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Ultrasonic attenuation and velocity studies of amorphous PdSiCu
625—629. Solid State Conm~unications, Vol.32,in pp. Pergan~nPress Ltd. 1979. Printed Great Britain.
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF AMORPHOUS PdSiCu H. Araki, G. Park, A. Hikata and C. Elbaum Metals Research Lab., Brown University, Providence, R.I. 02912, U.S.A. Received 20 August 1979 by J. Tauc Measurements of ultrasonic attenuation and velocity changes have been carried out on the metallic glass Pd 0 775Si0 665Cu0 06 as a function of amplitude, in the frequency range 10 to 90 MHz, for 0.3 < T < 10 K. The amplitude dependent attenuation changes observed in these studies are larger by a factor of 100 to 1000 than the values obtained from current two level system tunneling theory, with the use of parameters determined experimentally at higher frequencies by other workers. These attenuation changes have a linear (rather than quadratic) dependence on frequency and very weak T dependence (rather than lIT). These results are compared with data on vitreous silica obtained in the same range of frequencies and temperature.
2)has(henceforth been successful in The two level system TLS) tunexplaining thermal and acoustic properties neling modelthetheory~-~ of dielectric glasses, i.e., linear temperature dependence of the specific heat, quadratic ternperature dependence of thermal conductivity, log T dependence of ultrasonic velocity and amplitude dependent ultrasonic attenuation3). There is also a great deal of interest in investigating metallic glasses in order to check the ap— plicability of the same model to this case and numerous studies have been carried ~ With regard to ultrasonic properties, Bellessa and Bethoux6) reported the log T dependence of velocity change; amplitude dependence of the attenuation coefficient 7) and by was Golding reported etbyal.8). Qualitatively, metallic glasses seem to display Doussineau et al. thermal and ultrasonic properties similar to those of dielectric glasses. Quantitatively, however, differences have been reported~’8)and the problem has not been settled yet. In this note some new results on ultrasonic experiments on anorphous PdSiCu are reported and compared with results on vitreous silica Suprasil I. The amorphous Pd 0 775Si0 of 165Cu0 06 alloy was prepared by rapid quenching the melt into 0°Cwater. The specimens are cylinders 3 nun in diameter and lO-l~mm in length. Lithium nbbate crystals were used as transducers; these were bonded to the specimens with Dow Corning silicone grease. The temperature and amplitude dependence of the ultrasonic attenuation and velocity changes were measured between 0.3 and ~ 10 K using transverse waves at 10 to 90 MHz, and longitudinal waves at ‘~ 30 MHz. Precise measurements of the ultrasonic attenuation coefficient, a, and velocity change, M/v, have been made possible by using a newly developed pulse echo inethod~~.The resolutions of arnplitude and velocity change measurements are better than O.00l+ dB and 106, respectively. In order to verify whether any of the results were af— fected by spurious heating of the sample due to the ultrasonic signal, experiments were carried
pulses second (PPS). heating effects out withperrepetition rates No ranging from 1 to ~0 were found at the repetition rates of 10 and 20 PPS used in the measurements. A typical. temperature dependence of the attenuation coefficient for transverse waves at 25.1 MHz and four different amplitudes is shown in Fig. 1. As is seen from the graph, below about L~ K there is a definite negative ampli— tude dependence. More detailed results on the amplitude dependence at various temperatures are shown in Fig. 2. The experimental results are compared with the pr~ 1.ictions of the TLS tunneling model theory . This theory predicts for mA the expression: mA = aAOI(l ~ ~ where J and J are the input and the critical c. acoustic intensity, respectively. The data were found to agree very well with this functional form (see Fig. 2). The predicted form of mAO islO) 2/2pv3) ~ tanh (.~w/2kT) (2) mAO = (irnM where n, M are the density of states of TLS and the coupling constant between TLS and phonons, respectively, v is the acoustic wave velocity andthe the present other symbols have their usual meanings. In study4~ << 2kT, therefore mAO~ra/T. In order to compare the experimental results this prediction, obtained from the datawith by fitting~-~-~ to Eq. a were plotted
(~9
against temperature in Fig. is3, clearly which shows that the temperature dependence not l/T.
-
625
Similar dependences were found for the other frequencies; for T > 1 K, mAO tends to decrease With increasing temperature, but at lower ternperatures it tends to a constant value in all cases studied. Figure ‘~ shows mAO for various frequencies at 0.3 K. The frequency dependence is linear, rather than quadratic. In the same figure we plot the result by Doussineau et
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu
626
Vol. 32, No. 8
I
1.9
PdSiCu E
1.8
25.1MHz .
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TEMPERATURE.(K) Fig. 1 Temperature dependence of the attern~ation coefficient for 25.1 MHz transverse waves at four different amplitudes. Typical uncertainties in the results are about the size of the symbols.
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5.0K 4.2
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•
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—.-----.----.—-.-—-.-__._.j~~~ PdSICu
.5
TRANSVERSE
~
AMPLITUDE Fig. 2 Amplitude dependence of the attenuation coefficient for 25.1 MHz transverse waves at various temperatures. Fitted curves (Eq. (1)) are also shown. The arrows mark values of J obtained from the fitC ting. 7) for the same material at 720 MHz, but taken at 0.062 K. Their result falls on the al. linear extrapolation of our data; this strongly suggests that the temperature independent behaviour of a~ 0at low temperatures extends down to 60 mK with linear frequency dependence. The
broken line in the figure shows mA expected at 0.3 K from Eq. (2~based on the da~aof Doussineau et a17). In order to compare these results with the behaviour of dielectric glasses, experiments on vitreous silica Suprasil I were carried out in
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu
Vol. 32, No. 8
the same temperature and frequency range. No amplitude dependence in attenuation, within the accuracy of our experiment, was found for a 50
I
1.0
-
PdSICu
.~
TRANSVERSE
\
dB dynamic range (highest amplitude used is roughly the same as that for PdSiCu). This is not inconsistent with the predictions of the TLS theory, i.e., a 50 extrapolated to the present frequencies and temperatures from measure— 2/T dependence, is too small to the be obments at higher frequenciesl2~l3),on basis of an w served. The attenuation of longitudinal waves at 27.4 MHz was also measured in PdSiCu over a temperature range similar to that covered for transverse waves (see Fig. 5). A negative amplitude dependence of the attenuation was found; the total observed change was 0.015 ± 0.005 dB/cm at 0.3 K for a 36 dB dynamic range. In this regard we note that in the case of longitudinal waves the TLS theory predicts that m~ (Eq. 2) should be about one order of mag— ni~ude smaller and J about one order of magni— tude than forCtransverse provided that Mlarger is comparable for the two waves, cases7).
25.1 MHz \\
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0.1
+
-
o
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I
TEMPERATURE ( K )
In addition to the attenuation, velocity changes, Aviv, were measured at the same temperature and frequency ranges for various am-
Fig. 3 Temperature dependence of m~ 0for 25.1 MHz transverse waves. The broken line represents l/T dependence. I
10
•
I -
PdSICu
627
plitudes. The results for 42.6 MHz transverse waves are shown in Fig. 6. Below the maximum at ~ 2 K, Aviv, is linear in log T. This dependence has also been reported by other authors6) and agrees well with the TLS prediction~);
(0.062K)
9’
TRANSVERSE 0.3K
//
Av/v
=
2 2 (nM /pv ) log (T/T0)
(3)
/ /
E U
/
where T0 is an arbitrary reference temperature. Eq. (3) indicates no amplitude dependence in Aviv. The experimental results (Fig. 6 and
/ / / •
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-
measurements at the other frequencies), however, show that the slopes of Av/v against log T are amplitude dependent; the higher the am-
/ -
/ / / I
10
100
FREQUENCY C MHz)
1000
Fig. 4 Frequency dependence of mAO at 0.3K. The open circle represents the data of Ref. 7. The broken line shows a extra— polated from the data of Ret? 7, on the basis of Eq. (2).
plitude, the smaller slope.of the observed In summary, some the aspects ultrasonic properties of amorphous PdSiCu appear to be consistent with the TLS theory (negative amplitude dependence of attenuation for both modes and log T dependent velocity change), but there are definite discrepancies in frequency and temperature dependences of the attenuation change.
This research was supported by the National Science Foundation through the Materials Research Laboratory of Brown University and through Grant DMR77-l2249.
628
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu I —
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27.4 MHz LONGITUDINAL
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TEMPERATURE (K) Fig. 5 Temperature dependence of the attenuation coefficient at 27.1+ MHz longitudinal waves for two amplitudes.
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Vol. 32, No. 8
Vol. 32, No. 8
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu
629
REFERENCES
1.
2. 3.
4. 5. 6. 7.
P. W. Anderson, B. I. Halperin and C. M. Varma, Philosophical Magazine 25, 1 (1972), W. A. Phillips, Journal of Low Temperature Physics 7, 351 (1972). J. JNckle, Zeitschrift fuer Physik 257, 212 (1972). S. Hunklinger and W. Arnold, Physical Acoustics, Vol. XII, ed. M. P. Mason and R. N. Thurston, Academic Press, N. Y. (1976), p. 155. J. R. Matey and A. C. Anderson, Physical Review Bl6, 3406 (1977). J. E. Graebner, B. Golding, R. J. Schutz, F. S. L. Hsu and H. S. Chen, Physical Re— view Letters 39, 1480 (1977). G. Bellessa and 0. Bethoux, Physics Letters 62A, 125 (1977). P. Doussineau, P. Legros, A. Levelut and A. Robin, Journal of Physics (Paris) Letters 39, L-265 (1978).
8.
9. 10.
11.
12. 13.
B. Golding, J. E. Graebner, A. B. Kane and J. L. Black, Physical Review.aLetters 41, 1487 (1978). To be published. The difference of factor 2 from other papers comes from the difference in amplitude and intensity attenuation coefficient. In addition to a , the critical intensi— ties, ~ were o~ainedsimultaneously (see arrows in Fig. 2). 2 dependence. J~was found to have an approximately T S. Hunklinger, W. Arnold and S. Stein, Physics Letters 145A, 311 (1973). B. Golding, J. E~Graebnerand R. J. Schutz, Physical Review 814, 1660 (1976).
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF AMORPHOUS PdSiCu H. Araki, G. Park, A. Hikata and C. Elbaum Metals Research Lab., Brown University, Providence, R.I. 02912, U.S.A. Received 20 August 1979 by J. Tauc Measurements of ultrasonic attenuation and velocity changes have been carried out on the metallic glass Pd 0 775Si0 665Cu0 06 as a function of amplitude, in the frequency range 10 to 90 MHz, for 0.3 < T < 10 K. The amplitude dependent attenuation changes observed in these studies are larger by a factor of 100 to 1000 than the values obtained from current two level system tunneling theory, with the use of parameters determined experimentally at higher frequencies by other workers. These attenuation changes have a linear (rather than quadratic) dependence on frequency and very weak T dependence (rather than lIT). These results are compared with data on vitreous silica obtained in the same range of frequencies and temperature.
2)has(henceforth been successful in The two level system TLS) tunexplaining thermal and acoustic properties neling modelthetheory~-~ of dielectric glasses, i.e., linear temperature dependence of the specific heat, quadratic ternperature dependence of thermal conductivity, log T dependence of ultrasonic velocity and amplitude dependent ultrasonic attenuation3). There is also a great deal of interest in investigating metallic glasses in order to check the ap— plicability of the same model to this case and numerous studies have been carried ~ With regard to ultrasonic properties, Bellessa and Bethoux6) reported the log T dependence of velocity change; amplitude dependence of the attenuation coefficient 7) and by was Golding reported etbyal.8). Qualitatively, metallic glasses seem to display Doussineau et al. thermal and ultrasonic properties similar to those of dielectric glasses. Quantitatively, however, differences have been reported~’8)and the problem has not been settled yet. In this note some new results on ultrasonic experiments on anorphous PdSiCu are reported and compared with results on vitreous silica Suprasil I. The amorphous Pd 0 775Si0 of 165Cu0 06 alloy was prepared by rapid quenching the melt into 0°Cwater. The specimens are cylinders 3 nun in diameter and lO-l~mm in length. Lithium nbbate crystals were used as transducers; these were bonded to the specimens with Dow Corning silicone grease. The temperature and amplitude dependence of the ultrasonic attenuation and velocity changes were measured between 0.3 and ~ 10 K using transverse waves at 10 to 90 MHz, and longitudinal waves at ‘~ 30 MHz. Precise measurements of the ultrasonic attenuation coefficient, a, and velocity change, M/v, have been made possible by using a newly developed pulse echo inethod~~.The resolutions of arnplitude and velocity change measurements are better than O.00l+ dB and 106, respectively. In order to verify whether any of the results were af— fected by spurious heating of the sample due to the ultrasonic signal, experiments were carried
pulses second (PPS). heating effects out withperrepetition rates No ranging from 1 to ~0 were found at the repetition rates of 10 and 20 PPS used in the measurements. A typical. temperature dependence of the attenuation coefficient for transverse waves at 25.1 MHz and four different amplitudes is shown in Fig. 1. As is seen from the graph, below about L~ K there is a definite negative ampli— tude dependence. More detailed results on the amplitude dependence at various temperatures are shown in Fig. 2. The experimental results are compared with the pr~ 1.ictions of the TLS tunneling model theory . This theory predicts for mA the expression: mA = aAOI(l ~ ~ where J and J are the input and the critical c. acoustic intensity, respectively. The data were found to agree very well with this functional form (see Fig. 2). The predicted form of mAO islO) 2/2pv3) ~ tanh (.~w/2kT) (2) mAO = (irnM where n, M are the density of states of TLS and the coupling constant between TLS and phonons, respectively, v is the acoustic wave velocity andthe the present other symbols have their usual meanings. In study4~ << 2kT, therefore mAO~ra/T. In order to compare the experimental results this prediction, obtained from the datawith by fitting~-~-~ to Eq. a were plotted
(~9
against temperature in Fig. is3, clearly which shows that the temperature dependence not l/T.
-
625
Similar dependences were found for the other frequencies; for T > 1 K, mAO tends to decrease With increasing temperature, but at lower ternperatures it tends to a constant value in all cases studied. Figure ‘~ shows mAO for various frequencies at 0.3 K. The frequency dependence is linear, rather than quadratic. In the same figure we plot the result by Doussineau et
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu
626
Vol. 32, No. 8
I
1.9
PdSiCu E
1.8
25.1MHz .
•1
TRANSVERSE
z
17. •co~SO.&&L
2
~ 6è
4 I... Lii D 1.5 1.60.2
0.5~
00
.
I
£
2
•
0 •
—30dB I 68 dB 10 5 42dB — — —
TEMPERATURE.(K) Fig. 1 Temperature dependence of the attern~ation coefficient for 25.1 MHz transverse waves at four different amplitudes. Typical uncertainties in the results are about the size of the symbols.
__
5.0K 4.2
•
•
•
•
•
a
a
—.-----.----.—-.-—-.-__._.j~~~ PdSICu
.5
TRANSVERSE
~
AMPLITUDE Fig. 2 Amplitude dependence of the attenuation coefficient for 25.1 MHz transverse waves at various temperatures. Fitted curves (Eq. (1)) are also shown. The arrows mark values of J obtained from the fitC ting. 7) for the same material at 720 MHz, but taken at 0.062 K. Their result falls on the al. linear extrapolation of our data; this strongly suggests that the temperature independent behaviour of a~ 0at low temperatures extends down to 60 mK with linear frequency dependence. The
broken line in the figure shows mA expected at 0.3 K from Eq. (2~based on the da~aof Doussineau et a17). In order to compare these results with the behaviour of dielectric glasses, experiments on vitreous silica Suprasil I were carried out in
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu
Vol. 32, No. 8
the same temperature and frequency range. No amplitude dependence in attenuation, within the accuracy of our experiment, was found for a 50
I
1.0
-
PdSICu
.~
TRANSVERSE
\
dB dynamic range (highest amplitude used is roughly the same as that for PdSiCu). This is not inconsistent with the predictions of the TLS theory, i.e., a 50 extrapolated to the present frequencies and temperatures from measure— 2/T dependence, is too small to the be obments at higher frequenciesl2~l3),on basis of an w served. The attenuation of longitudinal waves at 27.4 MHz was also measured in PdSiCu over a temperature range similar to that covered for transverse waves (see Fig. 5). A negative amplitude dependence of the attenuation was found; the total observed change was 0.015 ± 0.005 dB/cm at 0.3 K for a 36 dB dynamic range. In this regard we note that in the case of longitudinal waves the TLS theory predicts that m~ (Eq. 2) should be about one order of mag— ni~ude smaller and J about one order of magni— tude than forCtransverse provided that Mlarger is comparable for the two waves, cases7).
25.1 MHz \\
__
E
\
•
__
\
0.1
+
-
o
I
I
‘
I
TEMPERATURE ( K )
In addition to the attenuation, velocity changes, Aviv, were measured at the same temperature and frequency ranges for various am-
Fig. 3 Temperature dependence of m~ 0for 25.1 MHz transverse waves. The broken line represents l/T dependence. I
10
•
I -
PdSICu
627
plitudes. The results for 42.6 MHz transverse waves are shown in Fig. 6. Below the maximum at ~ 2 K, Aviv, is linear in log T. This dependence has also been reported by other authors6) and agrees well with the TLS prediction~);
(0.062K)
9’
TRANSVERSE 0.3K
//
Av/v
=
2 2 (nM /pv ) log (T/T0)
(3)
/ /
E U
/
where T0 is an arbitrary reference temperature. Eq. (3) indicates no amplitude dependence in Aviv. The experimental results (Fig. 6 and
/ / / •
/ //
•
-
measurements at the other frequencies), however, show that the slopes of Av/v against log T are amplitude dependent; the higher the am-
/ -
/ / / I
10
100
FREQUENCY C MHz)
1000
Fig. 4 Frequency dependence of mAO at 0.3K. The open circle represents the data of Ref. 7. The broken line shows a extra— polated from the data of Ret? 7, on the basis of Eq. (2).
plitude, the smaller slope.of the observed In summary, some the aspects ultrasonic properties of amorphous PdSiCu appear to be consistent with the TLS theory (negative amplitude dependence of attenuation for both modes and log T dependent velocity change), but there are definite discrepancies in frequency and temperature dependences of the attenuation change.
This research was supported by the National Science Foundation through the Materials Research Laboratory of Brown University and through Grant DMR77-l2249.
628
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu I —
I
I.?
E
PdSICu
U
27.4 MHz LONGITUDINAL
z
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-
AALA
4
z
Ui 1.4
—42dB
I.4
•
—6dB
‘.3 0.5
0.2
I
2
5
tO
TEMPERATURE (K) Fig. 5 Temperature dependence of the attenuation coefficient at 27.1+ MHz longitudinal waves for two amplitudes.
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PdSICu —42
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TEMPERATURE (K) Fig. 6 Temperature dependence of the velocity changes at 1+2.6 MHz transverse waves for five different amplitudes.
Vol. 32, No. 8
Vol. 32, No. 8
ULTRASONIC ATTENUATION AND VELOCITY STUDIES OF PdSiCu
629
REFERENCES
1.
2. 3.
4. 5. 6. 7.
P. W. Anderson, B. I. Halperin and C. M. Varma, Philosophical Magazine 25, 1 (1972), W. A. Phillips, Journal of Low Temperature Physics 7, 351 (1972). J. JNckle, Zeitschrift fuer Physik 257, 212 (1972). S. Hunklinger and W. Arnold, Physical Acoustics, Vol. XII, ed. M. P. Mason and R. N. Thurston, Academic Press, N. Y. (1976), p. 155. J. R. Matey and A. C. Anderson, Physical Review Bl6, 3406 (1977). J. E. Graebner, B. Golding, R. J. Schutz, F. S. L. Hsu and H. S. Chen, Physical Re— view Letters 39, 1480 (1977). G. Bellessa and 0. Bethoux, Physics Letters 62A, 125 (1977). P. Doussineau, P. Legros, A. Levelut and A. Robin, Journal of Physics (Paris) Letters 39, L-265 (1978).
8.
9. 10.
11.
12. 13.
B. Golding, J. E. Graebner, A. B. Kane and J. L. Black, Physical Review.aLetters 41, 1487 (1978). To be published. The difference of factor 2 from other papers comes from the difference in amplitude and intensity attenuation coefficient. In addition to a , the critical intensi— ties, ~ were o~ainedsimultaneously (see arrows in Fig. 2). 2 dependence. J~was found to have an approximately T S. Hunklinger, W. Arnold and S. Stein, Physics Letters 145A, 311 (1973). B. Golding, J. E~Graebnerand R. J. Schutz, Physical Review 814, 1660 (1976).