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An x-ray back-reflection, rotating-camera technique has been used to obtain lattice constants and thermal expansivities of single-crystal silicon and calcium fluoride. Absolute expansivity was obtained over a broad range with an error less than 3 ppm. For silicon, this absolute method discriminates between earlier experiments showing some disagreement, and establishes with improved precision the temperature variation of the Grüneisen parameter γ in the region of particular interest (γ<0). For calcium fluoride the present x-ray measurements test a prediction of Ganesan and Srinivasan that γ should rise sharply below about 80°K. The prediction is not confirmed.

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We report new path-integral calculations and measurements of the kinetic energy of condensed helium and construct an overall dependence of kinetic energy on temperature for densities less than 70 atoms nm 23 . In the solid phase we find the kinetic energy is almost temperature independent and, surprisingly, has a smaller kinetic energy than the fluid near freezing at the same density. In the high temperature fluid phase, the excess kinetic energy decreases to zero very slowly because of pair scattering from the repulsive interatomic potential. [S0031-9007(96)00592-3] PACS numbers: 64.70.Dv, 61.12.Ex, 67.20.+k, 67.80.Gb The momentum distributions of the condensed isotopes of helium have been a matter of widespread interest for many years because of their connections with the theories of Bose condensation and of Fermi liquids. In this Letter we consider only the second moment of the momentum distribution, the kinetic energy E k . In contrast to the potential energy, the kinetic energy of a many-body system has distinctly different properties in the classical regime (Maxwellian), the quantum liquid, the crystal (Debye-like), the superfluid (Bose condensation), and for liquid 3 He (Fermi-liquid behavior). Helium is a nearly ideal system in which to study the variation of these quantum effects because of the wide range of densities, temperatures, and phases that can be achieved experimentally and retained stably in the laboratory (unlike, for example, nuclear matter or lasercooled ions). The kinetic energy is difficult to measure directly; inelastic (quasielastic) neutron scattering at high momentum transfers is probably the best way. On the theory side, the interatomic potential of helium is better known [1] than for any other atomic and molecular system, and for bosonic 4 He one has a well-developed and highly accurate simulation method, path integral Monte Carlo (PIMC) [2]. Hence, 4 He is the simplest quantum system for which to make accurate comparisons of theory and experiment.Here we make a critical comparison between various experiments and the PIMC theory and draw conclusions about the behavior of the kinetic energy upon melting and at higher temperatures. We first recapitulate our experimental and theoretical methods, and show that the results are in agreement. We then summarize our comprehensive picture of the kinetic energy of 4 He and comment on recent experiments.With the advent of intense pulsed neutron sources, direct measurement of single-particle momentum distributions is possible within the limit of the impulse approximation [3]. Then the dynamic structure factor S͑Q, E͒ for a target of mass m can be scaled to the longitudinal neutron Compton profile J͑ y, Q͒ using the variable y ͑m͞h 2 Q͒͑E 2h 2 Q 2 ͞2m͒Ô, whereÔ is a unit vector in the direction of the wave-vector transfer Q. Within this limit, S͑Q, E͒ is proportional to the longitudinal momentum distribution n͑ p͒. An early search [4] for a change in kinetic energy upon melting in 4 He used a comparison of pulsed neutron scattering from a liqui...

T h e simple ceramic processes of grinding and pelleting leave residual stresses in common materials such as SiOa and BaTi03. The magnitude of these stresses is easily detected by changes in the temperature of phase transitions ; such processes are enough to completely eliminate the phase transitions.

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