Effective Formation Energies Research Articles

Atomic defects and diffusion in intermetallic compounds with D03structure: an ab-initio study

Abstract The effective formation energies of vacancies and antistructure atoms in the D03 phase of FexAl1–x, FexSi1–x and NixSb1–x are calculated by means of the ab-initio electron theory and statistical mechanics. It is shown how the results of these calculations can be combined with available experimental data mainly from tracer diffusion studies, positron-annihilation experiments, quasielastic neutron scattering, and quasielastic Mossbauer studies to promote the understanding of the diffusion mechanisms in these materials.

The interaction and concentration of vacancies in NiAl

In stoichiometric NiAl, the concentration of thermal vacancies is unusually high because vacancy pairs form a low-energy triple defect consisting of two Ni vacancies and a Ni Al antisite defect. The formation energy of the triple defect has been calculated to be 2.28 eV and measured to be 2.18±0.3 eV. On the Al-rich side of stoichiometry, in addition to the thermal vacancies, there are even higher concentrations of constitutional vacancies. All the point defects interact elastically through the image pressure. In Al-rich Ni 45Al 55, the interaction is estimated to reduce the effective formation energy of a Ni vacancy by ∼0.1 eV.

Influence of Voids on the Accuracy of Measurement of Vacancy Concentration in NiAl and CoAl Intermetallic Compounds

The vacancy concentrations cv in the B2-type alloys of Ni1-xAlx (0.45≤x≤0.54) and Co1-xAlx (0.46≤x≤0.52) were determined by the measurements of lattice constant with X-ray diffraction and bulk density ρA using the Archimedes method. The measurements were performed at room temperature for various sizes of powder samples. The obtained density of ρA increased with decreasing powder size, and the resultant vacancy concentration decreased. The size dependence of ρA and a scanning electron microscopic observation indicated that the increase in ρA was due to the presence of voids in the powder samples. The reliable values of cv were estimated using a model that reduced the influence of voids. The effective formation energies of vacancy and antistructure atom were also estimated from the composition dependence of cv. The results of the estimation showed that the Al antistructure is the ground state of the defect structure at 0 K.

Atomic defects in FeCo: Stabilization of theB2structure by magnetism

The effective formation energies of atomic defects in the $B2$ phase of FeCo are calculated by a combination of the statistical mechanics with the ab initio density-functional electron theory with the local-spin-density approximation and the generalized-gradient approximation for the exchange-correlation functional. The effect of magnetism is required to stabilize the system against a spontaneous formation of antistructure atoms even in the stoichiometric case. The structural defects are antistructure atoms, and the effective energy for the formation of thermal antistructure atoms is much smaller than the effective formation energies for Fe and Co vacancies. The behavior of the atomic defects in this system consisting of two quite similar constituents appears to be much simpler than in the $B2$ transition-metal aluminides consisting of quite dissimilar constituents.

Atomic defects in the ordered compound B2-CoAl: A combination ofab initioelectron theory and statistical mechanics

For an ideal model of a homogeneous thermodynamically stable ordered compound $B2\ensuremath{-}{\mathrm{Co}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x},$ the effective formation energies of vacancies and antistructure atoms on both sublattices are calculated by a combination of ab initio electron theory and statistical mechanics. The results are compared with data for FeAl and NiAl obtained by the same procedure and with experimental results. The structural defects in ${\mathrm{Co}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ are Co antistructure atoms (for $x>0.5)$ and Co vacancies (for $x<0.5),$ albeit these latter defects are only slightly more favorable than Al antistructure atoms. This near balance possibly is responsible for conflicting experimental results obtained in real Al-rich samples. The dominant thermal excitations are also discussed.

Atomic defects in the ordered compoundB2-NiAl: A combination ofab initioelectron theory and statistical mechanics

For an ideal model of a homogeneous thermodynamically stable ordered compound $B2\ensuremath{-}{\mathrm{Ni}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ the effective formation energies and volumes of vacancies and antistructure atoms as well as the Ni and Al activities are calculated by a combination of the ab initio electron theory with a generalized grand canonical statistical approach. For nonstoichiometric compounds the structural defects are Ni vacancies (for $x<0.5)$ or Ni antistructure atoms on the Al sublattice (for $x>0.5).$ At stoichiometry $(x=0.5)$ the calculated effective Ni vacancy formation energy agrees quite well with experimental data. For $x<0.5$ the theory predicts a shrinkage of the sample with increasing temperature (superimposed to the usual anharmonic lattice expansion) due to thermal annihilations of structural Ni vacancies, in contrast to the experimental observation. The reason for this discrepancy is probably deviations of the structure of real $B2\ensuremath{-}{\mathrm{Ni}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ from the ideal model.

Theory of atomic defects and diffusion in ordered compounds, and application to B2-FeAl

By means of a generalized grandcanonical approach the relations between the effective formation energies, entropies and volumes of atomic defects in ordered compounds and the parameters characterizing the microscopic properties of the single defects are derived, whereby the microscopic parameters are calculated by the ab initio electron theory. The migration energies for several possible self-diffusion paths are determined by the transition-state theory in combination with the ab initio electron theory. Results are obtained for B2-Fe x Al 1− x at or close to stoichiometry, and they are compared with experimental data.

Atomistic Modeling of Interfacial Diffusion in the Lamellar Li0 TiAl

AbstractAtomistic simulation employing many-body central-force potentials was performed to elucidate the diffusion mechanisms in the bulk and at lamellar interfaces assuming a vacancy mechanism. First the self- diffusion of Ti and Al in stoichiometric structures was studied. It was found that the diffusion was faster along lamellar interfaces than in the bulk; the effective activation energy for the diffusion coefficient is about ∼15% lower. The simulations were then extended to investigate diffusion along lamellar boundaries with segregated Ti which is likely in Ti rich alloys. The surprising result is that diffusion remains practically unchanged when compared with the stoichiometric case. The reason is that while the path controlling the diffusion is different, the corresponding effective formation and migration energies are practically the same as in the stoichiometric case.

Atomic defects inD03-Ni3Sb: Anabinitiostudy

The effective formation energies and the effective formation volumes of atomic defects in the ordered compound Ni${}_{x}$Sb${}_{1\ensuremath{-}x}$ in the ${D0}_{3}$ structure are calculated by the statistical mechanics in combination with the ab initio electron theory. For the Sb-rich compounds the structural defect is the Ni vacancy on the $\ensuremath{\alpha}$ sublattice. The stoichiometric compound is a pentadefect system where on the average four Ni vacancies on the \ensuremath{\alpha} sublattice and one Ni antistructure atom are generated. The calculations strongly support the interpretation of results from neutron-scattering experiments.

Diffusion in Metals and Intermetallic Compounds: The Impact of AB-INITIO Calculations

ABSTRACTBy means of statistical mechanics the relations between the effective formation energies, entropies and volumes of atomic defects in ordered compounds which may be obtained experimentally and the parameters characterizing the microscopic properties of the single defects are derived, and the microscopic parameters are determined by the ab-initio electron theory. In a second step, the migration energies for possible self-diffusion paths are calculated by the transition-state theory in combination with the ab-initio electron theory. Results are reported for B2-FeAl and for Fe3Al, Ni3Sb and Fe3Si with D03 structure, and the impact of the calculations on the interpretation of experimental data is discussed.

Constitutional and Thermal Defects in Nickel Aluminides

ABSTRACTThe formation energies of intrinsic point defects and the interaction energies of possible defect pairs in NiA1 are calculated from first principles within an order-N, locally self-consistent Green's function method in conjunction with the multipole electrostatic corrections to the atomic sphere approximation. The theory correctly reproduces the ground-state properties of the off-stoichiometric NiAl alloys. The constitutional defects (antisite Ni atoms in Ni-rich and Ni vacancies in Al-rich NiAl) are shown to form ordered structures in the ground state, in which the defects of the same kind tend to avoid each other at the shortest separation distance on their sublattice. A mean-field theory is applied to calculate the equilibrium concentrations of thermal defects. The statistics of thermal defects is interpreted in terms of dominant composition-conserving complex defects which are shown to be triple defects in Ni-rich and nearly stoichiometric NiAl. In the Al-rich region a novel thermal excitation dominates where two constitutional Ni vacancies are replaced by one antisite Al atom. The number of vacancies, as well as the total number of point defects decrease with temperature in Al-rich NiAl. The boundary between the two regions is treated analytically. The vacancy concentration exhibits a minimum in its temperature dependence at the boundary. Similar analysis is applied to study constitutional and thermal defects in Ni3Al. The calculated effective vacancy formation energy in Ni3Al as a function of concentration is in excellent agreement with recent experimental data.

On the meaning of effective formation energies, entropies and volumes for atomic defects in ordered compounds

The statistical mechanics of atomic defects in ordered compounds is discussed within the framework of a generalized grandcanonical ensemble. To do this, grandcanonical defect formation parameters are introduced which characterize the properties of the respective single defects and which may be calculated by the ab initio electron theory. It is demonstrated that the commonly used effective formation parameters, defined via the temperature and pressure dependence of the defect concentrations, depend on the grandcanonical defect formation parameters of all the defects involved. They are in general complicated functions of the composition and do not have a simple physical meaning as in monoatomic crystals. This must be taken into account to avoid serious misinterpretations of experimental results.

Effective formation energies of atomic defects in D03Fe3Al: an ab-initio study

Abstract The effective formation energies of atomic defects in D0 3 Fe 3 Al are determined within the framework of a grand-canonical statistical method. The grand-canonical defect formation energies entering this method are calculated by the ab-initio mixed-basis pseudopotential method. Thermal vacancies appear on the α sublattice of the Fe atoms with an effective formation energy of 1.25 eV and on the Al sublattice (about 1.4 eV). The structural defects are Al antisite atoms on the γ sublattice of the Fe atoms or Fe antisite atoms on the Al sublattice.

Method for the determination of photostimulable defect center concentrations, production rates, and effective formation energies

A new method is proposed to determine radiation-induced defect center concentrations in solids which exhibit photostimulable luminescence. The technique relies on the determination of the number of photons released by spontaneous and photostimulated luminescence. A comparison with the x-ray-absorbed energy yields the effective formation energy of spontaneous luminescence photons and photostimulable centers. The method is applied representatively to BaFBr:Eu2+, which is utilized commercially as photostimulable x-ray storage phosphor in image plates for x-ray, γ-ray, electron, and neutron radiography. It is shown that in the utilized material on average 8 photostimulable F(Br−) centers (color centers based on bromine vacancies) and about 5 spontaneously emitted photons are generated by the absorption of 1 keV x-ray energy. Taking recent investigations into account which show that the x-ray generation of spontaneous luminescence and photostimulated luminescence centers is accompanied by the creation of approximately 36 nonphotostimulable defect centers, an average formation energy of about 20 eV per defect center can be calculated.

Point defect study of CuTi and CuTi2

The energies and configurations of interstitials and vacancies in the ordered compounds CuTi and CuTi2 were determined using atomistic simulation with realistic embedded-atom potentials. The formation energy of an antisite pair was found to be 0.385 and 0.460 eV in CuTi and CuTi2, respectively. In both compounds, the creation of a vacancy by the removal of either a Cu or Ti atom resulted in a vacant Cu site, with an adjacent antisite defect in the case of the Ti vacancy. The vacant Cu site in CuTi was found to be very mobile within two adjacent (001) Cu planes, with a migration energy of 0.19 eV, giving rise to two-dimensional migration. The vacancy migration energy across (001) Ti planes, however, was 1.32 eV, which could be lowered to 0.75 or 0.60 eV if one or two Cu antisite defects were initially present in these planes. In CuTi2, the vacancy migration energy of 0.92 eV along the (001) Cu plane was significantly higher than in CuTi. The effective vacancy formation energies were calculated to be 1.09 eV and 0.90 eV in CuTi and CuTi2, respectively. Interstitials created by inserting either a Cu or Ti atom had complicated configurations in which a Cu 〈111〉 split interstitial was surrounded by two or three Ti antisite defects. The interstitial formation energy was estimated to be 1.7 eV in CuTi and 1.9 eV in CuTi2.

Near-surface composition modifications in AgAuCu alloys by ion sputtering at elevated temperatures

Surface and subsurface compositional changes in a Ag40at%Au20at%Cu alloy at temperatures between 30 and 600°C were investigated using ion scattering spectroscopy. Upon heating the alloy, Cu and Au atoms segregated away from the surface. The entropies and enthalpies of Gibbsian segregation were determined to be 0.69 k and 0.134 eV for Cu, and − 0.21 k and 0.06 eV for Au, respectively, in the temperature range of 400–700°C. The time evolution of the surface compositions during 3 keV Ne + sputtering and corresponding steady-state compositional profiles were measured as a function of temperature. By comparing model calculations of near-surface compositional changes in the alloy with the experimental observations, useful information about the depth of origin of sputtered atoms and the defect properties in Ag-Au-Cu alloys was derived. The sputter fraction from the second atom layer was γ = 0.1; the effective vacancy formation energy was 1.12 eV; and the energies of vacancy and interstitial migration via Ag, Au and Cu were 0.66, 0.84 and 0.75 eV, and 0.06, 0.15 and 0.14 eV, respectively.

Calculation of Defect Properties of NiTi and FeTi

ABSTRACTThe energies and configurations of interstitials and vacancies in the B2 ordered compounds NiTi and FeTi were calculated using atomistic simulation. The stable configuration of a vacancy after the removal of an Ni atom was a vacant Ni site; similarly, the removal of an Fe atom in FeTi resulted in a vacant Fe site. Removal of a Ti atom in both compounds, however, resulted in a vacant Ni or Fe site and an adjacent antisite defect. The effective vacancy formation energies in NiTi and FeTi were calculated to be 1.48 and 1.07 eV, respectively. Interstitials in NiTi formed split <111> configurations consisting of a Ni-Ni dumbbell oriented in the <111> direction with one or two adjacent antisite defects. The Fe interstitial in FeTi had a similar configuration, except the dumbbell contained Fe atoms. The Ti interstitial in FeTi formed an <110> Fe-Fe dumbbell.

Predicting the structure and energy of a grain boundary in germanium

An ab initio molecular dynamics simulated quenching approach is used to study the properties of a (001) twist grain boundary in the Sigma =5 system in germanium. Interfacial total energies are mapped out over the entire range of possible relative in-plane translation states of the boundary. The analysis leads to predictions of the equilibrium translation state, the geometric structure, effective local volume and formation energy associated with this internal interface.

Equilibrium vacancies in Cu and Ag alloys with electropositive solutes

Abstract A new method is presented for the calculation of interaction energies of a vacancy-impurity pair and of higher-order complexes from the vacancy formation energy in pure metals and the concentration dependence of the effective formation energy in alloys. In terms of a modified complex model introduced by Berces and Kovacs, changes in the formation entropy of vacancy-impurity complexes compared with that of free vacancies as well as non-random solute distributions around vacancies are taken into account. The treatment is applied to effective vacancy formation energies as a function of alloying in several silver and copper systems with electropositive impurities obtained by resistivity measurements and positron annihilation. Vacancy impurity binding entropies of about k (Boltzmann's constant) are observed. The corresponding binding energies vary from −0·10 to −0·20 eV.

Vacancy‐Impurity Binding Energy and the Effective Vacancy Formation Energy as Determined from the Solidus Line for Binary Al‐Based Alloys

AbstractThe vacancy model of melting of metals has been used as a starting point for deriving the expressions permitting to determine the vacancy‐impurity binding energy, Ebv–i, and the effective vacancy formation energy from the knowledge of the solidus line for binary alloys. The calculated values of Ebv–i and E for binary Al‐based alloys show a fair agreement with the experimental data existing in the literature.