• Volume 10, Issue 1-2

March 1988,   pages  1-179

• Foreword

• Gauge theory of defects in the elastic continuum

A gauge theory of defects in an elastic continuum is developed after providing the necessary background in continuum elasticity and gauge theories. The gauge group is the three-dimensional (3D) Euclidean group [semi-direct product of the translation group T (3) with the rotation group SO (3)]. We obtainboth dislocations and disclinations by breaking of the translational invariance. Breaking of the rotational invariance is shownnot to lead to any interesting effects in a linear analysis. These results are shown to be consistent with the topological analysis which is briefly discussed at the end of the paper. Any defect given by the present theory acquires acore which removes the singularity of the stress field at the origin. The stress field agrees with the continuum result asymptotically, as is expected. Geometrical aspects of the deformed state of condensed matter are also briefly touched upon.

• Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector$$\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\rightharpoonup}}} {b} = (a/2, a/2,a/2 )$$ in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

• Some observations on defects in nematic liquid crystals

After briefly describing the usually observed defects in nematic liquid crystals, we give a summary of our observations on high strength line defects and a regular network of point disclinations on the nematic-isotropic interface.

• Defects in liquid crystals (II)

Defects in the disordered (uniaxial) liquid crystals, nematic, smecticA and cholesteric, and the use of topological analysis in classifying them, are discussed. While the latter is very successful in classifying defects in nematics, it fails to do so in the case of smecticA and cholesteric liquid crystals because of geometrical constraints. However, topological arguments have been partially successful in predicting some of the defects in cholesterics. The known features of the isotropic (cubic and amorphous) cholesteric blue phases are summarised and the various theoretical models picturing them as defect lattices, are also discussed briefly.

• The nature of dislocation motion in quasicrystals

Calculations in a hydrodynamic model of quasicrystal dynamics show that dislocation motion in these systems is impeded by a drag far greater than that in crystals.

• Random walk on a fibonacci chain

Random walk on a Fibonacci chain is studied both numerically and analytically. We demonstrate that the long-time behaviour is diffusive.

• Defects in conducting polymers

New types of defects such as solitons, polarons and bipolarons in conducting polymers have been discussed in this article. In the light of recent experimental results, the bipolaronic model of conduction has been re-examined. It is shown that more elaborate experiments are essential to confirm the hypothesis of charge transport via bipolarons in these newer synthetic metals.

• The kosterlitz-thouless transition and vortex dynamics

The physics of the Kosterlitz-Thouless vortex-unbinding transition in two-dimensional superfluids is discussed, and theN ×N Josephson junction array is considered as a prototype system. Dynamical behaviour is considered in two cases: (a) the complex impedance shows structure at a frequency-dependent transition temperature, similar to the dynamic susceptibility of a spin glass; (b) with a perpendicular non-uniform magnetic field, of a particular ‘self-similar’ hierarchical pattern, a scaling argument gives non-exponential relaxational dynamics of a prepared non-equilibrium vortex distribution.

• Study of crystal defects using ion channelling and channelling radiation

The channelling technique to study crystal defects is described and its applications to various kind of defects to study their atomistic nature have been reviewed. Special emphasis has been placed on the applications to extended defects like dislocations. Finally a related new technique being developed for the last few years, namely the channelling radiation technique has been discussed along with its applications to study the dislocations.

• Role of stacking faults in solid state transformations

This article illustrates the two different roles played by stacking faults in solid state transformations viz. (i) in accommodating part of the transformation strains as observed in the noble metal-based alloys undergoing martensitic transformations, and (ii) in providing a mechanism for changing the stacking sequence of layers in a variety of materials like SiC, ZnS, Co and its alloys, and certain steels. Diffraction patterns taken from the martensitic phases of noble-metal-based alloys as well as from SiC and ZnS crystals undergoing transformation from one close-packed modification to another reveal the presence of characteristic diffuse streaks. It is shown that from a theoretical analysis of the observed intensity distribution along streaked reciprocal lattice rows in terms of physically plausible models for the geometry and distribution of faults, one can make a choice between various possible routes for transformation. From simple computer simulation studies, it is shown that the observed arrest of transformations in SiC is essentially due to the insertion of stacking faults in a random space and time sequence leading to an irregular distribution of solitons.

• Deformation dynamics at low and ambient temperatures

The variation of tensile yield stress at a constant strain rate as a function of temperature for well-annealed pure metals show, with increasing temperatures, a rather sharp drop in yield stress (low temperature regime), followed by the intermediate temperature regime where yield stress decreases more slowly (and the ratio of yield stress to shear modulus remains more or less constant), which in turn is followed by the high temperature regime where the yield stress drops again rather sharply. The paper discusses the phenomenological framework for studying deformation dynamics in the low and intermediate temperature regimes. The approach adopted is the well-known state variable approach, where the evolutionary nature of deformation structure is described by one or more structure variables such that the current values of mechanical variables and structure variables together completely define the current state of deformation. A critical analysis of experimental results available suggest that at least for deformation at low strain rates, stress-rate is probably not a state variable of deformation. Thus deformation is most conveniently studied in terms of TASRA (thermally activated strain rate analysis) where the stress, plastic strain rate, temperature and structure are interrelated through a Gibb’s free energy for thermal activation by an Arrhenius equation. The stress-dependence of Gibb’s free energy and its maximum value then form the basis of identifying the rate-controlling obstacles. The need for careful experimentation and systematic analysis is illustrated by the example of low temperature deformation of hard hep metals. Modelling for the evolution of deformation structure is also touched upon.

• Deformation behaviour of materials—A phenomenological approach

The quantitative description of stress-strain behaviour through appropriate models for structural evolution of materials has been fairly successful in explaining both the monotonic and transient stress-strain behaviour of materials. Further exploration of this approach may lead to detailed understanding of evolution parameters and the influence of metallurgical variables. Thus, a quantitative method for alloy design for the purpose of structural applications at ambient and elevated temperature may emerge.

• Defects on surfaces

A brief review of various types of defects on surfaces and their role in surface reactions is presented. Particular emphasis is given on defects like steps/kinks and additives (promoters and poison).

• Vortices in superconductors

In type II superconductors where the London penetration depthλ is larger than the coherence lengthξ, there is a possibility of flux penetration inside the sample for magnetic field greater than$$H_{0_1 } \left( { = \frac{{\phi _0 }}{{4\pi \lambda ^2 }}ln \lambda /\xi , \phi _0 = \frac{{hc}}{{2e}}} \right).$$ The flux penetrates in the form of vortices with core of sizeξ. However these vortices differ from those in superfluid He4 in variation of currentj(r) circulating around them. For superconductorsj(r) ∼ 1/r only up to a distanceλ and then it falls exponentially whilev(r) ∼ 1/r for all distances in superfluids. The reason is that in superconductors vortex carries a magnetic flux which is screened by conduction electrons. This coupling of order parameter field (the pairing wavefunction) with the gauge field has many interesting implications for superconductors and for non-Abelian gauge theories. Some examples are as follows:

1. The energy of the vortices is reduced. The energy of vortex of lengthL (ind = 3 sample) is of orderL lnL for a superfluid, is of orderL in a superconductor, and (in ad = 2 sample) the energy of a vortex point which diverges like lnR (whereR is the size of the sample) in a superfluid becomes finite in a superconductor.

2. The superconducting-normal transition in three dimension is very weak first order, because the fluctuations of the gauge field, when summed over, add to Ginzburg Landau free energy a term proportional to |ψ|3, whereψ is the order parameter.

3. Because of the lnr behaviour of interaction energy of vortices, a two-dimensional superfluid sample can exhibit a Kosterlitz-Thouless type transition whereas a strictlyd = 2 superconductors should not have any. However for dirty superconducting films whereλ is large vortex binding-unbinding transition can be observed with quite a rich phase diagram.

The paper presented at the discussion meeting discusses the above in detail. Here we give only a brief summary of results and some relevant references.

• Recent observations and theoretical approaches for ordering of microdefects and clusters

Formation of ordered arrays of defects has been observed during irradiation for different irradiation conditions and in a wide class of materials. These range from ordering of void cavities, gas bubbles, solid inert gas bubbles, precipitates and formation of periodic walls of defect clusters. This paper gives a brief summary of these experimental observations and outlines the main features of the theoretical approach based on non-equilibrium stability of the irradiation process.

• # Bulletin of Materials Science

Current Issue
Volume 42 | Issue 5
October 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019