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The normal mode Gruneisen gamma parameters have been measured for several modes of vibration of potassium at 4.5K over the pressure range 0.001 to 4.1 kbar, by means of coherent inelastic neutron scattering experiments. The results are compared with six different theoretical calculations based on a variety of screened pseudopotential models for the interionic forces in this simple metal, including a very recent calculation described in the following paper by Taylor and Glyde (ibid., vol.6, no.10, p.1915 (1976)). There is overall qualitative agreement between several theories and experiment, but significant discrepancies exist for four particular normal modes. Significant differences are also found between the present results for certain low frequency transverse modes and the analogous gamma values derived from the pressure dependence of the elastic constant C44 at room temperature.

The contributions to the dynamic form factor S(Q, omega ) arising from interference between its one-phonon and multiphonon parts have been observed in the scattering of neutrons from potassium. Interference makes two qualitatively distinct contributions to S(Q, omega ). One is approximately proportional to the one-phonon part, S1(Q, omega ), and contributes scattering intensity largely within the one-phonon peak region. The other is asymmetric around the one-phonon frequency and for narrowly peaked phonon groups contributes intensity of opposite sign in the multiphonon region directly on each side of the one-phonon peak. Both contributions, and their dependence on wavevector Q and frequency omega , can be described by an anharmonic theory (Ambegaokar et al. (1965)) which includes interference between the one- and two-phonon parts of S(Q, omega ) via the cubic anharmonic term.

In contrast to the three finite-frequency peaks in the dynamical structure factor S(ate) predicted in a recent computer-simulation study of aluminum at 800 K, the line shape observed by means of neutron scattering is smooth and exhibits a single narrow peak at each wave vector. The observed line shape is, however, in agreement with approximate analytical calculations based on self-consistent-phonon theory, using the same interatomic force model as employed in the computer simulation. These comparisons suggest that exact computer simulation on a finite lattice can produce artificial peaks or oscillations not characteristic of the real solid. We find that these artificial peaks are associated with long-time noise in the computer simulation of S(Q,t); their efFect on S(Q,co) can be minimized by use of a damping function. The study of anharmonic effects in solids, that is, the ways in which the lattice vibrations deviate from harmonic excitations having sharply defined, temperature-independent frequencies, is a subject of continuing interest. These effects are important in solids at elevated temperatures and in materials which exhibit large zero-point oscillations. Up to about 1968, as described in a review by Cowley, work in this field was primarily concerned with the measurement and theoretical calculation of the shift and width of phonon frequencies as a function of temperature. The studies of aluminum' and potassium' are examples of thi. s work. Subsequently the effect of pressure on phonon modes, for example in Rb, ' has been studied, and several investigations have been made of a very characteristic anharmonic effect on the onephonon scattering of both x rays and neutrons — the so-called one-phonon-two-phonon interference effect, ' which has been reviewed by Glyde. ' Once again we may cite as examples both aluminum" and potassium, ' in addition to the pioneering work on KBr, '" and also the studies of the 'He sol1ls 12

Elastic and inelastic neutron scattering measurements have been made on a single crystal of β‐N2 at 55 K and a pressure of 400 MPa. The integrated intensities of 34 Bragg reflections were measured and analyzed in terms of symmetry‐adapted harmonics. None of the coefficients of the higher‐order harmonics could be determined and, within experimental error, the N2 molecule is randomly oriented. No well‐defined librational modes were observed and even translational acoustic phonons are broad. The line shapes of translational acoustic phonons propagating along the hexagonal axis are analyzed in terms of both Gaussian and Lorentzian line shapes and in terms of the Michel–Naudts theory of rotation–translation interactions. In terms of the latter theory, β‐N2 is in the slow relaxation regime and has a strong rotation–translation interaction. The temperature dependence observed for four of these line shapes suggests that the librational excitations are no longer overdamped at 46 K. Values for three of the elastic ...

An attempt to observe inelastic neutron scattering from short; wavelength charge fluctuation modes in molten potassium bromide is described. Measurements were made using a triple axis crystal spectrometer with fixed scattered neutron energy (19 THz, or 78.6 meV) and scans were recorded at scattering angles between 2 degrees and 7 degrees . An analysis of the results indicates weak shoulders on each side of the elastic peak, corresponding to energy transfers about 4 THz. A calculation of the expected scattering, based on the computer simulation results of Hansen and McDonald (1975) is described, and the neutron scattering results are discussed in the light of this calculation.

A very simple model for the lattice dynamics of CS2 is presented. This model is fully stable for a unit cell distorted by no more than 2% from the measured cell and gives good agreement with lattice mode frequencies obtained from optical studies. Coulombic forces appear not to be important for this structure. The molecular motion in modes for all the special points in the Brillouin zone is described through the use of an explicit notation. The group theoretical work of Grout el al. is extended to give the full selection rules for coherent inelastic neutron scattering. These rules show that certain modes can be measured with minimal interference from scattering from modes of different symmetry when certain experimental conditions are adopted, and therefore these rules will be of great use in the neutron scattering studies now in progress.

The frequency/wave-vector dispersion relation for normal modes of vibration propagating along the [00ζ], [ζζ0], and [ζζζ] directions in uranium dioxide at 296 °K has been determined by studying the coherent one-phonon scattering of slow neutrons from a single-crystal specimen. Analysis of the results shows that a simple rigid-ion model of the crystal with axially symmetric forces between near-neighbor ions can provide qualitative agreement with experiment. A more complicated model, in which the ionic polarizabilities are taken into account, is needed to obtain quantitative agreement with the dispersion curves and with the known dielectric properties. Such a model provides an interpolation formula for computing the frequency distribution function and other related quantities, such as the Debye–Waller factors and lattice specific heat. Information concerning the anisotropy of the Debye–Waller factor for the oxygen ions and the configuration of the "magnetic" electrons in UO2 is derived by comparing these calculations with the appropriate experimental data. The optic-mode frequencies and dielectric constants of UO2 are shown to satisfy the Lyddane, Sachs, and Teller relation. The slopes of the acoustic-mode branches at small wave vectors are consistent with independently measured elastic constants.

A beam of filtered neutrons with a mean wavelength of 8·4 A has been used to measure the total cross section of lead as a function of temperature from 290°k to 840°k. The cross section is found to vary linearly with temperature in both solid and liquid phases to within 1°k of the melting point. There is a jump in cross section at the melting point of (9·44 ± 0·6)%. The results in the solid are not in agreement with predictions based on the Debye theory.

The dispersion relation for the longitudinal acoustic lattice waves propagating in the direction of the hexad axis in (pyrolitic) graphite, at room temperature, has been determined by neutron spectrometry. The dispersion curve has very closely the form of a sine curve, with a maximum frequency of (3.84\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}${10}^{12}$ cps, for the zone-boundary phonon of wavelength $c=6.70$ \AA{}. The transverse acoustic lattice waves were less well determined, but show roughly similar behavior with a maximum frequency at the zone boundary of (1.3\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{12}$ cps. Values for certain elastic constants have been deduced from the measurements: in units of ${10}^{11}$ dyn/${\mathrm{cm}}^{2}$, ${C}_{33}=3.9\ifmmode\pm\else\textpm\fi{}0.4$, and ${C}_{44}=0.42\ifmmode\pm\else\textpm\fi{}0.2$.

The frequency wave-vector dispersion relation for the normal modes of vibration of ${\mathrm{Li}}^{7}$F at 298\ifmmode^\circ\else\textdegree\fi{}K has been measured by means of slow-neutron inelastic scattering techniques. Triple-axis crystal spectrometers at two reactor facilities at the Oak Ridge National Laboratory were employed, mostly in the "constant-Q" mode of operation. The results can be satisfactorily fitted by a seven-parameter dipole approximation model involving nearest-neighbor and second-nearest-neighbor ${\mathrm{F}}^{\ensuremath{-}}$-${\mathrm{F}}^{\ensuremath{-}}$ short-range forces, a variable ionic charge, and the polarizability of the ${\mathrm{F}}^{\ensuremath{-}}$ ions only. The applicability of other force models to ${\mathrm{Li}}^{7}$F is also discussed. Certain inconsistencies have been found between the slopes of the acoustic branches near q=0 and the appropriate velocities of sound as measured by ultrasonic techniques. It is believed that these arise from anharmonic effects. The frequency distribution of the normal modes has been computed with high precision from the best-fit dipole approximation model, together with related quantities such as the lattice heat capacity, entropy, and Debye-Waller factors for each ion. Combined (two-phonon) density-of-states functions have also been calculated; comparisons are made between these one- and two-phonon distribution functions and certain features observed in optical and infrared absorption experiments on LiF.

Measurements have been made of phonon frequencies and widths in β-brass at 296°K, 499°K, 714°K and 751°K, using neutron spectrometry. These properties vary smoothly with temperature and show no large discontinuities near the order-disorder phase transition. A possible correlation between the phonon lifetimes and the degree of short range order is discussed.

Recent neutron diffraction data are used to investigate triplet correlations in liquid argon by means of a method suggested by Egelstaff et al . A careful analysis is made of the errors involved and it is found that the superposition approximation generally overestimates the magnitude of triplet correlations and that the deviations are largest for nearest-neighbour triplet configurations.

The magnetic excitations of UO2 have been measured by inelastic neutron‐ scattering techniques with the triple‐axis crystal spectrometer at the C5 facility of NRU. On increasing the temperature, the neutron groups from the modes of higher (>1.5×1012 Hz) frequency decreased slightly in frequency, barely increased in width, but decreased markedly in intensity, and were not observable above TN[(30.5±0.5)°K for our specimen]. For example the results for the frequencies of the modes with scattering vector Q = (0.5, 0.5, 2.5)2π/a are (ν(T)×1012 Hz): ν(9) = 2.02±0.03, ν(21) = 2.00±0.04, ν(25.3) = 1.95±0.05, ν(27.0) = 1.75±0.05, ν(29.5) = 1.50±0.07. The neutron groups from the modes with lower frequencies decreased more markedly in frequency, but also showed little increase in width and were not observed above TN. The experiments indicate that the modes of lowest frequency which appeared to have almost zero frequency at TN are closely associated with the transition. These measurements, together with the strong ma...

The dispersion relation for the normal modes of vibration propagating along the [$\ensuremath{\zeta}00$], [$\ensuremath{\zeta}\ensuremath{\zeta}\ensuremath{\zeta}$], and [$0\ensuremath{\zeta}\ensuremath{\zeta}$] directions in a single crystal of pure gallium arsenide at 296\ifmmode^\circ\else\textdegree\fi{}K has been determined by neutron spectrometry. The frequencies (units ${10}^{12}$ cps) of specific modes are (a) (0,0,0): $\mathrm{TP} 8.02\ifmmode\pm\else\textpm\fi{}0.08$, $\mathrm{LO} 8.55\ifmmode\pm\else\textpm\fi{}0.20$; (b) (1,0,0): $\mathrm{TO} 7.56\ifmmode\pm\else\textpm\fi{}0.08$, $\mathrm{TA} 2.36\ifmmode\pm\else\textpm\fi{}0.015$, $\mathrm{LO} 7.22\ifmmode\pm\else\textpm\fi{}0.15$, $\mathrm{LA} 6.80\ifmmode\pm\else\textpm\fi{}0.06$; (c) (0.5,0.5,0.5): $\mathrm{TO} 7.84\ifmmode\pm\else\textpm\fi{}0.12$, $\mathrm{TA} 1.86\ifmmode\pm\else\textpm\fi{}0.02$, $\mathrm{LO} 7.15\ifmmode\pm\else\textpm\fi{}0.07$, $\mathrm{LA} 6.26\ifmmode\pm\else\textpm\fi{}0.10$. The results are analysed in terms of the dipole approximation model. Although a fairly complex version of this model provides a satisfactory description of most of the data, certain significant discrepancies remain. These indicate that the neglect of quadrupole interactions is a serious weakness of the dipole approximation model.