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Sound velocity in liquid silicon
Volume 72A, number 2
25June1979
PHYSICS LETTERS
SOUND VELOCITY IN LIQUID SILICON
N.M. K&IA and S. STEINEMANN Institut de Physique exp&imentale de I’Universitkde Lausanne, W-1015 Don&y, Switzerland Received 21 February 1979
The velocity of sound in liquid silicon has been measured from 1430°C up to 1800°C. The sound velocity increases with temperature, as found in most semi-metals and semiconductors in the liquid state just above the melting point.
1. Introduction. The semi-metal or semiconductor elements Ga, Si, Ge, Sb and Te are known to show anomalous behaviours near their melting points. They are character&d by a large entropy of fusion, and (a part in Te?) the packing (mass density) increases during the solid&liquid transition (see ref. [l]). It has been suggested that the structural reordering in the liquid is, in some of the above mentioned elements, incomplete at temperatures well above the melting point [2]. Sound velocity and mass density are appropriate parameters for studying this phenomenon, since they lead to the compressibility which is related directly to the structure. The density data for these elements are given by Crawley [3]. The sound velocity in liquid Ga, Sb, Bi and Te has been reviewed in refs. [2] and [4]. Tb liquid Ge has been investigated by Glazov et al. [S]. However measurements of the sound velocity in liquid Si are lacking, due to the high melting point of this element. The present work was undertaken to complete the studies of the compressibility of these “anomalous” elements, and thereby enriching the data concerning the physicochemical properties of the liquid Al-S1 system [6].
2. Experimental met&d and results. The experimental technique has been described elsewhere [7], only the general features are recalled. Measurements are carried out in a single-crystal-growing furnace whose driver systems allow easy positioning of the sound conductors. Good temperature control (*l’(Z) is obtained with the high-frequency heating system. The error on the absolute value of the sound velocity is 0.3% whilst
the reproducibility of the experiments is less than *O.l%. The liquid silicon (99.999% of purity) is contained in an aluminium oxide crucible (99.8% Al2O3). The buffer rods are made of high-density pure alumina. In these sound conductors, whose mean density is 3.91 g cm-j, it has been found that the attenuation is weak even at the high temperatures reached during this study. Fig. 1 shows the sound velocity as a function of temperature. Experiments need carefully controlled heating and cooling cycles to avoid thermal hysteresis or lag. These measurements gave a scatter which ranges from *OS% near the melting point to *0.3% near 1750°C; these figures are larger than the reproducibility of the technique in normal conditions. The procedure adopted
I lb00
lxlo
I
TWX
1800
1
VW
Fig. 1. Sound velocity in liquid silicon; the data can be approximated with the relation u = 3369.0 + 0.388 T, where u is in ms-’ and T is in “C!.At the melting point (=a1410°C) the extrapolated velocity is 3916 ms-‘.
Volume 72A, number 2
PHYSICS LETTERS
by Glazov et al. [5] for reaching structural equilibrium in liquid Ge, i.e. holding the melt for at least 3 hours at a constant temperature for each measurement, cannot be followed at the high temperatures needed during the present work. Nevertheless, measurements were done when the temperature equilibrium was established. This was ascertained by moving the thermocouple, attached to the upper buffer rod, without perturbing the stability of the PID-controller which regulates the output of the HF heating system. In the figure, the line represents the mean values of the measured velocities and the bars indicate their maximum scatter. The temperature dependence of the adiabatic compressibility f3 can be evaluated from the present measurements and the density data of Luca and Urbain [8]. In the temperature range investigated, the compressibility decreases and 13—1 (a~3/aT)is about equal to —3.4 X i0~K—1. 3. Conclusion. The anomalous behaviour of solid semi-metals and semiconductors when they melt, is generally attributed to (i) the structural reordering with a tendency toward a metal~likestructure and (ii) the increase of the number of free electrons. In liquid Ge it seems that the first mentioned mechanism dominates, since the Hall coefficient corresponds to four free electrons per atom [9]. In liquid Te the two mechanisms are simultaneously present [10]. The electrical resistivity of pure liquid silicon [11] and the electronic transport properties of the Al—Si liquid system [6] indicate that silicon behaves like a normal metal, with four free electrons per atom, in the liquid state. Accordingly, it is likely that the sound velocity anomaly observed, i.e. a positive temperature coefficient,
154
25 June 1979
is mainly due to the structural rearrangement. Near
the melting point, X-ray diffraction experiments show clearly that liquid Si and Ge do not have a metal-like structure [12]. The first (low) peak of the structure factor is non-symmetrical. This is interpreted as an indication for a dual-structure model; liquid Si and Ge are believed to be heterogeneous, consisting of two types of microregions with different packing densities. As the temperature increases, the regions with the crystal-like atomic arrangement are dissolved. The thermal lag observed in the sound velocity measurements can probably be linked with the kinetics of this structural rearrangement. This work was supported by “Alusuisse AG NeUhausen”, Switzerland. References [1] T.E. Faber,An introduction to the theory of liquid metals (Cambridge U.P., London, 1972) p. 80. [2] M.B. Gitis (1966) 131.and I.G. Mikhailov, Soy. Phys. Acoustics 12 [3] A.F. Crawley, Intern. Metall. Rev. 19 (1974) No. 180. [4] R.T. Beyer and E.M. Ring, Liquid metals chemistry and physics, ed. S.Z. Beer (Dekker, New York, 1972) p. 411. [5] V.M. Glazov, A.A. Aivazov and V.!. Timoshenko, Soy. Phys. Solid State 18 (1976) 684. [6] N.M. Kéita, Ph.D. Thesis Université de Lausanne (1977). [7] N.M. Kéita and S. Steinemann, J. Phys. C 11(1978) 4635. [8] L.D. Lucas and G. Urbain, Compt. Rend. 255 (1962)2414. [9] G. Busch and Y. Tiêche, Phys. Kond. Mater. 1(1963)78. [10] B. Cabane and J. Friedel, J. Phys. Radium 32 (1971) 73. [11] N.E. Cusack, Rep. Prog. Phys. 26 (1963) 361. [12] Y. Waseda and K. Suzuki, Z. Phys. B20 (1975) 339.
25June1979
PHYSICS LETTERS
SOUND VELOCITY IN LIQUID SILICON
N.M. K&IA and S. STEINEMANN Institut de Physique exp&imentale de I’Universitkde Lausanne, W-1015 Don&y, Switzerland Received 21 February 1979
The velocity of sound in liquid silicon has been measured from 1430°C up to 1800°C. The sound velocity increases with temperature, as found in most semi-metals and semiconductors in the liquid state just above the melting point.
1. Introduction. The semi-metal or semiconductor elements Ga, Si, Ge, Sb and Te are known to show anomalous behaviours near their melting points. They are character&d by a large entropy of fusion, and (a part in Te?) the packing (mass density) increases during the solid&liquid transition (see ref. [l]). It has been suggested that the structural reordering in the liquid is, in some of the above mentioned elements, incomplete at temperatures well above the melting point [2]. Sound velocity and mass density are appropriate parameters for studying this phenomenon, since they lead to the compressibility which is related directly to the structure. The density data for these elements are given by Crawley [3]. The sound velocity in liquid Ga, Sb, Bi and Te has been reviewed in refs. [2] and [4]. Tb liquid Ge has been investigated by Glazov et al. [S]. However measurements of the sound velocity in liquid Si are lacking, due to the high melting point of this element. The present work was undertaken to complete the studies of the compressibility of these “anomalous” elements, and thereby enriching the data concerning the physicochemical properties of the liquid Al-S1 system [6].
2. Experimental met&d and results. The experimental technique has been described elsewhere [7], only the general features are recalled. Measurements are carried out in a single-crystal-growing furnace whose driver systems allow easy positioning of the sound conductors. Good temperature control (*l’(Z) is obtained with the high-frequency heating system. The error on the absolute value of the sound velocity is 0.3% whilst
the reproducibility of the experiments is less than *O.l%. The liquid silicon (99.999% of purity) is contained in an aluminium oxide crucible (99.8% Al2O3). The buffer rods are made of high-density pure alumina. In these sound conductors, whose mean density is 3.91 g cm-j, it has been found that the attenuation is weak even at the high temperatures reached during this study. Fig. 1 shows the sound velocity as a function of temperature. Experiments need carefully controlled heating and cooling cycles to avoid thermal hysteresis or lag. These measurements gave a scatter which ranges from *OS% near the melting point to *0.3% near 1750°C; these figures are larger than the reproducibility of the technique in normal conditions. The procedure adopted
I lb00
lxlo
I
TWX
1800
1
VW
Fig. 1. Sound velocity in liquid silicon; the data can be approximated with the relation u = 3369.0 + 0.388 T, where u is in ms-’ and T is in “C!.At the melting point (=a1410°C) the extrapolated velocity is 3916 ms-‘.
Volume 72A, number 2
PHYSICS LETTERS
by Glazov et al. [5] for reaching structural equilibrium in liquid Ge, i.e. holding the melt for at least 3 hours at a constant temperature for each measurement, cannot be followed at the high temperatures needed during the present work. Nevertheless, measurements were done when the temperature equilibrium was established. This was ascertained by moving the thermocouple, attached to the upper buffer rod, without perturbing the stability of the PID-controller which regulates the output of the HF heating system. In the figure, the line represents the mean values of the measured velocities and the bars indicate their maximum scatter. The temperature dependence of the adiabatic compressibility f3 can be evaluated from the present measurements and the density data of Luca and Urbain [8]. In the temperature range investigated, the compressibility decreases and 13—1 (a~3/aT)is about equal to —3.4 X i0~K—1. 3. Conclusion. The anomalous behaviour of solid semi-metals and semiconductors when they melt, is generally attributed to (i) the structural reordering with a tendency toward a metal~likestructure and (ii) the increase of the number of free electrons. In liquid Ge it seems that the first mentioned mechanism dominates, since the Hall coefficient corresponds to four free electrons per atom [9]. In liquid Te the two mechanisms are simultaneously present [10]. The electrical resistivity of pure liquid silicon [11] and the electronic transport properties of the Al—Si liquid system [6] indicate that silicon behaves like a normal metal, with four free electrons per atom, in the liquid state. Accordingly, it is likely that the sound velocity anomaly observed, i.e. a positive temperature coefficient,
154
25 June 1979
is mainly due to the structural rearrangement. Near
the melting point, X-ray diffraction experiments show clearly that liquid Si and Ge do not have a metal-like structure [12]. The first (low) peak of the structure factor is non-symmetrical. This is interpreted as an indication for a dual-structure model; liquid Si and Ge are believed to be heterogeneous, consisting of two types of microregions with different packing densities. As the temperature increases, the regions with the crystal-like atomic arrangement are dissolved. The thermal lag observed in the sound velocity measurements can probably be linked with the kinetics of this structural rearrangement. This work was supported by “Alusuisse AG NeUhausen”, Switzerland. References [1] T.E. Faber,An introduction to the theory of liquid metals (Cambridge U.P., London, 1972) p. 80. [2] M.B. Gitis (1966) 131.and I.G. Mikhailov, Soy. Phys. Acoustics 12 [3] A.F. Crawley, Intern. Metall. Rev. 19 (1974) No. 180. [4] R.T. Beyer and E.M. Ring, Liquid metals chemistry and physics, ed. S.Z. Beer (Dekker, New York, 1972) p. 411. [5] V.M. Glazov, A.A. Aivazov and V.!. Timoshenko, Soy. Phys. Solid State 18 (1976) 684. [6] N.M. Kéita, Ph.D. Thesis Université de Lausanne (1977). [7] N.M. Kéita and S. Steinemann, J. Phys. C 11(1978) 4635. [8] L.D. Lucas and G. Urbain, Compt. Rend. 255 (1962)2414. [9] G. Busch and Y. Tiêche, Phys. Kond. Mater. 1(1963)78. [10] B. Cabane and J. Friedel, J. Phys. Radium 32 (1971) 73. [11] N.E. Cusack, Rep. Prog. Phys. 26 (1963) 361. [12] Y. Waseda and K. Suzuki, Z. Phys. B20 (1975) 339.