Interatomic bonds and the tensile anisotropy of trialuminides in the elastic limit: a density functional study for Al3(Sc, Ti, V, Cr)

The tensile anisotropy in the elastic limit of Al3(Sc, Ti, V, Cr) intermetallic compounds in both the L12 and D022 crystal structure has been investigated using first-principles density-functional calculations. In both crystal structures the main bonding character comes from the saturation of dominant d 3 (L12) and d 4 (D022) hybrid orbitals located on the TM atoms. The series Al3Sc → Al3V corresponds to gradual d-band filling and leads to a gradual increase of bond-strength and covalent bond formation. The magnetism of Cr breaks this trend in the Al3Cr compound (for both ferromagnetic and antiferromagnetic configurations). In this series, a trend towards an increased anisotropy of the elastic constants, Young modulus Y and Poisson ratio ν is observed. The easy and hard directions of tension can be simply identified by the variation of Y, which corresponds to the presence or absence of covalently bonded–Al–TM–chains. A high anisotropy of the Poisson ratio arises also from an alternation of atoms in the lateral directions and can be understood in the same terms.

[1]  de Fontaine D,et al.  Theoretical and experimental study of relaxations in Al3Ti and Al3Zr ordered phases. , 1995, Physical review letters.

[2]  Maher Moakher.  On the Averaging of Symmetric Positive-Definite Tensors , 2006 .

[3]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[4]  Blöchl,et al.  Improved tetrahedron method for Brillouin-zone integrations. , 1994, Physical review. B, Condensed matter.

[5]  K. Tominaga,et al.  Mechanical properties of L12 modified titanium trialuminides alloyed with chromium, iron and vanadium , 2002 .

[6]  K. Lu,et al.  Nanoindentation measurement of hardness and modulus anisotropy in Ni_3Al single crystals , 2002 .

[7]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[8]  J. D. Strand,et al.  A new look at bonding in trialuminides: reinvestigation of TaAl3. , 2003, Inorganic Chemistry.

[9]  P. Nash,et al.  Synthesis and properties of trialuminides with ultra-fine microstructures , 1992 .

[10]  J. Hafner,et al.  Electronic structure and interatomic bonding in Al10V , 2003 .

[11]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[12]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[13]  J. Nye.  Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .

[14]  K. Venkateswarlu,et al.  Microstructure, tensile strength and wear behaviour of Al–Sc alloy , 2004 .

[15]  M. Umemoto,et al.  Mechanical properties of nanocrystalline Ti–Al–X alloys , 2002 .

[16]  R. Hill.  The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[17]  B. M. Fulk.  MATH , 1992 .

[18]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[19]  M. Gibson,et al.  LOCAL SITE SYMMETRY AND ELECTRONIC STRUCTURE OF TRIALUMINIDE AND RELATED INTERMETALLIC ALLOYS PROBED BY SOLID-STATE NMR , 1998 .

[20]  Y. L. Page,et al.  Symmetry-general least-squares extraction of elastic coefficients from ab initio total energy calculations , 2001 .

[21]  Antonio Maria Cazzani,et al.  Extrema of Young’s modulus for cubic and transversely isotropic solids , 2003 .

[22]  F. Froes.  Structural intermetallics , 1989 .

[23]  D. Miracle,et al.  Mechanical behaviour of Al3Ti intermetallic and L12 phases on its basis , 2001 .

[24]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[25]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[26]  C. Fu.  Electronic, elastic, and fracture properties of trialuminide alloys: Al_3Sc and Al_3Ti , 1990 .

[27]  G Sines,et al.  The anisotropy of Young's modulus, shear modulus and Poisson's ratio in cubic materials , 1971 .

[28]  E. George,et al.  Deformation and Fracture of L12 Trialuminides , 1991 .

[29]  Pierre Villars,et al.  Pearson's handbook of crystallographic data for intermetallic phases , 1985 .

[30]  J. Hafner,et al.  Interatomic bonding, elastic properties, and ideal strength of transition metal aluminides: A case study for Al 3 ( V , Ti ) , 2005 .

[31]  J. B. Dunlop,et al.  Dilute intermetallic compounds. II. Properties of aluminium rich aluminium-transition metal phases , 1974 .

[32]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[33]  C. P. Chang,et al.  The strengthening effect of Al3Ti in ultrafine grained Al-Al3Ti alloys , 1999 .

[34]  M. Rovati.  On the negative Poisson’s ratio of an orthorhombic alloy , 2003 .

[35]  E. George,et al.  Brittle cleavage of L1_2 trialuminides , 1990 .

[36]  Remo Guidieri.  Res , 1995, RES: Anthropology and Aesthetics.

[37]  C. Lue,et al.  NMR Study of trialuminide intermetallics , 1998 .

[38]  K. Kumar.  Ternary intermetallics in aluminiumrefractory metal-X systems (X = V, Cr, Mn, Fe, Co, Ni, Cu, Zn) , 1990 .

[39]  P. Kao,et al.  The strengthening effect of Al3Ti in high temperature deformation of Al–Al3Ti composites , 1998 .

[40]  W. W. Scanlon,et al.  Intermetallic Compounds , 1963, Science.

[41]  A. Cazzani,et al.  Extrema of Young’s modulus for elastic solids with tetragonal symmetry , 2005 .

[42]  M. Yoo,et al.  Fundamental Aspects of Deformation and Fracture in High-temperature Ordered Intermetallics , 1991 .

[43]  J. Hafner,et al.  Covalent bonding and bandgap formation in intermetallic compounds: a case study for Al3V , 2002 .

[44]  S. Cowin,et al.  Averaging Anisotropic Elastic Constant Data , 1997 .

[45]  D. Farkas.  Interatomic potentials for Ti-Al with and without angular forces , 1994 .

[46]  G. Bester,et al.  Interpretation of ab initio total energy results in a chemical language: II. Stability of TiAl3 and ScAl3 , 2001 .

[47]  D. Miracle,et al.  The influence of Zr alloying on the structure and properties of Al 3 Ti , 2003 .

[48]  Representation of Elastic Behavior in Cubic Materials for Arbitrary Axes , 1970 .

[49]  K. Kimura,et al.  Elastic constants of TiAl3 and ZrAl3 single crystals , 1991, Journal of Materials Science.

[50]  J. B. Dunlop,et al.  Al 10 V: An Einstein Solid , 1973 .

[51]  R. Hoffman.  Solids and Surfaces: A Chemist's View of Bonding in Extended Structures , 1989 .

[52]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.