Energy of planar defects in the Ni<Subscript>3</Subscript>Al phase: Theory and experiment

The Ni₃Al phase with an L1₂ surperstructure exhibits a clearly pronounced positive temperature dependence of the yield stress. The nature of this phenomenon is still not clearly understood. The temperature dependence of the yield stress under consideration is determined, in many respects, by the structure of glide superdislocations and planar defects of these superdislocations involved in the L1₂ superstructure. A critical analysis is made of the current state of the art in the solution of the problem regarding the energy of antiphase boundaries in planes of an octahedron and a cube, as well as the energy of stacking faults in the Ni₃Al phase.     

Segregation of impurities and vacancies on phase and antiphase boundaries in alloys

The equilibrium distribution of low-concentration impurities or vacancies is investigated in the region of a coherent phase boundary or antiphase boundary in a binary alloy. A general expression for the free energy of an inhomogeneous multicomponent alloy, which generalizes the expression previously derived for a binary alloy, is presented. Explicit formulas for the impurity concentration profile c _im(x) in terms of the distribution of the principal components of the alloy near a boundary are obtained from this expression in the mean-field and pair-cluster approximations. The shape of this profile is determined by a “preference potential” P, which characterizes the attraction of an impurity to one of the alloy components, as well as by the temperature T and the phase transition temperature T c. At small values of P/T impurities segregate on a phase boundary, and the degree of this segregation, i.e, the height of the maximum of c _im(x), in the region of the boundary increases exponentially as the ratio T _c/T increases. For P ≠ 0 the c _im(x) profile near a phase boundary is asymmetric, and as P/T increases, it takes on the form of a “worn step.” The maximum on the c _im(x) curve then decreases, and at a certain |P|≳T _c it vanishes. Segregation on an antiphase boundary is investigated in the case of CuZn ordering in a bcc alloy. The form of c _im(x) near an antiphase boundary depends significantly both on the form of the potential P and on the stoichiometry of the alloy. At small P impurities segregate on an antiphase boundary, and at fairly large P “antisegregation,” i.e., a decrease in the impurity concentration on the antiphase boundary in comparison with the value within the antiphase domains, is also possible. Zh. éksp. Teor. Fiz. 112, 714–728 (August 1997)     

Atomic configurations of antiphase boundaries IN Lla superlattice alloys: APB of 1/2 <110> {110} type

An antiphase boundary of 1/2 <100> {110} type in equilibrium with atomic displacements is examined, such as occurs in an ordered alloy with Ll₂ superlattice. The effects from discrepancies in the atomic radii are evaluated along with those from differences in atomic interaction in a parallel simulation of the lattice states near planar defects in ordered Cu₃Au and Ni₃Fe. It is found that there are substantial differences in the local deformations at these boundaries by comparison with other types of planar defect: there are parallel planes involving compression and stretching together with oscillating atomic displacements perpendicular to the boundary, which die away at the eighth plane from the APB. It is found that the region of local deformation out to which the continuum theory of elasticity does not apply extends to ten planes of {110} type.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 49–52, July, 1987.     

Deformation-Induced Destruction of the Long-Range Order in Single Crystals of Ni3Fe Alloy

In the present work, x-ray diffraction and electron microscopy are used to investigate the state of a Ni₃Fe single crystal during plastic deformation. It is demonstrated that the observed destruction of long-range atomic order is accompanied with splitting of superdislocations and generation of single dislocations. The change of the long-range order parameter for single crystals deformed in the [001] direction estimated from the degree of splitting of superdislocations is in good agreement with x-ray measurements of this parameter. The destruction of long-range order for intermediate deformations < 40% is well described by the model of mechanical mixing of the alloy, the main role in which is played by the mechanisms of plane defect generation by shears along slip planes.     

Atomic configuration of antiphase boundaries in alloys

Computer simulation methods in the approximation of pairwise interatomic Morse potentials are used to calculate the atomic configurations and the energy of formation of 1/2 <110> {111} antiphase boundaries in ordered Cu₃Au and Ni₃Fe alloys. Atomic displacements result in considerable smearing of the first five planes closest to an antiphase boundary and a slip of atomic planes. These effects substantially reduce the energy of formation of antiphase boundaries. The influence of the size factor on the atomic configuration on the antiphase boundaries is discussed.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 2, pp. 43–47, February, 1985.In conclusion, the authors express their thanks to A. I. Tsaregorodtsev for useful discussion of this work.     

Simulation of the process of deformation-induced destruction of long-range order in alloys with an L12 superstructure

Plastic-deformation-induced destruction of long-range order in alloys with an L1₂ superstructure is considered. A mathematical model is suggested which takes into account the following mechanisms that lead to the destruction of long-range order: generation of superdislocations, generation of single dislocations, multiplication of antiphase boundaries (APBs) upon the conservative motion of dislocations, multiplication of APBs upon dislocation climb, formation of APB tubes on superdislocations, generation of point defects, and thermal ordering. A mathematical model of deformation strengthening and long-range order destruction with allowance for the change in the type of shear-forming dislocations from superdislocations to single dislocations is formulated.     

Electron-microscopic study of microcracks in single-crystal Ti<Subscript>3</Subscript>Al

Microcracks in a Ti₃ Al alloy subjected to indentation at room temperature were studied by transmission electron microscopy. The microcracks are shown to grow on \(\{ 0\overline 1 11\} \) pyramidal planes and in the slip bands of 2c + a superdislocations on \(\{ 20\overline 2 1\} \) and \(\{ 11\overline 2 1\} \) pyramidal planes. It is found that, due to the formation of a slip band in the basal plane at a microcrack tip, the propagating microcrack becomes steplike rather than straight. It is shown that a microcrack can nucleate at the line of intersection of \(\{ 11\overline 2 1\} \) pyramidal and \(\{ 0\overline 1 10\} \) prismatic planes.     

Temperature and velocity dependence of the mechanical properties of intermetallic compound Ni3Al. II

This paper examines the retardation of superdislocations in LI₂ superstructure, due to the capture by superpartial dislocations (SPD) of atomic defects on the slip plane, and also resulting from diffusion of atomic defects in PD. When the jogs formed by the settling of defects on dislocations remain nondissociated, the sliding of superdislocations is accompanied by the generation of displaced rows of atoms the maximum linear energy of which in the L1₂ superstructure amounts to v/b (v is the ordering energy, b the interatomic distance). The maximum magnitude of retardation of superdislocations, dependent upon generation of displaced rows, is twice as high on cubic planes as on octahedral planes. The estimations presented indicate that the diffusion settling of atomic defects on the SPD of sliding superdislocations can be a cause of the anomalous temperature dependence of flow stresses under high temperatures. Some effects associated with the possible dissociability of jogs on SPD are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 63–67, October, 1971.The authors express their thanks to É. V. Kozlov for helpful discussion.     

Dislocation retardation due to the destruction of short-range order in the L12 superstructure

The magnitude and temperature dependence of the dislocation retardation due to the destruction of short-range order are calculated in the quasichemical approximation. The atomic interaction in two coordination spheres and dislocation slip in cubic and octahedral planes are taken into account. The retardation stress for the first superdislocation is essentially the same in these planes for T < T _k (where T _k is the phase-transition temperature), while the retardation stress for subsequent superdislocations is much lower, so large planar accumulations of superdislocations may arise. The retardation stress is maximal at T = T _k , and for T > T _k the first dislocations should move in pairs. Comparison of the experimental cleavage stresses with calculated values shows that, by itself, superdislocation retardation due to correlation destruction cannot explain the behavior of the yield point.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 78–85, April, 1971.     

Slip transfer at coherent twin boundaries in Ni3Al and ordered Cu3Au

Slip transfer at coherent twin boundaries in L1₂-ordered alloys has been investigated by analysis of plastically deformed Cu₃Au and Ni₃Al specimens in a transmission electron microscope. A comparison between the ex situ deformed material and previous in situ experiments is made. In ordered Cu₃Au, antiphase boundaries induced by slip transfer have been found at a coherent twin boundary (CTB), similar to the in situ deformed material. On the other hand, in Ni₃Al superlattice intrinsic stacking faults (SISFs) were detected at CTBs which have not been observed in in situ deformed material. A possible mechanism for SISF formation is discussed. The transfer of slip, and the associated creation of stacking faults at CTBs in both materials is described in terms of absorption of superdislocations in the boundary and the general criteria for slip transfer at grain boundaries.     

Investigation of changes in the order parameters near antiphase boundaries in the Cu<Subscript>3</Subscript>Au alloy

Investigation of the specific features of order-disorder structural phase transitions in ordering alloys in the presence of antiphase boundaries of conservative and nonconservative types has been performed in a computer experiment by the example of the model Cu₃Au alloy. The distributions of the long-range and short-range order parameters in the planes parallel to antiphase boundaries have been obtained by the Monte Carlo method for different temperatures. The mechanisms of disordering near conservative and nonconservative boundaries in ordering alloys are revealed. It is shown that the effect of diffusion of superstructural parameters is significant near nonconservative antiphase boundaries in comparison with conservative boundaries. Obviously, nonconservative boundaries can make a relatively large contribution to the effect of positive temperature dependence of the yield strength of ordering alloys with the L1₂ superstructure.     

Formation of microcracks in an indented Ti<Subscript>3</Subscript>Al intermetallic compound

Microcracks in the Ti₃Al alloy indented at room temperature have been analyzed by electron microscopy. Analysis of the microstructure has revealed that microcracks propagate in the {0\(\overline 1 \)11} pyramidal planes and in the slip bands of the 2c + a superdislocations in the {20\(\overline 2 \)1} and {11\(\overline 2 \)1} pyramidal planes. It is found that the formation of a slip band in the basal plane at the microcrack tip leads to a change in the character of microcrack propagation from straight-line to steplike.     

The effect of antiphase domains on the energy spectra of special boundaries in alloys with the <Emphasis Type="Italic">L</Emphasis>1<Subscript>2</Subscript> superstructure

The special grain boundaries in ordering alloys with the L1₂ superstructure have been investigated by optical metallography and transmission diffraction electron microscopy. The relative energy of the boundaries Σ3 and Σ9 in Ni₃Fe alloy with a short-range order is determined. The energy of these boundaries in an alloy with long-range order is estimated. The energy of twin grain boundaries increases at the phase transitions A1 → L1₂ due to the formation of antiphase grain boundaries in those boundaries. The spectra of special boundaries over Σ and their distributions, depending on the relative energy, change as well. The average relative energy of special grain boundaries in alloys with the L1₂ superstructure increases with increasing the energy of antiphase boundaries.     

Nucleation of microcracks during dislocation interactions in a Ti<Subscript>3</Subscript>Al single crystal

Reactions between superdislocations involved in deformation in the basal, prismatic, and type-I and II pyramidal planes in single-crystal Ti₃Al are considered. The types of dislocation interactions are established that result in the formation dislocation barriers (microcrack nuclei). The force and energy conditions for microcracks to arise are found. The interaction between a and 2c + a superdislocations results in microcracks with the plane of opening lying in basal and pyramidal planes; the interaction of 2c + a superdislocations in different pyramidal planes results in the formation of microcracks in prismatic and pyramidal planes; and the interaction of a superdislocations in basal and/or pyramidal planes does not cause the formation of dislocation barriers. The types of microcracks are classified in terms of the orientation of deformation axes of single crystals, and the regions of the stereographic triangle are determined characterized by a preferential type of crack opening.     

Generalized stacking faults in model lattice of ordered Fe-Si alloys

The energies of the generalized stacking faults lying on {110} and {112} planes are calculated for Fe-Si alloys with the DO₃ long-range order for concentrations 10–25 at. % Si. In the used model, the interaction between atoms is described by the series of three central interatomic potentials fitted to experimental data. The lattice relaxations perpendicular to the stacking fault plane are considered. The displacement vectors corresponding to stable antiphase boundaries are found and some consequences for the structure of superdislocations in the DO₃ superlattice are mentioned.The author is indebted to Dr. F.Kroupa and Dr. L.Lejek for valuable discussion.     

Special features of the long-range order – short-range order phase transition in FCC-based alloys

Results of x-ray analysis of the long-range order in FCC-based alloys with L1₂, L1₂(M), L1₂(MM), and D1_a superstructures are generalized. Regularities of the behavior of the long-range order parameter and average size of the thermal and periodic antiphase boundaries (APB) are traced, main mechanisms of temperature order-disorder phase transition are elucidated, and influence of the thermal and periodic APB on the special features of the order-disorder phase transition is revealed. The character of change of the periodic antiphase boundary density determines the special features of the order-disorder phase transition in alloys with longperiod superstructures.     

T.E.M. study of Al2O3 metastable phases

Plasma spraying was employed to obtain rapidly solidified dense metastable alumina samples. They have been studied after being sprayed and in various annealed states by transmission electron microscopy and X-ray powder diffraction.

The so-called “γ” phase has been imaged by T.E.M. and exhibits a more or less ordered domain structure with quasi-periodic 1/4 <110> antiphase boundaries in the {100} planes of the defective spinel lattice.

Heating “γ” between 850 and 1050°C leads to more ordered intermediate phases. They are shown to appear through a two-dimensional antiphase periodic boundaries mechanism. Aluminum vacant sites are likely located along the antiphase planes and their concentration (Al_2.66□_0.33O₄) is consistent with the observed periodicities. The “δ” and “θ” forms are considered as variants of this structure.     

Spin waves transport across a ferrimagnetically ordered nanojunction of cobalt-gadolinium alloy between cobalt leads

A model calculation is presented for the spin wave scattering and coherent transport at the ferrimagnetically ordered cobalt-gadolinium alloy nanojunction between cobalt leads. The structural model for the amorphous alloy nanojunction [Co_1/2Gd_1/2]₃ is considered as an ordered alloy hcp structure of three (0001) atomic planes between the leads. To analyze the spin dynamics and spin wave scattering at the nanojunction boundary, the phase field matching method (PFMT) is implemented over the ground state of the system, in the Heisenberg Hamiltonian representation. The coherent reflection and transmission probabilities of spin waves from the cobalt leads incident onto the nanojunction boundary are calculated, and numerical results are presented for the coherent SW transport across the nanojunction over the entire range of their frequencies. The results are especially valid in the interval between nanometric SW wavelengths greater than the nanojunction width and macroscopic wavelengths. They demonstrate in particular, the possibility of the resonance assisted maxima for the SW transmission spectra owing to the interactions between the incident spin waves and the localized spin resonances on the nanojunction. This effect is general and may be observed at different characteristic frequencies and corresponding incident angles.     

Influence of the antiphase domain structure on the long-range atomic order parameter in the Ni3Mn alloy with superstructure L12

The antiphase domain structure in the Ni₃Mn alloy with superstructure L1₂ with various manganese contents has been studied. It has been found that a deviation of the alloy composition from the stoichiometry leads to the formation of manganese oxides at the antiphase domain boundaries and grain boundaries. With an increase in the antiphase domain sizes, the domain size distribution function changes from the normal to lognormal, and the degree of long-range atomic order decreases.     

Dislocation structure of intermetallic Ti3Al subjected to high-temperature deformation

Transmission electron microscopy was used to examine the dislocation structure of intermetallic Ti₃Al subjected to deformation at tempertures T = 1073–1273 K. The microstructure of samples subjected to high-temperature deformation is established to contain mobile superdislocations of a and 2c + a types, and single dislocations with Burgers vector [0001] are also observed on the prismatic planes. Possible models of destruction of barriers associated with 2c + a superdislocations on the pyramidal planes are discussed using the results of computer simulations of the structure of a superdislocation core in in Ti₃Al.