COMPUTER EXPERIMENTS ON PROPAGATION AND ELASTIC SCATTERING OF BEAMS OF DOWN – CONVERTING PHONONS
Gańcza W. M. 1, Obukhov I. A. 2, Paszkiewicz T. 3, Danilchenko B. A. 2
1 Institute of Theoretical Physics, University of Wrocław
pl. Maxa Borna 9, PL-50-204 Wrocław, Poland
2Institute of Physics, Ukrainian Academy of Sciences,
252650 Kiev, Ukraine
3Institute of Physics, University of Rzeszów
ul. Rejtana 16A, PL-35-310 Rzeszów, Poland
Received:
Received 5 July, 2001
DOI: 10.12921/cmst.2001.07.02.07-46
OAI: oai:lib.psnc.pl:519
Abstract:
We present the program MCAnScat which simulates propagation of beams of down-converting phonons in anisotropic cubic and isotropic media containing point mass defects. It is assumed that the excitation the phonon subsystem is low-level. The program produces time-of-flight spectrograms and phonon energy and quasi-momentum focusing patterns for samples having the form of a rectangular parallelepiped, as well as for cylindric and spherical specimens. Wave vectors of beam phonons belong to body angles ranging from 4π to zero. The axes of corresponding cones are arbitrarily oriented. When down-conversion processes are excluded the outcomes of experiments on initial spatially homogeneous states and on diffusive propagation of phonons are compared with exact results obtained for isotropic and cubic media. As an example of application of MCAnScat we study ballistic and diffusive propagation of beams of phonons in GaAs. The obtained results are in excellent agreement with theoretical and experimental findings.
Key words:
elastic scattering, heat pulses, Monte Carlo Methods, phonon down-conversion
References:
[1] M. Lax, V. Narayanamurti, R. C. Fulton, N. Holtzwarth, Phonon Scattering in Condensed Matter V, eds. A. C. Anderson, J. P. Wolfe, p. 335 (Springer, Heidelberg, 1986).
[2] H. J. Maris, Phys. Rev., B 41, 9736 (1990).
[3] D. V. Kazakovtsev, A. A. Maximov, D. A. Pronin, I. I. Tartakovskii, Sov. Phys. JETP, 71, 819
(1990).
[4] H. J. Maris, S. Tamura, Phys. Rev., B 47, 727 (1993).
[5] S. Tamura, Phys. Rev., B 48, 13502 (1993).
[6] Y. B. Levinson, Nonequilibrium Phonons in Nonmetallic Crystals, eds. W. Eisenmenger and
A. A. Kaplyanskii, p. 91 (Elsevier, Amsterdam, 1986).
[7] V. L. Gurevich, Transport in Phonon Systems (North-Holland, Amsterdam, 1986).
[8] W. M. Gańcza, T. Paszkiewicz, Comp. Phys. Comm., 85, 423 (1995).
[9] Cz. Jasiukiewicz, T. Paszkiewicz, Z. Phys. B -Condensed Matter, 77, 209 (1989).
[10] T. Paszkiewicz, M. Wilczyński, Z. Phys. B -Condensed Matter, 80, 287 (1990).
[11] T. Paszkiewicz, M. Wilczyński, Z. Phys. B -Condensed Matter, 80, 365 (1990).
[12] T. Paszkiewicz, M. Wilczyński, Z. Phys. B -Condensed Matter, 88, 5 (1992).
[13] T. Paszkiewicz, M. Wilczyński, Dynamical Properties of Solids, v. 7, Phonon Physics The Cutting Edge, eds. G. K. Horton and A. A. Maradudin, p. 257 (North Holland, Amsterdam, 1995).
[14] M. T. Ramsbey, S. Tamura, J. P. Wolfe, Phys. Rev., B 46, 1358 (1992).
[15] S. N. Ivanov, E. N. Khazanov, T. Paszkiewicz, A. V. Taranov, M. Wilczyński, Z. Phys.
B-Condensed Matter, 99, 535 (1996).
[16] W. M. Gańcza, T. Paszkiewicz, Computers Chem. 22, 21 (1998).
[17] J. P. Wolfe, Imaging Phonons (Cambridge University Press, Cambridge, 1998).
[18] A. G. Kozorezov, T. Miyasato, J. K. Wigmore, J. Phys.: Condens. Matter 8, 1 (1996).
[19] E. Held, W. Klein, R. P. Iluebener, Z. Phys., B 75, 279 (1989).
[20] J. C. Hensel, R. C. Dynes, Phys. Rev. Lett. 43, 1033 (1979).
[21] J. A. Shields, J. P. Wolfe, S. Tamura, Z. Phys., B 76, 295 (1989).
[22] Cz. Jasiukiewicz, D. Lehmann, T. Paszkiewicz, Z. Phys. B 86, 225 (1992).
[23] Yu. I Sirotin, M. P. Shaskolskaya, The Principles of Crystalophysics (Nauka, Moscow, 1979)
[in Russian].
[24] F. I. Fedorov, Theory of Elastic Waves in Crystals (New York, Plenum Press 1968).
[25] A. Duda and T. Paszkiewicz, Phys. Rev., B 61, 3180 (2000).
[26] A. Duda and T. Paszkiewicz, Physica, B 263-264, 63 (1999).
[27] S. Tamura, Phys. Rev., B 30, 610 (1984).
[28] L. J. Walpole, Proc. Roy. Soc., A 391, 149 (1984).
[29] A. G. Every, Phys. Rev., B 22, 1746 (1980).
[30] S. Tamura, Phys. Rev., B 27, 858 (1983).
[31] S. Tamura, Phys. Rev., B 30, 849 (1984).
[32] Cz. Jasiukiewicz, T. Paszkiewicz, D. Lehmann, Z. Phys. B-Condensed Matter, 96, 213 (1994).
[33] H. Goldstein, Classical Mechanics, Chapt. 4, Sect. 4.4. (Addison-Wesley, Reading, Mass., 1974),
[34] B. A. Danilchenko, D. V. Kazakovtsev, I. A. Obukhov, Zh. Exp. Teor. Fiz., 106, 1439 (1994).
[35] S. N. Ivanov, A. V. Taranov, E. N. Khazanov, Fiz. Tverd. Tela, 35, 3201 (1995).
[36] J. W. Tucker, V. W. Rampton, Microwave Ultrasonics in Solid State Physics (North-Holland,
Amsterdam, 1972).
[37] S. Tamura, Phys. Rev., B 31, 2574 (1985).
[38] S. Tamura, H. J. Maris, Phys. Rev. B 31, 2595 (1985).
[39] C. Jacoboni, C. Reggiani, Rev. Mod. Phys., 55, 645 (1983).
[40] B. A. Danilczenko, M. I. Slutskii, Sov. Phys. Solid State, 30, 21 (1988).
[41] B. A. Danilchenko, W. M. Gańcza, Cz. Jasiukiewicz, Phys. Rev., B 60, 6113 (1999).
[42] Die Kunst of Phonons, Lectures from the Winter School of Theoretical Physics, eds. T. Paszkiewicz, K. Rapcewicz (Plenum, New York, 1994).
[43] A. T. Lee, B. Cabrera, B. L. Daugheity, J. Penn, Phys. Rev. Letters, 71, 1395 (1993).
[44] B. A. Danilchenko, S. N. Ivanov, D. V. Poplavskii, A.V. Taranov, E. N. Khazanov, Sov. Phys.
JETP, 85, 179 (1997).
We present the program MCAnScat which simulates propagation of beams of down-converting phonons in anisotropic cubic and isotropic media containing point mass defects. It is assumed that the excitation the phonon subsystem is low-level. The program produces time-of-flight spectrograms and phonon energy and quasi-momentum focusing patterns for samples having the form of a rectangular parallelepiped, as well as for cylindric and spherical specimens. Wave vectors of beam phonons belong to body angles ranging from 4π to zero. The axes of corresponding cones are arbitrarily oriented. When down-conversion processes are excluded the outcomes of experiments on initial spatially homogeneous states and on diffusive propagation of phonons are compared with exact results obtained for isotropic and cubic media. As an example of application of MCAnScat we study ballistic and diffusive propagation of beams of phonons in GaAs. The obtained results are in excellent agreement with theoretical and experimental findings.
Key words:
elastic scattering, heat pulses, Monte Carlo Methods, phonon down-conversion
References:
[1] M. Lax, V. Narayanamurti, R. C. Fulton, N. Holtzwarth, Phonon Scattering in Condensed Matter V, eds. A. C. Anderson, J. P. Wolfe, p. 335 (Springer, Heidelberg, 1986).
[2] H. J. Maris, Phys. Rev., B 41, 9736 (1990).
[3] D. V. Kazakovtsev, A. A. Maximov, D. A. Pronin, I. I. Tartakovskii, Sov. Phys. JETP, 71, 819
(1990).
[4] H. J. Maris, S. Tamura, Phys. Rev., B 47, 727 (1993).
[5] S. Tamura, Phys. Rev., B 48, 13502 (1993).
[6] Y. B. Levinson, Nonequilibrium Phonons in Nonmetallic Crystals, eds. W. Eisenmenger and
A. A. Kaplyanskii, p. 91 (Elsevier, Amsterdam, 1986).
[7] V. L. Gurevich, Transport in Phonon Systems (North-Holland, Amsterdam, 1986).
[8] W. M. Gańcza, T. Paszkiewicz, Comp. Phys. Comm., 85, 423 (1995).
[9] Cz. Jasiukiewicz, T. Paszkiewicz, Z. Phys. B -Condensed Matter, 77, 209 (1989).
[10] T. Paszkiewicz, M. Wilczyński, Z. Phys. B -Condensed Matter, 80, 287 (1990).
[11] T. Paszkiewicz, M. Wilczyński, Z. Phys. B -Condensed Matter, 80, 365 (1990).
[12] T. Paszkiewicz, M. Wilczyński, Z. Phys. B -Condensed Matter, 88, 5 (1992).
[13] T. Paszkiewicz, M. Wilczyński, Dynamical Properties of Solids, v. 7, Phonon Physics The Cutting Edge, eds. G. K. Horton and A. A. Maradudin, p. 257 (North Holland, Amsterdam, 1995).
[14] M. T. Ramsbey, S. Tamura, J. P. Wolfe, Phys. Rev., B 46, 1358 (1992).
[15] S. N. Ivanov, E. N. Khazanov, T. Paszkiewicz, A. V. Taranov, M. Wilczyński, Z. Phys.
B-Condensed Matter, 99, 535 (1996).
[16] W. M. Gańcza, T. Paszkiewicz, Computers Chem. 22, 21 (1998).
[17] J. P. Wolfe, Imaging Phonons (Cambridge University Press, Cambridge, 1998).
[18] A. G. Kozorezov, T. Miyasato, J. K. Wigmore, J. Phys.: Condens. Matter 8, 1 (1996).
[19] E. Held, W. Klein, R. P. Iluebener, Z. Phys., B 75, 279 (1989).
[20] J. C. Hensel, R. C. Dynes, Phys. Rev. Lett. 43, 1033 (1979).
[21] J. A. Shields, J. P. Wolfe, S. Tamura, Z. Phys., B 76, 295 (1989).
[22] Cz. Jasiukiewicz, D. Lehmann, T. Paszkiewicz, Z. Phys. B 86, 225 (1992).
[23] Yu. I Sirotin, M. P. Shaskolskaya, The Principles of Crystalophysics (Nauka, Moscow, 1979)
[in Russian].
[24] F. I. Fedorov, Theory of Elastic Waves in Crystals (New York, Plenum Press 1968).
[25] A. Duda and T. Paszkiewicz, Phys. Rev., B 61, 3180 (2000).
[26] A. Duda and T. Paszkiewicz, Physica, B 263-264, 63 (1999).
[27] S. Tamura, Phys. Rev., B 30, 610 (1984).
[28] L. J. Walpole, Proc. Roy. Soc., A 391, 149 (1984).
[29] A. G. Every, Phys. Rev., B 22, 1746 (1980).
[30] S. Tamura, Phys. Rev., B 27, 858 (1983).
[31] S. Tamura, Phys. Rev., B 30, 849 (1984).
[32] Cz. Jasiukiewicz, T. Paszkiewicz, D. Lehmann, Z. Phys. B-Condensed Matter, 96, 213 (1994).
[33] H. Goldstein, Classical Mechanics, Chapt. 4, Sect. 4.4. (Addison-Wesley, Reading, Mass., 1974),
[34] B. A. Danilchenko, D. V. Kazakovtsev, I. A. Obukhov, Zh. Exp. Teor. Fiz., 106, 1439 (1994).
[35] S. N. Ivanov, A. V. Taranov, E. N. Khazanov, Fiz. Tverd. Tela, 35, 3201 (1995).
[36] J. W. Tucker, V. W. Rampton, Microwave Ultrasonics in Solid State Physics (North-Holland,
Amsterdam, 1972).
[37] S. Tamura, Phys. Rev., B 31, 2574 (1985).
[38] S. Tamura, H. J. Maris, Phys. Rev. B 31, 2595 (1985).
[39] C. Jacoboni, C. Reggiani, Rev. Mod. Phys., 55, 645 (1983).
[40] B. A. Danilczenko, M. I. Slutskii, Sov. Phys. Solid State, 30, 21 (1988).
[41] B. A. Danilchenko, W. M. Gańcza, Cz. Jasiukiewicz, Phys. Rev., B 60, 6113 (1999).
[42] Die Kunst of Phonons, Lectures from the Winter School of Theoretical Physics, eds. T. Paszkiewicz, K. Rapcewicz (Plenum, New York, 1994).
[43] A. T. Lee, B. Cabrera, B. L. Daugheity, J. Penn, Phys. Rev. Letters, 71, 1395 (1993).
[44] B. A. Danilchenko, S. N. Ivanov, D. V. Poplavskii, A.V. Taranov, E. N. Khazanov, Sov. Phys.
JETP, 85, 179 (1997).
