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T h e value of ΔΗ® for Fe is estimated indirectly. a b 1. Experimental Methods There are relatively few techniques capable of accurately measuring the equilibrium concentration of vacancies. As a rule, one measures only the enthalpy of formation as the result of varying some specific property which reflects the concentration as a function of temperature. A. Quenching T h e most common technique applied to metals for the measurement of vacancy concentrations is to quickly quench a wire made from the material of interest from a succession of temperatures and measure the change in electrical resistance at liquid He temperature, which is proportional to the change in vacancy concentration, which in turn is a function of the initial annealing temperature.

Phys. 15, 1 (1943), goes far beyond the mathematical knowledge needed for this text. Nevertheless, C h a p t e r 1, pages 1-20 is one of the best and most rigorous derivation of the relation b e t w e e n diffusion and r a n d o m walks. II Point Defects in Elemental Crystalline Substances All real crystals are imperfect containing both line and point defects and this chapter is devoted to their energetics because of their frequent and important role in solid state diffusion. The former, most commonly referred to as dislocations, have a minor influence on the chemistry of solids; although they are dominant in governing the strength properties and are frequently influential in the nucleation of phase transformations; we will consider their influence upon diffusion briefly in a later chapter.

C. Positron Annihilation Another technique which has been used successfully for determining the enthalpy of vacancy, and even divacancy, formation is based upon positron-electron annihilation. Unlike the conventional quenching tech­ nique, positron annihilation can measure defect concentrations under equi­ librium conditions and over wider ranges of temperature than dilatometric methods. 511 MeV gamma rays. If the electron and positron annihilate as free (unbound) particles and without appreciable relative kinetic energy, the two gamma rays will be emitted in exactly opposite J .

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