Hirokazu Koizumi

Plastic flow stress of b.c.c. transition metals and the Peierls potential

Analysis of the temperature dependence of the flow stress of the b.c.c. metals α-Fe, Nb, Mo and Ta reveals their Peierls potentials. They are dam-like with a flat maximum or even have an intermediate minimum, but they are never sinusoidal. The elastic energy of the activated bulges in the dislocations is fully taken into account in a quasi-anisotropic calculation by making it trapezoidal. In the thermally activated configuration the amplitude of the bulge (the height of a kink pair) is the lattice periodicity a, double activation to 2a is excluded.

Kink pair nucleation and critical shear stress

Abstract The activation energy ΔH ∗ for forming a rectangular kink pair in a dislocation on a Peierls potential is calculated. If the potential is smooth and has only one minimum, the energy ΔH ∗ (τ) decreases monotonously with the applied stress τ. If the potential has the shape of a camel-hump, with an intermediate minimum, discontinuities appear in ΔH ∗ (τ) . When the top of the potential is nearly flat or has a shallow minimum, the ΔH ∗ (τ) curve has a hump, causing a hump in the temperature dependence of the critical shear stress.

Dislocation Model of Amorphous Germanium

From a point of view that a crystal containing many dislocations can be a model of an amorphous solid, the structure of amorphous Ge has been generated on a computer by introducing many screw dislocations regularly into a diamond lattice. It is expected that the radial distribution function for the distance smaller than the period of the dislocation array is little influenced by the regularity and is mainly determined by the core structure of dislocations. In relaxing the atom positions to minimize the total energy, the Keating potential was used for the interatomic interactions. It is found that the radial distribution function for the dislocation density of 0.25 b per atomic volume or 4.4×10 14 cm -2 agrees well with experiments. The reduced intensity function was also calculated. Agreement with experiments is good, except that it shows the higher first peak than experiments.

Core structure of a screw dislocation in a diamond-like structure

Abstract The core structure of a screw dislocation in the diamond lattice has been calculated with the Stillinger-Weber potential for the interatomic interaction. The non-dissociated screw dislocation positioned at the centre of a unit hexagon normal to the dislocation line is a stable configuration A. A perfect screw centred on a longer edge of the unit hexagon is also a stable configuration B. Configuration B is more stable and has a lower energy than configuration A. Dissociated configurations of width w = na (a is the repeat distance in the slip direction and n = 1, 2, 3,…) are also stable. The geometrical feature of configuration B explains the cross-slip observed in III-V compounds at low temperatures. The Peierls stress of the perfect screw dislocation is 0.044G, where G is the shear modulus. This value corresponds to the experimental values of III-V compounds deduced from the temperature dependence of the critical shear stress at low temperatures.

Nucleation of trapezoidal kink pairs on a Peierls potential

Abstract The activation energy ΔH∗ for forming a kink pair of trapezoidal shape in a dislocation in a Peierls potential is calculated by considering the long-range elastic interaction between the dislocation segments. The shapes and energies obtained in this three-parameter model closely resemble those obtained from the continuous line-tension approximation, except at low stresses where ΔH∗ is well approximated by a square-root-dependence on the stress. If the potential is smooth, the stress dependence of the activation energy is also smooth. For a camel-hump potential, with an intermediate minimum, a discontinuity appears in the stress-dependence.

Temperature dependence of the flow stress of III-V compounds

Abstract An interpretation for the temperature dependence of the plastic flow stress of III–V compounds is presented, invoking only non-dissociated screw dislocations. With the aid of the Stillinger-Weber potential for the interatomic interaction, the Peierls potential of a non-dissociated screw dislocation is deduced in twodimensional space normal to the dislocation line. A saddle-point configuration and the formation energy of a kink pair are calculated in three-dimensional space. The relation obtained between the flow stress T c and temperature T under a constant strain rate describes the experimental T c−T relation of III–V compound well: a strong T dependence at highT c and low T, a stronger T dependence at low Tc and high T, and a plateau-like T c at intermediate T. The hump in the T c−T relation is interpreted as a transition between different paths of the non-dissociated screw dislocation: a planar path and a zigzag path in the (111) plane.

Temperature dependence of the plastic flow stress of covalent crystals

Abstract A model is presented to explain the steep temperature dependence of the plastic flow stress τc(T), of highly covalent crystals of α-Al2O3, Si and GaAs. The model assumes high and steep Peierls potentials: Vp(x) = Px2 + Qxn (n > 2) for x < a/2, a being the period. The kink pair formation energy ΔH(τ) is calculated from the elastic interaction energy of a trapezoidal kink pair. The calculation predicts narrow and abrupt kink pairs. The activation energy ΔH(τ) obtained describes the experimental relation log τc = A - BT with constants A and B. The results suggest that the kink pair formation is the rate controlling process of dislocation motion in covalent crystals.

Inertial motion and multi-kink pair formation of dislocations on the Peierls potential

The motion of a dislocation overcoming the Peierls potential is investigated by integrating the equation of motion. The behaviour of the segment following the nucleation of the first pair of kinks changes drastically from overdamping to underdamping at a critical value of the applied stress τ. When τ is smaller than a critical value τ*, the migration of kinks is dominant and the whole segment falls into the next valley of the Peierls relief to complete single kink pair formation. On the contrary, when τ, due to inertia the centre part of the bowed out segment overcomes the second maximum of the Peierls relief, and continues to overcome the succeeding maxima dynamically, resulting in multi-kink pair formation. The critical stress τ* is about 0τ7τp in the absence of friction, τp being the Peierls stress. It increases with increasing friction. The possibility to observe the multi-kink pair formation is discussed for f.c.c. metals, b.c.c. metals and ionic crystals.

A Dislocation Model of Amorphous Metals

A dislocation model of amorphous metals is constructed to meet the requirement of global connectivity. Noncrystalline nature of atomic configurations at the screw dislocation core is discussed in connection with Bernal polyhedra and rings of fivefold symmetry which have been found in the dense random packing models. Relative population of trigonal prisms to that of tetragonal dodecahedra is determined by different degrees of symmetry breaking of the core structure. Pair distribution functions are calculated for the dislocation model after relaxation of atom positions and a good agreement with experiments is obtained for the dislocation density of 10 14 ∼10 15 cm -2 . For the high density the core structure is found to keep nearly the same local configuration as that of an isolated dislocation, and, thus, the dislocation model contains many Bernal polyhedra.

Emission of elastic waves from a dislocation in a 2-D discrete lattice

Abstract A dislocation moving in a lattice emits elastic waves, as it accelerates and decelerates due to the lattice periodicity. In this work, simulations of this process in a 2-D discrete square lattice are presented. Under a small applied stress, the dislocation motion from an unstable position to the next stable position is accompanied by emission of dipolar waves, followed by quadrupolar emission when it oscillates around the stable position. When the applied stress is larger than 70% of the Peierls stress, the dislocation overcomes the Peierls hills, and after moving a few atomic distances it achieves a steady motion with alternating forward motion and “hesitation” or oscillation, accompanied by radiations of dipolar and quadrupolar waves.