Tham khảo tài liệu 'mesoscopic non-equilibrium thermodynamics part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Phonon Participation in Thermodynamics and Superconductive Properties of Thin Ceramic Films 321 where Hs 2M EE p y 0 VMM x nx ny Pnx ny Nz 1 ECa E unxnv 0 nx ny a 2 a nx ny Nz nx ny Nz 1 u a unx ny Nz 2 unx ny 1 ua unx ny 0 a unx ny 0 a unx 1 ny 0 a unx ny 0 a unx 1 y 0 4 a unx ny 0 a unx ny 1 0 a unx ny 0 a nx ny 1 0 nx ny Nz a 2 nx ny Nz Hb X unx 1 ny Nz nx ny Nz a unx 1 ny Nz a 2 un n nx ny Nz a 2 unx ny 1 Nz 2M EE pZ nyn nx ny 2 1E c X a Nz E E nx ny a 1 n 1 nn a 2 un n n a unx 1 ny nz a 2 un n n unx ny 1 n Nz a unx ny nz a nx ny 1 nz a unx ny nz 5 F 2 E unx ny nz 1 z 2 nz a a 2 un n n a un n n 1 a 2 un_ n nx ny Nz 1 u nx ny Nz unx nv 1 n a unx ny 2 We have decided to use the approach of Heisenberg s equations of motion Tosic et al. 1992 Setrajcic et al. 1992 Setrajcic Pantic 1994 for the determination of possible frequencies energy spectrum and the states of phonons. We start from the following system of the equations of motion for the phonon displacements - for nz 0 2 unx ny 0 ila unx 1 ny 0 unx-1 ny 0 unx ny 1 0 unax ny-1 0 unax ny 1 - 6uníx nyỌ 0 6 - for 1 nz Nz 1 2 unx ny nz íỉa unx 1 ny nz unx 1 ny nz unx ny 1 nz unx ny 1 nz unax ny nz 1 unax ny nz 1 unx ny n 0 7 322 Thermodynamics - for nz Nz u a nx ny Nz 2 a a a unx 1 ny Nz unx-1 nv Nz unx nv 1 Nz unx nv-1 Nz unx nv Nz-1 - 6unx nv N - 8 where Qa ựCa M. The solution of this system of Nz 1 homogeneous differential-difference equations for phonon displacements can be looked for in the form of the product of an unknown function along z-axis and harmonic function of the position within XY-plane known from the bulk solutions . TO 1 a t V id ia kxnx kyny -it w 4 a 4 a 4 a fk 9 unx ny nz t L dw e 4nz 4nz 4nz kz w . 9 kx ky kz- Substituting this expression into the equations 6-8 we obtain R a 4a a R a a 0 0 4na-1 R4 4na 1 nz -1 nz nz 1 0 10 4Nz 2 R 4Nz-1 4Nz 0 4 Nz 1 R 4 a 0 where w _ _ ọakx . 0 ak R W 4Fkxky 2 Wa w Fkxky sin2 sin2 . 11 In this way the system of Nz 1 differential-difference equations 6-8 .
