Electronic structure, phase stability, and cohesive properties of Ti 2 X Al ( X = N b , V , Zr ) (original) (raw)
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Physical Review B, 2007
The phase stability of B2 Ti 3 Al 2 X ͑X =Nb or V͒ and slightly rearranged atomic structures is examined by first-principles calculations. The ground-state energy calculations show instability in some of the Ti 3 Al 2 X configurations against the structure type of atomic displacement. We use electronic density of states and Mulliken population analysis to understand the hybridization between the atoms and the electronic origin of the stability or instability of each system. In order to estimate the strength of each bond, the heats of formation for several compounds are calculated. We find that the strength of the transition metal-Al bond increases from V to Nb to Ti, with Ti-V and Ti-Nb being weakly unstable. By examining several atomic configurations, it is shown that the stability of each structure is directly related to the number of Ti-Al bonds in each configuration. It is confirmed that the formation of the phase in Ti 3 Al 2 X is a combined displacive-replacive transformation. The crystal structure parameters, such as lattice constants and bulk modulus, are calculated and compared with available experimental data.
Solid State Communications, 2013
The crystallographic structure and stability of the a 00 phase relative to the a and b phases in Ti-x M (M ¼Ta, Nb, V, Mo) alloys are investigated by using the first-principles exact muffin-tin orbital method in combination with the coherent potential approximation. We show that, with increasing concentration of the alloying elements, the structure of the orthorhombic-a 00 phase evolutes from the hcp-a to the bcc-b phase, i.e., the lattice parameters b/a and c/a as well as the basal shuffle y decreases from those corresponding to the a phase to those of the b phase. The compositional a=a 00 and a 00 =b phase boundaries are determined by comparing the total energies of the phases. The predicted a=a 00 phase boundaries are about 10.2, 10.5, 11.5, 4.5 at% for Ti-V, Ti-Nb, Ti-Ta, and Ti-Mo, respectively, in reasonable agreement with experiments. The a 00 =b phase boundaries are higher than the experimental values, possibly due to the absence of temperature effect in the first-principles calculations. Analyzing the electronic density of states, we propose that the stability of the a 00 phase is controlled by the compromise between the strength of the covalent and metallic bonds.
Structural stability of intermetallic phases in the Ga–Ti system
Calphad, 2011
The total energies of intermetallic compounds in the Sn-Ti system are calculated employing electronic density-functional theory (DFT) using pseudopotentials constructed by the projector augmented waves (PAW) method in the generalized gradient (GGA) approximation for the exchange and correlation energy. The calculations are performed for the experimentally observed compounds at their ideal stoichiometry as well as for structures which are stable in systems of early transition metals or rare earth elements with p-elements of columns IIIB, IVB, and VB. The calculated formation enthalpy of the hexagonal Sn 5 Ti 6 compound is slightly less exothermic than the value obtained by direct reaction calorimetry. For the stable intermetallic compounds, the calculated zero-temperature lattice parameters agree well with those obtained experimentally at ambient temperature. More, for stable phases with unit cell-internal degree(s) of freedom, the results of ab initio calculations show good agreement when compared with data obtained by structural analysis of X-ray diffraction. The composition dependence of the enthalpies of formation is slightly asymmetric. The electronic densities of state of the D8 8 -Sn 3 Ti 5 compound have been computed; the curve shows the hybridization of Sn 5p states with Ti 3d states. The stability of the intermetallic compounds in the Ti-Sn system is due to this hybridization.
Electronic structure and chemical bonding in Ti2AlC investigated by soft x-ray emission spectroscopy
The electronic structure of the nanolaminated transition metal carbide Ti 2 AlC has been investigated by bulk-sensitive soft x-ray emission spectroscopy. The measured Ti L, C K and Al L emission spectra are compared with calculated spectra using ab initio densityfunctional theory including dipole matrix elements. The detailed investigation of the electronic structure and chemical bonding provides increased understanding of the physical properties of this type of nanolaminates. Three different types of bond regions are identified; the relatively weak Ti 3d -Al 3p hybridization 1 eV below the Fermi level, and the Ti 3d -C 2p and Ti 3d -C 2s hybridizations which are stronger and deeper in energy are observed around 2.5 eV and 10 eV below the Fermi level, respectively. A strongly modified spectral shape of the 3s final states in comparison to pure Al is detected for the buried Al monolayers indirectly reflecting the Ti 3d -Al 3p hybridization. The differences between the electronic and crystal structures of Ti 2 AlC, Ti 3 AlC 2 and TiC are discussed in relation to the number of Al layers per Ti layer in the two former systems and the corresponding change of the unusual materials properties.
Phase Relations and Crystal Structure of τ6-Ti2(Ti0.16Ni0.43Al0.41)3
Inorganic Chemistry, 2011
Ti 2 (Ti 0.16 Ni 0.43 Al 0.41) 3 is a novel compound (labeled as τ 6) in the Ti-rich region of the TiÀNiÀAl system in a limited temperature range 870 < T < 980°C. The structure of τ 6-Ti 2 (Ti,Ni,Al) 3 was solved from a combined analysis of X-ray single crystal and neutron powder diffracton data (space group C2/m, a = 1.85383(7) nm, b = 0.49970(2) nm, c = 0.81511(3) nm, and β = 99.597(3)°). τ 6-Ti 2 (Ti,Ni,Al) 3 as a variant of the V 2 (Co 0.57 Si 0.43) 3-type is a combination of slabs of the MgZn 2-Laves type and slabs of the Zr 4 Al 3-type forming a tetrahedrally close-packed FrankÀKasper structure with pentagonÀtriangle main layers. Titanium atoms occupy the vanadium sites, but Ti/Ni/Al atoms randomly share the (Co/Si) sites of V 2 (Co 0.57 Si 0.43) 3. Although τ 6 shows a random replacement on 6 of the 11 atom sites, it has no significant homogeneity range (∼1 at. %). The composition of τ 6 changes slightly with temperature. DSC/DTA runs (1 K/min) were not sufficient to define proper reaction temperatures due to slow reaction kinetics. Therefore, phase equilibria related to τ 6 were derived from X-ray powder diffraction in combination with EPMA on alloys, which were annealed at carefully set temperatures and quenched. τ 6 forms from a peritectoid reaction η-(Ti,Al) 2 Ni þ τ 3 þ R 2 T τ 6 at 980°C and decomposes in a eutectoid reaction τ 6 T η þ τ 4 þ R 2 at 870°C. Both reactions involve the η-(Ti,Al) 2 Ni phase, for which the atom distribution was derived from X-ray single crystal intensity data, revealing Ti/Al randomly sharing the 48f-and 16cpositions in space group Fd3m (Ti 2 Ni-type, a = 1.12543(3) nm). There was no residual electron density at the octahedral centers of the crystal structure ruling out impurity stabilization. Phase equilibria involving the τ 6 phase have been established for various temperatures (T = 865, 900, 925, 950, 975°C, and subsolidus). The reaction isotherms concerning the τ 6 phase have been established and are summarized in a SchultzÀScheil diagram.
Ti-Al-V ternary phase stability at elevated temperatures
Scripta Metallurgica et Materialia, 1992
Ternary a_d,'J_itions of the beta isomorphous elements, Nb, V, Me and Ta, have long been known to improve the ambient tempcratare ductility and fracture toughness of 0r2 (Ti3A1) and"/(TiA1) intermetallic alloys [1 -4]. In the former the increase has begn related to the stabilization of the ductile [3 phase, while the latter enhancement has been related to changes in tetragonality, unit cell volume, twin density and/or electronic structure. Control of the mechanical properties of ternary and more complex tz2(Ti3 A1)and ?(Ti AI) intermetallic alloys will require optimization of their prior thermomechanical history. Such control can be achieved through a knowledge of relevant high temperature phase equilibria; indeed, establishment of appropriate phase equilibria in the Ti-A1-Nb ternary system continues to be the subject of an extensive investigation at the University of Wisconsin .
First-principles study of ω-phase formation in the Ti 3 Al 2 V system
Journal of Physics: Condensed Matter, 2007
Using first-principles methods, the phase stability of the underlying bodycentered-cubic (bcc) structure of Ti 3 Al 2 V and slightly rearranged atomic structures are investigated. The calculated ground-state energies show an instability in the ternary Ti 3 Al 2 V alloy with respect to the ω structure-type atomic displacement. A Mulliken population analysis shows strong bonding between the transition metals and Al. It is shown that Ti-Al is the strongest bond and that ω-type displacements increase the population overlap for this bond and reduce the energy of the system. The first-principles calculations are extended to finite temperature and various contributions to the free energy are calculated within the quasiharmonic approximation. It is shown that, at high temperatures, the bcc structure is stabilized by the contribution of the low-energy modes to lattice entropy. In agreement with experiment and in contrast to the Ti-Al-Nb system, we find that the metastable B8 2 structure cannot form in this alloy.
An empirical theoretical investigation into phase and structural behaviour in Ti–Al alloys
Materials Science and Technology, 2010
According to the average lattice and atom models of the empirical electron theory of solids and molecules (EET), effects of interstitial impurities on valence electron structures and phase transformation of Ti-Al alloys are analysed. Furthermore, the descendant degree of bond energy, melting point, and liquidus temperatures affected by interstitial impurities are calculated based on the bond energy formula of the EET. Moreover, the main controversial experimental results on the phase transformation in Ti-Al alloys are explained well. It is demonstrated that because of the effects of interstitial impurities, atom states increase, bond structures are seriously anisotropic, which results in very complex phase transformations in intermediate Al content. It is also shown that the melting point and liquidus temperatures decrease due to interstitial impurities, and the average decreased degree can be estimated very well using the EET.
Structural stability of intermetallic phases in the Sn–Ti system
Calphad-computer Coupling of Phase Diagrams and Thermochemistry, 2009
The total energies of intermetallic compounds in the Sn-Ti system are calculated employing electronic density-functional theory (DFT) using pseudopotentials constructed by the projector augmented waves (PAW) method in the generalized gradient (GGA) approximation for the exchange and correlation energy. The calculations are performed for the experimentally observed compounds at their ideal stoichiometry as well as for structures which are stable in systems of early transition metals or rare earth elements with p-elements of columns IIIB, IVB, and VB. The calculated formation enthalpy of the hexagonal Sn 5 Ti 6 compound is slightly less exothermic than the value obtained by direct reaction calorimetry. For the stable intermetallic compounds, the calculated zero-temperature lattice parameters agree well with those obtained experimentally at ambient temperature. More, for stable phases with unit cell-internal degree(s) of freedom, the results of ab initio calculations show good agreement when compared with data obtained by structural analysis of X-ray diffraction. The composition dependence of the enthalpies of formation is slightly asymmetric. The electronic densities of state of the D8 8-Sn 3 Ti 5 compound have been computed; the curve shows the hybridization of Sn 5p states with Ti 3d states. The stability of the intermetallic compounds in the Ti-Sn system is due to this hybridization.