Fundamental Aspects of Nuclear Reactor Fuel Elements (Tid by D. Olander

By D. Olander

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1 _(_L3] 33 particles in each energy state: 1 nj - exp[(e --p)/kT] + 1 where j denotes a particular electron state (specified by the three translational quantum numbers and the spin quantum number) and p is the chemical potential of the electron gas. The latter is determined from the condition that the sum of the Tj must be equal to the total number of conduction electrons in the solid (Eq. [ r1 =(9e 2 )1 (@ 3d The minus sign in Eq. 7 indicates that the electronic charge uniformly distributed about the point positive charge is a lower energy configuration than the separated point charges.

The cohesive energy of the metal is obtained by evaluating the total energy at r, = roeq: 27/4 )%e 4 m Ecoh = U(roeq) =--- 40 ]-- •--=-5eV 11 Experimental values of Ecoh from Eq. 22) (which is the ionization energy, I) should be small. 21) is called the electron affinity, A. 24) COHESIVE ENERGY OF SOLIDS for which energy equal to I + A is required. , I+ A is not negative). However, electron transfer proceeds readily in the solid because of the additional stabilizing effect of the electrostatic attraction of the oppositely charged ions when they are close together.

42 according to the method described in connection with Eq. 16 yields the expression for Z given by Eq. 19. Differentiation of Eq. 19 with respect to hvi and insertion into Eq. 45 yields Ji- (ehvi/kT [- (j ihvp +... + jihpi +... 43) The average number of phonons in a particular state i may be obtained by treating P as a distribution function: ji (i, . ii... Jii j3N-) P(0h ... 46) which is the Planck distribution function, or the distribution function for Bose-Einstein particles with zero chemical potential.

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