Shunya Ishioka

Diffusion mechanisms in ordered alloys—a detailed analysis of six-jump vacancy cycle in the B2 type lattice

Abstract The diffusion coefficients of A and B atoms in the B2 type AB alloy are derived for the case that highly correlated vacancy jump cycle is operative. The effective frequencies of 100- and 110-type jumps of A and B atoms are expressed in terms of frequencies for individual vacancy jumps; the calculation is made by applying the concept of the mean first passage time known in the theory of stochastic processes. The correlation factors for diffusion of A and B atoms are calculated as a function of the wrong bond energy. The present analysis provides a sound and quantitative basis for the discussion of the ratio of diffusion coefficients for two types of atoms, D A D B , in ordered alloys.

The core structure of 1/3⟨1123⟩ {1122} edge dislocations in h.c.p. metals

Abstract A computer simulation has been carried out for the core structure of a 1/3⟨1123⟩ {1122) edge dislocation using the truncated Lennard-Jones (12–6) potential. The core is composed of two distinct structural units which can be interpreted in terms of {1121) and {1122) twins. This core structure differs markedly from that proposed by Rosenbaum (1964).

The core structures of a ⅓〈1 123〉{1122} edge dislocation under applied shear stresses in an h.c.p. model crystal

Abstract The behaviour of a ⅓〈1 123〉{1122} edge dislocation under the effect of an external shear stress applied on {1122} planes has been studied by computer calculation. Before the application of the external stress, the dislocation has either of two typos of core configuration; one spreads as two twin faults on {1121} and {1122} planes (type I) and the other as a stacking fault with a fault vector of b/2, hounding partial cores still having the same twin faults as in the type-I core (type II). When the shear stress is applied in a direction that corresponds to tension along the c axis, the {1121) twin develops from both types of core under suitable conditions. When the stress is applied in the opposite direction, the type-I core changes into type-II; the dislocation moves as an extended dislocation without development of the {1122} twin. The results are interpreted and discussed in the light of experimental observations on deformation in h.c.p. metals.

Random walks on diamond and hexagonal close packed lattices

Abstract Random walks on the diamond (dia.) and the hexagonal close packed (h.c.p.) lattices are discussed in terms of random walk generating functions for non-Bravais lattices composed of two sublattices. The number of visits to the origin, P(0; 1), for the two lattices is related to that of the face centred cubic (f.c.c.) lattice by P(0; 1) dia. = 4/2P(0; 1) t.c.c. , P(0; 1) h.c.p. = P(0; 1) f.c.c. , The correlation factors for tracer diffusion in the h.c.p. lattice have been calculated rigorously by using the result of random walk calculations, which confirms the values obtained by Compaan and Haven (1958).

Motion of a 1/3〈1123〉 screw dislocation in a model h.c.p. lattice

Abstract A computer-simulation study has been made of the behaviour of a 1/3〈1123〉 screw dislocation under the effect of applied shear stresses, using a truncated Lennard-Jones potential. As has been shown elsewhere, the stress-free dislocation assumes various core configurations spreading over {1011}, {1122} or several combinations of these planes. Regardless of its core configurations, the dislocation glides on the {1122} plane under the shear stress applied in the direction corresponding to the compression parallel to the c axis, while it glides on the {1011} plane under the shear stress applied in the opposite direction. The result is discussed in the light of the macroscopic behaviour of h.c.p. metals.

The core structure of a 1/3〈1 123〉 screw dislocation in h.c.p. metals

Abstract Atomistic calculations are made for a 1/3〈1 123〉 screw dislocation, using a truncated Lennard-Jones (12–6) potential. A variety of core configurations are formed depending on initial conditions. They can be interpreted as combinations of two types of elementary structures; one corresponds to an extension of the core along {1011}, and the other along 〈1122〉 planes, each bounded by partial dislocations with the Burgers vectors b/2 (= 1/6〈1 123〉). The fault energies on the {1011} and {1122} planes are almost the same, which is consistent with the appearance of various core configurations. The planar fault bounded by partials is not a simple stacking fault but has transition layers, which are caused by shuffling movements of atoms normal to the fault vector. The shear displacement accompanying the fault, however, occurs stepwise at the fault and the partials are not zonal. This is in sharp contrast to the dissociation models for the dislocation so far proposed.

Effect of oxygen on diffusion of manganese in α-titanium

Abstract Diffusion coefficients of 54Mn in single crystal α-Ti have been measured over the temperature range from 878 to 1135 K. It has been confirmed that manganese exhibits fast diffusion, which is about three orders of magnitude faster than self-diffusion in α-Ti. Temperature dependence of 54Mn diffusivities parallel and perpendicular to the c axis is, respectively, expressed as D∥ = (4.9 ± 1.9) × 10−6exp(−160.5 ± 2.7 kJmol−1/RT) m2s−1, D⊥ = (6.0±1.3)× 10−5 exp(−189.2 ± 1.6 kJmol−1/RT) m2s−1. Effect of oxygen on Mn diffusion in polycrystal α-Ti has also been investigated. The addition of oxygen suppresses the Mn diffusion, which is interpreted as blocking effect of oxygen.

Random walks and correlation factor in diffusion in a three-dimensional lattice with coordination number 8

Abstract Random-walk properties are calculated for a three-dimensional lattice with coordination number B. The new lattice consists of the mid-points of the edges of a simple-cubic lattice. Since niobium and oxygen atoms in niobium monoxide arrange themselves in this way, the lattice is referred to as the NbO lattice. The values of the return probability pr and correlation factor / for tracer diffusion via the vacancy mechanism are compared with those for other three-dimensional lattices so far reported; pr decreases and / increases with increasing coordination number of the lattices. It is suggested that the determination of the correlation factors for the Nb or O diffusivities in NbO is helpful in clarifying the mechanism of diffusion.

Isotope effect for anomalous fast diffusion

Abstract The very small isotope effect is characteristic of the so-called anomalous fast diffusion of metallic solutes in metals. Consistency is critically re-examined between the small isotope effect and the interstitial (or interstitial-type) mechanism which is most popularly accepted. It is shown that the isotope-effect coefficient E for the interstitial diffusion can be regarded as a kind of average of the ‘kinetic factors’ for all kinds of jumps. The origin of the small ‘kinetic factors’ is discussed on the basis of the Vineyard rate theory. It is pointed out that there are two possible types of the saddle-point configuration: ‘stable’ and ‘unstable’. If interstitial solutes move via the ‘stable’ configuration, the interstitial mechanism is consistent with the small isotope effect. A few comments are made on previous arguments on the isotope effect.

Integral methods in the calculation of correlation factors for impurity diffusion

Abstract A new method of calculating correlation factors in impurity diffusion is developed. The method, which is based on the theory of random walks on an imperfect lattice, yields a rigorous result within the framework of the adopted model. The expressions for the correlation factors in the five- (or four-) vacancy jump frequency model are given for the b.c.c., f.c.c. and diamond-structure lattices.