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Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase field crystal model which takes into account relaxation of atomic density (as a slow thermodynamic variable) and atomic flux (as a fast thermodynamic variable). Such model covers slow and rapid regimes of interfaces propagation at small and large driving forces during solidification. In example of BCC crystal lattice invading the homogeneous liquid, dynamical regimes of crystalline front propagating along the selected crystallographic directions are studied. The obtained velocity and the velocity sequences for different faces are compared with known results. © 2020 Elsevier B.V.

In the framework of numerical calculations and analytical expansion in the transfer integral between the next-nearest neighbors t' and the direct antiferromagnetic (AFM) gap , the metal-insulator transition criterion is obtained, the Hartree-Fock and slave boson approaches being used. In the case of a square lattice, there is an interval of t' values, for which the metal-insulator transition is a first-order transition, which is due to the Van Hove singularity near the center of the band. For simple and body-centered cubic lattices, the transition from the insulator AFM state occurs to the phase of an AFM metal and is a second-order phase transition; it is followed by a transition to a paramagnetic metal. These results are modified when taking into account the intersite Heisenberg interaction which can induce first-order transitions. © Published under licence by IOP Publishing Ltd.

The metal–insulator transition (MIT) for the square, simple cubic, and body-centered cubic lattices is investigated within the t–t′ Hubbard model at half-filling by using both the generalized for the case of spiral order Hartree–Fock approximation (HFA) and Kotliar–Ruckenstein slave-boson approach. It turns out that the magnetic scenario of MIT becomes superior over the non-magnetic one. The electron correlations lead to some suppression of the spiral phases in comparison with HFA. We found the presence of a metallic antiferromagnetic (spiral) phase in the case of three-dimensional lattices. © 2016, Springer Science+Business Media New York.

Prototype tantalum coatings, electrochemically deposited from a molten salt onto 20-mm interior bore steel liners, exhibited superior wear and erosion behavior compared to chromium coatings. The liners were subjected to cyclic exposures of high temperature, pressure, and an aggressive chemical environment. X-ray analysis of the coatings revealed a low-hardness, randomly-oriented, body-centered-cubic, alpha-phase tantalum. Formation of tantalum oxides (predominantly Ta2O5), swaging due to the low-hardness of the coatings, a 2-micrometers layer consisting of tantalum and carbon at the tantalum/steel interface, and surface compressive residual stresses were observed. Cylindrical magnetron sputtering systems were constructed to coat 45-mm interior bore steel cylinders to protect them from wear and erosion. X-ray diffraction, scanning electron microscopy, photomicrography, and hardness analysis of several sputter-deposited tantalum specimens revealed coatings consisting of soft body-centered-cubic alpha-phase and hard tetragonal beta-phase tantalum., Presented at the 26th International Conference on Metallurgical Coatings, and Thin Films, San Diego, CA, 12-16 April 1999. Published in Surface Coatings and Technology.

This report presents the results of an investigation of elevated temperature irradiation swelling in refractory metals with an objective of understanding swelling mechanisms in these materials and demonstrating practicality of swelling-resistant materials. The study was divided into three phases. During the first phase, a theoretical model was developed for the swelling in body-centered cubic (bcc) metals. The model was based on chemical reaction rate formalism. Calculations were carried out on on a model material, niobium, which was selected for the study. Experimental and theoretical work was conducted to determine the swelling mechanism. Niobium was irradiated with Nb(++) ions to a dose of 50 dpa and swelling was determined by transmission electron microscopy. A peak swelling at 900C of 7% was observed. No swelling was observed above 1300C. The experimental data were compared to those predicted by the theoretical model. Reasonable agreements were obtained between the experimental and theoretical swelling curve when niobium-oxygen interaction was included. Sink strength ratios were also calculated from the data. The theoretical model was extended during the second phase to include loop growth/ shrinkage in bcc metals. During the third phase of the program, two alloys, Nb- 5Hf and Nb-5W, were irradiated with Nb(++) alone and with Nb(++) + He(+) over a temperature range of 800 - 1350C.

We examine model cluster structures by applying the simple Hueckel method to spherically symmetric clusters whose atoms are constrained to occupy cubic (simply, body-centered or face-centered) and hcp lattice positions. The Hueckel orbitals are organized into energy shells, many of which remain well separated even at 500-600 atom cluster sizes. The classical droplet model provides a good fit to cluster atomization energies, which then correctly extrapolate to the bulk cohesive energy predicted by tight binding calculations. Energy level distributions for cubic lattice show that features characteristic of a tight binding solid become fully evident in clusters containing as few as 100 atoms. A particular example is the high density of states found for the Fermi level of bcc clusters, vestiges of which might suffice to confer on suitable materials an enhance electrical conductivity. (AW), Prepared in cooperation with California Institute of Technology, Pasadena, CA. and City University of New York, NY.

The primary objective of this investigation was the derivation of binary phase diagrams by means of a statistical mechanical model called the Cluster Variation Method. In particular, phase equilibrium as a function of the ratio between the values of second and first neighbor effective pair interactions, the ratio being the only physical input to the computer codes. The resulting phase diagrams are important for the purpose of analyzing experimentally determined alloy phase diagrams. Keywords: Cluster Variation; Solid Solutions; Statistical Mechanics; Mathematical Models; Phase Diagrams. (Author).

In this letter we assess the accuracy of the LSDA in describing the magnetic and structural ordering in 3d transition metals, based on total energy calculations for fcc and bcc iron as a function of volume and type of magnetic order. The local spin density approximation (LSDA) in describing the magnetic and structural ordering in iron is tested based on a series of total energy calculations using the general potential LAPW (linearized augmented plane wave) method. We find that ferromagnetism is stable in the bcc phase, while antiferromagnetism, which is degenerate with the nonmagnetic state, is stable in the fcc phase. However, our results show that the fcc phase is 867 K lower in energy than the bcc phase, which indicates a fundamental deficiency of LSDA in describing the magnetic interactions in transition metals., Prepared in cooperation with College of William and Mary, Williamsburg, VA. Dept. of Physics under Grant NSF-DMR81-20550.

The objective of this program was the understanding of the role of alloying elements in promoting ductility in BCC metals. The program considered the roles of both increased cohesive strength of solids and enhanced plastic deformation in improving the resistance of a solid to fracture. Various approaches were used to evaluate changes that could affect the fracture behavior. These included estimates of true surface energy and fracture stress using interatomic potential functions, and the effect of plastic deformation using a model crack that allowed plastic deformation at the crack tip. Measurements were made of elastic constants, magnetic susceptibility, and fracture energies of pure metals and alloys. Several alloys were studied including Fe-Si, W-Re, W-Ta, Nb-Zr, and Nb-Hf.

Mechanical testing in tension and compression has been done on single crystals of tantalum and tantalum-base interstitial and substitutional solid solutions involving a wide range of crystallographic orientations. These experiments were complemented by analyses of slip lines and dislocation structures by optical and high voltage electron microscopy, respectively. The research has established many aspects of the relative roles of the Peierls stress of extended screw dislocations and solution hardening in determining the low temperature strength of body-centered cubic materials. The major findings include (a) establishing the importance of the normal stress on low temperature strength of bcc materials; (b) determination of the large effects of solutes on the orientation dependence of yielding, the stress differential in tension and compression, slip and twin systems, and primary screw dislocation structure, distribution, density and cross glide; and (c) determination that the widths of extended screw dislocations in bcc materials are very small.

The general purpose of this research program has been two-fold: (1) to determine the brittle fracture characteristics, mainly, of several steel and titanium materials; and, (2) to develop via appropriate constitutive relations a detailed description of the ductile-brittle transition behaviour which is exhibited by certain BCC and HCP metals. The brittle fracture behaviour of these materials was directly measured by tensile testing at 4.2K. Compression tests at 4.2K were performed, also, so as to establish the nature of whatever plastic deformation behaviour might be induced in the absence of applied tensile stresses.

A theoretical calculation has been made of the temperature dependence of the force-constant changes at the (001) free surface of body-centered cubic crystals. The changes arise from anharmonic effects. The procedure consists of first calculating the dynamical displacements by evaluating the Helmholtz free energy including anharmonic terms with the aid of many-body theoretical techniques and then calculating the change in force constants in the vicinity of a crystal surface produced by the cubic anharmonic terms in the crystal potential energy. Numerical estimates of the force-constant changes have been made for alpha-iron using a model consisting of Lennard-Jones 6-12 type central interactions up to second neighbors. The influence of surface force-constant changes on such effects as the surface-mode frequencies, the temperature dependent surface mean-square displacements and the stability of a crystal surface are discussed.

The research was concerned with studying the structure, the mechanical properties and the decomposition of Ti and Zr b.c.c. (e.g. Zr-Nb, Ti-V) solid solutions. The experimental techniques used in this study were electron microscopy, electron diffraction, elastic constant measurements and single crystal tensile testing. The purpose of this Final Report is to review the highlights of the research and point out important results.

B6 octahedra, which consist of six boron atoms in an octahedral arrangement, are important structural units in such materials as the metal hexaborides and the recently discovered boron-metal WANGNOL alloys. The X(alpha) Scattered Wave Method has been used to calculate the electronic properties of both an isolated octahedron and the effects of external environment. The latter has been investigated by surrounding a B6 octahedron by various configurations of atoms representing the local structure of the metal hexaboride and alloy materials. Results obtained from these calculations have been used to provide an explanation of the difference in properties between the metal hexaborides and the WANGOL alloys in terms of the difference in local bonding properties of the two materials. The bonding in the metal hexaborides is shown to be primarily ionic-covalent, while that of the WANGNOL alloys is found to be more ionic-metallic. This difference in bonding is shown to lead to quite different electronic and mechanical properties in the two classes of materials.

We use a modified Kadanoff's variational method to calculate the phase diagram of an Ising model with random vacancies on one of two interpenetrating sublattices of the isotropic square (SQ) and body-centered cubic (BCC) lattices. We find second order phase transitions only for T0. The transition temperature to very good approximation decreases linearly with impurity (i.e. vacancy) concentration at small concentration. This agrees with the linear decrease observed in other systems. A plausible explanation of the absence of first order transitions for T0 is given. The relation of our models to certain percolation problems is similar to that of some spin models studied by Syozi. Thus our results allow an estimate of critical probabilities for percolation. (Author)

Using computer simulation, the authors have attempted to relate the macroscopic fracture properties of bcc iron to phenomena on the atomic scale. Although bonds can be made to rupture in the computer model (brittle fracture), the predicted cleavage plane is the (100) plane. This discrepancy is attributed to the approximations made in the flexible boundary. (Author), Presented at the International Conference (3rd) on Fracture (3rd), Munich, 8-13 April 73.

The deformation and strengthening of bcc Ti-Mo alloys has been investigated by examining single crystals of Ti-12-1/2 wt.% Mo. A change in deformation mode from twinning to slip occurs when single phase crystals are aged to precipitate omega phase. In the single phase solution treated condition, the crystals deform by (332) <113> twinning. When omega phase is present the crystals deform by <111> slip. The occurrence and formation of alpha phase in Ti-Mo-Al alloys has also been investigated. The relationship between Burgers and non-Burgers alpha phase is discussed with regard to mechanisms of formation and kinetics of the transformation. (Author)

The stress-velocity relations for screw and mixed dislocations in high purity niobium were studied at 298K and 196K. Etch pitting methods were used to reveal the dislocation positions after stress pulses in tension and compression. Attention was particularly directed towards establishing any asymmetry in the motion of dislocations on the (112). No asymmetry was observed for either screw or mixed dislocations moving on the (112). The motion at 298K at low stresses was limited by extrinsic barriers while that at 196K and high stresses seemed limited by intrinsic dislocation drag. (Author)

A calculation is submitted of the diffusion coefficient of atoms which have penetrated into the internodes of body-centered cubic crystalline lattice of a binary alloy which may be in an ordered state., Trans. of Zhurnal Tekhnicheskoi Fiziki (USSR) v24 n10 p1802-1811 1954.

Solutions for the maximum resolved shear stresses on twinning systems in fcc and bcc crystals in tension and compression are presented and discussed. Additional data are included on the relative magnitudes of shear stresses on secondary systems. Conventions for the specification of twinning systems are described and discussed.

The high temperature thermodynamic data obtained on ternary carbides having the sodium-chloride type structure have been correlated with the bonding and mechanical properties of these carbides. The metal-metal bonding on the metal sublattice in the carbide is the same as in the binary body-centered cubic metals. The variation of the carbon-carbon interaction energy and the metal- carbon interaction energy indicates that the metal-carbon bonds are localized bonds. From the variation of the difference in metal-carbon interaction energy with composition the compressibility of the carbides at elevated temperature can be calculated. The values are in excellent agreement with values derived from room temperature mechanical properties measurements., See also Part 1, AD700765.

Surface vibration modes for the (001) surface of monatomic bcc crystals are examined using a simple model which allows for full cubic anisotropy and which exactly fits the second-order elastic constants. For both the semi-infinite crystal and the crystal slab approaches, the effect of anisotropy is examined for iron, vanadium and isotropic tungsten. For each crystal a surface mode with shear-horizontal (SH) polarization is found below the SH bulkband along the (100) direction but not along the (110) direction. For long wavelength, the frequency of this surface mode departs from the bulk band edge as the inverse cube of wavelength and the localization depth is proportional to the inverse square of wavelength. A surface mode with SH polarization is found above the SH bulkband in both the (100) and (110) directions for vanadium. In addition to the Rayleigh waves, a number of short wavelength surface modes with sagittal-plane polarization are found for each crystal. (Modified author abstract)

The temperature and shear strain rate dependences of the flow stresses measured for single crystals or polycrystals of alpha-iron, molybdenum, and niobium are compared on the basis of the thermal activation-strain rate analysis (TASRA). Of particular concern is the TASRA parameter, the 'activation volume', which is shown to follow a reciprocal dependence on the thermal component of shear stress, with fair accuracy. (Author Modified Abstract), Prepared in cooperation with Oxford Univ. (England).

New techniques for computing intensity distributions from atomic arrangements with defects in periodicity were applied to a variety of models in an attempt to reproduce in detail the diffuse neutron diffraction pattern of a Zr-20 wt. % Nb alloy quenched from 1273K. The model which succeeds is described, and its kinematic intensity sum is derived. The resultant computed diffuse intensity distribution is compared with experiment. (Author), Prepared in cooperation with Oak Ridge National Lab., Tenn. Metals and Ceramics Div. Sponsored in part by Atomic Energy Commission.

Little information is available on coherent twin boundary energies of bcc metals. This is due to the difficulty in recognizing annealing twins in bcc metals because of their unique morphology and to their rarity because of their relatively high interfacial energy. The purpose of this investigation is to show through surface morphology measurements that the interfaces of a bcc deformation twin will, upon annealing, achieve as low an interfacial energy as a coherent annealing twin.

Many practical Ti, U and Zr-base alloys have microstructures that result from transformations originating in b.c.c. solid solutions. In recent years there has been a considerable amount of research performed on these alloys at industrial, government and university laboratories. The purpose of the conference was to bring together for a few days all the people active in this area of research, in order to exchange current and rapidly developing ideas. Summaries of the invited and contributed papers are assembled., Sponsored in part by Office of Naval Research, Arlington, Va.

Computer simulations were performed to locate the equilibrium positions and binding energies of interstitial He, Ne, Ar, Kr, and Xe in a tungsten crystal. Heavy interstitial atoms in tungsten share a lattice site with the atom that normally occupies that site and form what is called a split interstitial. Three characteristic interstitial sites were located relative to each lattice site tested. The distance of the impurity atom from the site was seen to vary roughly inversely with its mass, and the displacement of the lattice atom increased with the mass of the impurity atom. The foreign atom in its interstitial position was tested to determine the minimum initial kinetic energy needed to escape the lattice, as well as the optimum escape direction. (Author)

The temperature dependence of the mean square displacements for atoms on the (100) and (110) surfaces of chromium has been studied theoretically using the harmonic approximation. Calculations were carried out for crystals with periodic boundary conditions in two directions and free boundary conditions in the third direction using a Born-Von Karman model with central interactions up to third nearest neighbors and non-central angular stiffness interactions between nearest and next nearest neighbors. The values of the force constants were chosen to give good fits to the elastic constants and to the bulk phonon dispersion curves in the three major directions (100), (110) and (111). The ratio of the mean-square displacements at a surface to that in the bulk was calculated as a function of temperature for both the (100) and (100) surfaces. The theoretical results are compared with the available experimental data from low-energy electron diffraction. (Author)

The energy required to form a twin in Nb has been experimentally determined to be of the order 1 billion ergs/cc. This high energy has been explained in terms of a continuous nucleation theory which also accounts for the observed morphology of twins in B.C.C. transition metals and the heat evolved in the process. (Author)

Simple models for describing the elastic constants of b.c.c. crystals in terms of force constants for stretching and bending of bonds are discussed. It is concluded that observed elastic constants are compatible with a model comprising a volume-dependent term and central force terms between nearest neighbours and next-nearest neighbours in the strain energy. (Author)

A mathematical procedure is presented for applying the Born stability criteria to the determination of the mechanical stability of cubic crystals in the presence of applied forces and deformations. The general procedure is suitable for use in conjunction with a computer and is independent of the specific model of interatomic interactions that can be used in numerical calculations. Specific calculations are performed for a body-centered cubic (B.C.C.) crystal lattice with a uniaxial tensile force applied perpendicularly to a face of a unit cell. The atoms in the crystal are assumed to interact through a 2-body Morse interatomic potential function appropriate to B.C.C. iron. Two ranges of stability are found to exist: a B.C.C. phase and body-centered tetragonal phase (B.C.T.). For the B.C.T. phase, the lattice remains stable for values of tensile strain up to about 7%, with corresponding strength. These values are close to the measured tensile characteristics of fine iron whiskers. (Author)

An analytical study is made of face-shear and thickness-twist waves propagating along the (100) and (110) directions of a body-centered cubic lattice plate bounded by a pair of (001) surfaces. The behavior of the waves in the (110) direction is similar to that found previously for analogous waves in the (100) direction of simple-cubic and face-centered cubic plates. In the (100) direction of the body-centered cubic plate, the situation is quite different. Near the halfway point of the first Brillouin zone, the lowest symmetric mode and the lowest antisymmetric mode are predominantly surface modes and the remaining modes group together in a narrow, high frequency band-pass. The results of numerical computations are exhibited for iron and tungsten. (Author)

The research performed in this laboratory is primarily concerned with the interaction of ultrasound with nuclear and electron spins in solids. The present report describes (1) the detailed studies made under the contract of the elastic, magneto-elastic, F19 nuclear acoustic resonance and Mn19 nuclear acoustic resonance in the cubic antiferromagnet, RbMnF3; and (2) the study, as a function of temperature, of the anomalies in the elastic properties and nuclear acoustic resonance in bcc metal crystals.

Faulting on (211) planes has been reported in filings of many b.c.c. materials based on differences in the broadening of various peaks in the x-ray powder pattern. These experiments have been repeated in this work using (a) recent techniques for correcting for various experimental errors and (b) new derivations of effects of faults on other planes. The results indicate that there are no faults produced by filing in Fe, beta-brass, and Mo-Re alloys. For Nb there are faults on (110), and concentration varies inversely with the interstitial content. (Author)

The research accomplishments of a two year study of the Peierls-barrier are reported. Metals deform plastically principally by movement of dislocations and the Peierls-barrier is one of the impediments to such motion. Earlier work had indicated that the Peierls-barrier depends mainly on three parameters. The present work shows that these reduce to two parameters which are so closely related as to constitute a single complex parameter, a complex width where the real part is ordinary width and the imaginary part is the separation of partials if the dislocation is dissociated. (Author)

A preliminary account is given of sharp 'rays' and related intensity structure revealed by high resolution classical calculations of atomic scattering from an ordered monolayer. Factors related to use of structural features of the intensity maxima for investigation of atom-surface interaction fields are discussed. (Author)

The report discusses a mechanism for the work hardening phenomena occurring in iron base alloys., Prepared in cooperation with Calif. Univ., Los Angeles, Calif. Dept. of Engineering.

Assuming metals to be isotropic, infinitely large, homogeneous, and continuous elastic media, the tetrahedral and octahedral position energies of such interstitial impurity atoms as C, N, O, and H in body-centered cubic metals Fe, W, Mo, Ta, and Nb are calculated by using the concept of the elastic dipole. Calculation results show that the remaining atoms are all located at octahedral positions, except that H occupies the tetrahedral position in W, Mo, Ta, and Nb. Also, a critical radius has been found to determine whether interstitial atoms are in the tetrahedral or the octahedral position. In the last part, activation energy for diffusion of interstitial atoms among octahedral sites is calculated, and results obtained all rather closely agree with previous workers' experimental data. (Author), Edited trans. of Wu Li Hsueh Pao (Mainland China) v22 n3 p281-293 1966.

The objective of this program has been to elucidate the fundamental mechanisms of high-rate plastic deformation of metals. Single crystal specimens of an fcc metal (Cu) and a bcc metal (Nb) were deformed; the macroscopic yielding behavior was noted for each material as a function of strain rate, and the structures of the deformed crystals were studied by metallographic techniques. In addition to the single-crystal work, a study was made of the character of slip bands in polycrystalline iron and a mild steel as a function of temperature. This permitted comparisons to be made between the behavior of different bcc metals. (Author)

Certain Ti and Zr solid solutions containing the omega phase exhibit intensity distributions in reciprocal space which are partly diffuse. In an effort to understand the structural meaning of these diffraction patterns, the authors have developed new methods for the evaluation of the kinematic intensity sum for certain kinds of atomic arrangements which are not quite periodic. The methods are illustrated by their application to a simple model for these alloy systems. The model successfully reproduces some but not all of the features of observed intensity distributions. (Author), Prepared in cooperation with Oak Ridge National Lab, Tenn.

The report presents the results of an investigation to ascertain the role of alloying elements on the brittle fracture behavior of the bcc metals, with special emphasis on iron, molybdenum, and tungsten. (Author)

Much of the work this year has been concerned with the detailed exploration of the critical region for different models. The form of the function h(x) in the scaling-law equation of state for the two and three dimensional Ising models was calculated. The results of the calculation have been compared with experiment and with empirical formulae. It was found possible to account theoretically for the spurious unphysical singularities in the low temperature series for the Ising model which mask the true critical behaviour. Low temperature series for the spin 1 Ising model have been derived. The numerical results are consistent with the hypothesis that the indices beta and delta are spin-independent. For the problem of non close packed dimers on a lattice, series expansions have been derived as in the Ising problem and they have been used to establish the behaviour of monomer-dimer equilibrium. Detailed research has been undertaken into the Green's function for random walks on the bcc lattice. A number of exact formulae have been derived using generalized hypergeometric functions which could be of use in several branches of solid state physics. Finally, a careful analysis of the form of correction terms to critical behaviour in the Ising model has been carried out. This enables a precise definition of the critical region to be made. (Author)