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6. LOW-TEMPERATURE PROPERTIES OF NON-CRYSTALLINE SOLIDS

6. LOW-TEMPERATURE PROPERTIES OF NON-CRYSTALLINE SOLIDS T > 1 K : other low-frequency excitations, “soft modes”, and the Soft-Potential Model. T > 1 K ?. U. Buchenau e t al ., Phys.Rev. B34 , 5665 (1986). Basic assumptions of the SOFT-POTENTIAL MODEL:.

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6. LOW-TEMPERATURE PROPERTIES OF NON-CRYSTALLINE SOLIDS

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  1. 6. LOW-TEMPERATURE PROPERTIES OF NON-CRYSTALLINE SOLIDS T > 1 K: other low-frequency excitations, “soft modes”, and the Soft-Potential Model

  2. T > 1 K ? U. Buchenau et al.,Phys.Rev. B34, 5665 (1986)

  3. Basic assumptions of the SOFT-POTENTIAL MODEL: V(x) = W (D1 x + D2 x2 + x4 ) (i) The soft modes can on average be characterized by a single energy W (ii) D1 and D2 are randomly distributed around the origin of the D1 - D2 plane:  P(D1 , D2) = P(0, 0) Ps (iii) The interaction between the soft modes and the sound waves is bilinear in the displacement of the soft mode and in the strain field of the sound wave: Vl,t = l,txl,t

  4. V(x) = W (D1 x + D2 x2 + x4 ) D2 < 0 V(x) = Wx4 D2=D1=0 D2 > 0

  5. TUNNELING MODEL  SOFT POTENTIAL MODEL  SPM universal constants:

  6. SOFT-POTENTIAL MODEL: Specific heat

  7. SPM fit: { ,

  8. M.A.R. ,Philos. Mag. (2004)

  9. CALCULATION OF THE THERMAL CONDUCTIVITY ( ) ( ( ) ( )

  10. Tc SPM M.A.R. and U. Buchenau, Phys. Rev. B55, 5749 (1997)

  11. L. Gil et al.,Phys. Rev. Lett.70, 182 (1993)

  12. Ioffe-Regel limit: phonon localization when its mean free path decreases down to half the wavelength: for Brillouin scattering: SPM

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