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Photonic metamaterials are man-made materials with "lattice constants" smaller than the wavelength of light. Tailoring the properties of their functional building blocks (atoms) allows one to go beyond the possibilities of usual materials. For example, magnetic dipole moments at optical frequencies (mune1) become possible. This aspect substantially enriches the possibilities of optics and photonics and forms the basis for the so-called negative-index metamaterials. Here, we describe the underlying physics and review the recent progress in this rapidly emerging field

Canada's pre-eminent neutron source since 1957 has been the NRU reactor at Chalk River. It is unlikely to operate beyond the year 2005. In 1994, AECL prepared the case and concept for a new research reactor, the Irradiation Research Facility (IRF), to replace NRU. The IRF was developed with the dual purpose of meeting the needs of both R&D programs to support existing and advanced CANDU® designs and also of condensed matter science and materials research using extracted neutron beams. In November 1995, AECL began a pre-project engineering programme to develop the design of the facility and to begin the safety analysis and “up-front” licensing process. The dual-purpose concept continues to be pursued and the design modified, to achieve maximum performance in the most cost-effective manner. The planned neutron-beam facilities, which include a cold source and a guide hall, will greatly enhance Canada's programs of neutron-beam research and applications. The current status of the IRF design and of efforts to secure funding for the neutron-beam components will be presented.

We analyse surface-to-bottom profiles of temperature, salinity, light attenuation coefficient and acoustic (150 kHz) backscatter intensity collected in June 1990 in the vicinity of the central hydrothermal vent field on Endeavour Ridge in the northeast Pacific. Data from coincident deep plankton net tows corroborate earlier speculation (Thomson et al., 1991, Journal of Geophysical Research, 96, 4839-4844) that the 100 m thick acoustic scattering layer found near 1.9 km depth in this region consists of a dense concentration of macrozooplankton living near the top of the plume-contaminated bottom waters. Peak (≈10 dB) acoustic anomalies in the June 1990 backscatter layer were located near the top of the plume at depths of 1800–2000 m throughout the principal 60 km2 study area. The scattering layer contained a high Zooplankton biomass of 21 mg m−3 and maximum species richness of 83 taxa. In all profiles, the backscatter intensity decreased to anomalously low values beneath the core of the plume. The presence of the backscatter layer 12 km to the east of the vent site is evidence for Zooplankton layering beyond the immediate confines of the ridge. We conclude that pelagic and deep-sea Zooplankton congregate near the top of the plumecontaminated bottom waters in the vicinity of the ridge to take advantage of increased concentrations of chemosynthetic bacteria, fine-grained particles and other nutrients carried vertically upward by the buoyant portions of the plume. The Zooplankton depletion below the central core of the spreading hydrothermal plume indicates that Zooplankton avoid elevated concentrations of hydrothermally-derived minerals and other chemicals inherent to the main body of the plume.

We investigated the propagation of femtosecond laser pulses through a metamaterial that has a negative index of refraction for wavelengths around 1.5 micrometers. From the interference fringes of a Michelson interferometer with and without the sample, we directly inferred the phase time delay. From the pulse-envelope shift, we determined the group time delay. In a spectral region, phase and group velocity are negative simultaneously. This means that both the carrier wave and the pulse envelope peak of the output pulse appear at the rear side of the sample before their input pulse counterparts have entered the front side of the sample.

By measuring and calculating oblique-incidence transmittance spectra of a negative-index photonic metamaterial layer, the authors infer the in-plane dispersion relation of the magnetization wave. From the geometry and the dispersion shape, the authors conclude that coupling is predominantly via magnetic dipoles for wave propagation along the magnetic-dipole direction. These magnetization waves are the classical analog of magnon excitations of quantum-mechanical spins.

A three-dimensional, barotropic, finite element model is used to calculate the tidal flows in eastern Juan de Fuca Strait and the southern Strait of Georgia. The harmonics of eight constituents are computed and compared with those from previous finite difference models and those from historical tide gauge and current meter observations. Root-mean-square differences between observed and calculated sea level amplitudes are within 2.0 cm for all constituents, and the phases are within 4.0° for all constituents except K2. Horizontal currents from the model are found to reproduce the observed vertical variations in shear except in regions where stratification effects and internal tides exist. In particular, the model representation of currents at six stations in the Canadian Tide and Current Tables (volume 5) is accurate. The pattern of tidal residual currents has much more detail than previous, coarser resolution models, and numerous eddies are predicted. Computed energy flux fields reveal that over a 29-day period only 38% of the tidal power entering Juan de Fuca Strait is transmitted into the southern Strait of Georgia, and of the 39% entering Haro Strait, 36% is dissipated within the strait itself.

We have used a tethered oceanic profiling package consisting of a conductivity-temperature-depth (CTD) sensor, transmissometer and acoustic Doppler current profiler (ADCP) to investigate the plume emanating from a known hydrothermal vent site at a depth of 2200 m near the crest of Endeavour Ridge in the northeast Pacific Ocean. Acoustic profiles obtained in August 1988 about 3 km to the southwest of the vent site revealed the presence of an intense scattering layer centered at approximately 1870 m depth near the top of the neutrally buoyant portion of the plume. Peak intensity anomalies in the 100-m-thick scattering layer ranged from 10 to 15 dB and were of comparable magnitude to upper ocean values observed in the euphotic zone. Below the top of the plume, backscatter intensities were significantly below background levels. We speculate that the strong backscatter layer consists of highly mobile macrozooplankton which congregate near the top of the plume to take advantage of the increased concentrations of nutrients originating with vertical buoyant transport of chemosynthetic bacteria and fine-grain particles from the vent site. At the same time, the animals are able to avoid toxic levels of hydrothermally derived metals and sulfur inherent to the main body of the plume.

Inelastic neutron scattering experiments in tetragonal KNb${\mathrm{O}}_{3}$ show a high anisotropy in some regions of the phonon dispersion relation and the existence of strong one-dimensional intercell correlations between atomic motions along the [100] and [010] directions, in agreement with x-ray diffuse-scattering measurements in the same phase. The transverse phonon modes propagating normally to these directions of strong correlations, that is, with polarization vectors parallel to them, are relatively soft, not only near the zone center but all the way to the zone boundary. Comparison of these results with the Raman, neutron, and x-ray data obtained in the other phases suggests a description of the ferroelectric phase transition mechanism in KNb${\mathrm{O}}_{3}$ in terms of soft modes and dynamic correlations in each phase.

The power of neutron scattering methods to probe the dynamical behaviour of atoms and molecules in solids is illustrated by several examples taken from the now enormous literature on phonons, related excitations and phonon interactions in perfect and not so perfect crystals. The seminal role played by the soft mode concept is stressed. Although references are made to early investigations in some areas, the emphasis is on the last decade of research. Nearly all of this research has been carried out at steady state reactor sources with triple axis crystal spectrometers.

Neutron diffraction experiments on small particles of lead in the pores of Vycor glass are described. The small particles have a coherence length of (107 ± 20) Å; there is only a slight increase in the lattice parameter as compared with bulk lead, but an analysis of the intensity of the diffraction peaks reveals that there is an increase in the average amplitude of vibration of 28%. At least 80% of the lead in the glass is present in the crystalline state and contributes to the coherent diffraction.

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 coherent, elastic neutron scattering from polycrystalline samples of SF6 and CBr4 in their plastic phases has been measured. The powder line component of the neutron distributions has been analysed in terms of Debye-Waller factors to give information about the orientational disorder in the solids. An extensive diffuse scattering component is also observed in CBr4. The scattering calculated for a simple model of the molecular disorder in CBr4 agrees reasonably well with this observed diffuse scattering, but improvements in the model are clearly necessary.

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.

The frequencies of selected intermolecular modes of vibration and libration in a single crystal of deuterated ammonia (ND3) have been measured by the technique of coherent inelastic neutron scattering, at temperatures of 20 and 95 K. The results are compared with the previous optical measurements at the Γ point, and with calculations based on two different models for the intermolecular potential function. A detailed assessment of these data leads to a set of mode frequencies for the Γ, R, and M points. The elastic constants are calculated from the measured acoustic mode dispersion curves propagating along the three major symmetry directions. The existing intermolecular force models are in good qualitative agreement with experiment, but significant discrepancies remain to be resolved by future theoretical refinements.

The technique of inelastic neutron scattering has been used to determine translational and librational lattice modes in a single crystal of solid nitrogen in the cubic $\ensuremath{\alpha}$-phase at 15 K. The measurements were concentrated at the high-symmetry points $\ensuremath{\Gamma}$, $R$, and $M$, where the degeneracies ease the task of symmetry assignments to the observed modes. The assignment was made on the correlation of the observed structure-factor variation with force-model predictions. The calculations were based on a general potential function which includes Lennard-Jones or six-exponential-type interactions as well as electric quadrupole forces. Good agreement was found between both the observed frequencies and the observed intensities and their calculated counterparts. The temperature dependence of selected modes has been established and it is compared to a recent self-consistent phonon calculation.

Measurements of the effective absorption coefficient μ have been made, for a range of neutron energies, of large single crystal specimens of quartz, silicon and sapphire, at 300 K and 80 K. The effectiveness of such filters is given by the ratio of μ for (unwanted) epithermal neutrons to that for the desired thermal neutron beam. Our results indicate that sapphire is significantly more effective than either quartz or silicon for a wide range of neutron energies.

The structural and dynamical properties of the orientationally disordered solid SF6 have been studied. The present understanding of this state is discussed in terms of the microscopic nature of the orientational disorder, the influence of steric repulsion, and the concept of orientational frustration. A possible mechanism is considered for the phase transition to an ordered structure.

The wave vector and temperature dependences of transverse acoustic modes propagating along the [001] and polarized along the [100] orthorhombic axis in KNbO3 have been studied by means of coherent inelastic neutron scattering methods. The results are consistent with previous elastic constant and neutron scattering measurements. The mechanism of the orthorhombic-tetragonal phase transition is discussed in the light of all these data.

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

The neutron diffraction pattern of liquid D20 has been investigated at pressures up to 9·1 kbar at 25°C and 15·6 kbar at 85°C using an aluminium alloy pressure vessel of novel design. The corrected neutron counts were scaled by a constant factor so that our low-pressure measurements agreed with the best absolute measurements of the structure factor at low pressure. The structure factors were Fourier transformed to give the neutron-weighted pair distribution functions G(r). The principal conclusions drawn from the results are as follows. (1) The amplitudes of the peaks in the radial distribution function greatly increase under pressure, showing that there is an increase in the correlations of molecular positions and orientations. A graph of 4πr 2 G(r) against pressure shows no evidence that the first-neighbour coordination number increases by much more than the density. The number of near neighbours at 15·6 kbar and 85°C appears to be about 6·4. The volume of melting of ice VII near the triple point of 81·...

The nature of the spin correlations in Zn1−cMncTe alloys for several values of c has been studied by neutron powder diffraction as a function of temperature T between 2 and 300 K. Results have been obtained for c=0.376, 0.565, 0.594, and 0.68. The correlations are weak at low c and high T, but intensify progressively as c increases and/or T decreases. For c as high as 0.68, the experiments do not indicate any phase transition to a fully ordered magnetic structure, but the appearance of broad, intense magnetic diffuse scattering peaks at particular positions suggests a strong tendency towards antiferromagnetic ordering of type III. The results are analyzed in terms of a theory of the magnetic scattering from magnetic ions surrounded by near‐neighbor shells of correlated spins. Comparison is also made with the correlations expected from an ordered type III structure modified by various exponential functions of a correlation length κ(c). Application of a magnetic field up to 2 Tesla to the c=0.594 specimen p...

The scattering density distribution in β-N 2 at 1.2 kbar has been determined by neutron scattering methods. Diffuse scattering has been observed as a function of pressure. Calculations of the diffuse scattering on the assumption of randomly oriented N 2 molecules are in poor agreement with the experimental observation.

The frequencies of normal modes belonging to the Sigma 4 and G4 branches in potassium at 4.3K have been measured by means of coherent inelastic neutron scattering experiments. No evidence was found in the Sigma 4 branch of the anomaly predicted in a recent theoretical calculation based on a rather sophisticated pseudopotential model. It is likely that this anomaly arises from a particular mathematical problem in calculating the Sigma 4 normal mode frequencies, and that when this problem is avoided, the model provides an excellent description of the observed frequencies. The parameters of a widely used phenomenological model have been re-evaluated in the light of all the phonon frequency data now available for potassium.

The spin correlations between Mn ions in Zn1−cMncTe alloys have been measured as a function of temperature and concentration. The spin correlations follow the same sign sequence as for a type III antiferromagnet out to seven shells of neighbours. Complete long range magnetic order was not observed for any c or T.

The frequencies of particular intermolecular modes of vibration and libration in single crystals of solid carbon disulphide have been measured by coherent inelastic neutron and Raman scattering techniques 148K. Measurements were made at the special points in the Brillouin zone Gamma , S, R, Z, A, Q and Y and, including earlier infrared results, 37 of the 42 distinct frequencies at these points have been identified. Six of the ten dispersion curves along Lambda (001) have been measured and three dispersion curves have been outlined along Delta (100). Values of the elastic constants C11, C33, C44and C55have been determined from the acoustic branches. The present results are compared with calculations based on two different models for the interatomic potentials. Both models calculate the general level of the intermolecular frequencies to be too high and the bandwidth of the frequencies to be too large. Neither model can be considered an adequate description of the present results.

Collective excitations in the orientationally disordered phase of SF6 have been studied by inelastic neutron scattering and molecular dynamics simulation techniques. Experimental measurements to observe acoustic modes were made along the high symmetry directions at temperatures of 100 K and 200 K. The excitations observed showed little evidence of discrete peaks but were all broad and overdamped. They showed little temperature dependence. The dynamical structure factors S(Q, ω) calculated from the simulation are in qualitative agreement with the observed spectra but quantitatively show discrepancies. For smaller wave vectors than those studied experimentally the calculations show the existence of well-defined, long wavelength acoustic phonons. The wave vector at which the transition occurs between propagating and overdamped excitations was found to be temperature dependent. The results are interpreted in terms of the concept of orientational frustration. Some difficulties in the application of molecular d...

The construction and calibration of a new analyser crystal having automatically variable curvature about a vertical axis is described. The use of this analyser in several types of measurements of elastic and inelastic neutron scattering, made with the IN3 three-axis crystal spectrometer at the I.L.L. High Flux Beam Reactor, is discussed in relation to the performance expected theoretically. The curving of the crystal allows a large increase of neutron count rates (by a factor of 5) without any corresponding loss of energy resolution by means of a specific focusing technique. The employment of this device in general requires some care in order to avoid spurious effects; it is nevertheless easy to use and should be most valuable in experiments where the Q - dependence of the neutron scattering is not too important.

Lattice dynamics of La 11 B 6 was studied on the neutron triple axis spectrometers at HFIR. The acoustic and optical modes were measured in the high symmetry directions. The rotary motion of the B 6 molecule was measured only near the zone boundaries but shows no softening. Instead, very flat low frequency La modes were observed. The agreement with the elastic constants and the temperature dependence of specific heat is satisfactory. In YbB 6 , the elastic constants and specific heat were measured. Both results give the quite different feature from those of LaB 6 , no softening of C 12 and more softened flat low frequency Yb modes, due to the lack of the metallic bonds.

The dispersion curves for phonons propagating along the trigonal axis of the layer-structure emiconductor Bi2Te3 at 77 K have been determined by coherent inelastic neutron scattering techniques. Analysis of these results in terms of a simple interplanar force model shows a) that the forces between adjacent planes of Te atoms are comparable to those between nearest neighbour planes of Bi and Te and b) that foreces between next-nearest-neighbour planes have to be considered. In addition, a limited number of phonons were measured at 300 K and some low-frequency modes propagating along the bisectrix within the planes were determind. The results are compared, where possible, with previous Raman scattering, infrared reflection, and elastic constant measurements.

A pressure vessel for neutron diffraction of liquids up to 20 kbar is described. It was made of one or two aluminum‐alloy cylinders, having ultimate strengths of ∼6.5 kbar, that were supported radially by three steel supporting rings, which left two 6‐mm‐wide gaps for the passage of neutrons. The cylinders were supported longitudinally by a force of 300 tonnes applied to the ends of the vessel by a hydraulic press. The experimental fluid was pressurized in another vessel and piped into the diffraction vessel.

The circumferential distributions of axial, hoop, and radial residual strains in a bent INCOLOY-800* tube have been measured by neutron diffraction. High residual axial tensile strains are observed just above the neutral axis with corresponding compressive strains just below the neutral axis. There are marked and systematic differences in the amount of strain in grains with a [001] direction aligned along the axis of the tube and those with a [111] direction aligned along the tube axis. Model calculations show that these differences originate in the different yield points and elastic moduli for different crystallographic directions.

An investigation of the plastic phases of polycrystalline specimens of sulphur hexafluoride (SF6) and carbon tetrabromide (CBr4) by neutron elastic scattering and neutron diffraction experiments is reported. A theory of neutron diffraction in plastic crystals, which treats the Bragg scattering and the diffuse scattering from a unified point of view, is developed and applied in the interpretation of the neutron results. The Debye-Scherrer peaks are analysed, both by a cumulant expansion technique and a cubic harmonic analysis, to determine the crystal structures of the plastic phase which are found to be body-centred cubic (space group Im3m) for SF6 and face-centred cubic (space group Fm3m) for CBr4. The bond-orientation distribution function, f(Ω), has maxima in the directions for SF6 and in the directions for CBr4. Since, in both cases, f(Ω) is appreciably different from zero for all orientations, it is apparent that significant thermal reorientation takes place in both these crystals. The tr...

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.

A selection of normal modes of vibration and libration in a single crystal of (${\mathrm{ND}}_{4}$${)}_{2}$${\mathrm{SnCl}}_{6}$ is studied at several temperatures by means of thermal neutron inelastic scattering techniques. In particular, the behavior of the longitudinal rotary mode of the ${\mathrm{SnCl}}_{6}$ octahedra is investigated and compared with the ``soft-mode'' behavior of this libration in other antifluorite crystals. We also observe the lowest-lying librational mode of the ${\mathrm{ND}}_{4}$${\mathrm{}}^{+}$ ions, and find it to be dispersionless. Values are obtained for the elastic constants of (${\mathrm{ND}}_{4}$${)}_{2}$${\mathrm{SnCl}}_{6}$ from the slopes of the low-frequency acoustic-mode dispersion curves.

The first two authors have measured the dispersion curves for phonons whose wave vector lies along the symmetry lines $\ensuremath{\Sigma}$ and $Z$ in the Brillouin zone. The measurements were made by the method of inelastic neutron scattering. With the aid of these new results the latter two authors have determined the shell-model parameter $\ensuremath{\delta}$ which could not be determined from the previously measured dispersion curves along the lines $\ensuremath{\Delta}$ and $\ensuremath{\Lambda}$. A figure is given which summarizes all the measured dispersion curves of diamond and gives the most recently calculated shell-model fit to the data. Because of the large size of this parameter $\ensuremath{\delta}$, it was necessary to recompute some of the thermodynamic and optical properties of diamond previously reported by the last two authors elsewhere. Thermodynamic quantities such as the Debye temperature were very little affected, but some of the critical-point frequencies used in the analysis of the two-phonon infrared absorption spectrum had to be altered. A corrected table of critical points is given.

The frequency-wave-vector dispersion relation, $\ensuremath{\nu}(\mathrm{q})$, for the normal vibrations of a nickel single crystal at 296\ifmmode^\circ\else\textdegree\fi{}K has been measured for the [$00\ensuremath{\zeta}$], [$0\ensuremath{\zeta}\ensuremath{\zeta}$], [$\ensuremath{\zeta}\ensuremath{\zeta}\ensuremath{\zeta}$], and [$0\ensuremath{\zeta}1$] symmetric directions using inelastic neutron scattering. The results can be described in terms of the Born-von K\'arm\'an theory of lattice dynamics with interactions out to fourth-nearest neighbors. The shapes of the dispersion curves are very similar to those of copper, the normal mode frequencies in nickel being about 1.24 times the corresponding frequencies in copper. The fourth-neighbor model was used to calculate the frequency distribution function $g(\ensuremath{\nu})$ and related thermodynamic properties.

The usefulness of group theoretical methods in the study of the normal modes of vibration in crystals is illustrated by applying them to the case of solid carbon dioxide. Emphasis is placed on a detailed explanation of how to obtain the irreducible representations and basis vectors for selected normal mode wave vectors. These examples have been chosen specifically to show how to treat (i) zone boundary points in non-symmorphic space groups and (ii) various effects of time-reversal symmetry. Compatibility relations and the gradients of dispersion curves at the zone boundaries are also discussed. The group theoretical analyses are presented in a straightforward manner suitable for practical application, without detailed proofs or justifications.

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.