A comprehensive set of interatomic potential parameters for modeling natural apatite crystals is presented. These potentials build on those previously used in research on apatites with new potentials fitted empirically to crystal structures and their properties using the GULP program. We demonstrate that the new potentials produce good models for the different compounds used for fitting, as well as for several natural apatites. Also presented are predicted enthalpies of mixing of strontium and calcium apatites and predicted cation site preferences in strontium calcium fluorapatite.

Interatomic potential models for natural apatite crystals: Incorporating strontium and the lanthanides

The Raman spectra of tetragonal TbPO4 (zircon-type I41/amd structure, D4h19 space group) have been measured at ambient conditions and under variable pressure up to 155 GPa inside a diamond anvil cell (DAC) Assignment of the Raman active modes of the tetragonal phase has been carried out based on polarized measurements from a single oriented crystal of TbPO4 at ambient conditions The abrupt Raman mode discontinuities and the appearance of numerous new Raman peaks at a pressure Pc≈95 GPa have provided strong evidence for a first-order phase transition to a lower crystal symmetry, most likely monoclinic The high-pressure structure appears to be more compact compared to the tetragonal one, and is retained upon bringing the crystal to ambient pressure

Raman study of tetragonal TbPO4 and observation of a first-order phase transition at high pressure

The room-temperature elastic constants of ErVO4 were considerably smaller than those of isostructural silicate and phosphate analogs. The generally “less-rigid” crystalline lattice and weaker metal-oxygen bond-strength in the RVO4 (R = rare earth elements) phases indicates that these materials are of interest for potential applications as an interphase component in toughened oxide ceramic composites.

Brillouin-Scattering Study of the Elastic Constants of ErVO4

The rare-earth oxide compound (tetragonal zircon structure) is investigated using the extended susceptibility formalism, which considers at any temperature all of the features of the crystalline electric field within the ground-state multiplet in the joint analysis of the magnetic, magnetoelastic and elastic properties. The magnetoelastic coefficients are determined from third-order magnetic susceptibility, parastriction and elastic constant measurements for the different symmetry modes. The dominant magnetoelastic coupling is associated with the orthorhombic -symmetry; however, tetragonal and symmetry-lowering modes are also observed to give rise to noticeable effects, in particular in the thermal expansion. The close coherency between the magnetoelastic coefficients in and is then emphasized: the tetragonal magnetoelastic coefficients are sizeable and all of the magnetoelastic couplings keep the same sign and order of magnitude in the two phosphates. This coherency appears to be valid throughout the large family of rare-earth zircons. Through these two examples, the occurrence of a quadrupolar ordering is then discussed as being governed by the crystalline electric field, and the role of undercritical quadrupolar interactions is emphasized in .

Magnetic and magnetoelastic properties of

Comparative analysis is performed for the magnetoelastic contributions to thermal expansion of two groups of rare-earth zircons: phosphates RPO4 (R=Y,Tb–Yb) and vanadates RVO4 (R=Pr, Nd, Gd–Yb). Significant magnetoelastic anomalies of thermal expansion are observed and magnetoelastic contributions are found in regard to the corrections for the changes of the phonon contributions throughout the series of RPO4 and RVO4. Magnetoelastic contributions to thermal expansion are demonstrated to be well accounted for by the temperature dependences of the quadrupole moments of rare-earth ions both in phosphates and vanadates. The fully symmetric magnetoelastic coefficients are determined for all the rare-earth compounds under investigation; they are of the same sign and comparable magnitude in vanadates and phosphates, whereas the magnetoelastic contributions are opposite in sign for two isomorphous groups of rare-earth zircons.

Magnetoelastic contribution to thermal expansion of rare-earth zircons

The rare-earth oxide compound ${\mathrm{HoVO}}_{4}$ (tetragonal zircon structure) is investigated in the extended susceptibility formalism, which includes all the features of the crystalline electric field in the analysis of the magnetic, magnetoelastic, and elastic properties as a function of temperature. The characteristic behavior of the first-order magnetic susceptibility allows us to refine the values of the crystalline electric-field parameters and to determine the strength of the magnetic interactions. The magnetoelastic coefficients are then found from third-order magnetic susceptibility, parastriction, and elastic-constants measurements for the different symmetry modes. Their coherency with values determined for ${\mathrm{TbPO}}_{4}$ is then emphasized: They have the same sign and order of magnitude; in particular the magnetoelastic coefficients for the tetragonal symmetry are sizable in these rare-earth oxides in contrast to the case of rare-earth intermetallics. The unusual temperature dependence of the third-order magnetic susceptibility along the tetragonal axis is a precursor of the level crossing in high magnetic fields associated with a magnetization jump of about 8${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ at 11.4 T, which we study as a function of temperature down to 0.1 K. The existence of a two-step jump of the magnetization at low temperatures, if not driven by mechanical stresses, remains an intriguing result.

Magnetoelastic properties and level crossing in HoVO4.

The magnetic and magnetoelastic properties (third-order magnetic susceptibility and parastriction) of ${\mathrm{TbPO}}_{4}$, which has the zircon-type tetragonal structure, are analyzed in the paramagnetic phase. The susceptibility formalism is then used to describe all the symmetry-lowering modes in a rare-earth insulator. The dominant magnetoelastic coupling is associated with the \ensuremath{\delta} symmetry and is, at least partly, responsible for the transition occuring at 2.15 K in the antiferromagnetic phase and clearly dominates the \ensuremath{\gamma}-symmetry mode. However, none of the different symmetry-lowering modes can be completely neglected and we determine parameters for the \ensuremath{\alpha}1 and \ensuremath{\alpha}2 tetragonal modes and the \ensuremath{\varepsilon} monoclinic mode. Owing to the close vicinity of the first excited singlet to the ground-state doublet, the \ensuremath{\alpha} quadrupolar interactions play an important role in determining the temperature dependence of the level spacing at low temperature, in particular in the ordered phases. The determination of all the magnetoelastic modes of ${\mathrm{TbPO}}_{4}$ is an essential step towards the understanding of the complex magnetic properties in the ordered phases, where numerous interactions coexist.

Z. Kazei

Papers

Magnetoelastic properties and level crossing in HoVO4.

Magnetic and magnetoelastic properties in tetragonal TbPO 4