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110. On the approach to equilibrium of quantum gases
EQUATION OF STATE
S 169
complete series of solid solutions in a system where the pure components have different crystal structures, cubic for solid argon and hexagonal for fl-nitrogen. A determination of the condensed phase diagram in this system b y thermal analysis has indicated the existence of a thermal halt of the peritectic type. Optical examination of the solids formed from argon-nitrogen mixtures has further demonstrated a change in structure as would be expected from a peritectic system. 1) Din, Goldman and Monroe, Proceedings Commission I, 9th International Congress of Refrigeration, 1-003, Paris (1955).
110. On t h e a p p r o a c h to e q u i l i b r i u m of q u a n t u m g a s e s . I. PRIGO'GINE and P. RgSlBOIS. Universit6 Libre de Bruxelles, Belgium. W e study the approach to equilibrium of an homogeneous quantum gas. W e suppose the concentration sufficiently low for the equilibrium properties to be described by a perfect Bose-Einstein (or Fermi-Dirac) gas. Starting from the formal solution of the V o n lqeumann equation and using diagram techniques, we derive a transport equation; the transition probabilities are complex functions of the occupation numbers when realistic interactions (like hard spheres interactions) are used. We find in this way, apart from the well known terms of the Uhlenbeck-Uehling type, describing the effect of the statistics on the final states, new terms due to symmetry effects in the intermediate states. This formalism is used to study the problem of singularities in the transport properties at the A-point.
VI. T R A N S P O R T
PHENOMENA
IN SOLIDS
U l . H e a t c o n d u c t i v i t y of LiF w i t h v a r y i n g c o n c e n t r a t i o n s R. BERMAN. Clarendon Laboratory, Oxford, England.
of 6Li and 7Li.
Although the scattering of single phonons by isotopes can be calculated, the evaluation of the resulting thermal resistance is difficult because this involves the whole spectrum of m u t u a l l y interacting phonons. Z i m a n 1) has shown how an upper limit of resistance can be calculated; for relatively small isotope scattering the actual resistance will be equal to this, b u t for larger concentrations the resistance should increase less rapidly t h a n c(1 -- c). Measurements in progress on LiF crystals, in which the 8Li concentration varies from 5 to 90%, confirm this theory: as c (or 1 -- c) approaches zero the resistance agrees well with the upper limit, and with c increasing the resistance falls below proportionality to c(l -- c). For c = 0.5 the resistance is about one-tenth of the calculated upper limit. 1) Ziman, J. M., Canad. J. Phys. 34 (1956) 1256.
112. T h e l a t t i c e h e a t c o n d u c t i v i t y of c o p p e r - z i n c a l l o y s . Miss J. N. LOMER and H. IV[.ROSENBERG. The Clarendon Laboratory, Oxford, England. The heat conductivity of copper-zinc single crystals (with up to 30% Zn) has been measured in the range 2 to 90°K and from tb".se results the lattice heat conductivity,
S 169
complete series of solid solutions in a system where the pure components have different crystal structures, cubic for solid argon and hexagonal for fl-nitrogen. A determination of the condensed phase diagram in this system b y thermal analysis has indicated the existence of a thermal halt of the peritectic type. Optical examination of the solids formed from argon-nitrogen mixtures has further demonstrated a change in structure as would be expected from a peritectic system. 1) Din, Goldman and Monroe, Proceedings Commission I, 9th International Congress of Refrigeration, 1-003, Paris (1955).
110. On t h e a p p r o a c h to e q u i l i b r i u m of q u a n t u m g a s e s . I. PRIGO'GINE and P. RgSlBOIS. Universit6 Libre de Bruxelles, Belgium. W e study the approach to equilibrium of an homogeneous quantum gas. W e suppose the concentration sufficiently low for the equilibrium properties to be described by a perfect Bose-Einstein (or Fermi-Dirac) gas. Starting from the formal solution of the V o n lqeumann equation and using diagram techniques, we derive a transport equation; the transition probabilities are complex functions of the occupation numbers when realistic interactions (like hard spheres interactions) are used. We find in this way, apart from the well known terms of the Uhlenbeck-Uehling type, describing the effect of the statistics on the final states, new terms due to symmetry effects in the intermediate states. This formalism is used to study the problem of singularities in the transport properties at the A-point.
VI. T R A N S P O R T
PHENOMENA
IN SOLIDS
U l . H e a t c o n d u c t i v i t y of LiF w i t h v a r y i n g c o n c e n t r a t i o n s R. BERMAN. Clarendon Laboratory, Oxford, England.
of 6Li and 7Li.
Although the scattering of single phonons by isotopes can be calculated, the evaluation of the resulting thermal resistance is difficult because this involves the whole spectrum of m u t u a l l y interacting phonons. Z i m a n 1) has shown how an upper limit of resistance can be calculated; for relatively small isotope scattering the actual resistance will be equal to this, b u t for larger concentrations the resistance should increase less rapidly t h a n c(1 -- c). Measurements in progress on LiF crystals, in which the 8Li concentration varies from 5 to 90%, confirm this theory: as c (or 1 -- c) approaches zero the resistance agrees well with the upper limit, and with c increasing the resistance falls below proportionality to c(l -- c). For c = 0.5 the resistance is about one-tenth of the calculated upper limit. 1) Ziman, J. M., Canad. J. Phys. 34 (1956) 1256.
112. T h e l a t t i c e h e a t c o n d u c t i v i t y of c o p p e r - z i n c a l l o y s . Miss J. N. LOMER and H. IV[.ROSENBERG. The Clarendon Laboratory, Oxford, England. The heat conductivity of copper-zinc single crystals (with up to 30% Zn) has been measured in the range 2 to 90°K and from tb".se results the lattice heat conductivity,