Prediction of high-temperature point defect formation in TiO2 from combined ab initio and thermodynamic calculations

A computational approach that integrates ab initio electronic structure and thermodynamic calculations is used to determine point defect stability in rutile TiO₂ over a range of temperatures, oxygen partial pressures and stoichiometries. Both donors (titanium interstitials and oxygen vacancies) and acceptors (titanium vacancies) are predicted to have shallow defect transition levels in the electronic-structure calculations. The resulting defect formation energies for all possible charge states are then used in thermodynamic calculations to predict the influence of temperature and oxygen partial pressure on the relative stabilities of the point defects. Their ordering is found to be the same as temperature increases and oxygen partial pressure decreases: titanium vacancy → oxygen vacancy → titanium interstitial. The charges on these defects, however, are quite sensitive to the Fermi level. Finally, the combined formation energies of point defect complexes, including Schottky, Frenkel and anti-Frenkel defects, are predicted to limit the further formation of point defects.     

Point defects and diffusion in ordered alloys: An ab initio study of the effect of vibrations

We present a detailed investigation of the influence of atomic vibrations on the point defect and diffusion properties of ordered metallic alloys, by means of ab initio calculations with density-functional theory. Considering the case of Ni₂Al₃ which provides a rich panel of defect-related properties, our study reveals that the behaviour of this compound is largely monitored by self-interstitials, whereas such defects are usually ignored in metallic compounds. The vibration free energies are obtained for the full set of point defects of Ni₂Al₃, showing that these quantities are strongly defect-dependent, and significantly modify the free energy of the compound in an intricate composition-dependent manner. The second key-issue is the first ab initio full analysis of attempt frequencies, via the coupling of vibration analysis and saddle-point search for significant atomic jumps. This analysis indicates that attempt frequencies range over several orders of magnitude and exponentially increase with migration energies. We show the importance of these factors in reaching realistic composition-dependent diffusion coefficients.     

Thermodynamic stability of Co–Al–W L12 γ′

Co-based superalloys in the Co–Al–W system exhibit coherent L1₂ Co₃(Al,W) γ′ precipitates in an face-centered cubic Co γ matrix, analogous to Ni₃Al in Ni-based systems. Unlike Ni₃Al, however, experimental observations of Co₃(Al,W) suggest that it is not a stable phase at 1173 K. Here, we perform an extensive series of density functional theory (DFT) calculations of the γ′ Co₃(Al,W) phase stability, including point defect energetics and finite-temperature contributions. We first confirm and extend previous DFT calculations of the metastability of L1₂ Co₃(Al_0.5W_0.5) γ′ at 0 K with respect to hexagonal close-packed Co, B2 CoAl and D0₁₉ Co₃W using the special quasi-random structure (SQS) approach to describe the Al/W solid solution, employing several exchange/correlation functionals, structures with varying degrees of disorder, and newly developed larger SQSs. We expand the validity of this conclusion by considering the formation of antisite and vacancy point defects, predicting defect formation energies similar in magnitude to Ni₃Al. However, in contrast to the Ni₃Al system, we find that substituting Co on Al sites is thermodynamically favorable at 0 K, consistent with experimental observation of Co excess and Al deficiency in γ′ with respect to the Co₃(Al_0.5W_0.5) composition. Lastly, we consider vibrational, electronic and magnetic contributions to the free energy, finding that they promote the stability of γ′, making the phase thermodynamically competitive with the convex hull at elevated temperature. Surprisingly, this is due to the relatively small finite-temperature contributions of one of the γ′ decomposition products, B2 CoAl, effectively destabilizing the Co, CoAl and Co₃W three-phase mixture, thus stabilizing the γ′ phase.     

First-principles calculations of structural energetics of Cu–TM (TM = Ti,Zr, Hf) intermetallics

A systematic and comprehensive study of cohesive properties of Cu–TM (TM = Ti, Zr, Hf) intermetallics is carried out using a first-principles method. Specifically, the total energies and equilibrium cohesive properties of 95 intermetallics in the Cu–TM (TM = Ti, Zr, Hf) systems are calculated employing electronic density-functional theory (DFT), ultrasoft pseudopotentials and the generalized gradient approximation for the exchange-correlation energy. The intermetallic phases considered in our first-principles investigation are classified as stable, metastable and virtual types. The concentration dependence of the heat of formation (ΔE_f) in the Cu–Ti system is only slightly asymmetric, while in the Cu–Zr and Cu–Hf systems they are distinctly asymmetric, being skewed towards the Cu-rich side with a minimum in ΔE_f at Cu₁₀TM₇. Based on the observed differences between ab initio and calorimetric heat of formation, we conclude that additional careful experiments are needed to validate ab initio alloy energetics. We also note that the calphad model parameters representing alloy energetics vary significantly from one assessment to another in these systems. For the stable intermetallics, the calculated zero-temperature lattice parameters agree to within ±1% of experimental data at ambient temperature. For the stable phases with unit cell-internal degree(s) of freedom, the results of ab initio calculations show a good agreement when such data are available from X-ray and other diffraction results. For intermetallic compounds where no such experimental data are available, we provide optimized unit cell geometries which may be verified in future experiments. For most structures we also provide zero-temperature bulk moduli and their pressure derivatives, as defined by the equation of state. The bonding between Cu and Zr is discussed based on the analyses of density of states and bonding charge densities in Cu₅Zr and CuZr.     

The effect of native point defect thermodynamics on off-stoichiometry in β-Mg17Al12

The mechanical strength of Mg–Al–Zn alloys can be affected by a fine spatial dispersion of β-Mg₁₇Al₁₂ precipitates in the Mg matrix. In an effort to understand the phase stability and the unusual asymmetric off-stoichiometry observed in β-Mg₁₇Al₁₂, we have performed a series of first-principles density functional theory (DFT) calculations of bulk and defect properties of Mg₁₇Al₁₂. Specifically, we consider native point defects (i.e. vacancies and anti-sites) in all four sublattices of Mg₁₇Al₁₂, i.e. 2a, 8c, 24g (Mg) and 24g (Al). The T = 0 K static energies of defect Mg₁₇Al₁₂ supercells indicate that anti-site defects are energetically favored over vacancies, and the lowest anti-site defect formation energies are in 24g sites for both Al_Mg and Mg_Al. These Al-rich and Mg-rich anti-site defect formation energies are similar in magnitude, and thus do not explain the asymmetric off-stoichiometry of Mg₁₇Al₁₂. We also investigate the effect of atomic vibrations via DFT phonon calculations on native point defect free energies of Mg₁₇Al₁₂ and combine these entropic contributions with the point defect formation energies to evaluate the thermodynamics of off-stoichiometry in this phase. We find that the formation of the Al_Mg anti-site is not strongly stabilized by vibrational entropy. Thus, we conclude that the observed asymmetry in the off-stoichiometry of the β-Mg₁₇Al₁₂ phase in the Mg–Al phase diagram is not explained by simple native point defect thermodynamics, and must involve a more complicated defect formation mechanism, such as multi-defect clustering.     

Pitting corrosion of intermetallic compound Ni3(Si,Ti) with 2 at% Mo in sodium chloride solutions

The pitting corrosion of Ni₃(Si,Ti) with 2 at% Mo consisting of a single intermetallic compound Ni₃(Si,Ti) phase of L1₂ structure and a two phase mixture of L1₂ and fcc nickel solid solution was investigated as functions of test temperature and chloride concentration in sodium chloride solutions by using a potential step method and compared with that of intermetallic compound, Ni₃(Si,Ti). The pitting potential obtained for the Ni₃(Si,Ti) with 2 at% Mo decreased with increasing chloride concentration and test temperature. A critical chloride concentration below which no pitting corrosion took place was found to exist and to decrease with increasing test temperature. The specific pitting potential at the critical chloride concentration also decreased with increasing test temperature. The pitting potential of Ni₃(Si,Ti) with 2 at% Mo was higher than pure nickel, but lower than that of Ni₃(Si,Ti). A critical chloride concentration was found to be lower than that of Ni₃(Si,Ti), whereas the specific pitting potentials at the critical chloride concentration was found to be higher than that of Ni₃(Si,Ti). Pitting corrosion occurred in the two phase mixture region.     

Stability and elastic properties of L12-(Al,Cu)3(Ti,Zr) phases: Ab initio calculations and experiments

The total energies and equilibrium cohesive properties of L1₂, DO₂₂ and DO₂₃ structures along Al₃Ti–Al₃Zr and Al₃X–Cu₃X (X = Ti, Zr) sections are calculated from first principles employing electronic density-functional theory (DFT), ultrasoft pseudopotentials and the generalized gradient approximation. Calculated heats of formation are consistent with a narrow field of stability of the L1₂ structure at 12.5 at.% Cu for ternary (Al,Cu)_0.75Zr_0.25 and (Al,Cu)_0.75Ti_0.25 intermetallics at low temperatures. Experimentally, samples homogenized at 1000 °C establish a more extensive stability field for the L1₂ phase in quaternary alloys with Cu concentrations ranging from 6.7 to 12.6 at.% Cu. Two L1₂ phases were observed in as-cast alloys with near equal amounts of Ti and Zr, as well as alloys homogenized at 1000 °C. Good agreement is obtained between calculated and measured values of lattice parameters and elastic moduli. These results demonstrate high accuracy of ab initio calculations for phase stability, lattice parameters and elastic constants in multicomponent trialumide intermetallics.     

Density-Functional-Theory Study of Cohesive,Structural and Electronic Properties of Ni-Sb Intermetallic Phases

This work has its roots in a long-term theoretical research line aimed at developing a complete database with structural, thermodynamic, cohesive and elastic properties of the intermetallic compounds (ICs) of the type Me_aX_b where Me = Cu, Ni and X = In, Sn and Sb. The paper reports the results of an ab initio study of various phases occurring in the Ni-Sb phase diagram, viz., the low-temperature Ni₃Sb (orthorhombic oP8), the high-temperature Ni₃Sb (cubic cF16), Ni₅Sb₂ (monoclinic mC28), NiSb (hexagonal hP4) and the NiSb₂ (orthorhombic oP6) compounds. The molar volume, bulk modulus and its pressure derivative, the electronic density of states (DOS) and the energy of formation from the elements of these compounds are calculated ab initio using the relativistic projected augmented wave (PAW) method implemented in the VASP code. The Local Density Approximation of Ceperley and Alder and the Generalized Gradient Approximation due to Perdew and Wang are adopted to treat the exchange and correlation energies. Detailed comparisons between the current and previously reported theoretical and experimental values are reported.     

Modeling of phase stability of the fcc phases in the Ni–Ir–Al system using the cluster/site approximation method coupling with first-principles calculations

A combined CSA (cluster/site approximation)/FP (first-principles) calculation approach was employed to investigate the phase stability and thermodynamic properties of the face-centered cubic (fcc) phases of the Ni–Ir–Al system. For the constituent binaries of the Ni–Ir–Al system, enthalpies of formation of the Ni_xIr_1−x, Ni_xAl_1−x and Ir_xAl_1−x fcc compounds were calculated by first-principles approach at x = 0.75, 0.5 and 0.25 at 0 K, respectively. The pair exchange energies of the Ni–Ir and Al–Ir systems in the CSA model were obtained from FP calculated enthalpies of formation, while those for the Ni–Al binary were adopted from previous work. Thermodynamic model parameters of the fcc phases for the Ni–Ir–Al ternary system were then obtained from the constituent binaries via extrapolation. The calculated isothermal section at 1573 K is in good agreement with the experimental data within the uncertainties of the calculations and experiments.     

Oxygen incorporation in M2AlC (M = Ti,V, Cr)

Oxygen incorporation in the MAX phases Ti₂AlC, V₂AlC and Cr₂AlC was studied by ab initio calculations. Comparing the calculated energies for oxygen incorporation indicates that oxygen substitutes for carbon in Ti₂AlC and V₂AlC, but is incorporated interstitially in the Al layer of Cr₂AlC, even for carbon-deficient Cr₂AlC. To evaluate these predictions, combinatorial d.c. sputtering was used to deposit thin films with different oxygen concentrations. Two phase regions of Cr₂AlC and Cr₂Al were investigated in order to study oxygen incorporation in carbon-deficient Cr₂AlC. X-ray strain analysis data indicate that the a and c lattice parameters increase with oxygen content. These trends are in good agreement with the change in lattice parameters predicted by ab initio calculations and therefore corroborate the notion of interstitial oxygen incorporation in Cr₂AlC. A metastable solubility limit for oxygen of 3.5 at.% was determined experimentally. This is the first report on interstitial oxygen in a MAX phase and may be of relevance during the initial stages of oxidation.     

First-principles calculations for stability of atomic structures of Al-rich AlX (X=Sc–Zn) alloys,including AlMn quasicrystal: II. Medium-ranged interactions of X pairs in Al

The AlMn quasicrystal (QC) is a metastable phase with quasiperiodic arrangement of Mackay icosahedrons (MIs) (Al₄₂Mn₁₂, a vacancy at the center) and is stabilized by the the addition of Si. We give qualitative discussions for the micromechanism of the stability of the atomic structures of MI in AlMn QC, as well as the Al-rich AlX (X=Sc, V, Cu, Zn) alloys, by using the ab initio calculations for point defects in Al(fcc), where the minority elements in the AlX alloys are considered as impurities. We show: (1) the atomic structure of MI may be stabilized by the medium-ranged interaction of Mn pairs, which is strongly attractive around the interatomic distance of 4.9 Å, which is close to the observed interatomic distance for the first-neighbor Mn–Mn pairs in MI. (2) Magnetism plays an important role around the interatomic distance 7.5 Å, which is close to the interatomic distance of second-neighbor Mn–Mn pairs in MI. We also discuss the effect of a vacancy and Si impurities in MI.     

In situ visualization of Ni–Nb bulk metallic glasses phase transition

We report the results of in situ investigation of the structural evolution and crystallization behavior of Ni-based bulk metallic glass. The X-ray diffraction, transmission electron microscopy, nanobeam diffraction, differential scanning calorimetry, radial distribution function and scanning tunneling microscopy (STM)/spectroscopy techniques were applied to analyze the structure and electronic properties of Ni_63.5Nb_36.5 glasses before and after crystallization. According to our STM measurements, the primary crystallization originally starts with the Ni₃Nb phase formation as a leading eutectic phase. It was shown that surface crystallization differs drastically from bulk crystallization due to the possible surface reconstruction. The mechanism of Ni_63.5Nb_36.5 glass alloy two-dimensional crystallization was suggested, which corresponds to the local metastable (3 × 3) ?  Ni(1 1 1) surface phase formation. The possibility of different surface nanostructures developing by annealment of the originally glassy alloy in an ultrahigh vacuum at a temperature lower than the bulk crystallization temperature was shown. The increase of the mean square surface roughness parameter R_q while transforming from a glassy to a fully crystallized state can be caused by concurrent growth of Ni₃Nb and Ni₆Nb₇ bulk phases. The simple empirical model for the estimation of Ni_63.5Nb_36.5 cluster size was suggested, and the value obtained (about 8 Å) is in good agreement with the corresponding STM measurements (8–10 Å).     

The crystal structure of the β′ phase in Al–Mg–Si alloys

The crystal structure of β′, one of the metastable phases formed during precipitation hardening of Al–Mg–Si (6xxx) alloys, has been determined using electron diffraction (ED). With the aid of high-resolution electron microscopyimages and the composition estimated from energy dispersive X-ray analysis, an initial model for the structure of the β′ phase was obtained. The data from digitally recorded ED patterns were then used for a least-squares refinement of the atomic parameters of the model with a software program package developed in Delft (MSLS), taking into account dynamic scattering. The β′ structure has a composition of Mg₉Si₅. The unit cell is hexagonal, space group P6₃/m, with unit cell parameters a = 0.715 nm and c = 1.215 nm. The composition and structure were confirmed by ab initio calculations.     

Structure,phase stability and elastic properties in the Ti1–xZrxN thin-film system: Experimental and computational studies

The composition-dependence of the structure and elastic properties of ternary Ti_1–xZr_xN alloys is systematically investigated by combining thin film growth and ab initio calculations. Single-phase Ti_1–xZr_xN thin films (0 ? x ? 1) with a rocksalt structure have been deposited using dc reactive magnetron sputtering at T_s = 300 °C in Ar/N₂ plasma discharges. The structure, stress state and phase stability upon thermal annealing were studied by X-ray diffraction (XRD), while the acoustic and elastic properties were measured using Brillouin light spectroscopy, picosecond ultrasonics and nanoindentation. First-principles pseudopotential calculations of the total energy, lattice constants, bulk modulus, and single-crystal elastic constants C_ij for several cubic ordered structures of Ti_1–xZr_xN alloys were also carried out. The positive values of the computed formation energies indicate that the homogeneous Ti_1–xZr_xN alloys can be only stabilized at high temperatures. However, the magnetron-sputtered thin films were found to retain their as-grown single-phase cubic structure during post-deposition annealing at 850 °C for 3 h. The calculated equilibrium lattice parameters are in good agreement with the stress-free lattice parameters a₀ determined experimentally from XRD using the sin²ψ method: they both exhibit a positive deviation from Vegard-like linear interpolation. The calculated bulk modulus, elastic constants and Poisson’s ratio gradually decrease from TiN to ZrN. These computed values were used to interpret the experimentally derived elastic constants and Young’s modulus as functions of composition.     

First-principles studies of defects,mechanical properties and electronic structure of Cr-based Laves phases

First-principles calculations have been performed to investigate the defects, mechanical properties and electronic structure of MCr₂ (M = Nb, Ti and Zr) Laves phases. The results show that the ternary additive of V preferentially substitutes the Cr site and Zr the Nb site in NbCr₂. W has a weak site preference on the Cr site in NbCr₂. The ternary site substitutions are related to the electronic structure of NbCr₂. Further calculations of the densities of states and charge density distribution of TiCr₂ show that a strong covalent bonding between the small atoms (Cr) along the Kagome net forms a tetrahedral electronic network, which is a common feature for the electronic structure in Laves phases. Mechanical properties, such as elastic constants, elastic moduli and stacking fault energies of ZrCr₂, were calculated additionally. The intrinsic and extrinsic stacking fault energies of ZrCr₂ are found to be 112 mJ m⁻² and 98 mJ m⁻², respectively.     

Surface segregation of Pt in γ′-Ni3Al: A first-principles study

We performed first-principles slab calculations based on the density functional theory to investigate the surface segregation behavior of Pt on the clean (1 0 0), (1 1 0) and (1 1 1) surfaces of γ′-Ni₃Al. The results clearly indicate that Pt has a strong tendency to surface segregate in all three low-index surface orientations. Such a conclusion is in complete agreement with a recent experimental finding that Pt segregates to the clean Ni₃Al(1 1 1) surface. The tendency of Pt to surface segregate also helps to explain why Pt addition is beneficial to the oxidation resistance of Ni₃Al.     

Isothermal section of the Er–Fe–Al ternary system at 800 °C

Physico-chemical analysis techniques, including X-ray diffraction and Scanning Electron Microscope–Energy Dispersive X-ray Spectroscopy, were employed to construct the isothermal section of the Er–Fe–Al system at 800 °C. At this temperature, the phase diagram is characterized by the formation of five intermediate phases, ErFe_12?xAl_x with 5 ≤ x ≤ 8 (ThMn₁₂-type), ErFe_1+xAl_1?x with ?0.2 ≤ x ≤ 0.75 (MgZn₂-type), ErFe_3?xAl_x with 0.5 < x ≤ 1 (DyFe₂Al-type), Er₂Fe_17?xAl_x with 4.74 ≤ x ≤ 5.7 (TbCu₇-type) and Er₂Fe_17?xAl_x with 5.7 < x ≤ 9.5 (Th₂Zn₁₇-type), seven extensions of binaries into the ternary system; ErFe_xAl_3?x with x < 0.5 (Au₃Cu-type), ErFe_xAl_2?x with x ≤ 0.68 (MgCu₂-type), Er₂Fe_xAl_1?x with x ≤ 0.25 (Co₂Si-type), ErFe_2?xAl_x with x ≤ 0.5 (MgCu₂-type), ErFe_3?xAl_x with x ≤ 0.5 (Be₃Nb-type), Er₆Fe_23?xAl_x with x ≤ 8 (Th₆Mn₂₃-type), and Er₂Fe_17?xAl_x with x ≤ 4.75 (Th₂Ni₁₇-type) and one intermetallic compound; the ErFe₂Al₁₀ (YbFe₂Al₁₀-type).     

Ternary Sm–Al–Ni bulk metallic glasses

The present paper is concerned with the formation of the ternary Sm-based Sm–Al–Ni bulk metallic glasses. Composition design is carried out using our e/a- and cluster-related criteria. Three bulk metallic glasses, Sm₅₄Al₂₃Ni₂₃, Sm₅₆Al₂₂Ni₂₂ and Sm₅₈Al₂₁Ni₂₁, are obtained by suction casting into rods with diameter of 3 mm. All of them share a constant e/a = 1.5 and fall along the e/a-constant composition line in the ternary composition diagram. The Sm₅₄Al₂₃Ni₂₃ BMG exhibits the best thermal stability and glass-forming ability, which is located at the intersecting point of the e/a-constant line and the Sm₇Ni₃–Al cluster line.     

Laves phases in the ternary systems Ti–{Pd,Pt}–Al

Formation and crystal structure of Laves phases in the systems Ti–{Pd,Pt}–Al were investigated employing XPD (X-ray powder diffraction), XSCD (X-ray single crystal diffraction) and EPMA (electron probe microanalysis) techniques. Laves phases with MgZn₂ type (space group: P6₃/mmc) and its variant with the Nb(Ir,Al)₂-type (a√3 × a√3 × c supercell of MgZn₂-type, space group: P6₃/mcm) were found in both systems. Formation of a particular structure type is dependent on temperature and composition. Laves phases with the Nb(Ir,Al)₂-type form around 25 at.% of Pd,Pt at 950 °C. The MgZn₂-type Laves phase Ti(Pt,Al)₂ was not observed at 950 °C, but it forms in as-cast alloys at a slightly lower Pt content, Ti_37.8Pt_19.0Al_43.2. In the Ti–Pd–Al system at 950 °C the MgZn₂-type phase exists at the Pd-poor side of the homogeneity region whilst the Nb(Ir,Al)₂-type phase is slightly richer in Pd. Phase relations associated with the Ti–Pt–Al Laves phase were established at 950 °C and reveal a new compound TiPtAl that derives from hexagonal ZrBeSi-type (ordered Ni₂In-type, a = 0.43925(4) nm, c = 0.54844(5); space group P6₃/mmc; R_F2 = 0.015 from single crystal data). Atom distribution in the compound shows a slight deviation from full atom order Ti(Pt_0.97Al_0.03)(Al_0.98Pt_0.02).