Point defects and their properties in FeAl and FeSi alloys

Positron annihilation as well as differential dilatometric measurements were performed to measure the vacancy concentration in FeAl and FeSi. The highest vacancy concentration is found at the stoichiometric B2 composition with more than 3.5% at the melting point in FeAl. Additionally, diffusion and isotope effect experiments were carried out in B2 FeAl to obtain information about the diffusion mechanism. The isotope effect decreases when the material transforms from D0₃ to B2. The effective formation volume of the defects in the B2 phases is larger (1.4Ω) than one atomic volume Ω and is related to a defect involving more than one vacancy. The effective migration enthalpy of 0.5–1.8 eV as well as the effective formation enthalpy of 0.7–1.02 eV vary with the concentration of the alloys in an opposite manner. The results for the FeAl system suggest that different defect types may operate as diffusion vehicles in the different phases. The mobility of the defects dominates the thermomechanical behavior of FeAl alloys. The defect production during mechanical deformation of FeAl alloys is divided into two parts. The annealing out of mechanically produced defects occurs on the same time rate as that of thermal defects.     

High-temperature atomic defect properties and diffusion processes in intermetallic compounds

Data on thermal vacancy formation in intermetallic compounds obtained from positron lifetime spectroscopy yield high effective formation enthalpies H^F_V in close-packed structures and low values in bcc-type structures which can be well understood theoretically. The vacancy migration enthalpy H^M_V could be determined at high temperatures for B2-FeAl by studying the equilibration process after temperature changes. As demonstrated here in a comparative study on B2-FeAl the thermal formation and migration of defects can also be sensitively investigated by time-differential length-change studies after temperature changes in the vicinity of the equilibration temperatures. The present vacancy data can explain the wide variation of the transition metal self-diffusivities in intermetallic compounds. For B2-FeAl it is shown that the high-temperature mechanical properties are closely linked to the formation of thermal defects as evidenced by the temperature variation of the yield stress anomaly and its time dependence after fast heating.     

Constitutional and thermal defects in B82–SnTi2

Vacancy and antisite defect formation energies in B8₂–SnTi₂ are calculated by an ab initio approach. Three sublattices are introduced to account for the B8₂ structure. A statistical model based on a mean-field approximation is developed in the canonical ensemble. The defect concentrations are calculated as function of temperature and deviation from stoichiometry. For stoichiometric B8₂–SnTi₂ alloys, the dominant thermal defects are composed of one antisite Ti atom and three Ti vacancies. In the Sn-rich B8₂–SnTi₂, the constitutional defects are Ti vacancies; the thermal defect below 1000 K is an interbranch where Ti vacancies are replaced by Sn antisites; at high temperatures, it is a four point-defect comprising one Ti antisite and three Ti vacancies. In the Ti-rich B8₂–SnTi₂, the constitutional defects are antisite Ti atoms and the thermal defect is a four point defect comprising one Ti antisite and three Ti vacancies. The effective defect formation enthalpies are derived at low temperature. The Gibbs energy as well as the Sn and Ti chemical potentials in B8₂–SnTi₂ phase are obtained as function of composition for various temperatures. The extension of the one-phase domain of B8₂–SnTi₂ in the Sn–Ti phase diagram is discussed.     

Changes in the potential and vibrational energies upon the formation of vacancies in oxygen-doped cores of crystallite-conjugation regions of polycrystalline 4d and 5d BCC transition metals

The changes in the potential (u _cmpl) and vibrational (?_cmpl) energies and the signs of changes in the interatomic spacings (Δa _cmpl) upon the formation of vacancies in oxygen-alloyed (OA) cores of crystallite-conjugation regions (CCR) in polycrystalline 4d and 5d transition metals Mo, Ta, and W have been determined. The potential energy upon the formation of vacancies (upon the formation of vacancy complexes with oxygen atoms—vacO complexes) in the OA cores of CCRs in polycrystalline Mo, Ta, and W increases (u _cmpl are positive), as upon the formation of vacancies in pure CCR cores of transition bcc d metals. The vibrational energy upon the formation of vacancies in OA CCR cores in polycrystalline Mo, Ta, and W decreases (?_vacO are negative). The negative sign of changes in the vibrational energy upon the formation of vacancies in the OA CCR cores in Mo, Ta, and W (?_vacO < 0) agrees with the independent determinations of the sign of changes in the vibrational energy in the OA CCR cores in polycrystalline tungsten (?_vacO)_W using Mössbauer measurements of the Debye temperature. The signs of changes in the interatomic spacings upon the formation of vacancies in the OA CCR cores in polycrystals of Mo, Ta and W are negative (Δa _VacO < 0), in contrast to positive (0 < Δa _BCC) changes in the interatomic distances in the nearest neighborhood of vacancies formed in pure CCR cores in Mo, Ta, and W.     

Solute and vacancy segregation to a/4<1 1 1> and a/2<1 0 0> antiphase domain boundaries in Fe3Al

Segregation of solute atoms and vacancies to antiphase domain boundaries (APDBs) in Fe–Al alloys near the stoichiometry Fe₃Al (Fe–22–28 at.% Al) was studied using a phase-field model based on the Bragg–Williams approximation. Local equilibrium vacancy concentration was determined from experimental data for vacancy formation enthalpy and the configurational entropy of vacancies assuming that the formation enthalpy is independent of long-range order and chemical composition. Fe atoms and vacancies segregate to APDB with the phase-shift vector a/2<1 0 0>(D0₃-APDB) in crystals with stoichiometric composition (Fe–25 at.% Al) and with the Fe-rich composition, whereas both of them tend to be depleted in Al-rich crystals. On the other hand, Fe atoms and vacancies both segregate on APDBs with the phase-shift vector a/4<1 1 1>(B2-APDB) in all compositions studied. The effects of vacancy segregation on APDB energy and thickness is negligibly small; however, the vacancy concentration at the center of APDBs can be up to 80% larger than in the bulk, and therefore it is anticipated that the mobility of APDBs can be significantly affected by the segregation of vacancies as well as by that of solute atoms.     

Crystallite-conjugation regions and adjacent lattice regions in polycrystalline iridium: III. Enthalpies of formation of vacancies and the energies of interaction of partners in vacancy complexes with oxygen formed in the cores of crystallite-conjugation regions in polycrystalline iridium

The interatomic spacings in the cores of crystallite-conjugation regions (CCRs) and adjacent lattice regions (ALRs) of polycrystals either decrease or increase upon alloying of nominally pure metals with oxygen and vacancy complexes with oxygen (mVacO, where m is the number of vacancies in the complex) that are formed during annealing. These changes in the interatomic spacings lead to an increase or decrease in the isomer shifts δ of the components of the Mössbauer spectra of atomic probes ⁵⁷Fe that are localized in the CCR cores and ALRs of polycrystals [1–6]. The enthalpies Q _mcmpl1, of formation of vacancy-oxygen complexes mVacO in the CCR cores have been measured for Ir and Cr polycrystals, and the enthalpies Q _Vac,1 of formation of vacancies in CCR cores have been determined for Ta, W, Ir, and Cr polycrystals. The enthalpies E _mcmpl of the interaction between the partners of the complexes increase with increasing number m of vacancies in the complexes.     

Thermal vacancy formation in Co-based Heusler-type alloys Co2MnZ (Z = Si, Ge, Sn)

Thermal vacancy formation was studied for the Heusler-type ferromagnetic alloys Co₂MnZ (Z = Si, Ge, Sn) as a function of temperature (773–1273 K) by the density, electrical resistivity and positron annihilation measurements. The vacancy concentration increased with increase in quenching temperature and particularly, a high vacancy concentration exceeding 2% was observed in Co₂MnGe and Co₂MnSn. Estimated vacancy formation and migration energies were comparable with those for B2-type FeAl and CoGa alloys with high vacancy concentration. Further, the vacancy type and the vacancy site were examined for alloys quenched from 773 K. As a result, it was suggested that the mono-vacancies are randomly distributed over the lattice sites.     

Lattice gas decomposition model for vacancy formation correlated with B2 atomic ordering in intermetallics

Thermal vacancy formation correlated with atomic ordering was modelled in B2-ordering A–B binary intermetallics. Ising Hamiltonian was implemented with a specific Bragg–Williams-type thermodynamic formalism for thermal vacancy formation based on the phase equilibria in a lattice gas composed of atoms and vacancies. It has been demonstrated that for pair-interaction energetics favouring vacancy formation on A-atom sublattice, equilibrium concentrations of vacancies and antisite defects result mutually proportional in well defined temperature ranges. The effect observed in both stoichiometric and non-stoichiometric binary alloys was interpreted as a tendency for triple defect formation. In B-rich non-stoichiometric binary alloys vacancy concentration did not extrapolate to zero at temperature approaching zero, which indicated the formation of constitutional vacancies. Energetic conditions for the occurrence of the effects were analysed in detail.     

Accelerating disorder–order transitions of FePt by preforming a metastable AgPt phase

Many approaches had been reported to successfully reduce the transition temperature of FePt from A1 to L1₀ phase, though without detailed knowledge. In this work, we deposited the metastable AgPt layer adjacent to the Fe layer and addressed the importance of vacancies in the disorder–order transition of FePt at reduced temperatures on the basis of a kinetic diffusion model. The decomposition of the metastable AgPt phase, creating excess vacancies during the post-deposition annealing process, accelerated the intermixing between Fe and Pt and the nucleation of L1₀ FePt. The evolution of phase transformation from AgPt–Fe to L1₀ FePt–Ag was monitored by in situ high temperature X-ray diffractometry and was also validated by first-principles calculations. The intermixing between Fe and Pt and the nucleation of L1₀ FePt after annealing at 230 °C were directly observed by transmission electron microscopy and grazing incidence X-ray diffractometry, respectively. With the assistance of the decomposition of AgPt, we obtained a (0 0 1)-dominated L1₀ FePt film with an out-of-plane coercivity as large as 13.3 kOe after annealing at a temperature as low as 350 °C. The principles of the proposed method can be applied for versatile disorder–order phase transitions.     

The stress anomaly in FeAl–Fe3Al alloys

The anomalous stress peak observed near 500–600 °C in Fe–Al alloys has now been convincingly explained using a model of hardening by immobile thermal vacancies on the lower temperature side of the peak and the loss of hardening as these vacancies become mobile at higher temperatures. The large numbers of vacancies required for such hardening are associated with compositions close to stoichiometry, i.e. 40–50%Al, raising the question of whether such a vacancy hardening model can be adopted for Fe₃Al alloys, which show a similar stress peak anomaly. Examination of data on vacancy formation over the entire range of composition, Fe–Fe₃Al–FeAl, shows that, indeed, a vacancy hardening model appears capable of explaining the stress anomaly for both FeAl and Fe₃Al.     

Defect structures in ZrCo2 Laves phase

Point defect structures in the C15 ZrCo₂ alloys were studied by bulk density and X-ray lattice parameter measurements. It was found that, for the ZrCo₂ alloys quenched from 1000°C, the lattice parameter increases linearly as the Zr content increases up to 33.3 at.% Zr. The lattice parameter of the Laves phase remains constant for the alloys with Zr content higher than 33.3 at.%, indicating that the solubility range of Zr in ZrCo₂ on the Zr-rich side is essentially zero. The constitutional defects were found to be of the anti-site type. Thermal vacancies exhibiting a maximum at the stoichiometric composition were observed in the ZrCo₂ Laves phase alloys after quenching from 1250 and 1000°C, with higher thermal vacancies obtained from 1250°C. The defect structures in the ZrCo₂ phase may be correlated to the relative magnitude of formation enthalpies for anti-site and quadruple defects in this compound. Thermal vacancy concentration at a level of 1% in ZrCo₂ does not affect fracture toughness at room temperature.     

First-Principles Calculations of Defect Structures in B2 AlCo and GaCo

First-principles electronic structure calculations have been performed for defect structures in nonstoichiometric B2 AlCo and GaCo. To determine the type of constitutional defects, the compositional dependence of the energy of formation and lattice parameter was obtained by calculations employing supercells of various sizes (16 and 32 atoms) as well as special quasirandom structures (SQSs) developed for random pseudobinary A_1?x B _x C with compositions x = 0.25 and 0.5. According to the results, Co vacancies are the constitutional point defects in the Al-rich side of both B2 AlCo and B2 GaCo, while Co vacancies present the minimum energy for the Ga-rich side. For the Co-rich side of both B2 AlCo and B2 GaCo, the Co antisite is the most stable defect. To investigate the thermal defect concentrations at finite temperature, we adopted the Wagner–Schottky model using enthalpies of formation of point defects obtained from the SQS approach. The present results suggest that the predominant thermal defects in AlCo are of complex type whereas for GaCo they are of interbranche Co type. The results of these calculations show agreement with available theoretical and experimental data.     

Deformation-induced point defects in NiAl single crystals

NiAl single crystals, oriented for single slip, were deformed at room temperature to a strain of 2%, and were subsequently annealed in the temperature range of 673–873 K (T/T_m=0.35–0.45). In as-deformed samples, dislocation substructures consist of jogged edge and screw dislocations, and prismatic loops. Densities of vacancy- and interstitial-type loops are about equal. Annealing causes shrinkage and disappearance of the interstitial loops and significant growth of the vacancy loops. These observations suggest that excess vacancies are present after room temperature deformation. These non-equilibrium point defects may result from non-conservative motion of jogged screw dislocations.     

Microstructural evolution and mechanical properties of an Nb–16Si in-situ composite with Fe additions prepared by arc-melting

This paper deals with phase constitutions, microstructural evolutions, and mechanical properties of Nb–16Si–xFe in-situ composites (where x = 2, 4, 6 at.%, referred as to 2Fe, 4Fe and 6Fe alloys, hereafter) prepared by arc-melting. It is found that with additions of Fe, Nb₄FeSi silicide arises and microstructures of as-cast samples are consisted of dendritic-like Nb_SS phase, Nb₃Si block, and Nb₄FeSi matrix in the 2Fe and 4Fe alloys, and of the dendritic-like Nb_SS phase and Nb₄FeSi matrix in the 6Fe alloy. When heat-treated at 1350 °C for 100 h, part of the Nb₃Si phase decomposes in the 2Fe and 4Fe alloys, and the 6Fe alloy shows no change in microstructure as compared with the as-cast one. The Nb₄FeSi silicide is found to be brittle, its fracture toughness and elastic modulus are first obtained, having values about 1.22 MPa m^1/2, and 310 GPa, respectively. The fracture toughness of the bulk as-cast and heat-treated Nb–16Si–xFe samples are changed slightly by the Fe additions, which is in a range of 9.03–10.19 MPa m^1/2. It is interesting that at room temperature, strength is improved by the Fe additions, whereas at 1250 °C and 1350 °C the strength decreases. As the Fe content increased from 2 at.% to 6 at.%, for example, the 0.2% yield strength increases from 1410 MPa to 1580 MPa at room temperature, decreases from 479 MPa to 385 MPa at 1250 °C.     

Optical properties of heusler alloys Co2FeSi, Co2FeAl, Co2CrAl, and Co2CrGa

The results of an investigation of optical properties and the calculations of the electronic structure of Co₂FeSi, Co₂FeAl, Co₂CrAl, and Co₂CrGa Heusler alloys are presented. The main focus of our attention is the study of the spectral dependence of the real part (?₁) and imaginary part (?₂) of the dielectric constant in the range of wavelengths λ = 0.3–13 μm using the ellipsometric method. An anomalous behavior of the optical conductivity σ(ω) has been found in the infrared range in the Co₂CrAl and Co₂CrGa alloys, which differs substantially from that in the Co₂FeSi and Co₂FeAl alloys. The results obtained are discussed based on the calculations of the electronic structure.     

Possibilities of random vacancy distribution and antisite atom recovering in the point defect mechanism in B2-type intermetallics

Point defect behavior in B2-type intermetallic compounds is investigated from thermodynamic point of view based on the Bragg–Williams method. The model is developed by taking new point defect formation mechanism, random vacancy distribution (RVD) and antisite atom recovering (ASAR) processes, into consideration, which was proposed based on the current findings in X-ray and in situ neutron diffraction studies for B2 FeAl. Free energy expressions for pure states of the antisite defect (ASD), RVD, triple defect (TRD) and ASAR and also those for hybrid state between the RVD, TRD and ASAR are obtained. From these expressions, the condition for appearance of the RVD and ASAR behavior is considered. Numerical results are given for three cases which show the different point defect behaviors due to composition and temperature. The first case indicates a creation of a substantial high concentration of the A-vacancy only in the B-rich composition region, as observed in B2 NiAl. This situation, however, is interpreted by the ASAR process by B antisite atom, not by the TRD process. In the second case, RVD like behavior appears in the A-rich region. This resembles the observation in B2 FeAl, but it is not by an appearance of the pure RVD state. ©     

空位对Cu/Sn无铅焊点界面元素扩散的影响

界面柯肯达尔空洞形成的过程伴随着空位的形成与扩散,对空位行为的研究有利于深入理解界面扩散和空洞形成过程. 运用分子动力学方法模拟Cu/Cu₃Sn界面上空位对扩散的影响,计算空位形成能、扩散势垒及空位扩散激活能. 结果表明,相同条件下含空位的模型发生扩散的几率要高于不含空位的模型. 另外,计算表明铜晶体的空位形成能大于Cu₃Sn晶体中铜空位的形成能;Cu₃Sn晶格中不同晶位的Cu空位(Cu1空位和Cu2空位)的形成能比较接近,但均小于锡的空位形成能. 此外,对Cu/Cu₃Sn界面的空位扩散势垒及空位扩散激活能的计算结果表明,Sn原子的空位扩散激活能高于Cu原子.     

Effect of η-phase and FeAl composition on the mechanical properties of WC–FeAl composites

This study investigated the effects of η-phase generation and the binder phase composition of iron aluminide (FeAl) on the mechanical properties of tungsten carbide–iron aluminide (WC–FeAl) composites. The η-phase was generated in the composites when the WC–FeAl powder was highly oxidized before sintering in a vacuum. The presence of the η-phase resulted in the degradation of mechanical properties such as transverse rupture strength (TRS) and indentation fracture toughness (IFT). In addition, FeAl composition varied mainly as a result of α-Al₂O₃ formation. The iron-rich side of FeAl in binder phase improved the TRS and IFT. It was concluded that control of the η-phase generation and an appropriate FeAl composition are very important to maintain high TRS and IFT in the WC–FeAl system.     

Changes in the vibrational energies and interatomic spacings upon the formation of vacancies in the volumes and in the cores of crystallite-conjugation regions of polycrystalline transition metals with cubic lattices

The changes in the vibrational energies and the signs of changes in the interatomic spacings upon the formation of vacancies in the bulk of metal and in the cores of the crystallite-conjugation regions (CCR) in polycrystalline transition metals with bcc and fcc lattices have been determined. The vibrational energy increases upon the formation of a vacancy in the bulk of metal because of a positive “relaxation” contribution to the change in the force constant of the atoms surrounding a vacancy. Positive “relaxation” contributions to the changes in the force constants and, correspondingly, an increase in the vibrational energy of the atoms surrounding a vacancy arise also upon the formation of “split” vacancies (S vacancies) in the cores of CCRs of polycrystalline transition metals with a face-centered cubic lattice. The positive “relaxation” contributions to the changes of the force constant of atoms in the region of localization of S vacancies are caused by a decrease in the interatomic spacings upon their formation, just as upon the formation of conventional vacancies in the bulk of metals. The vibrational energy of the nearest environment of the vacancies that are formed in the CCR cores in the polycrystalline d transition metals with a bcc lattice decreases because of a negative “relaxation” contribution to the change in the force constants. The cores of the high-angle CCRs in polycrystalline d transition metals with a bcc lattice are characterized by a negative internal pressure. Therefore, vacancies with positive relaxation volumes ν_BCC > 0 are formed in them, causing an increase in the interatomic distances in the nearest environment of such vacancies.     

Investigation of point defect migration in Fe–Al alloys by means of fast Doppler broadening technique

In order to study the migration of point defects in Fe–Al alloys within the range of 25–40 at.% Al quenching experiments were carried out. The equilibration process was observed by means of Doppler broadening of the 511 keV positron annihilation peak using a ²²Na positron emitter. Annealing at different temperatures in B2′ and in D0₃ structure, respectively, permits the determination of effective migration enthalpies H^M_eff. Whereas annealing the Fe-25 at.% Al alloy in D0₃ structure and annealing the Fe-40 at.% Al alloy in B2 structure yields only one migration enthalpy of H^M_eff=0.45 eV and H^M_eff=1.2 eV, respectively, in Fe-30 at.% Al as well as in Fe-35 at.% Al two recovery stages could be observed. In Fe-30 at.% Al an early recovery stage is associated with H^M_eff =1.0 eV and a late one with H^M_eff=1.3 eV. In Fe-35 at.% Al the early stage is dominated by H^M_eff=0.9 eV and H^M_eff=1.8 eV, the late one by H^M_eff=1.8 eV and H^M_eff=1.7 eV for recovery in B2- and D0₃-structure, respectively.