We performed inelastic neutron-scattering measurements on powdered Ni3Al. The alloy was prepared in two states of chemical order: (1) with equilibrium L1(2) order, and (2) with disorder (the material was a fee solid solution prepared by high-energy ball milling). Procedures to convert the energy loss spectra into approximate phonon density of states (DOS) curves for Ni3Al in the two states of chemical order were guided by Born-von Karman analyses with force constants obtained from previous single-crystal experiments on L Ii-ordered Ni,AI and fee Ni metal. The main difference in the phonon DOS of the ordered and disordered alloys occurs near 39 meV, the energy of a peak arising from optical modes in the ordered alloy. These high-frequency optical modes involve primarily the vibrations of the aluminum-rich sublattice. The disordered alloy, which does not have such a sublattice, shows much less intensity at this energy. This difference in the phonon DOS around 39 meV is the main contributor to the difference in vibrational entropy of disordered and ordered Ni3Al, which we estimate to be S-vib(dis)-S-vib(ord) = (+0.2+/-0.1)k(B)/atom at high temperatures.

The magnetic critical fluctuations in the d=2 random-exchange antiferromagnet ${\mathrm{Rb}}_{2}$${\mathrm{Co}}_{0.7}$${\mathrm{Mg}}_{0.3}$${\mathrm{F}}_{4}$ have been studied by neutron diffraction at temperatures both above and below the N\'eel temperature ${T}_{N}$=40.8 K. At temperatures above ${T}_{N}$, the line shape of the critical scattering is well described by the Lorentzian form, and the critical exponents \ensuremath{\nu} and \ensuremath{\gamma} for the inverse correlation length ${\ensuremath{\kappa}}^{+}$=${\ensuremath{\kappa}}_{0}^{+}$\ensuremath{\Vert}t${\ensuremath{\Vert}}^{\ensuremath{\nu}}$ and the staggered susceptibility ${\ensuremath{\chi}}^{+}$=${C}_{0}^{+}$\ensuremath{\Vert}t${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ are in good agreement with the values for the pure d=2 Ising model.The critical exponent \ensuremath{\beta}, which, along with the critical amplitude ${M}_{0}$, describes the temperature dependence of the d=2 long-range antiferromagnetic order just below ${T}_{N}$ through M=${M}_{0}$\ensuremath{\Vert}t${\ensuremath{\Vert}}^{\ensuremath{\beta}}$ is also in good agreement with the value of \ensuremath{\beta} for the pure d=2 Ising model. Furthermore, the combination of critical amplitudes ${R}_{s}$=${C}_{0}^{+}$(${\ensuremath{\kappa}}_{0}^{+}$${)}^{2}$/${M0}^{2}$, which, from the hypothesis of two-scale-factor universality, is a universal quantity also agrees well with the values of ${R}_{s}$ for the pure d=2 Ising model and the value of ${R}_{s}$ found experimentally for the pure d=2 Ising antiferromagnet ${\mathrm{K}}_{2}$${\mathrm{CoF}}_{4}$. The line shape of the critical scattering below ${T}_{N}$ has been analyzed both by using a Lorentzian form and by using the form proposed by Tarko and Fisher for the pure d=2 Ising model below ${T}_{N}$.The analysis using the Lorentzian form leads to a physically unreasonable description of the critical scattering below ${T}_{N}$ and hence to the conclusion that the Lorentzian form is an inappropriate description of the critical scattering below ${T}_{N}$ in a d=2 random Ising system. The results of the analysis using the Tarko-Fisher form provide a better description of the critical scattering below ${T}_{N}$ and the critical exponents for the inverse correlation length ${\ensuremath{\kappa}}^{\mathrm{\ensuremath{-}}}$=${\ensuremath{\kappa}}_{0}^{\mathrm{\ensuremath{-}}}$\ensuremath{\Vert}t${\ensuremath{\Vert}}^{\ensuremath{\nu}}$ and the staggered susceptibility ${\ensuremath{\chi}}^{\mathrm{\ensuremath{-}}}$=${C}_{0}^{\mathrm{\ensuremath{-}}}$\ensuremath{\Vert}t${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ agree well with the values for the pure d=2 Ising model. However, the values of the universal critical amplitude ratios ${\ensuremath{\kappa}}_{0}^{\mathrm{\ensuremath{-}}}$/${\ensuremath{\kappa}}_{0}^{+}$ and ${C}_{0}^{+}$/${C}_{0}^{\mathrm{\ensuremath{-}}}$, which result from this latter analysis, differ significantly from the values for the universality class of the pure d=2 Ising model. This difference in the amplitude ratios may arise because the d=2 random Ising model is in a different universality class than the pure d=2 Ising model or because the Tarko-Fisher form for the line shape may not be appropriate for the d=2 random Ising model below ${T}_{N}$.An investigation of this latter possibility using a modified version of the Tarko-Fisher form which preserved the amplitude ratio of the inverse correlation lengths at the pure d=2 Ising model value suggests that this is a strong possibility.

Results of inelastic neutron scattering experiments on a stage-2 and -4 graphite-${\mathrm{SbCl}}_{5}$ intercalation compound are reported. A one-dimensional Born---von K\'arm\'an model is applied to interpret the data. Comparison of the results for ${\mathrm{SbCl}}_{5}$-intercalated graphite with other recently reported neutron data for intercalation compounds suggests systematic trends in the magnitudes of the interactions.

A clear splitting, present only at low temperatures, is observed where the unperturbed phonon curve crosses the C${\mathrm{N}}^{\ensuremath{-}}$ ${T}_{1\mathrm{u}}$ and ${T}_{2\mathrm{u}}$ levels in a KCl crystal doped with 6\ifmmode\times\else\texttimes\fi{}${10}^{19}$ C${\mathrm{N}}^{\ensuremath{-}}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Calculated dispersion curves require coupling constants which agree within experimental uncertainty with those determined ultrasonically. The absence of the splitting at high temperatures can be explained because the phonon gain and loss processes in the interaction with the C${\mathrm{N}}^{\ensuremath{-}}$ level cancel almost completely.

The frequencies of certain normal modes of vibration of the graphite lattice have been studied on samples of high-quality pyrolytic graphite by coherent, inelastic-neutron-scattering techniques. Some of the data are not compatible with certain restrictions imposed by the valence-bond model as presented by Young and Koppel. Therefore, the data have been analyzed in terms of a simple axially symmetric, Born-von K\'arm\'an force-constant model. The results show that appreciable interactions exist between third nearest neighbors in the basal plane. The force model has been used to calculate a frequency distributio function and the lattice specific heat of graphite. These calculations are in excellent agreement with the specific heat measured for natural graphite in the temperature range 1.5-300\ifmmode^\circ\else\textdegree\fi{}K.

The spin-wave dispersion relation for the $c$ direction of dysprosium metal in the ferro-magnetic phase at 78\ifmmode^\circ\else\textdegree\fi{}K and in the helical magnetic phase at 98\ifmmode^\circ\else\textdegree\fi{}K has been measured by triple-axis neutron spectrometry. The energy gap measured in the ferromagnetic phase at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}=0$ is in poor agreement with that calculated from the macroscopic magnetostriction and crystal-field anisotropy constants. The Fourier-transformed exchange interaction $J(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})\ensuremath{-}J(0)$ in the ferromagnetic phase posses a peak near the wave vector that gives the periodicity of the helical structure just above the Curie temperature.

Spin-wave dispersion relations have been measured in high-symmetry directions for metallic Gd. Analysis shows that at least five interplanar constants are required for a satisfactory fit to the data. The energy gap at $q=0$ is unmeasurably small. In the $c$ direction the measured dispersion curve gives directly the Fourier-transformed exchange interaction $J(0)\ensuremath{-}J(q)$. This exhibits no other extreme value except that at the origin.

Phonon frequencies for wave vectors along the principal symmetry directions in copper have been determined at 49 and 298\ifmmode^\circ\else\textdegree\fi{}K from neutron inelastic-scattering measurements. In general, the temperature dependences of the frequencies were found to be smaller for the higher-frequency modes. For the lower frequencies ($\ensuremath{\nu}\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}{10}^{12}$ cps), the frequency changes measured are consistent with the 3-4% changes estimated from the isothermal elastic constants. For higher frequencies the relative changes are much smaller, often being 1% or less. Axially symmetric force models, which included interactions to the sixth nearest neighbors, were fitted to the data and have been used to calculate a frequency distribution function $g(\ensuremath{\nu})$ at each temperature. A comparison of the temperature dependences of the moments of these distributions with various Gr\"uneisen parameters leads to the conclusion that Cu does not satisfy the assumption of the quasiharmonic model. The Debye temperature ${\ensuremath{\Theta}}_{C}$ versus temperature curve calculated with the 49\ifmmode^\circ\else\textdegree\fi{}K $g(\ensuremath{\nu})$ is in excellent agreement with results from specific-heat measurements in the entire 0 to 298\ifmmode^\circ\else\textdegree\fi{}K range. A fairly strong temperature dependence for the widths of some well-focused phonons was observed.

x-ray intensity data have been obtained from aluminum single crystals at temperature intervals that were small enough to allow determination of $\frac{d(\mathrm{ln}I)}{\mathrm{dT}}$ in the 100-300\ifmmode^\circ\else\textdegree\fi{}K temperature range. From these measurements the temperature dependence of $\frac{\mathrm{dM}}{\mathrm{dT}}$ (or ${M}^{\ensuremath{'}}$), the temperature derivative of the Debye-Waller factor $M$ was determined. These derivatives are related in a straightforward way to the frequency distribution $g(\ensuremath{\nu})$ and hence to an equivalent characteristic temperature ${\ensuremath{\Theta}}_{{M}^{\ensuremath{'}}}$. Comparisons of experimental results with calculations based on actual approximate frequency distributions for aluminum indicate that the sensitivity of ${\ensuremath{\Theta}}_{{M}^{\ensuremath{'}}}$ to the shape of the frequency distribution can be experimentally significant. These experimental results for ${\ensuremath{\Theta}}_{{M}^{\ensuremath{'}}}$ are in very good agreement with calculations based on a frequency distribution derived by means of an 8-neighbor Born-von K\'arman force model from a previously reported analysis of neutron inelastic scattering data. Calculations using a simple one-neighbor force model based only on elastic constants were inadequate. In the 100-300\ifmmode^\circ\else\textdegree\fi{}K range the entire temperature dependence of the experimental ${\ensuremath{\Theta}}_{{M}^{\ensuremath{'}}}$ can be accounted for by anharmonicity associated with thermal expansion. The experimental and analytical techniques used make possible the determination, at a given temperature, of a relatively accurate and unambiguous value for ${\ensuremath{\Theta}}_{{M}^{\ensuremath{'}}}$. The determination does not depend on ${\ensuremath{\Theta}}_{{M}^{\ensuremath{'}}}$ values at other temperatures.

The experimental phonon-dispersion curves of aluminum at 80\ifmmode^\circ\else\textdegree\fi{}K and at 300\ifmmode^\circ\else\textdegree\fi{}K have been analyzed in terms of axially symmetric Born-von K\'arm\'an force-constant models, including 8 nearest neighbors. The resulting models have been used to compute a frequency distribution function $g(\ensuremath{\omega})$ at each temperature from which various thermodynamic properties have been derived. The specific-heat curve predicted by the $g(\ensuremath{\omega})$ appropriate to 80\ifmmode^\circ\else\textdegree\fi{}K fits excellently the experimental results in the temperature range 20 to 80\ifmmode^\circ\else\textdegree\fi{}K. At higher temperatures the experimental results deviate from this calculated curve and approach the curve appropriate to $g(\ensuremath{\omega})$ at 300\ifmmode^\circ\else\textdegree\fi{}K. Similar behavior is found for the experimental Debye-Waller coefficient in the range above 100\ifmmode^\circ\else\textdegree\fi{}K. It is concluded that inelastic-neutron-scattering data and thermodynamic data are compatible in the range of sufficiently low temperatures where deviations from the quasiharmonic approximation are small, provided a good force-constant model as well as a statistically adequate $g(\ensuremath{\omega})$ are available. There is evidence that the quasiharmonic approximation in aluminum is invalid at room temperature at least for the extreme low-frequency part of $g(\ensuremath{\omega})$.