The non-Arrhenius migration of interstitial defects in bcc transition metals

Thermally activated migration of defects drives microstructural evolution of materials under irradiation. In the case of vacancies, the activation energy for migration is many times the absolute temperature, and the dependence of the diffusion coefficient on temperature is well approximated by the Arrhenius law. On the other hand the activation energy for the migration of self-interstitial defects, and particularly self-interstitial atom clusters, is very low. In this case a trajectory of a defect performing Brownian motion at or above room temperature does not follow the Arrhenius-like pattern of migration involving infrequent hops separated by the relatively long intervals of time during which a defect resides at a certain point in the crystal lattice. This article reviews recent atomistic simulations of migration of individual interstitial defects, as well as clusters of interstitial defects, and rationalizes the results of simulations on the basis of solutions of the multistring Frenkel–Kontorova model. The treatment developed in the paper shows that the origin of the non-Arrhenius migration of interstitial defects and interstitial defect clusters is associated with the interaction between a defect and the classical field of thermal phonons. To cite this article: S.L. Dudarev, C. R. Physique 9 (2008).     

IBA calculations on the even-even Pt isotopes

By performing least-squares-fit calculations on the energy spectra of the even-even ^186–196Pt isotopes, the IBA model I and the IBA model II are compared on an equal footing. It is found that both model I and model II can fit energy spectra and absolute B(E2) transition rates reasonably well. Model II shows a distinct improvement in the energy spectra of β-bands of heavier nuclei in the isotope series. It is suggested that for regions far from the closed shells model I may be used to simulate model II as a useful phenomenological probing tool.     

Peierls potential for crowdions in the bcc transition metals

We present the first derivation of the analytic expression for the Peierls-Nabarro potential for crowdion migration using the double sine-Gordon model. The analysis is guided by the group-specific trend in the shapes of the periodic lattice potentials calculated for the body-centered-cubic transition metals in groups 5B and 6B of the periodic table. We combine density-functional calculations of the crowdion's profile and environment with an extended version of the analytical Frenkel-Kontorova model, and determine the effective potential experienced by the defect's center of mass. This reveals important underlying differences between the metals in these groups, which are inaccessible to either the numerical or analytical approaches alone, and accounts for the previously unexplained significantly higher crowdion migration temperatures observed in the metals of group 6B relative to those of group 5B.     

Quadrature effects on the accuracy of flux calculations in realistic atmospheres

We have investigated the accuracy of five different quadrature methods—equal steps in θ, equal steps in cos θ, Gaussian, double Gaussian and Gauss-Lobatto—on the accuracy of fluxes in realistic aerosol atmospheres, using the Gauss-Seidel method. In addition, a range of Gaussian quadrature stream numbers from two to 32 were compared. The atmospheric models considered are those recently presented by Lenoble, with the exception that we have used Henyey-Greenstein phase functions in place of Mie. Our results should be easily reproduceable by any other workers interested in similar realistic atmospheres. A table of Gauss-Lobatto weights and points is provided as an appendix.     

Radiation damage in bcc metals studied by TDPAC

The time-differential perturbed angular correlation (TDPAC) method is an excellent tool for the study of radiation damage in metals and it has been applied successfully to many fcc metals. Recently, some investigations have been performed with bcc metals, where it is more difficult to obtain reliable results because the open lattice easily absorbs many impurities. After a short general introduction to the field, the power of the TDPAC method is demonstrated by showing in detail recent results obtained by our group in Bonn for the bcc metal tungsten. Finally, the present situation for all non-ferromagnetic bcc metals is summarized.     

Shell-model calculations for the zinc isotopes

Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, 0}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits outside a closed “⁵⁶Ni” core. The effective Hamiltonian used was one obtained by Koops and Glaudemans from a fit to Ni and Cu level energies. An average absolute deviation of 0.19 MeV between the calculated and experimental ground-state binding energies is obtained for the A = 62?68 Zn isotopes. Good agreement is also found between most calculated and experimental excitation energies and spectroscopic factors for single-nucleon transfer for the low-lying levels in these nuclei. Experimentally known B(E2) values are generally well reproduced by the present model with effective charges of 1.0 ± 0.1 and 1.6 ± 0.2 for the neutron and proton, respectively. Magnetic dipole as well as Gamow-Teller transitions are not well accounted for by these calculations and seem to be sensitive to excitations of the ⁵⁶Ni core.     

Cavity formation at indium impurities in bcc metals

The defect formation in the bcc metals W and Mo above annealing stage III and the influence of rare gases on this process were investigated by means of the perturbed angular correlation technique using¹¹¹In as radioactive probe. In both metals a relatively high electric field gradient (EFG) could be observed at the indium site, characterized by the quadrupole interaction frequencies υ_Q=263 MHz, ν=0 and υ_Q=220 MHz, ν≈0.15 for W and Mo, respectively. The observations are assigned to the growth of threedimensional vacancy clusters at the probe atoms with the indium atoms situated in the inner surface of this cavities, thus experiencing the corresponding surface EFG.     

The effect of shear stress on the screw dislocation core in bcc metals

The screw dislocation core structure in bcc metals under an external shear stress is investigated using the model of generalized splitting as an approximation of the Peierls-Nabarro model of screw dislocation dissociated on three {110} slip planes. The shear stress for which the core structure in this model is unstable is found.     

Treatment of bcc transition metals on a modified CGW model

The vibrational spectrum and specific heat of three bcc transition metals -iron, chromium and tungsten are computed on the basis of modified Clark-Gazis-Wallis angular force model which considers volume forces of Krebs' nature. The calculations are made using the Blackman's root sampling technique for a discrete subdivision in wave-vector space. The calculated lattice specific heats and the effective Debye temperatures are compared with the available experimental data. The results show a reasonably satisfactory agreement with the experimental observations.The authors are highly thankful to Dr.Jyoti Prakash, Dr. S.Chandra for helpful discussions. One of them (H. L. K.) is thankful to C. S. I. R. India for the award of J. R. F. The computational facilities received from the I. I. T. Kanpur are also acknowledged.     

Phonon dispersion for the bcc metals Mo and Cr

In this paper the phonon dispersion for the bcc metals Mo and Cr is calculated based on the pair potentials obtained from cohesive energies and the Slater-Kirkwood- type three body interaction. In the calculation of the pair potentials the Möbius transform in the number theory is used and the cohesive energy is evaluated by the LMTO method. The results show a good agreement with inelastic neutron scattering data and indicate that the three-body interaction is necessary to account for the phonon dispersion.     

Dislocation structure and deformation hardening of bcc metals

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 23–34, March, 1991.     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

Shell-model calculations on Ni and Cu isotopes

Binding energies, excitation energies and spectroscopic factors have been calculated for^57–67Ni and^58–68Cu in an unrestricted (2p_3/2, lf _5/2,2p_1/2) shell-model space. The effective two-body matrix elements are obtained from the modified surface delta interaction (MSDI) and from a least-squares fit to experimental binding and excitation energies (ASDI). The average deviation between about 100 experimental and calculated energies is 0.14MeV for MSDI and 0.08 MeV for ASDI. Excitation energies of high-spin states are given also. Spectroscopic factors have been calculated for all single-nucleon transfer reactions on stable Ni or Cu targets leading to Ni or Cu isotopes. For spectroscopic factors larger than 0.4 the average deviation between theory and experiment is about 30%. The experimentally observed and calculated spectroscopic strengths are compared by using sum rules and are found to be consistent. An extensive compilation has been made of experimental data on energies,J ^π assignments and spectroscopic factors.     

Electronic selection rules controlling dislocation glide in bcc metals

The validity of the structure-property relationships governing the low-temperature deformation behavior of many bcc metals was brought into question with recent ab initio density functional studies of isolated screw dislocations in Mo and Ta. These relationships were semiclassical in nature, having grown from atomistic investigations of the deformation properties of the group V and VI transition metals. We find that the correct form for these structure-property relationships is fully quantum mechanical, involving the coupling of electronic states with the strain field at the core of long a/<2111> screw dislocations.     

Pressure-volume calculation in bcc metals using Born stability criteria

A simple analytical two-body potential φ(r) = −Ar ⁻ⁿ + B exp(−pr ^m) is considered for P-V calculations in bcc metals using Born stability criteria. It is shown that the stability of bcc metals can be expressed uniquely as a function of a parameter q (discussed in the text). The P-V calculations are done in ten bcc metals. The calculations are compared with the experimental data of shock-wave measurements and also with other potential available. It is found out that the present potential is better than the other two-body potentials in case of bcc metals. Further, the calculations done for TOEC and the first pressure derivative of SOEC are found in good agreement with the reported results.     

Variational calculations on the hydrogen molecular ion

We present high-precision non-relativistic variational calculations of bound vibrational—rotational state energies for the H⁺ ₂ and D⁺ ₂ molecular ions in each of the lowest electronic states of Σ _g , Σ _u , and Π _u symmetry. The calculations are carried out including coupling between Σ and Π states but without using the Born—Oppenheimer or any adiabatic approximation. Convergence studies are presented which indicate that the resulting energies for low-lying levels are accurate to about 10^?13. Our procedure accounts naturally for the lambda-doubling of the Π _u state.     

Variational calculations of realistic models of nuclear matter

We report variational calculations of nuclear matter with a semi-realistic Reid v₁₂ model, and a realistic v₁₄ model of the two-nucleon interaction operator. The v₁₄ model fits the available nucleon-nucleon scattering data up to 425 MeV lab energy, and has relatively weak L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions in addition to the standard central, tensor and ($\text{L}\text{·}\text{S}$). The L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions are treated semiperturbatively; their contribution reduces the overbinding of nuclear matter. However, the equilibrium k_F = 1.7 fm^?1 and E₀ = ?17.5 MeV obtained with the v₁₄ model are both higher than their empirical values k_F = 1.33 fm^? and E₀ = ?16 MeV. We assume that the difference between the calculated and empirical E(ρ) is entirely due to three-nucleon interactions (TNI). The TNI contributions are phenomenologically added to the nuclear matter energy, and their parameters are adjusted to obtain the correct equilibrium energy, density and compressibility. The required TNI contributions appear to be of reasonable magnitude.