Hcp-fcc Phase Transition Research Articles

Fcc–hcp phase coexistence in Al at high pressures: Explanation in terms of density of states

The density of states (DOS) of fcc and hcp structures of Al has been calculated for normal and high pressures. It has been found that the DOS of both structures, near the Fermi level, is similar over a range of compressed volumes close to the fcc–hcp transition volume ( V/ V 0∼0.53). This similarity is the reason for the reported coexistence of fcc–hcp phases over a wide range of pressures near the fcc–hcp phase transition. All calculations have been performed using the FP-LAPW method with GGA.

Theoretical study of FCC–HCP phase coexistence and phase stability in Al by FP-LAPW method with GGA for exchange and correlation

Zero pressure properties, phase stability and phase coexistence have been studied for Al. Possible high pressure phases of Al are examined by comparing the total internal energies and enthalpies for three structures:FCC, BCC and HCP. The energies are calculated using the density function formalism and the full potential linear augmented plane wave (FPLAPW) method. Perdew-Burke-Ernzerhof 96 parameterization of Generalized Gradient Approximation (GGA) is used for exchange and correlation. Zero pressure lattice constants and the bulk modulus have been calculated for three phases of Al, and show good agreement with published experimental results. Our results for the minimum energy c/ a ratio for hcp match well with the experimental value. Coexistence of FCC–HCP phases for a wide range of pressures near phase transformation is indicated by volume–energy curves, in agreement with a recent powder X-ray diffraction experiment. The calculated lattice parameters at high pressures show good agreement with reported experimental values. The computed transition pressure and volume for FCC–HCP phase transition is also in reasonable agreement with experiment. Finally, we have also calculated the FCC–BCC and BCC–HCP transition pressures and compared our results with reported theoretical results. These results show that the Perdew-Burke–Ernzerhof GGA, along with FP-LAPW, gives reasonably accurate results for aluminum over a large range of pressures.

Pressure-induced structural phase transition in rare-earth trihydrides. Part III. Systematics: General and geometric approach

Systematics of hcp–fcc phase transition observed in a series of lanthanide and yttrium trihydrides has been established. Based on the established systematics the prediction of the hcp–fcc transition pressure for the rest of the lanthanide trihydrides has been made. The role of H–H repulsive interaction as a probable transition promoter is discussed.

Lattice sums and their phase diagram implications for the classical Lennard-Jones model

High-accuracy lattice sums have been evaluated for the Lennard-Jones 12-6 pair potential, without cutoffs, in the close-packed fcc and hcp lattices. The results confirm the small relative stability of hcp at low pressure, and locate precisely the first-order phase transition at zero temperature to the fcc structure. The reduced pressure pσ3/ε at this transition is approximately 878.476… , with both structures having been compressed to about one-half of their zero-pressure volumes. On account of its lower symmetry compared to fcc, the hcp lattice spontaneously distorts from the ideal close-packed geometry to lower its energy by a tiny amount. For low compressions, this distortion involves expansion within close-packed planes, and shrinkage in the perpendicular stacking direction. However this spontaneous distortion changes sign shortly before reaching the compression required for the hcp–fcc phase transition, vanishing at a volume ratio (compared to zero pressure) of about 0.537.

Exchange-Coupled Spin-Fluctuation Theory: Application to Fe, Co, and Ni.

Finite-temperature properties are modeled for the itinerant-electron ferromagnets Fe, Co, and Ni by employing a spin-fluctuation theory where the modes are coupled by interatomic exchange interactions. Our method is based on the density functional theory using the local density approximation. The latter yields all parameters derived from constrained ground-state properties of noncollinear spin configurations to calculate ab initio the Curie temperatures, the magnetic susceptibilities, and, furthermore, the hcp-fcc phase transition of Co. Our results are in fair agreement with experimental data.

HCP-FCC Phase Transition in Co-Ni Alloys Studied With Magneto-Optical Kerr Spectroscopy

ABSTRACTWe have studied 100nm thick electron beam evaporated Co1-xNix alloy films in the composition range 0 ≤ x ≥ 1 using magneto-optical spectroscopy and magnetic anisotropy measurements. For films with x ≈ 0.2 we have also investigated the dependence of these quantities on the growth temperature, which was varied in the range 27 ≤ TG ≥ 408°C. Both as function of the Ni content x and the growth temperature TG we observe the anticipated hcp → fcc phase transition, e.g. by monitoring the magneto-crystalline anisotropy constant Ku, 1, which changes continuously from values of ≈ 0.3MJ/m3 for Co rich hcp alloys (0 ≤ x ≥ 0.25) to ≈ -0.05MJ/m3 for Ni rich fcc alloy films, in good agreement with bulk literature data. The new and most striking result, however, is observed in the polar magneto-optical Kerr and ellipticity spectra, which were measured in the photon energy range 0.8 ≤ hv ≥ 5.5eV. Changes by up to about 40% in Kerr rotation for films of constant composition and magnetization are observed when the structure changes from hcp → fcc. This demonstrates the sensitivity of magneto-optical effects to structural changes, making Kerr spectroscopy a useful electronic and physical structure probe.

Coherent modulated structure during the martensitic hcp-fcc phase transition in Co and in a CoNi alloy.

Diffuse neutron-scattering experiments on the martensitic fcc-hcp phase transition in single crystals of pure cobalt and Co-32% Ni reveal the presence of satellites around (111) fcc reflections within a temperature range where the fcc and hcp phases coexist. The satellites indicate a modulation of the (111) fcc lattice planes with a wavelength $\ensuremath{\lambda}=6{d}_{111}$. This result can be explained by the occurrence of an intermediate structure where platelike nuclei of the hcp phase are coherently inserted into the fcc matrix.

Evolution with pressure of the hcp-fcc phase transition in solid 4He

We first analyze recent measurements of the Raman scattering of hcp solid 4He, using well-known self-consistent phonon approximations; that illustrates the difficulties encountered in the description of highly anharmonic solids. We then confirm the prediction of Holian et al. that the hcp-fcc transition line should curve back on the T = 0 K axis between 1 and 2.5 GPa.

Observation of the hcp-fcc phase transition inHe3

The hcp-fcc phase transition has been studied in $^{3}\mathrm{He}$ from the triple point at 17.65 K and 1560 bars to 6.3 kbar with the use of an optical method. The transition line is found to be linear above 2.5 kbar with a slope of 617 bar/K. The transition kinetics, hysteresis, and width are similar to those of the transition in $^{4}\mathrm{He}$, indicating a martensitic transition.

Circular polarization of the spectral thermal emission from ferromagnets

An experimental study on a new magneto-optic effect, the partially circular polarization of the spectral thermal i.r. and vis emission from the ferromagnets iron, cobalt and nickel is presented. Measurements have been performed at photon energies from 0.2 to 2.0 eV and at temperatures between 600 and 1100 K. Results are correlated to parameters of the magneto-optic Kerr effect. The circular polarization is proportional to the magnetization, vanishes above the Curie temperature and changes sign at 1.3eV for iron, at 1.8eV for cobalt and at 0.3 eV for nickel. In addition, the circular polarization of the spectral thermal emission was studied at the hcp-fcc phase transition of cobalt at 700 K, where no Kerr-effect data are available. Finally, another new magneto-optic effect on the spectral thermal emission is suggested on the basis of the present investigation.

Predictions of the solid-parahydrogen phase diagram

The hcp-fcc phase transition of parahydrogen is predicted on the basis of a quantum cell model, which was successful in matching experimental data on helium. The hcp-fcc-fluid triple point is estimated to occur near 23 K and 0.35 kbar. The phase line is then predicted to curve over and intercept the pressure axis at 0 K, at a pressure of about 11 kbar (1.1 GPa).

Lattice dynamics of hcpHe4at high pressure

The neutron-inelastic-scattering technique was used to measure the phonon dispersion relations in two high-density crystals of hcp $^{4}\mathrm{He}$ with molar volumes of 11.61 and 9.41 ${\mathrm{cm}}^{3}$/mol. These densities are on the order of twice that of $^{4}\mathrm{He}$ at 30 bars. The crystals were grown from the melt in the fcc phase, and cooled across the fcc-hcp phase transition. The observed phonon spectra show anharmonic effects much less prominent than those observed in earlier measurements at 21 ${\mathrm{cm}}^{3}$/mol. In particular, multiphonon interference effects were not found to be very pronounced, while multiphonon scattering appeared to influence phonon line shapes strongly for large wave-vector and energy transfers. Elastic constants d\ifmmode \dot{e}\else \.{e}\fi{}termined from the initial slopes of the dispersion curves were found to be in good agreement with those calculated by Goldman using the first-order self-consistent-phonon theory. The dependence on volume of the phonon energies is discussed with reference to the earlier studies at 21.1 and 16.0 ${\mathrm{cm}}^{3}$/mol. No significant dispersion of mode Gr\uneisen parameters was found unlike the case of fcc He. Gr\uneisen parameters were found to depend on volume approximately in a manner given by Ahlers for the thermodynamic Gr\uneisen parameter.

Predictions of the solid helium phase diagram

The hcp-fcc phase transition of helium is predicted on the basis of a quantum mechanical, anharmonic, anisotropic cell model calculation. The small heat of transition agrees with experiment within the uncertainty in the knowledge of the pair potential. The phase line is extended beyond present experimental range by introducing lattice dynamics corrections, which are increasingly important at high densities. The phase line is predicted to curve over and intersect the pressure axis at 0 °K at about 20 000 atm. This behavior of the phase line is independent of the quantitative results of the models used here, since the harmonic approximation, which becomes exact in the high-density limit, requires that fcc be stable relative to hcp. Anharmonic lattice dynamic correlations are shown to be essential to the prediction of the bcc-hcp transition. They are introduced here via a correlated cell model. For the highly accurate cell model calculations several numerical methods of solution are compared.