Lattice stability of Ca, Sr and Yb disilicides

In this paper a study of the lattice stability of Ca, Sr and Yb disilicides is reported. The structural stability of six different prototype lattices was investigated by means of density functional theory calculations and pseudopotentials within the generalized-gradient approximation using the VASP code. The high-pressure equilibria for the CaSi₂ and SrSi₂ have been described deriving the transition pressures, the structural properties, the bulk moduli and the heats of formation for the various polymorphs. Results are discussed together with the experimental literature. For the ytterbium disilicide a specific study of the Si vacancies in the hR3 ground state structure was carried out. Six different supercells derived from the primitive hexagonal cell were considered and full atomic and lattice relaxations were performed in order to predict the energetically most favorable structure. The formation of vacancies in the Si-sublattice is driven by the lowering of the density of states at the Fermi energy. A new mP22 lattice is proposed to describe the structure of the defective YbSi_2 − x phase: the resulting stoichiometry is Yb₄Si₇.     

Structural,elastic, electronic,and thermodynamic properties of intermetallic Zr2Cu: A first-principles study

Three competing structures (C11_b, C16 and E9₃) of intermetallic Zr₂Cu have been systematically investigated by first-principles calculations and quasi-harmonic Debye model. Both the calculated equation of states (EOS) and pressure–enthalpy results indicate a structural phase transition from C11_b to C16 phase at around 11–14 GPa. The calculated equilibrium crystal parameters and elastic constants are in consistence with available experimental or theoretical data. All three phases are mechanically stable according to the elastic stability criteria, and ductile according to Pugh's ratio, while the ambient-stable C11_b phase shows a higher elastic anisotropy. Furthermore, differences in the nature of bonding between three competing structures are uncovered by electron density topological analysis. C11_b Zr₂Cu possesses an intriguing pseudo BaFe₂As₂-type structure with the charge density maxima at Zr tetrahedral interstices serving as Fe-position pseudoatoms; C16 Zr₂Cu contains Zr-pair configurations bonded through bifurcated Zr–Zr bonding paths; while the E9₃ phase has only conventional straight bonding. Additionally, through quasi-harmonic Debye model, the pressure and temperature dependences of the bulk modulus, specific heat, Debye temperature, Grüneisen parameter and thermal expansion coefficient for three phases are obtained and discussed.     

First-principle calculations of the electronic,elastic and thermoelectric properties of Ag doped CuGaTe2

To improve the performance of a thermoelectric material CuGaTe₂, element Ag is doped to replace element Ga and we investigate the electronic structure, phase stability, elastic and thermoelectric properties of CuGa_1−xAg_xTe₂ (x = 0, 0.25 and 0.5) via first-principles method. The phase stability of CuGa_1−xAg_xTe₂ is discussed by analyzing the formation energy, cohesive energy and elastic constants. The calculated sound velocities decrease with the increase of Ag content, which is favorable for reducing the lattice thermal conductivity. The analysis of band structures shows that the replacement of Ga by Ag makes CuGaTe₂ undergo a direct-indirect semiconductor transition. The Ag doping induces steep density of states in valence band edge, which is beneficial for increasing the carrier concentration and improving thermoelectric performance of CuGaTe₂.     

Temperature-dependent mechanical properties of alpha-/beta-Nb5Si3 phases from first-principles calculations

The temperature-dependent structural properties and anisotropic thermal expansion coefficients of α-/β-Nb₅Si₃ phases have been determined by minimizing the non-equilibrium Gibbs free energy as functions of crystallographic deformations. The results indicate that the crystal anisotropy of α-Nb₅Si₃ phase is much more temperature dependence than that of β-Nb₅Si₃ phase. The total/partial density of states of α-/β-Nb₅Si₃ phases are discussed in detail to analyze their electronic hybridizations. It is demonstrated that the bonding of the two phases is mainly contributed from the hybridization between Nb-4d and Si-3p electronic states. The temperature-dependent mechanical properties of α-/β-Nb₅Si₃ phases are further investigated via the quasi-harmonic approximation method in coupling with continuum elasticity theory. The calculated single-crystalline and polycrystalline elasticity shows that both phases are mechanically stable and exhibit the intrinsic brittleness. The results also suggest that α-Nb₅Si₃ phase possesses a superior ability of compression resistance but an inferior ability of high-temperature resistance of mechanical properties than those of β-Nb₅Si₃ phase. The bonding features of α-/β-Nb₅Si₃ phases are discussed by means of charge density difference analysis in order to explain the difference of the temperature-dependent mechanical properties between the two phases.     

Electronic structure and ferromagnetism of Fe11NiSi4, Fe11CoSi4, Fe11CrSi4 and Fe3Si from first principles

Based on the density functional theory (DFT), the plane-wave pseudopotential method was used to calculate structural stabilities, electronic structures, and ferromagnetism of Fe₃Si, Fe₁₁NiSi₄, Fe₁₁CoSi₄ and Fe₁₁CrSi₄ intermetallic compound. This study showed that the Fe₁₁NiSi₄ and Fe₁₁CrSi₄ phase are more stable than Fe₃Si phase, especially Fe₁₁NiSi₄, but decreased with Fe₁₁CoSi₄ phase. Calculating the density of states and the Mulliken electronic populations showed that Fe₁₁NiSi₄ had the highest structural stability because of its Fermi level, which was close to the bottom of the pseudo-gap. Fe₁₁NiSi₄ also had the largest Mulliken population, which increased the metallic bonding of the alloying system. The total magnetic moments of Fe₁₁NiSi₄, Fe₁₁CoSi₄ and Fe₁₁CrSi₄ were 20.04μ_B, 19.98μ_B, and 18.81μ_B, respectively. These magnetic moments mainly originated from the 3d spin polarization of Fe and those of additional atoms.     

Density functional study of the mechanical and phonon properties of Al12X (X = Mo,Tc, Ru,W, Re,and Os) compounds

By means of first principles calculations, we have studied the structural, elastic, and phonon properties of the Al₁₂X (X = Mo, Tc, Ru, W, Re, and Os) compounds in cubic structure. The elastic constants of these compounds are calculated, then bulk modulus, shear modulus, Young's modulus, Possion's ratio, Debye temperature, hardness, and anisotropy value of polycrystalline aggregates are derived and relevant mechanical properties are compared with the available theoretical ones. Furthermore, the phonon dispersion curves, mode Grüneisen parameters, and thermo-dynamical properties such as free energy, entropy and heat capacity are computed and the obtained results are discussed in detail.     

Infrared brazing of Ti50Ni50 shape memory alloy using pure Cu and Ti–15Cu–15Ni foils

Infrared brazing of Ti₅₀Ni₅₀ using two brazing filler metals was investigated in the study. Three phases, including Cu-rich, CuNiTi (Δ) and Ti(Ni,Cu), were observed in the Ti₅₀Ni₅₀/Cu/Ti₅₀Ni₅₀ joint after brazing at 1150 °C. The Cu-rich phase was rapidly consumed in the first 10 s of brazing, and the eutectic mixture of CuNiTi and Ti(Ni,Cu) phases were subsequently observed in the joint. Samples brazed for longer time resulted in less CuNiTi and more Ti(Ni,Cu) phases in the joint. The existence of CuNiTi phase deteriorated the shape memory effect of the joint, but Ti(Ni,Cu) could still preserve shape memory behavior even alloyed with a large number of Cu. Therefore, higher shape recovery ratio was observed for specimens brazed for a longer time period. Extensive presence of Ti₂(Ni,Cu) phase was observed in Ti₅₀Ni₅₀/Ticuni^®/Ti₅₀Ni₅₀ joint upon brazing the specimens up to 1150 °C. The bending test could not be performed due to the inherent brittleness of Ti₂(Ni,Cu) matrix. Moreover, the stable Ti₂(Ni,Cu) phase was difficult to be removed completely by increasing either brazing time and/or temperature.     

A first principles study of structural and mechanical properties of Ti2AlZr intermetallic

The present work describes the structural and mechanical behaviour of three phases namely B2, D0₁₉ and O phases of Ti₂AlZr intermetallic using first principles density functional theory (DFT) within generalized gradient approximation (GGA). The equilibrium lattice constant values of B2, D0₁₉ and O phases are in good agreement with the experimental and theoretical data, respectively. Formation energy of O phase is minimum followed by D0₁₉ and B2. Bonding characteristics of these phases have been explained based on electronic density of states and charge density. All the three phases satisfy the Born stability criteria in terms of elastic constants and are associated with ductile behaviour based on G/B ratios. The B2 phase exhibits very high anisotropy in comparison to those of the D0₁₉ and O.     

Size dependent phase transformation in atomized TiAl powders

The paper focuses on the phase transformation of undercooled Ti–48Al (at.%) droplets atomized by high pressure gas. The microstructural evolution was analyzed using the transient nucleation theory in combination with the microstructural examinations. The primary phase, final phase volume fraction and the hardness are related to the droplets size to provide fundamental understanding. The competitive formation of the primary phases α and β are strongly controlled by the droplets size, and a critical diameter of about 25 μm was identified corresponding to an undercooling of 102 K. The final phase volume fraction of γ increased with the increase of powder size from 12% to 85%. The highest hardness with the value of 652 HV was obtained for powder of 50 μm in diameter.     

Structural stability of Fe-based topologically close-packed phases

Precipitates of topologically close-packed (TCP) phases play an important role in hardening mechanisms of high-performance steels. We analyze the influence of atomic size, electron count, magnetism and external stress on TCP phase stability in Fe-based binary transition metal alloys. Our density-functional theory calculations of structural stability are complemented by an analysis with an empirical structure map for TCP phases. The structural stability and lattice parameters of the Fe–Nb/Mo/V compounds are in good agreement with experiment. The average magnetic moments follow the Slater-Pauling relation to the average number of valence-electrons and can be rationalized in terms of the electronic density of states. The stabilizing effect of the magnetic energy, estimated by additional non-magnetic calculations, increases as the magnetic moment increases with band filling for the binary systems of Fe and early transition metals. For the case of Fe₂Nb, we demonstrate that the influence of magnetism and external stress is sufficiently large to alter the energetic ordering of the closely competing Laves phases C14, C15 and C36. We find that the A15 phase is not stabilized by atomic-size differences, while the stability of C14 is increasing with increasing difference in atomic size.     

First-principles investigation of the Cu–Ni,Cu–Pd,and Ni–Pd binary alloy systems

Phase diagrams of copper–nickel–palladium binary alloys were determined by density functional theory cluster expansion method. The system has both magnetic and non-magnetic binaries and subtle phase coexistence areas between similar and different kind of lattice types. Furthermore, the CuPd binary has several ordered structures. Cluster expansion models were constructed by heuristic cluster selection for all of the fcc structures and for the CuPd_bcc structure. Both configurational and magnetic phase diagrams were determined. Small amount of nickel magnetize fcc palladium to 0.26 μ_B from which the magnetic moment rises almost linearly to that of pure Ni. In CuNi, 0.46 x-Ni is needed for the magnetic transition. In CuPd alloy in 0 K, configurational free energy difference between bcc and fcc lattice resulting to phase separation is only about 1.1 kJ/mol-atoms. Low temperature energetics and magnetic phase diagrams have good quantitative agreement with available experimental and theoretical results. Finite temperature properties of the alloys are in good qualitative agreement with experimental results.     

Energy of formation, lattice parameter and bulk modulus of (Ni,X)Ti alloys with X = Fe, Pd, Pt, Au, Al, Cu, Zr, Hf

An analysis of the ternary ‘bridge’ Ni_50−yX_yTi₅₀ alloys with X = Fe, Pd, Pt, Au, Al, Cu, Zr, and Hf was performed using the BFS method for alloys. The lattice parameter, bulk modulus and energy of formation were determined for all the intermediate states in the (B2) transition NiTi to XTi.     

Crystal structure, phase stability and elastic properties of the Laves phase ZrTiCu2

The crystal structure of the ternary Laves phase ZrTiCu₂ with unusual stoichiometry has been determined from combined refinement of X-ray powder, X-ray single crystal and neutron powder intensity data. The derived structure is of type MgZn₂ (space group P6₃/mmc) with lattice parameters a = 0.51491(3) nm, c = 0.82421(8) nm. Crystal symmetry and composition reveal a high degree of atomic disorder, because Ti and Zr atoms share the 4f sites, whereas Ti and Cu atoms are found at the 6h sites. The 2a sites, however, are exclusively occupied by Cu. Lattice parameters for alloys Zr_1−xTi_1−xCu_2+2x (annealed at 800 °C) as a function of the concentration of Cu for a constant ratio of Zr/Ti = 1 vary in a nonlinear way, which is consistent with the described complex atomic substitution mechanism. At a load of 2 N the micro-hardness was measured to be 7.5 ± 0.3 GPa, which is significantly larger than for most of the binary Ti–Cu or Zr–Cu phases. By a density functional theory ab initio approach the site preferences of Zr, Ti and Cu were calculated indicating that a random mixture of Ti and Cu atoms at the 6h lattice sites is a key factor to stabilize the proposed structure, which is unique for a Laves phase. Lattice parameters, elastic constants and shear moduli for polycrystalline ZrTiCu₂ were also derived. The Vickers hardness of 6.2 GPa was estimated by applying a correlation between shear modulus and hardness. Data as calculated by the ab initio approach are in good agreement with the experimental findings.     

Debye temperature, self-diffusion and elastic constants of intermetallic compounds

The Debye temperature of a material is a suitable parameter to describe phenomena of solid-state physics which are associated with lattice vibrations. It basically depends on the elastic constants. In recent work a simple method was put forward that allows one to derive precise Debye temperatures of crystals with cubic, hexagonal and tetragonal symmetry from the elastic constants. The type of chemical binding does not play any role. It is one aim of the present work to apply this method to various intermetallic compounds, i.e. to critically analyse published Debye temperatures and to calculate hitherto unknown values. It is a further aim to show that the activation energy of self-diffusion is also connected with the elastic constants by a simple law at least for the cubic B2 and L1₂ intermetallics, as it was recently found for face-centred cubic metals. Some consequences for high-temperature plasticity are discussed.     

Transformation temperature changes due to second phase precipitation in NiTi-based shape memory alloys

This study investigated changes in the martensite start temperature (M_s) of NiTi-based shape memory alloys as a result of second phase precipitation. Precipitation of the second phase leads to a change in the matrix chemical composition and may alter the electron concentration (c_v) of the matrix. When the electron concentration of the matrix increases, the transformation temperature decreases, whereas the M_s temperature rises when the c_v of the matrix decreases. Additionally, if the precipitation does not result in a significant variation of the c_v of the matrix, the variation in M_s is small (<15 °C). In the present work it is shown that alteration of the M_s temperature as a result of precipitation is mainly due to the change in electron concentration of the matrix. The extrinsic effect of the precipitates on M_s is also discussed on the basis of their quantities in the as-quenched and aged microstructures and the strain energy induced in the matrix.     

Glass formability of W-based alloys through thermodynamic modeling: W–Fe–Hf–Pd–Ta and W–Fe–Si–C

Computational thermodynamics, based on the CALculation of PHAse Diagram (CALPHAD) method, can be an efficient way to predict phase stabilities in multi-component engineering materials. By calculating the stability of the liquid phase at low temperatures, this method could be a useful and cost-effective tool for the design of bulk metallic glasses. Based on the thermodynamic modeling of the constituent binary and ternary systems of W with Fe, Hf, Pd, Ta, Si, or C, thermodynamic databases are built to search for W-based metallic glasses in these alloying systems. Modeling of intermetallic phases combines input from first-principles total energy calculations and predictions of finite temperature properties from the Debye–Grüneisen model. Several plausible W-rich glass-forming alloys are identified in the W–Fe–Si–C quaternary system.     

Effects of X (V, W, Mo, Hf, Ta, Zr) additions on the ideal cleavage fracture of Cr2Nb: First-principles determination

The effects of the additive elements X (V, W, Mo, Hf, Ta and Zr) on the ideal cleavage fracture of the C15 Cr₂Nb were investigated using the first-principles method. The brittle cleavage energy G_c and critical stress σ_c were calculated. The results show that V on Cr sites and X (W and Zr) on Nb sites can increase the cleavage strength of Cr₂Nb, while X (W and Mo) on Cr sites and X (Mo, Ta and Hf) on Nb sites can reduce the cleavage strength of Cr₂Nb. Our results are consistent with available experimental ones. We also find that the effect of the element W on the cleavage strength of Cr₂Nb strongly depends on its site preference in Cr₂Nb. The charge densities induced by the additive elements X were also calculated in order to reveal the origin of the effects of X on the ideal cleavage fracture of Cr₂Nb.     

Physical properties of the InPd intermetallic catalyst

The intermetallic phase InPd is a candidate material for the use as a catalyst in the methanol steam reforming process. To study the connection between the catalytic properties of the surface and the structural and electronic properties of the bulk, we have grown single crystals of the InPd phase by the Czochralski method and determined their electronic, thermal, magnetic and hydrogen-absorption properties. By growing crystals from a high-temperature solution, we could crystallize a slightly off-stoichiometric In-rich composition In_1.04Pd_0.96, which contained a significant amount of constitutional defects in the lattice (Pd vacancies on the Pd sublattice) to retain the CsCl-type structure. The strongly inhomogeneously broadened ¹¹⁵In NMR spectrum and the high residual (T → 0) electrical resistivity confirmed the presence of constitutional defects. Single crystals of InPd do not absorb hydrogen, as requested for a good hydrogenation catalyst material. Calculated electronic density of states (DOS) shows large contribution of Pd(d) states at the Fermi level. Application of the electron localizability indicator reveals ionic and multi-centre In–Pd interactions stabilizing the crystal structure. The electrical and thermal conductivities of InPd show metallic character, whereas the thermoelectric power and the Hall coefficient both show positive sign, revealing that InPd is a predominant hole-type conductor. The calculated electronic DOS at the Fermi energy is in a good agreement with the experimental value determined from the low-temperature specific heat. Magnetic measurements have shown that InPd is a diamagnet. All results are compared to the chemically related intermetallic compound GaPd. The active–site-isolation concept for increased catalytic selectivity is discussed in relation to the InPd and GaPd structures.     

Thermodynamic modeling of Ru–Zr and Hf–Ru systems

In this paper, an assessment of the binary Ru–Zr and Hf–Ru systems is presented. The thermodynamic evaluation is based on diagrammatic investigations and high-temperature calorimetric measurements for the formation of the three intermediate compounds. The present work proposes thermodynamic modeling of the binaries calculated according to the CALPHAD method and carried out using the PARROT module in the Thermo-Calc software. The liquid phase and the solution phases (Ru)-HCP-A3, (Zr)-HCP-A3, (βZr)-BCC-A2, (Hf)-HCP-A3 and (βHf)-BCC-A2 are treated as substitutional solutions. The intermetallic Laves phase Ru₂Zr-C14 is modeled with the sublattice formalism. The RuZr-B2 and HfRu-B2 phases are treated as ordered phases originating, respectively, from (βZr)-BCC-A2 and (βHf)-BCC-A2 disordered phases. Considering the relative uncertainty of experimental data due to high temperatures, a good agreement is obtained between calculated and experimental phase diagrams. The optimized set of coefficients and the calculated isothermal section are provided.