TA1[110] phonon dispersion and martensitic phase transition in ordered alloys Fe3Pt

In a previous neutron scattering study, we had observed that the TA phonon softening in L1₂-ordered ferromagnetic Fe₇₂Pt₂₈ Invar is pronounced at the zone boundary M-point and leads to an antiferrodistortive phase transition at low temperatures. Here, we report on similar neutron scattering investigations on two ordered crystals with higher Fe content to investigate the relation between the TA phonon softening and the martensitic transformation, which occurs in Fe-rich ordered Fe-Pt. We find that the TA phonon softening, especially at the M-point zone boundary, does not depend on the composition of the investigated crystals. In Fe_74.5Pt_25.5, however, the antiferrodistortive phase transition temperature is enhanced due to tetragonal strain preceding the martensitic transition. In Fe₇₇Pt₂₃ a precursor driven premartensitic phase transition is not observed. The structure of the martensite is, however, influenced by the soft mode lattice instability of the austenite. This would explain the origin of structural details found previously for Fe₃Pt thermoelastic martensite. Received 18 January 1999 and Received in final form 11 March 1999     

Formation of a new dynamical mode in -uranium observed by inelastic x-ray and neutron scattering

Phonon dispersion curves were obtained from inelastic x-ray and neutron scattering measurements on alpha-uranium single crystals at temperatures from 298 to 573 K. Both measurements showed a softening and an abrupt loss of intensity in the longitudinal optic branch along [00zeta] above 450 K. Above the same temperature a new dynamical mode of comparable intensity emerges along the [01zeta] zone boundary with energy near the top of the phonon spectrum. The new mode forms without a structural transition but coincides with an anomaly in the mechanical deformation behavior. We argue that the mode is an intrinsically localized vibration and formed as a result of a strong electron-phonon interaction.     

Features of the structure and dynamics of Me1−x (NH4) x SCN (Me = K, Rb) mixed crystals

Neutron scattering is used to study the structure and dynamics of Me_{1 − x} (NH₄) _x SCN (Me = K, Rb) mixed crystals along the concentration section of 0.0 < x < 1.0 at room temperature 10 and 290 K. Phase transitions in Me_{1 − x} (NH₄) _x SCN mixed crystals are analyzed by neutron powder diffraction. The measured spectra of inelastic incoherent neutron scattering from mixed crystals in a concentration range of 0.0 < x < 1.0 at 10 are transformed into the generalized phonon density of states G(E) in the one-phonon incoherent approximation. Using G(E), we determine the changes in ammonium ion dynamics during phase transitions. Low energy resonance and local translational (two bands) and librational (two bands) modes are observed in the disordered rhombic phase at 10 K. The low energy resonance mode is not found in the ordered monoclinic phase at 10 K, though the local translational mode in the form of two bands and the local librational mode in the form of four bands are present there. The low energy resonance mode appears due to hybridization of the phonon spectrum of the host crystal with rotational tunneling modes of the split librational ground state of the impurity’s molecular ammonium ion.     

Nuclear spin conversion of methane in pure and rare-gas mixed crystals

Spin species conversion has been observed by means of neutron scattering. Methane, matrixisolated in rare-gas crystals has been investigated by measuring the time dependence of the detailed balance factor of inelastic neutron spectra. The temperature dependence of conversion rates in the interval between 2 and 5 K turns out to be stronger than predicted by a single phonon process. In general, conversion times are of the order of hours in this temperature region. The influence of the matrix is well described by a coupled phonon density of states. Crystals of pure and krypton doped methane have been examined by measuring the time dependence of the total neutron scattering cross section. For pure methane, the temperature dependence of the conversion rates shows two regimes for both free rotator and ordered molecules. Below 5 K, the behavior is described by a single phonon process and above by an Arrhenius law. Rates are enhanced by krypton dotation, which is explained by changed level spacings due to orientational disorder.     

Lattice dynamics of cubic PbTiO3 by inelastic neutron scattering

High-temperature dispersion relations of the phonon modes in a cubic PbTiO₃ single crystal have been investigated along the [ξ 0 0] and [ξ ξ 0] directions by inelastic neutron scattering. Above T _c, the phonon dispersions are only temperature-dependent close to the Brillouin zone centre where the mode softening comes through. The measurements indicate large cubic anisotropy of the elastic tensor and relatively low anisotropy of the soft mode dispersion. The differences from an earlier inelastic neutron scattering study are discussed.     

Collective excitations in solid hydrogen as observed by incoherent neutron scattering

Incoherent neutron scattering experiments are reported at a number of scattering angles for solid H₂ using the time-of-flight technique. The samples had an ortho concentration ofX0.91 and the temperatures were 4.2, 2.2 and 1.2 K. The recorded scattering functions exhibit the elastic line, the ortho-para conversion line, the phonon spectrum on the energy-gain side of the neutrons and finally the phonon spectrum on the energy-loss side. Analysis of the data shows multiple scattering to be very important especially at small scattering angles. Accordingly, the results of an extensive calculation are reported that include up to four-fold scattering. The phonon spectrum that brings calculation and experiment in agreement at all angles is presented. It is concluded from the comparison between the spectra at various temperatures that unexpectedly the samples have always remained in the hexagonal close-packed phase even below the usual transition temperature into the cubic phase. Comparison is made with the spectrum (also in thehcp phase) obtained from coherent neutron scattering. The high-energy phonon tail, to be expected for quantum crystals, is observed and is qualitatively consistent with that in a similar spectral density derived theoretically from ortho-para conversion data under pressure. No evidence of a libron spectrum atT=2.2 K for a sample withX=0.91 could be found, which is consistent with the absence of the cubic orientationally ordered phase in these experiments.Supported in this research by a grant from the National Science Foundation     

Elastic neutron scattering and dielectric behaviour of 4% brominated betaine calcium chloride dihydrate (BCCD)

We report a combined experimental study by means of elastic neutron scattering and dielectric measurements of a partially deuterated and brominated BCCD (Betaine Calcium Chloride Dihydrate) crystal. The lowest-temperature phase is one-dimensional modulated and characterized by the coexistence of different commensurate domains (with = 1/4, 4/17, 2/9 and 1/5 on cooling), but with a clear predominance of the five-fold phase. A huge global thermal hysteresis of the wave-vector of the modulation, attaining values of about 9 K in the incommensurate phase and up to 15 K in the “harmless” low temperature part of the phase diagram, is observed up to . The role of lattice defects on this phenomenon is discussed. Similarly to the behaviour of the pure compound, the structural modulation evolves on cooling towards a soliton regime (growth of third and fifth-order satellite peaks), probably with respect to a non-stabilized non-modulated ferroelectric phase. The critical temperatures deduced from dielectric constant and pyroelectric current measurements are in very good agreement with those obtained from neutron scattering. The dielectric anomaly observed in at K, and known as the “-anomaly”, could not be related with any special feature detected in the neutron data, and in particular no correlation between this anomaly and the appearance of the soliton regime can be established. Received 26 October 1998     

Origin of negative thermal expansion in cubic ZrW2O8 revealed by high pressure inelastic neutron scattering

Isotropic negative thermal expansion has been reported in cubic ZrW2O8 over a wide range of temperatures (0-1050 K). Here we report the direct experimental determination of the Grüneisen parameters of phonon modes as a function of their energy, averaged over the whole Brillouin zone, by means of high pressure inelastic neutron scattering measurements. We observe a pronounced softening of the phonon spectrum at P = 1.7 kbar compared to that at ambient pressure by about 0.1-0.2 meV for phonons of energy below 8 meV. This unusual phonon softening on compression, corresponding to large negative Grüneisen parameters, is able to account for the observed large negative thermal expansion.     

On the cross-over from half-metal to normal ferromagnet in NiMnSb

Magnetism and transport properties of the semi-Heusler compound NiMnSb are re-examined in great details. A wide set of experiments (elastic and inelastic neutron scattering, static magnetic measurements, magnetoresistance, Hall effect, thermopower, FMR) have been performed on polycrystals, single crystals or single-crystalline thin films, and the results are analysed. Special emphasis is given to the magnetic excitations and to the relaxation mechanisms in this metallic ferromagnet. At low temperatures, all experimental results hint at the existence of a fully spin-polarized conduction band (half metallic state). At higher temperature (T > 80 K), but well below the Curie temperature (730 K), a cross-over to a usual metallic ferromagnetic state is evidenced and discussed. Received 10 January 2000     

Spin wave propagation in the domain state of a random field magnet

Inelastic neutron scattering with high wave-vector resolution has characterized the propagation of transverse spin wave modes near the antiferromagnetic zone center in the metastable domain state of a random field Ising magnet. A well-defined, long wavelength excitation is observed despite the absence of long-range magnetic order. Direct comparisons with the spin wave dispersion in the long-range ordered antiferromagnetic state reveal no measurable effects from the domain structure. This result recalls analogous behavior in thermally disordered anisotropic spin chains but contrasts sharply with that of the phonon modes in relaxor ferroelectrics. Received 2 November 2002 / Received in final form 4 February 2003 Published online 11 April 2003 RID="a" ID="a"leheny@pha.jhu.edu     

Adiabatic electron-phonon interaction and high-temperature thermodynamics of A15 compounds

Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V3Si, V3Ge, and V3Co at temperatures from 10 to 1,273 K. It was found that phonons in V3Si and V3Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V3Co have a normal softening behavior. First-principles calculations show that this anomalous increase in phonon frequencies at high temperatures originates with an adiabatic electron-phonon coupling mechanism. The anomaly is caused by the thermally induced broadening of sharp peaks in the electronic density of states of V3Si and V3Ge, which tends to decrease the electronic density at the Fermi level. These results show that the adiabatic electron-phonon coupling can influence the phonon thermodynamics at temperatures exceeding 1,000 K.     

Large harmonic softening of the phonon density of states of uranium

Phonon density-of-states curves were obtained from inelastic neutron scattering spectra from the three crystalline phases of uranium at temperatures from 50 to 1213 K. The alpha-phase showed an unusually large thermal softening of phonon frequencies. Analysis of the vibrational power spectrum showed that this phonon softening originates with the softening of a harmonic solid, as opposed to vibrations in anharmonic potentials. It follows that thermal excitations of electronic states are more significant thermodynamically than are the classical volume effects. For the alpha-beta and beta-gamma phase transitions, vibrational and electronic entropies were comparable.     

Effects of non-equilibrium polar optic phonons and the band non-parabolicity on small signal high-frequency hot electrons ac mobility in narrow gap semiconductors in high magnetic fields

The small signal high-frequency ac mobility of hot electrons in n-HgCdTe in the extreme quantum limit at low and high temperatures have been calculated considering the non-equilibrium phonon distribution as well as the thermal phonon distribution .The energy loss rate has been calculated considering only optical phonon scattering while the momentum loss rate has been calculated considering acoustic phonon scattering and piezoelectric scattering together with polar optical phonon scattering and separately considering only the polar optical scattering. The results have been discussed and compared. It has been observed that at 20 K, the normalized mobility considering all the three scattering mechanisms differs appreciably from that considering only the polar optical phonon scattering. However, at 77 K, there is no difference in the normalized mobility. This establishes the fact that at higher temperature, the effect of acoustic phonon scattering and piezoelectric coupling is negligible, compared to the polar optical phonon scattering. So the ac mobility considering only polar optical phonon scattering has been studied at 77 and 20 K. The ac mobility is found to remain constant up to 100 GHz and thereafter it started decreasing at higher frequencies at 77 K whereas the ac mobility reduces at much lower frequencies at lower temperature at lower field. The non-parabolicity of the band structure enhances the normalized mobility.     

Spectrum of vibrational frequencies of crystalline tungsten at temperatures of 293 and 2400 K

The slow neutron inelastic scattering spectra for a refractory (T _melt = 3680 K) Group VI transition metal of the Periodic Table, namely, tungsten, were measured for the first time in the range from room temperature to 2400 K. Measurements of the neutron scattering spectra of tungsten were performed on a DIN-2PI time-of-flight spectrometer installed at the IBR-2 reactor (Dubna, Russia). The sample was heated in a TS3000 K high-temperature thermostat. The spectrum of vibrational frequencies of the crystal lattice of tungsten at temperatures of 293 and 2400 K was determined from the measured neutron scattering spectra by the iterative method. A softening of the frequency spectrum of tungsten was observed with increasing temperature. This was explained by the increasing role of vibrational anharmonicity effects at high temperatures. The experimental results were compared with model calculations of the frequency spectrum of tungsten.     

Studies of high-temperature electron–phonon interactions with inelastic neutron scattering and first-principles computations

Several recent studies of phonons combining inelastic neutron scattering and first-principles calculations are summarized. Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V₃Si, V₃Ge, and V₃Co at temperatures from 10 K to 1273 K. It was found that phonons in V₃Si and V₃Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V₃Co have a normal softening behavior. Additional measurements of the phonon DOS of BCC V alloys were performed, and it was found that a stiffening anomaly present in pure V is suppressed upon introduction of extra d-electrons by alloying. First-principles calculations of the electronic and phonon densities of states show that in both these systems, the anomalous phonon stiffening originates with an adiabatic electron–phonon coupling mechanism. The anomaly is caused by the thermally-induced broadening of sharp peaks in the electronic density of states, which tends to decrease the electronic density at the Fermi level. These results illustrate how the combined use of first-principles calculations and inelastic neutron scattering provides powerful insights into couplings of excitations in condensed-matter.     

Magnetization studies of the nuclear spin ordered phases of solid <Superscript>3</Superscript>He in silver sinters

Solid ³He, in the bcc lattice between 34 and 100 bar, exhibits two nuclear magnetic ordered phases in the sub-mK temperature range, the so called U2D2 low (magnetic) field phase and the “high field phase” above 0.4 T. To determine the exact spin structure of these phases we started a project of neutron scattering from the ordered solid in collaboration with the Hahn-Meitner Institute, Berlin, and other European and US groups. For this experiment it is crucial to grow a single crystal within the sinter needed for cooling the solid to temperatures of the order of 500 μK (or even twenty times lower in the case of the hcp lattice which is formed above 100 bar) and to keep it there long enough to measure a magnetic neutron reflection. We studied the growth of crystals in Ag sinters of different pore size and with different growth speeds to find an optimal way to obtain single crystalline samples. As a first diagnostic step we performed pulsed NMR measurements in the ordered phases of solid ³He in a sinter of 2700 Å particle size down to temperatures of 450 μK at various molar volumes. We could keep the samples in the ordered state for as long as 140 h. The second method we used was SQUID magnetometry. For the low field phase T_N was indicated by a drop of the intensity, both in the NMR signal and in the dc magnetization, whereas in the high field phase an increase of about 30% was observed below the ordering temperature. For the fabrication of the sinters a packing fraction of 50% and subsequent annealing proved to be very favorable to obtain cold ordered solid. Furthermore, we find that a paramagnetic surface contribution from a few monolayers of ³He exists down to 500 μK in addition to the bulk magnetization.     

Anharmonic dynamical behaviour in bcc zirconium

We present inelastic neutron scattering measurements of the low energy and strongly damped phonons in the high temperature bcc phase of zirconium. These phonons were investigated at different scattering vectors but equivalent phonon wave vectors in different Brillouin zones or along different but equivalent paths in the same Brillouin zone. Neither the observed differences in intensity nor in line shapes can be explained by the coherent one-phonon scattering law . This leads to an apparent violation of the fundamental symmetry of lattice dynamics. Taking into account the strong anharmonicity of these phonons, interferences between one- and multi-phonon scattering are held responsible for these effects. Measurements in different scattering planes reveal that due to the symmetry of the bcc lattice, these effects can only be observed in certain directions. Received: 24 December 1997 / Received in final form: 9 March 1998 / Accepted: 19 March 1998     

TiC lattice dynamics from ab initio calculations

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in a supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes. Received 23 February 1998     

Elastic and anelastic relaxations in the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3: II. Strain-order parameter coupling and dynamic softening mechanisms

Elastic and anelastic behaviour of single crystal and ceramic samples of Pb(Mg(1/3)Nb(2/3))O(3) has been investigated at frequencies of ~0.1-1.2 MHz through the temperature interval 10-800 K by resonant ultrasound spectroscopy (RUS). Comparison with data from the literature shows that softening of the shear modulus between the Burns temperature and the freezing interval is independent of frequency. The softening is attributed to coupling between acoustic modes and the relaxation mode(s) responsible for central peaks in Raman and neutron scattering spectra below the Burns temperature, and can be described with Vogel-Fulcher parameters. Shear elastic compliance and dielectric permittivity show similar patterns of temperature dependence through the freezing interval, demonstrating strong coupling between ferroelectric polarization and strain such that the response to applied stress is more or less the same as the response to an applied electric field, with a frequency dependence consistent with Vogel-Fulcher-like freezing in both cases. Differences in detail show, however, that shearing induces flipping between different twin orientations, in comparison with the influence of an electric field, which induces 180° flipping: the activation energy barrier for the former appears to be higher than for the latter. Below the freezing interval, the anelastic loss also has a similar pattern of evolution to the dielectric loss, signifying again that essentially the same mechanism is involved in the freezing process. Overall softening at low temperatures is attributed to the contributions of strain relaxations due to coupling with the local ferroelectric order parameter and of coupling between acoustic modes and continuing relaxational modes of the polar nanostructure. Dissipation is attributed to movement of boundaries between PNRs or between correlated clusters of PNRs. Overall, strain coupling is fundamental to the development of the characteristic strain, dielectric and elastic properties of relaxors.     

Magnetic and elastic properties of CeAg

Magnetic and elastic measurements in single crystals of CeAg and Ce_0.09La_0.91 Ag are presented. The magnetic susceptibility of Ce_0.09La_0.91 Ag can be quantitatively interpreted with taking Γ₈ as the ground state of the crystal field split $\text{J =}\text{5}\text{2}$ state of the Ce³⁺-ion. In CeAg we confirm a ferromagnetic phase transition at T_c = 5.3 K and a structural transition at 15 K. This latter one is clearly observed with the elastic constant measurements where c₁₁ - c₁₂ exhibits appreciable softening. This structural transition is probably due to a phonon softening at the zone boundary. The magnetic properties of CeAg, especially the small magnetic moment in the ordered region, are discussed.