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By M Ristic, K Gernoth

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21) T From the partial Gibbs energy of formation g(P, T ), the partial free volume of vacancy formation is given by v(P, T ) = − ∂g ∂P . (22) T At a given P , V , and T , equilibrium vacancy content c is independent of whether the state was reached under isobaric or isochoric conditions or some other path, and hence there f = g. At this state one therefore has p=− ∂g ∂P T ∂P ∂V = −v T ∂P ∂V = T v BT , V (23) where BT is the isothermal bulk modulus. A useful empirical relation involves the isothermal bulk modulus.

S. T. O. Simmons: (to be published). 83. A. V. O. Simmons: J. Non–Cryst. Solids 205–207, 216 (1996). 84. A. O. Simmons: Phys. Rev. B 36, 97 (1987); Phys. Rev. B 37, 5058 (1988). N. O. Simmons: J. Low Temp. Phys. 68, 125 (1987). The One- and Two-Body Densities of Crystalline Matter and Bragg and Diffuse Scattering of Neutrons and X-Rays Klaus A. O. Box 88, Manchester M60 1QD, United Kingdom Abstract. This work presents a theoretical treatment of the Bragg and diffuse scattering of an incident double-beam of neutrons or X-rays from crystalline matter.

References 1. O. Simmons: Z. Naturforsch. 48a, 415 (1993). 2. O. Simmons: ‘Neutron experiments on helium’. In: Erforschung der Dynamik kondensierter Materie mit Synchrotronstrahlung, ed. by E. Burkel, W. Sch¨ ulke (Univ. Rostok, Rostock 1998), Vol II, pp. F4/1–33. 3. C. M. O. Simmons: Z. Naturforsch. 48a, 433 (1993). 4. M. C. O. Simmons: Phys. Rev. Lett. 77, 115 (1996). 5. A. Gernoth: ‘The One- and Two-Body Densities of Crystalline Matter and Bragg and Diffuse Scattering of Neutrons and X-Rays’.

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Particle Scattering, X-Ray Diffraction And Microstructure Of Solids And Liquids by M Ristic, K Gernoth

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