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The variation of elastic properties, e.g., elastic constants, bulk modulus, and shear modulus of dilute Ni-base superalloys due to alloying elements (X's) and temperature, has been studied via first-principles calculations. Here, 26 alloying elements are considered: Al, Co, Cr, Cu, Fe, Hf, Ir, Mn, Mo, Nb, Os, Pd, Pt, Re, Rh, Ru, Sc, Si, Ta, Tc, Ti, V, W, Y, Zn, and Zr. It is found that (i) both the bulk and shear moduli of Ni-X decrease approximately linearly with increasing equilibrium volume, especially within each group of 3d, 4d, or 5d transition-metal alloying elements; (ii) all alloying elements considered herein increase the ratio of bulk to shear modulus (i.e., the ductility) and the elastic anisotropy of the Ni-X alloys; and (iii) the largest decrease of elastic properties of Ni is caused by alloying element Y. It is observed that the change of elastic properties of Ni due to various alloying elements is traceable from the distribution of (magnetization) charge density, for instance the spherical distribution of charge density facilitates shear deformation, resulting in a lower shear-related property. Using a proposed quasistatic approach based on the predicted elasticity-volume-temperature relationship, the isothermal and the isentropic elastic properties are predicted for the dilute Ni-X alloys at finite temperatures, displaying a decreasing trend with respect to temperature for each Ni-X system. Computed elastic properties are in favorable accord with available experimental data. [ABSTRACT FROM AUTHOR]

The effects of alloying elements (Co, Cu, Fe, Ge, Hf, Mg, Mn, Ni, Si, Sr, Ti, V, Y, Zn, and Zr) on elastic properties of Al have been investigated using first-principles calculations within the generalized gradient approximation. A supercell consisting of 31 Al atoms and one solute atom is used. A good agreement is obtained between calculated and available experimental data. Lattice parameters of the studied Al alloys are found to be depended on atomic radii of solute atoms. The elastic properties of polycrystalline aggregates including bulk modulus (B), shear modulus (G), Young's modulus (E), and the B/G ratio are also determined based on the calculated elastic constants (cij's). It is found that the bulk modulus of Al alloys decreases with increasing volume due to the addition of alloying elements and the bulk modulus is also related to the total molar volume (Vm) and electron density (nAl31x) with the relationship of nAl31x=1.0594+0.0207√B/Vm. These results are of relevance to tailor the properties of Al alloys. [ABSTRACT FROM AUTHOR]

Abstract: Influence of temperature on the elastic properties of Mg2X (X=Si, Ge, Sn, and Pb) compounds, has been studied using first-principles calculations, within the generalized gradient approximation, and compared with the available experimental data in the literature. Elastic stiffness coefficients calculated with respect to volume (c ij (V)) have been correlated to the equilibrium volume as a function of temperature V(T) from phonon calculations to obtain temperature dependence of elastic stiffness coefficients c ij (T). A good agreement between the thus predicted elastic constants and experimental data has been achieved. The general trend in the bulk modulus (B), shear modulus (G) and Young''s modulus (E) seen for the compounds is Mg2Ge>Mg2Si>Mg2Sn>Mg2Pb. Elastic anisotropy, fracture toughness and stiffness of the compounds have been analyzed as a function of temperature based on their anisotropic ratio (2c 44/(c 11–c 12)), product of bulk modulus and volume (B × V 1/3), and Young''s modulus. The results obtained herein provide a better understanding of the elastic behavior of antifluorite compounds as a function of temperature. The methodology used in this work acts as a benchmark for future first-principles work that involves calculating elastic constants as a function of temperature. [Copyright &y& Elsevier]

Abstract: The influence of different alloying elements on the lattice parameters and elastic properties of Mg solid solution has been studied using first-principles calculations within the generalized gradient approximation. The solute atoms employed herein are Al,Ba,Ca,Cu,Ge,K,Li,Ni,Pb,Si,Y and Zn. A supercell consisting of 35 atoms of Mg and one solute atom is used in the current calculations. A good agreement between calculated and available experimental data is obtained. Lattice parameters of Mg–X alloys are found to be dependent on the atomic radii of the solute atoms. A correlation between the bulk modulus of Mg–X alloys and the nearest-neighbor distance between Mg and X is shown. Addition of solute atoms belonging to the s-block and p-block of the periodic table results in a lower bulk moduli than d-block elements. A strong dependence of the elastic modulus of Mg–X alloys on the elastic properties of the solute atoms is also observed. Using the bulk modulus/shear modulus ratio (B/G), the change in the ductility of Mg due to the addition of the solute atom is briefly described. Linear regression coefficients for the elastic constants of each of the alloys are obtained as a tool for predicting the trend in the elastic properties of Mg as a function of concentration of the solute atoms. [Copyright &y& Elsevier]

First-principles results for the full set of elastic constants (stiffnesses) c ij of cementite, Fe3C, revealed an extreme elastic anisotropy with a very small c 44 amounting to only about 1/10 of c 55 and c 66. Synchrotron X-ray diffraction stress measurements were performed on Fe3C layers grown on α-Fe exhibiting a planar state of compressive residual stress. These data exhibit a characteristic hkl-dependence of the stress-induced reflection shifts, and provide experimental proof for the extreme elastic anisotropy of Fe3C. [Copyright &y& Elsevier]

Abstract: The three independent single-crystal elastic-stiffness constants C ij of cubic γ′-Fe4N (face-centred cubic (fcc)-type iron substructure) have been calculated by first-principles methods using the density functional theory: C 11 =307.2GPa, C 12 =134.1GPa and C 44 =46.0GPa. The Zener elastic-anisotropy ratio, A =2C 44/(C 11 − C 12)=0.53, is strikingly less than 1, implying 〈100〉 as stiffest directions, whereas all fcc metals show A >1. This elastic anisotropy is ascribed to the ordered distribution of N on the octahedral interstitial sites. X-ray diffraction lattice-strain measurements for a set of different h k l reflections recorded from γ′-Fe4N1−y layers on top of α-Fe confirmed the “abnormal” elastic anisotropy of γ′-Fe4N1−y . Stress evaluation, yielding a compressive stress of about −670MPa parallel to the surface, was performed on the basis of effective X-ray elastic constants determined from the calculated single-crystal elastic constants C ij and allowing a grain interaction intermediate between the Reuss and the Voigt models. [Copyright &y& Elsevier]