Generalized Susceptibility of Mixed Dislocation in Ferroelastics near Structural Phase Transition

Abstract:

Bending vibrations of a mixed dislocation in ferroelastics near structural phase transition were considered. It was assumed that the dislocation line performs small bending vibrations near equilibrium position. Complete system of equations describing the vibrations of a mixed dislocation near the structural phase transition is written. Based on these set of equations describing the vibrations of a crystal with a dislocation near the structural phase transition, written equations for dynamics of the mixed dislocation in linear approximation of dislocation displacement. Fourier transform of these equations is satisfied. Expression for Peach-Kohler force acting on the dislocation is obtained, and linear response function (generalized susceptibility) of the mixed dislocation in ferroelastics is found.

• Periodical: Key Engineering Materials (Volume 887)
• Pages: 610-615
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.887.610
• Online since: May 2021
• Authors: V.V. Dezhin*
• Keywords: Bending Vibrations, Ferroelastics, Generalized Susceptibility, Mixed Dislocation

References

[1] A.D. Bruce, R.A. Cowley, Structural Phase Transition, Taylor & Francis, London, (1981).

[2] E.K.H. Salje, Phase Transitions in Ferroelastic and Co-elastic Crystals, Cambridge University Press, Cambridge, (1990).

[3] V.K. Wadhawan, Introduction to Ferroic Materials, CRC Press, Boca Raton, (2000).

[4] E.K.H. Salje, Ferroelastic materials, Annual Review of Materials Research. 42 (2012) 265-283.

[5] L.D. Landau, E.M. Lifshtz, Course of Theoretical Physics, Vol 5, Statistical Physics Part 1, Butterworth-Heinemann, Oxford, (1980).

[6] V.L. Ginzburg, A.P. Levanyuk, A.A. Sobyanin, Comments on the region of applicability of the Landau theory for structural phase transitions, Ferroelectrics. 73 (1987) 171-182.

DOI: 10.1080/00150198708227916

[7] A.P. Levanyuk, A.S. Sigov, Defects and Structural Phase Transitions, Gordon and Breach Science Publishers, New York, (1988).

[8] A.P. Levanyuk, V.V. Osipov, A.S. Sigov, A.A. Sobyanin, Change of defect structure and the resultant anomalies in the properties of substances near phase-transition points, Sov. Phys. JETP. 49 (1979) 176-188.

[9] I.M. Dubrovskii, M.A. Krivoglaz, Phase transitions of the second kind in crystals containing dislocations, Sov. Phys. JETP. 50 (1979) 512-520.

[10] A.P. Levanyuk, A.S. Sigov, A.A. Sobyanin, The influence of defects on the properties of solids near phase transition points, Ferroelectrics. 24 (1980) 61-66.

DOI: 10.1080/00150198008238623

[11] M.V. Belousov, B.E. Volf, The effect of dislocations on the phase transition and scattering of light near the phase transition in a NH4Br crystal, Sov. Phys. JETP Lett. 31 (1980) 317-321.

[12] V.I. Alshitz, M.D. Mitlyanskii, Interaction of moving dislocation with a soft phonon mode in a displacement-type phase transition, Sov. Phys. JETP. 51 (1980) 1042-1044.

[13] A.P. Levanyuk, N.V. Shchedrina, Anomalies of the phonon drag of dislocations near phase transition points, Sov. Phys. Solid State. 25 (1983) 1338-1341.

[14] Yu.M. Kishinets, A.P. Levanyuk, A.S. Sigov, Dislocation contribution to the anomalies of physical properties of crystals near the points of structural phase transition, Sov. Phys. Crystallogr. 30 (1985) 487-490.

[15] A.E. Koshelev, Dislocations and structural phase transitions involving an increase in the elementary cell, Sov. Phys. JETP. 64 (1986) 1099-1104.

[16] Yu.M. Kishinetz, A.P. Levanyuk, A.I. Morosov, A.S. Sigov, Dislocatioj-induced anomalies of physical properties of crystals near structural phase transition, Ferroelectrics. 79 (1988) 27-30.

DOI: 10.1080/00150198808229391

[17] V.V. Gorbunov, V.N. Nechaev, Retardation of dislocations by the Cherenkov mechanism in crystals with a soft mode, Soviet Physics Journal. 31 (1988) 1002-1006.

DOI: 10.1007/bf01101171

[18] A.A. Boulbitch, P.E. Pumpyan, Local phase transition at a moving dislocation, Sov. Phys. Crystallogr. 35 (1990) 156-158.

[19] A.L. Korzhenevskii, R. Bausch, R. Schmitz, Dynamic instability of dislocations due to nucleation of a new phase, Phys. Rev. E 63 (2001) 056105.

DOI: 10.1103/physreve.63.056105

[20] A.L. Korzhenevskii, R. Bausch, R. Schmitz, Dislocation drag close to a phase transition, Phys. Rev. B 67 (2003) 100103.

DOI: 10.1103/physrevb.67.100103

[21] T. Ninomiya, Dislocation vibration and phonon scattering, J. Phys. Soc. Japan. 25 (1968) 830-840.

DOI: 10.1143/jpsj.25.830

[22] T. Ninomiya, Eigenfrequencies in a dislocated crystal, in: J.A. Simmons, R. de Wit, R. Bullough (Eds.), Fundamental aspects of dislocations theory, Vol 1, US Nat. Bur. Stand. Spec. Publ. 317, Washington, 1970, pp.315-357.

[23] V.V. Dezhin, V.N. Nechaev, A.M. Roshchupkin, Generalized dislication susceptibility in a crystal with soft mode, Fizika Tverdogo Tela. 32 (1990) 810-817.

[24] V.V. Dezhin, V.N. Nechaev, A.M. Roshchupkin, Generalized susceptibility of dislocations in ferroelectrics and ferromagnetics, Z. für Kristallographie. 193 (1990) 175-197.

DOI: 10.1524/zkri.1990.193.3-4.175

[25] I.L. Bataronov, V.V. Dezhin, V.N. Nechaev, Dynamic characteristics of dislocations in soft-mode crystals, Bull. Russian Academy Sciences: Physics. 62 (1998) 1223-1227.

[26] V.N. Nechaev, V.V. Dezhin, The bending vibrations equation of a screw dislocation in ferroelastic near the phase transition point, Vestnik Tambovskogo Universiteta. Ser.: Estestv. i tehnich. nauki. 21(3) (2016) 1188-1190.

DOI: 10.20310/1810-0198-2016-21-3-1188-1190

[27] V.V. Dezhin, V.N. Nechaev, Generalized susceptibility of a screw dislocation in ferroelastics near structural phase transition, J. Phys.: Conf. Ser. 1391 (2019) 012161.

DOI: 10.1088/1742-6596/1391/1/012161

[28] E. Kröner, Der fundamentale Zusammenhang zwischen Versetzungsdichte und Spannungsfunktionen, Z. Phys. 142 (1955) 463-475.

DOI: 10.1007/bf01375082

[29] L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, Vol 7, Theory of Elasticity, Butterworth-Heinemann, Oxford, (1986).

[30] I.L. Bataronov, V.V. Dezhin, On the natural small vibrations of dislocation in an isotropic medium, J. Phys.: Conf. Ser. 936 (2017) 012035.

DOI: 10.1088/1742-6596/936/1/012035