AbstractThe lattice dynamics of a fully‐deuterated single crystal of s‐triazine is investigated using the technique of coherent inelastic neutron scattering. Detailed measurements of the temperature dependence of the dispersion of the soft acoustic mode associated with the ferroelastic phase transition are reported and compared with the qualitative behaviour of other acoustic modes. The results are in agreement with an analysis of the acoustic dynamical matrix for this material which predicts that in the high‐temperature phase the combination of elastic constants C2eff = 1/2(C11 − C12) C44 − C214 should become unstable on cooling towards the transition temperature. This effective elastic constant is found to have a temperature dependence of the form Ceff = C0(T − T0) with C0 = 3.404 × 106 Nm−2K−1 and T0 = 172.4 K. Measurements of some optic mode frequencies are also reported.

The elastic transition in s-triazine (C3N3H3) from a trigonal (R3c) high temperature (low pressure) structure to a monoclinic (C2/c) low temperature (high pressure) phase has been investigated at pressures up to 5 kbar using neutron scattering techniques. Neutron diffraction was used to measure the pressure dependence of the order parameter and inelastic scattering to study the softening of the transverse acoustic phonon modes on three isotherms. In both cases the effect of pressure on the transition is found to be described primarily by that on the temperature of the transition.

We have carried out a comprehensive experimental and theoretical study of the inelastic scattering in the one-dimensional near-Heisenberg antiferromagnet ${(\mathrm{C}{\mathrm{D}}_{3})}_{4}$NMn${\mathrm{Cl}}_{3}$ (TMMC) at low temperatures, $0.3<~T<~2.5$ K, in magnetic fields varying between 0 and 70 kOe; the field is applied perpendicular to the chain axis. In zero field at long wavelengths we observe two sets of excitations, a low-energy acoustic branch corresponding to spin motion within the dipolar-determined easy plane and a high-energy optical branch corresponding to oscillations out of the plane. For magnetic fields greater than 30 kOe and $T\ensuremath{\simeq}2$ K we observe as many as four distinct excitations---the two one-magnon modes plus two sharp excitations at higher energies. Our theroretical analysis suggests that the two higher-energy modes correspond to two-magnon processes in the longitudinal response function. The theory, which is done within the harmonic approximation expanding out to fourth order in the magnon operators, gives a good qualitative description of the data but underestimates the two-magnon intensities by a factor of 2 or 3. We also observe a marked anticrossing of the one- and two-magnon branches; this latter result shows that anharmonic effects are quite important in the spin dynamics. Finally at $T=0.3$ K and zero field we observe a gap of 0.1 meV in the acoustic spin-wave dispersion relation due to a very small in-plane anisotropy field of 71 \ifmmode\pm\else\textpm\fi{} 30 Oe.

In a recent paper we reported a neutron scattering study of the random one-dimensional (1D) Heisenberg antiferromagnetic ${({\mathrm{CD}}_{3})}_{4}\mathrm{N}{\mathrm{Mn}}_{c}{\mathrm{Cu}}_{1\ensuremath{-}c}{\mathrm{Cl}}_{3}$, with $c=0.93$ and $0.85$. The main emphasis was on the static properties. In the present publication we present the results and analyses of extended quasielastic and inelastic neutron scattering experiments at temperatures down to 0.3 K. The low-temperature behavior of the inverse correlation length $\ensuremath{\kappa}$ and staggered susceptibility $\ensuremath{\chi}(Q=\ensuremath{\pi})$ of the $c=0.93$ specimen indicates that the exchange ${J}_{\mathrm{C}\mathrm{u}\ensuremath{-}\mathrm{C}\mathrm{u}}$ between pairs of ${\mathrm{Cu}}^{++}$ ions is ferromagnetic. Well-defined spin-wave-like excitations are observed for wave vectors larger than a critical wave vector ${q}_{\mathrm{cr}}$. The low-temperature measurements indicate that ${q}_{\mathrm{cr}}$ is governed by the percolation limit ${\ensuremath{\kappa}}_{c}$ of $\ensuremath{\kappa}$ itself, indicating that the observed excitations are associated with the pure ${\mathrm{Mn}}^{++}$ segments. We have carried out spin-wave perturbation calculations and computer simulations of the spin-dynamical properties of the dilute classical Heisenberg chain at $T=0$. These two calculations are in good agreement with each other. No Ising resonances, associated with states at chain ends, were found in these calculations. These resonances occur in similar systems in higher dimensions but are shown not to occur in 1D because of the singular nature of the density of states at the band edges. For $q>{q}_{\mathrm{cr}}$, the observed inelastic scattering response is quantitatively accounted for by means of the perturbation calculations. For $q\ensuremath{\sim}{q}_{\mathrm{cr}}$ the experimentally measured line shapes are in qualitative agreement with the computer simulations.

We present in this paper the results of a detailed neutron scattering investigation at various temperatures of the dynamical properties of the linear-mercury-chain compound ${\mathrm{Hg}}_{3\ensuremath{-}\ensuremath{\delta}} \mathrm{As}{\mathrm{F}}_{6}$. The main emphasis has been put on the nature of the response function of the Hg chains at higher temperatures ($T\ensuremath{\gtrsim}150$ K). The results are analyzed and discussed in terms of new theoretical results obtained by Emery and Axe, and it is found that the behavior of the Hg chains in this temperature region is one-dimensional liquidlike, in accordance with theoretical predictions. Below ${T}_{c}=120$ K where three-dimensional long-range order is established among the Hg ions, the transverse phononlike excitations in the Hg chains with displacement along the chain develop a small (\ensuremath{\sim} 0.1 meV) energy gap at finite wave vector. This feature makes it straightforward to demonstrate the absence of elastic scattering in the sheets of scattering from the Hg chains. We have measured at room temperature acoustic As${\mathrm{F}}_{6}$ sublattice phonons in the $\ensuremath{\Delta}(\ensuremath{\zeta}00)$ and the $\ensuremath{\Lambda}(00\ensuremath{\zeta})$ directions. The observed dispersion slope of the transverse branch along $\ensuremath{\Delta}$ polarized along $\ensuremath{\Lambda}$ is about 25% smaller than that of the transverse branch along $\ensuremath{\Lambda}$ polarized along $\ensuremath{\Delta}$, in apparent disagreement with elasticity theory which predicts both modes to be governed by ${C}_{44}$. We show that this behavior can be qualitatively explained by the anisotropic coupling between Hg chains and the host lattice, leading to a much smaller elastic regime in the $\ensuremath{\Lambda}$ direction than in the $\ensuremath{\Delta}$ direction.

The molecular crystal s-triazine, C3N3H3, is known to undergo a transition from a trigonal to a monoclinic structure when cooled below Tc=200K. Inelastic neutron scattering measurements have been carried out on a single crystal of s-triazine at various temperatures. A pronounced softening of transverse modes governed by the elastic constant c44 is observed in the vicinity of Tc. The phonon response remains underdamped at energies down to at least 0.07 meV and no 'central peak' is observed. The transition seems to be slightly first order ('quasi-continuous') in accordance with recent observations, while it has been reported to be of second order at higher pressures.

By means of neutron scattering, we have measured magnetic excitations in the linear-chain antiferromagnet TMMC at T =1.8 K. An energy gap is observed at q=0 associated with zz-spin correlations, thus giving direct evidence for the importance of the dipolar xy anisotropy for the spin dynamics at low temperatures. A finite magnetic field applied perpendicular to the chains creates a second q=0 gap. There are substantial discrepancies between field dependence of the spin-wave dispersion and the predictions of linear spin-wave theory.

Inelastic neutron scattering measurements of Hg-chain excitations in Hg3−σAsF6 are presented. Below Tc = 120 K, where the Hg-ions develop an ordered sublattice, a small but well-defined gap in the Hg-chain dispersion develops at finite q. The response of the Hg-chains does not involve an elastic component indicating the absence of defect or impurity-interactions along the chains.

Tin tetraiodide was chosen for a temperature and pressure dependent lattice dynamical study because of its pronounced anharmonic properties. The variation of the Raman spectrum with temperature from 100K to 298K has been measured using a single-crystal specimen. The temperature dependence of the mode frequencies and linewidths are given together with symmetry assignments. Further measurements were made at room temperature using a powdered sample under pressure, showing considerable variation in internal as well as external modes. Isochoric and isobaric temperature shifts, relative pressure shifts and Gruneisen parameters are obtained from these data. The group theory for this system is presented. The authors' analysis was confirmed by extensive lattice dynamical calculations, first using a model in which the molecules were assumed to be rigid units, and then using a model which gave the internal modes as well as the lattice modes. The pressure variation was also calculated using both models.

We have carried out inelastic neutron scattering on Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2N(${\mathrm{C}}_{5}$${\mathrm{D}}_{5}$), at $T=1.2$ K and at magnetic fields up to 70 kOe. The spin dynamics of this typical $s=\frac{1}{2}$ one-dimensional Heisenberg antiferromagnet have previously been investigated at zero magnetic field by Endoh et al., using neutron scattering. They observed a spectrum of magnetic excitations in close agreement with the spectrum of lowest excited states as calculated exactly by des Cloizeaux and Pearson (dCP). The marked asymmetry in the line shape of the neutron response previously observed is carefully reexamined and is shown to be a true effect, in agreement with several theoretical predictions. At high magnetic field, a broadening of the neutron response is observed, especially pronounced at the antiferromagnetic zone boundary, where the peak smears out at 70 kOe. For wave vectors near an antiferromagnetic Bragg point a decrease in the peak energy is observed for increasing field, lending qualitative support to the calculations of Ishimura and Shiba of the field dependence of the dCP states.

The Mössbauer spectrum of ilvaite was measured between 115 K and 898 K, and the energy dispersive X-ray powder pattern was measured between 300 K and 1 123 K. Below 500 K the Mössbauer spectrum varies strongly with temperature while the X-ray spectrum remains unchanged. The results are interpreted by electron exchange between nearly identical Fe-sites in ilvaite.

The intensity I of the 119Sn Mossbauer line in SnI4 was measured from 100K to 300K at atmospheric pressure and at 200K at a pressure of 2 kbar. At low temperatures, the slope delta of lnI versus temperature is independent of temperature. Applying a Debye model with rigid motion of the SnI4 molecules, one obtains an unusually low value of the Debye temperature ( theta =49K) which, however, is confirmed by ultrasonic measurements (57K). Above 170K, an increasing deviation from linearity of lnI versus temperature is observed. Furthermore, at higher pressure, a large increase of the Mossbauer intensity at 200K is observed. These two observations indicate that volume changes strongly influence the lattice dynamics. They are explained by a quasiharmonic model using a Gruneisen parameter equal to gamma =4+or-1.5.

The intensity I of the 119Sn Mossbauer line in SnI4 was measured from 100K to 300K at atmospheric pressure and at 200K at a pressure of 2 kbar. At low temperatures, the slope delta of lnI versus temperature is independent of temperature. Applying a Debye model with rigid motion of the SnI4 molecules, one obtains an unusually low value of the Debye temperature ( theta =49K) which, however, is confirmed by ultrasonic measurements (57K). Above 170K, an increasing deviation from linearity of lnI versus temperature is observed. Furthermore, at higher pressure, a large increase of the Mossbauer intensity at 200K is observed. These two observations indicate that volume changes strongly influence the lattice dynamics. They are explained by a quasiharmonic model using a Gruneisen parameter equal to gamma =4+or-1.5.

Thermal decomposition products of the Mohr salt (NH4)2Fe(SO4)2·6H2O have been studied and identified using the Mössbauer effect, X-ray diffraction, infrared spectroscopy, and the gravimetric and thermal differential methods. It has been found that the Mohr salt heated for 96 hr. in air at 520K changes to a single substance identified as NH4Fe(SO4)2 with a single Mössbauer line (width 0.30 mm/sec; isomeric shift 0.30 mm/sec). When the Mohr salt is heated for 1 hr. in air at 770 K it changes to Fe2(SO4)3 with a single Mössbauer line (width 0.33 mm/sec; isomeric shift 0.31 mm/sec) strikingly similar to line of NH4Fe(SO4)2.

Non-Lorentzian diffusion-broadened Mossbauer lines are reported for two different systems: (i) SnO2 particles in silicon grease; and (ii) Fe(C5H7O2)3 dissolved in 1,3-propanediol. Both results are discussed as superpositions of Lorentzians each representing a particular situation of a Mossbauer nucleus. A model for the interpretation of the SnO2 result is presented. Agreement is found assuming that rotational diffusion of the SnO2 particles is dominating.