Macroscopic Elastic Properties of Textured ZrN--AlN Polycrystalline Aggregates: From Ab initio Calculations to Grain-Scale Interactions

Despite the fast development of computational materials modelling, theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this communication we use a supercell-based approach to obtain the elastic properties of random solid solution cubic ZrAlN system as a function of the metallic sublattice composition and texture descriptors. The employed special quasi-random structures are optimised not only with respect to short range order parameters, but also to make the three cubic directions $[1\,0\,0]$, $[0\,1\,0]$, and $[0\,0\,1]$ as similar as possible. In this way, only a small spread of elastic constants tensor components is achieved and an optimum trade-off between modelling of chemical disorder and computational limits regarding the supercell size is achieved. The single crystal elastic constants are shown to vary smoothly with composition, yielding $x\approx0.4$-0.5 an alloy constitution with an almost isotropic response. Consequently, polycrystals with this composition are suggested to have Young's modulus independent on the actual microstructure. This is indeed confirmed by explicit calculations of polycrystal elastic properties, both within the isotropic aggregate limit, as well as with fibre textures with various orientations and sharpness. It turns out, that for low AlN mole fractions, the spread of the possible Young's moduli data caused by the texture variation can be larger than 100 GPa. Consequently, our discussion of Young's modulus data of cubic ZrAlN contains also the evaluation of the texture typical for thin films.Comment: 10 pages, 6 figures, 3 table

Non-existence of stationary two-black-hole configurations: The degenerate case

In a preceding paper we examined the question whether the spin-spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. Based on the solution of a boundary value problem for two separate (Killing-) horizons and a novel black hole criterion we were able to prove the non-existence of the equilibrium configuration in question. In this paper we extend the non-existence proof to extremal black holes.Comment: 18 pages, 2 figure

Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table

Infrared astronomical satellite (IRAS) catalogs and atlases. Volume 1: Explanatory supplement

The Infrared Astronomical Satellite (IRAS) was launched on January 26, 1983. During its 300-day mission, IRAS surveyed over 96 pct of the celestial sphere at four infrared wavelengths, centered approximately at 12, 25, 60, and 100 microns. Volume 1 describes the instrument, the mission, and data reduction

Ab initio explanation of disorder and off-stoichiometry in Fe-Mn-Al-C kappa carbides

Carbides play a central role for the strength and ductility in many materials. Simulating the impact of these precipitates on the mechanical performance requires the knowledge about their atomic configuration. In particular, the C content is often observed to substantially deviate from the ideal stoichiometric composition. In the present work, we focus on Fe-Mn-Al-C steels, for which we determined the composition of the nano-sized kappa carbides (Fe,Mn)3AlC by atom probe tomography (APT) in comparison to larger precipitates located in grain boundaries. Combining density functional theory with thermodynamic concepts, we first determine the critical temperatures for the presence of chemical and magentic disorder in these carbides. Secondly, the experimentally observed reduction of the C content is explained as a compromise between the gain in chemical energy during partitioning and the elastic strains emerging in coherent microstructures

Band gap and band parameters of InN and GaN from quasiparticle energy calculations based on exact-exchange density-functional theory

We have studied the electronic structure of InN and GaN employing G0W0 calculations based on exact-exchange density-functional theory. For InN our approach predicts a gap of 0.7 eV. Taking the Burnstein-Moss effect into account, the increase of the apparent quasiparticle gap with increasing electron concentration is in good agreement with the observed blue shift of the experimental optical absorption edge. Moreover, the concentration dependence of the effective mass, which results from the non-parabolicity of the conduction band, agrees well with recent experimental findings. Based on the quasiparticle band structure the parameter set for a 4x4 kp Hamiltonian has been derived.Comment: 3 pages including 3 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Had the planet mars not existed: Kepler's equant model and its physical consequences

We examine the equant model for the motion of planets, which has been the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for each orbit a velocity which satisfies Kepler's second law and Hamilton's hodograph, and a centripetal acceleration with an inverse square dependence on the distance to the sun. If this dependence is assumed to be universal, Kepler's third law follows immediately. This elementary execice in kinematics for undergraduates emphasizes the proximity of the equant model coming from Ancient Greece with our present knowledge. It adds to its historical interest a didactical relevance concerning, in particular, the discussion of the Aristotelian or Newtonian conception of motion

Exciting prospects for solids: Exact-exchange based functionals meet quasiparticle energy calculations

Focussing on spectroscopic aspects of semiconductors and insulators we will illustrate how quasiparticle energy calculations in the G0W0 approximation can be successfully combined with density-functional theory calculations in the exact-exchange optimised e ective potential approach (OEPx) to achieve a first principles description of the electronic structure that overcomes the limitations of local or gradiant corrected DFT functionals (LDA and GGA)

Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes

We study general S2xS1 Gowdy models with a regular past Cauchy horizon and prove that a second (future) Cauchy horizon exists, provided that a particular conserved quantity $J$ is not zero. We derive an explicit expression for the metric form on the future Cauchy horizon in terms of the initial data on the past horizon and conclude the universal relation A\p A\f=(8\pi J)^2 where A\p and A\f are the areas of past and future Cauchy horizon respectively.Comment: 17 pages, 1 figur