Growth of 4He-Crystals at mK-Temperatures

Liquid-solid interface of ⁴ He has been investigated down to mK-temperatures using an optical interferometer in combination with a sensitive pressure gauge. The c- facets with 5–100 screw dislocations/cm ² grew with spiral growth which can be understood by including inertial terms and localization of steps to the standard theory. Crystals without screw dislocations revealed two novel growth mechanisms. At growth rates > 1 nm/s, these high-quality crystals grew in a burst-like manner, creating abruptly 200–2000 new atomic-layers. At rates below 0.5 nm/s, the c- facet revealed slow, continuous growth. Studies of a- facets yielded a velocity vs. pressure dependence which can be explained by spiral growth. The shape of the c- facet was monitored down to 2 mK without any evidence of the freezing of kinks. Pressure measurements down to our minimum temperature did not show any anomalies connected with the supersolid transition. Indications of new faceting transitions were not observed down to 2 mK.     

Theoretical evaluation of the role of crystal defects on local equilibrium and effective diffusivity of hydrogen in iron

ABSTRACT

Hydrogen diffusion and trapping in ferrite is evaluated by quantum mechanically informed kinetic Monte Carlo simulations in defective microstructures. We find that the lattice diffusivity is attenuated by two to four orders of magnitude due to the presence of dislocations. We also find that pipe diffusivity is vanishingly small along screw dislocations and demonstrate that dislocations do not provide fast diffusion pathways for hydrogen as is sometimes supposed. We make contact between our simulations and the predictions of Oriani's theory of ‘effective diffusivity’, and find that local equilibrium is maintained between lattice and trap sites. We also find that the predicted effective diffusivity is in agreement with our simulated results in cases where the distribution of traps is spatially homogeneous; in the trapping of hydrogen by dislocations where this condition is not met, the Oriani effective diffusivity is in agreement with the simulations to within a factor of two.

This paper is part of a thematic issue on Hydrogen in Metallic Alloys     

Screw dislocation pile-ups at and near a planar interface of a two-phase system

The method of continuously distributed dislocations is used in analyzing the behaviour of pile-ups of screw dislocations in two-phase systems. Two types of pile-ups are analyzed, namely, a pile-up of screw dislocations of length ‘L’ situated at a distance ‘a’ from the interface for $\text{L/2a <}\text{1}\text{2}$ and two pile-ups of screw dislocations of length L situated one above the other at a distance of separation h for $\text{L/2a <}\text{1}\text{2}$. The effect of the shear modulus of the second phase and the pile-up parameters on the behaviour of the pile-ups is discussed. Conclusions have been drawn on the fracture behaviour of the two-phase systems.     

Force between two parallel screw dislocations and application to linear screw dislocation pileups—Gauge theory results

An analytic expression for the force between two parallel screw dislocations, derived earlier on the basis of the gauge theory of dislocations, has been used to investigate the static distribution of a given numberN of parallel screw dislocations confined between two immobile dislocation obstacles. It is shown that in the limit of a continuous distribution of dislocations the equilibrium condition leads to a Fredholm integral equation of first type which does not admit any nontrivial solution. Implication of this result is discussed. For a finite number of dislocations, the ratio (η) of the obstacle separation to the core radius is an important parameter governing the nature of solution of the discrete equation. It is found that for a givenN, there is a critical valueη _c below which there does not exist any solution.     

Vertical dislocations in Ge films selectively grown in submicron Si windows of patterned substrates

The structural properties of straight screw dislocations extended in the [001] direction formed in squared- and line shaped- Ge(001) films selectively grown on submicron regions of Si(001) substrates were investigated by transmission electron microscopy. The screw dislocations propagating as a result of spiral surface growth were redirected toward the SiO₂ sidewalls. This redirection is linked to the formation of facets such as {111} facets in the growing Ge films. In the process of strain relaxation upon annealing, the screw dislocations were dissociated into dislocations with Burgers vectors of the a/2<110> type, which glided on the {111} surfaces and disappeared.     

Dislocation etching of GaSe single crystals

Dislocation etching of GaSe single crystals was investigated by using a dilute chromic-sulphuric acid mixture, when conical etch pits were revealed on the (0001) surfaces. At the apices of spiral growth hills, bunches of spiral dislocations were revealed, proving that it is not a single screw dislocation of large Burgers vector, but a bunch of co-operating screw dislocations that were responsible for the spiral growth formations of large step-height. In the case of GaSe crystals, grown by vapour transport methods, dislocation densities of 10² to 10⁶ cm⁻² were found. The Bridgman crystals investigated were completely free from non-basal dislocations.     

The effect of nitrogen on the structure and mobility of dislocations in Fe-Ni-Cr austenite

The structure and the critical resolved shear stress for the motion of the straight a/2110 edge and screw dislocations in Fe-Ni-Cr and Fe-Ni-Cr-N austenite have been analysed using the conjugate gradient method to minimize the potential energy of the crystal and the embedded atom method to quantify atomic interactions at 0 K. In Fe-Ni-Cr austenite both the edge and the screw dislocations dissociate along one of the {111} planes forming a stacking-fault ribbon. The ribbon widths are comparable to their values calculated using continuum theory. Dissociated edge and screw dislocations require very similar levels of shear stress for their motion. In Fe-Ni-Cr-N austenite, the structure of the dislocation core of the a/2110 edge dislocation does not seem to be significantly affected by the presence of nitrogen. In sharp contrast, the core structure of the dissociated a/2110 dislocation undergoes a major change, resulting in spreading of the core on to two or more non-parallel planes. As a result, a significantly higher level of stress is required for the motion of a screw than an edge dislocation. Under certain conditions the interaction of nitrogen atoms with screw dislocations can result in pinning of the dislocations. The potential mechanism for the motion of the pinned screw dislocations by formation and motion of edge-type kinks is briefly discussed.     

Angular momentum of the fields of a few-mode fiber. III. Optical Magnus effect, Berry phase, and topological birefringence

It is shown that, on the one hand, the evolution of the angular rotation of the lines of nodes of the CP₁₁ mode is a manifestation of the optical Magnus effect in a few-mode fiber with a parabolic refractive index profile, and, on the other hand, the additional phase γ _b =±δβ ₂₁ z in CV and IV vortices is the Berry topological phase, which arises as a result of the cyclic change in the orientations of the orthogonal axes of dislocations. The splitting of the propagation velocities of orthogonal circularly polarized CV⁺ and IV⁻ modes in an LV vortex in a parabolic fiber is a manifestation of the phenomenon of topological birefringence of a few-mode fiber. The azimuth of the linear polarization of a vortex undergoes continuous angular rotation. In an optical fiber with a stepped index profile the CP₁₁ mode forms circularly polarized edge dislocation over lengths which are multiples of half the beat length, and over lengths which are odd multiples of the quarter beat length it forms linearly polarized fields with a purely screw dislocation. This transformation of edge and screw dislocations can be regarded formally as conversion of the polarizational angular momentum into orbital angular momentum. The conversion of angular momentum is a reflection of the dynamical unity of the optical Magnus effect and the Berry topological phase in the fields of a few-mode fiber. Pis’ma Zh. Tekh. Fiz. 23, 59–67 (December 12, 1997)     

X-ray topographic analysis of dislocations and growth bands in a melt grown gadolinium gallium garnet crystal

A melt grown crystal of gadolinium gallium garnet containing dislocations with a density of about 3 × 10³ / cm² was analyzed by X-ray diffraction topography. Most of the dislocations appear to have Burgers vectors in the 〈111〉 direction parallel to the growth axis. These dislocations make relatively small angles with the growth axis so they are predominantly screw in character. Some evidence for the existence of decorated edge dislocations was found. In addition, anisotropy of growth band contrast was observed. This effect is interpreted in terms of elastic stresses between bands of different lattice parameter.     

Comparison of glide mechanisms in hcp Ti and Ti3Al

Several dislocation glide mechanisms are studied in Ti and Ti₃Al by means of in situ straining experiments in a transmission electron microscope at various temperatures. The prismatic glide of α titanium occurs by the jerky motion of straight screw a-dislocations subjected to a frictional force. An explanation for the discontinuity in the temperature dependence of the corresponding activation area is proposed, on the basis of the experimentally measured variation of the corresponding dislocation jump length. In Ti₃Al, superlattice 2a-dislocations exhibit two different dissociation modes in prismatic planes corresponding to highly different antiphase boundary energies. The properties of these two types of dislocation are compared and discussed. It is shown that the motion of 2c+a superlattice dislocations in pyramidal planes is controlled by a new mechanism: the self-nucleation of small-size obstacles as the result of irreversible atomic displacements. The tension/compression asymmetry observed between type 1 and type 2 pyramidal planes is finally discussed.     

Collective Pinning of a Flux-Line Lattice with Screw Dislocations

The energy of screw dislocations of a flux-line lattice in Type-II superconductors is calculated taking account of dispersion of the tilt modulus. On the basis of this calculation, the collective-pinning theory for the plastic case, proposed by Mullock and Evetts, leads to correlation lengths of a flux-line lattice much shorter than that for the elastic case leads, and much better theoretical fits to experimental results in Nb ₃ Ge and 2H-NbSe _2–x S _x are obtained. Furthermore, the intermediate state between three-dimensional disorder and two-dimensional disorder in a flux-line lattice is predicted when the screw dislocations trigger the dimensional crossover.     

Dislocation etching in molybdenite

An etchant to reveal the non-basal dislocations on the (0001) faces of MoS₂ single crystals has been established. Evidence concerning the ability of this etchant to reveal the sites of non-basal screw dislocations is also given.     

Effect of Screw Dislocations on the Roughening Transition

The behaviour of the interface of a crystal which is threaded with parallel screw dislocations is analysed in the limits of weak and strong coupling of the interface to the underlying lattice. If the dislocations are distributed as closely spaced pairs of opposite sign the interface is faceted at low temperatures, and undergoes the roughening transition in the weak coupling limit. In contrast, if the dislocations are distributed entirely at random the interface seems to have a glassy, non-faceted low temperature state, and undergoes the super-roughening transition in the weak coupling limit.     

The image force on the screw dislocation around a crack of finite size

On the basis of the result of Smith [Proc. R. Soc. 305A, 384 (1967)], we analyse the elastic interaction between a screw dislocation and a crack of finite length. The image force on the screw dislocation and the crack extension force are considered. The effects of the dislocations inside the crack and the curvature of the crack are also discussed. In addition, the location of the screw dislocation is extended from the crack surface to the inclined plane. Some special cases are treated here and the results are compared with those of the other reports.     

Typical hillocks and spirals on flux-grown DyFeO3 crystal surfaces

Multi-sided and almost rectangular growth hillocks on (1 1 0) faces of flux-grown DyFeO₃ crystals are illustrated. Some such hillocks exhibit spiral growth layers originating from the summits of hillocks. Spiral growth layers originating from more than one initiation centre interact, giving rise to closed loop, interlocked and interlaced or other complex growth formations. The origin of the multi-sided hillocks is attributed to preferential growth at the sites of screw dislocations in DyFeO₃ crystals. Defects other than screw dislocations also stimulate growth on (1 1 0) faces of DyFeO₃ crystals. An example of this is offered. The mechanism of independent growth on (1 1 0) faces of these crystals is discussed.     

Atomistic simulation of dislocation core structure and dynamics in Fe–Ni–Cr–N austenite

Atomistic computer simulations based on the use of the conjugate gradient and molecular dynamics methods were employed to determine the core structure and dynamics of the a/2 <1 0 0> edge and screw dislocations in Fe-Ni-Cr and Fe-Ni-Cr-N austenites. The embedded-atom method was used to quantify the interactions between iron, nickel, chromium and nitrogen atoms. In Fe-Ni-Cr austenite, both the edge and screw dislocations dissociate along one of the {1 1 1} planes, forming stacking fault ribbons. The ribbon widths were found to be comparable to their values calculated using the continuum theory. The analysis of dislocation dynamics showed that the phonon drag interferes more with the motion of screw dislocations, reducing their mobility in comparison with the mobility of edge dislocations. In Fe-Ni-Cr-N austenite, the structure of the dislocation core of the a/2 <1 1 0> edge dislocation does not seem to be significantly affected by the presence of nitrogen. In sharp contrast, the core structure of the dissociated a/2 <1 1 0> screw dislocation undergoes a major change, resulting in spreading of the core on to two or more non-parallel planes. As a result, mobility of the screw dislocations is substantially lower than that of the edge dislocations. This finding is consistent with the experimental observations that the dislocations are predominantly of the screw character in Fe-Ni-Cr-N austenite. This revised version was published online in November 2006 with corrections to the Cover Date.     

Dynamics of field dislocations and disclinations in a few-mode optical fiber. III. Circularly polarized CP11 modes and L disclinations

It has been found experimentally and theoretically that when a stepped-index few-mode optical fiber is excited by a circularly polarized Gaussian beam, linearly polarized pure edge L _x and L _y disclinations are generated in the guided wave fields. The azimuths of the linear polarization of these disclinations rotate in the direction opposite to the rotation of the disclination axes. When the axes of the L _x and L _y disclinations are mutually orthogonal, a pure screw dislocation is created. When the axes are collinear, the L _x and L _y disclinations annihilate and a pure uniform circularly polarized edge dislocation is generated, its axis coinciding with the axis of the disclinations. Reversal of the circular polarization of the excitation changes the sign of the angles of orientation of the pure edge dislocations and disclinations, and also reverses the azimuth of the linear polarization and reverses the sign of the topological charge of the pure screw dislocation. The physical mechanism for the rotation of the disclination and dislocation axes is attributed to the optical Magnus effect in a few-mode fiber. The rotation of the plane of polarization of the L _x and L _y disclinations and the screw dislocation reflects the appearance of the Berry topological phase accompanied by a cyclic change in the orientation of these disclination axes. Pis’ma Zh. Tekh. Fiz. 23, 14–20 (March 12, 1997)     

Screw dislocations interacting with a partially debonded interface in cylindrically anisotropic composites

Interaction between screw dislocations and a partially debonded interface in cylindrically anisotropic composites subjected to uniform stress at infinity is investigated in this paper. Using Muskhelishvili’s complex variable method, the closed forms of complex potentials are obtained for a screw dislocation and a screw dislocation dipole located inside either matrix or inhomogeneity. Explicit expressions of stress intensity factors at the crack tips, image forces and image torques acting on dislocation or the center of dipole are provided. The results show that the crack and dislocation geometry combination plays an important role in the interaction between screw dislocations and interface crack. Furthermore, it is found that the anisotropy of solids may change the shielding and anti-shielding effects arising from screw dislocations and the equilibrium position of screw dislocations. The presented solutions are valid for anisotropic, orthotropic or isotropic composites and can be reduced to some novel or previously known results.     

Dislocations in GaAs p-i-n diodes grown by hydride vapour phase epitaxy

Hydride vapour phase epitaxy grown all-epitaxial p-i-n structures were studied by synchrotron X-ray topography. Three types of process induced dislocations were found: short threading dislocations, long straight interfacial dislocations and circular arc dislocations. The majority of the dislocations observed are short straight threading dislocations, the density of which is typically about 5000 cm⁻². The dislocations at the p-i interface are long straight lines parallel to [110]. They are screw dislocations having their Burgers vector parallel to [110], calculated from the contrast analysis of the well resolved dislocation images. One sample also showed a dense misfit dislocation network at the n-side. However, no misfit dislocations were seen in the back-reflection topographs of the n-side of the other samples, which shows that it is possible to grow a misfit-dislocation free n-type GaAs layer onto the substrate side of a hydride vapour phase epitaxy grown GaAs surface after proper substrate removal.     

The effect of dislocations on the roughening transition in the weak coupling approximation

The analysis of the roughening transition proposed by Nozières and Gallet is extended to interfaces threaded with either randomly placed screw dislocations or dislocation loops. In both cases we consider a low density of dislocations which intersect normally with the surface leading to a local deformation of the crystal planes and to the formation of small steps in the interface. We show that dislocation loops do not change the roughening transition significantly: it still remains within the Kosterlitz-Thouless universality class of phase transitions. In contrast, randomly placed screw dislocations modify the phase transition: the Kosterlitz-Thouless transition is rounded on a length scale of order the spacing of dislocations. However there is a transition at a slightly lower temperature for randomly placed screw dislocations: the superroughening transition. This conclusion is only valid if the dislocations are randomly placed, not if they are distributed as closely spaced pairs of opposite sign.