudinal and shear wave velocities are negative and constant at higher temperatures, and decrease at low temperatures to zero below 5 K - behaviour quite different to that observed [6] in vitreous silica. No evidence has been found for the existence of two-level systems in these chalcogenide glasses.

Acknowledgements The authors wish to acknowledge Dr. C.B. Thomas and Dr. L. Rogers who supplied the specimens and to thank J. Crawshaw for assistance with some of the experiments.

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