Stacking Characteristics of Close Packed Materials

It is shown that the enthalpy of any close packed structure for a given element can be characterised as a linear expansion in a set of continuous variables $\alpha_n$ which describe the stacking configuration. This enables us to represent the infinite, discrete set of stacking sequences within a finite, continuous space of the expansion parameters $H_n$. These $H_n$ determine the stable structure and vary continuously in the thermodynamic space of pressure, temperature or composition. The continuity of both spaces means that only transformations between stable structures adjacent in the $H_n$ space are possible, giving the model predictive and well as descriptive ability. We calculate the $H_n$ using density functional theory and interatomic potentials for a range of materials. Some striking results are found: e.g. the Lennard-Jones potential model has 11 possible stable structures and over 50 phase transitions as a function of cutoff range. The very different phase diagrams of Sc, Tl, Y and the lanthanides are understood within a single theory. We find that the widely-reported 9R-fcc transition is not allowed in equilibrium thermodynamics, and in cases where it has been reported in experiments (Li, Na), we show that DFT theory is also unable to predict it

quasiharmonic equations of state for dynamically-stabilized soft-mode materials

We introduce a method for treating soft modes within the analytical framework of the quasiharmonic equation of state. The corresponding double-well energy-displacement relation is fitted to a functional form that is harmonic in both the low- and high-energy limits. Using density-functional calculations and statistical physics, we apply the quasiharmonic methodology to solid periclase. We predict the existence of a B1--B2 phase transition at high pressures and temperatures

Mass-radius relationships for exoplanets

For planets other than Earth, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass-radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass-radius and mass-pressure relations for key materials whose equation of state is reasonably well established, and for differentiated Fe/rock. We find that variations in the equation of state, such as may arise when extrapolating from low pressure data, can have significant effects on predicted mass- radius relations, and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets. Kepler-10b is apparently 'Earth- like,' likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass-radius curves for H2O and CH4, suggesting an 'icy' composition with a relatively large core or a relatively large proportion of H2O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity. HAT-P-2b is slightly denser than the mass-radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number. CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5+1.2-1.0 TPa. The central pressure in CoRoT-7b is probably close to 0.8TPa, though may be up to 2TPa.Comment: Added more recent exoplanets. Tidied text and references. Added extra "rock" compositions. Responded to referee comment

The effects of a varus unloader brace for lateral tibiofemoral osteoarthritis and valgus malalignment after anterior cruciate ligament reconstruction: A single case study

We investigated the immediate effects of a varus knee brace on knee symptoms and knee-joint biomechanics in an individual with predominant lateral tibiofemoral joint osteoarthritis (TFJOA) and valgus malalignment after anterior cruciate ligament (ACL) reconstruction. A varus unloader brace was prescribed to a 48-year-old male with predominant lateral radiographic and symptomatic TFJOA and valgus malalignment eight-years following ACL reconstruction. During a step-down task, the participant rated knee pain, task-difficulty, knee-stability and knee-confidence on four separate visual analogue scales. Quantitative gait analysis was conducted during self-selected walking trials under three test conditions in a randomized order: (i) no brace; (ii) brace without frontal plane adjustment (no varus re-alignment); and (ii) brace with frontal plane adjustment (varus re-alignment). Post-processing of gait data involved calculation of knee kinematics and net joint moments for the reconstructed limb. The participant reported improved pain (3%), task difficulty (41%), stability (46%) and confidence (49%) when performing the step-down task with the brace. The varus brace resulted in immediate reductions in knee abduction angle (24%) and internal rotation angle (56%), and increased knee adduction moment (18%). These findings provide preliminary evidence for potentially beneficial effects of bracing on knee-symptoms and biomechanics in individuals with lateral TFJOA after reconstruction

Theoretical and computational study of high pressure structures in barium

Recent high pressure work has suggested that elemental barium forms a high pressure self-hosting structure (Ba IV) involving two `types' of barium atom. Uniquely among reported elemental structures it cannot be described by a single crystalline lattice, instead involving two interpenetrating incommensurate lattices. In this letter we report pseudopotential calculations demonstrating the stability and the potentially disordered nature of the `guest' structure. Using band structures and nearly-free electron theory we relate the appearance of Ba IV to an instability in the close-packed structure, demonstrate that it has a zero energy vibrational mode, and speculate about the structure's stability in other divalent elements.Comment: 4 pages and 5 figures. To appear in PR

Pressure-induced metallization in solid boron

Different phases of solid boron under high pressure are studied by first principles calculations. The $\alpha$-B$_{12}$ structure is found to be stable up to 270 GPa. Its semiconductor band gap (1.72 eV) decreases continuously to zero around 160 GPa, where the material transforms to a weak metal. The metallicity, as measured by the density of states at the Fermi level, enhances as the pressure is further increased. The pressure-induced metallization can be attributed to the enhanced boron-boron interactions that cause bands overlap. These results are consist with the recently observed metallization and the associated superconductivity of bulk boron under high pressure (M.I.Eremets et al, Science{\bf 293}, 272(2001)).Comment: 14 pages, 5 figure

Dynamical properties of Au from tight-binding molecular-dynamics simulations

We studied the dynamical properties of Au using our previously developed tight-binding method. Phonon-dispersion and density-of-states curves at T=0 K were determined by computing the dynamical-matrix using a supercell approach. In addition, we performed molecular-dynamics simulations at various temperatures to obtain the temperature dependence of the lattice constant and of the atomic mean-square-displacement, as well as the phonon density-of-states and phonon-dispersion curves at finite temperature. We further tested the transferability of the model to different atomic environments by simulating liquid gold. Whenever possible we compared these results to experimental values.Comment: 7 pages, 9 encapsulated Postscript figures, submitted to Physical Review

A computational study of the configurational and vibrational contributions to the thermodynamics of substitutional alloys: the Ni3Al case

We have developed a methodology to study the thermodynamics of order-disorder transformations in n-component substitutional alloys that combines nonequilibrium methods, which can efficiently compute free energies, with Monte Carlo simulations, in which configurational and vibrational degrees of freedom are simultaneously considered on an equal footing basis. Furthermore, by appropriately constraining the system, we were able to compute the contributions to the vibrational entropy due to bond proportion, atomic size mismatch, and bulk volume effects. We have applied this methodology to calculate configurational and vibrational contributions to the entropy of the Ni3Al alloy as functions of temperature. We found that the bond proportion effect reduces the vibrational entropy at the order-disorder transition, while the size mismatch and the bond proportion effects combined do not change the vibrational entropy at the transition. We also found that the volume increase at the order-disorder transition causes a vibrational entropy increase of 0.08 kB/atom, which is significant when compared to the configurational entropy increase of 0.27 kB/atom. Our calculations indicate that the inclusion of vibrations reduces in about 30 percent the order-disorder transition temperature determined solely considering the configurational degrees of freedom.Comment: Already submitte

The Effect of Lattice Vibrations on Substitutional Alloy Thermodynamics

A longstanding limitation of first-principles calculations of substitutional alloy phase diagrams is the difficulty to account for lattice vibrations. A survey of the theoretical and experimental literature seeking to quantify the impact of lattice vibrations on phase stability indicates that this effect can be substantial. Typical vibrational entropy differences between phases are of the order of 0.1 to 0.2 k_B/atom, which is comparable to the typical values of configurational entropy differences in binary alloys (at most 0.693 k_B/atom). This paper describes the basic formalism underlying ab initio phase diagram calculations, along with the generalization required to account for lattice vibrations. We overview the various techniques allowing the theoretical calculation and the experimental determination of phonon dispersion curves and related thermodynamic quantities, such as vibrational entropy or free energy. A clear picture of the origin of vibrational entropy differences between phases in an alloy system is presented that goes beyond the traditional bond counting and volume change arguments. Vibrational entropy change can be attributed to the changes in chemical bond stiffness associated with the changes in bond length that take place during a phase transformation. This so-called ``bond stiffness vs. bond length'' interpretation both summarizes the key phenomenon driving vibrational entropy changes and provides a practical tool to model them.Comment: Submitted to Reviews of Modern Physics 44 pages, 6 figure