Linear Specific Heat of Disordered Solids at Low Temperatures

Thermal expansion of glasses at low temperatures

“…Equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11) and (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) give (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) in good functional agreement with experimental data and a previous handwaving derivation. The total tunneling GrUneisen parameter (Equation (1-13)) can be evaluated using the mean-value theorem as…”

“…( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The GrUneisen parameter associated with the asymmetry, y!J., may be assumed to be "normal" ( (the symmetric case), y(!J., !J.) will be approximately y(!J.)…”

“…This requires that a minimum value of 6 (!\ . ) be adopted to prevent Equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) and (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) from o om1n…”

Thermal expansion of glasses at low temperatures

“…( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] in good functional agreement with experimental data and a previous handwaving derivation. The total tunneling Gruneisen parameter (Equa tion (1-13)) can be evaluated using the mean-value theorem as…”

“…Several theories (5)(6)(7)(8)(9)(10)(11)(12)(13) have been proposed to explain the unusual thermal behavior of glasses at low temperature, with the simple postulate of a slowly varying continuous distribution in energy of two level states (14)(15)(16)(17) giving the best agreement with existing experimental data.…”