K. Sangwal

On the reverse indentation size effect and microhardness measurement of solids

Abstract The reverse type of indentation size effect (ISE), where the apparent microhardness increases with increasing applied test load, was critically examined for the experimentally reported data for a number of single crystals differing in crystal structure and chemical bond, using the theoretical models reported in the literature. The analysis revealed that the indentation-induced cracking model, initially proposed to explain the reverse ISE, is not satisfactory. Examination of the data from the standpoint of the models of the normal ISE showed that, in the case of the reverse ISE, a specimen does not offer resistance or undergo elastic recovery, as postulated in some of the models, but undergoes relaxation involving a release of the indentation stress along the surface away from the indentation site. It was found that, for the comparison of microhardness of a face along different directions, of different planes or that of the same face of the crystals of the same substance subjected to different thermal treatment, the Meyer law and the Hays–Kendall approach are not reliable but that the proportional specimen resistance and elastic/plastic deformation response models give similar results. It was also found that the reverse ISE phenomenon occurs only in materials in which plastic deformation is predominant. The possible origins of the occurrence of reverse ISE are suggested.

Effects of impurities on crystal growth processes

The mechanisms of adsorption of impurities during the growth of bulk crystals are surveyed. The impurities considered are foreign substances deliberately added to or inherently present in a growth medium. After a brief introduction to different growth models, the nature of impurities and types of impurity effects on growth kinetics, adsorption of impurities on F faces at relatively low and high impurity concentrations is first discussed. Here mechanisms of adsorption at kinks in steps and surface terrace in the presence of low concentrations of one impurity and two competitive impurities are presented. Then the concepts of adsorption of impurities involving the formation of two-dimensional impurity layer and three-dimensional impurity clusters as growth promotors on a growing face are developed. Thereafter the mechanism of adsorption of impurities on S and K faces and the determination of the adsorption mechanism on a growing face from the kinetic data are discussed. Finally, impurity effects on surface morphology of bulk crystals, and growth morphodroms of alkali halides are briefly reviewed.

On the estimation of surface entropy factor, interfacial tension, dissolution enthalpy and metastable zone-width for substances crystallizing from solution

Abstract Surface entropy factors, interfacial tensions, dissolution enthalpies and metastable zone-widths for substances crystallizing from solutions are estimated and compared with literature values. It is shown that the expression relating surface entropy factor with heat of melting, melting point and crystal solubility predicts reliable values of surface entropy factors and interfacial tensions. In combination with the equation for critical supersaturation given by the classical nucleation theory, the same equation also predicts satisfactory values of metastable zone-widths for compounds growing from solutions.

Growth kinetics and surface morphology of crystals grown from solutions : Recent observations and their interpretations

Abstract Observations reported since 1980 on the kinetics of growth and surface morphology of crystals obtained from solutions are reviewed and interpreted from the standpoint of crystal growth theories. After a brief introduction to the theories of crystal growth, first the kinetics of growth are surveyed and confronted with the crystal growth theories. Here the origins of deviations in the linear dependences of inclination of growth hillocks and rate of displacement of their growth steps on super saturation are analysed and explained in terms of kink nucleation at steps and solute accumulation at kinks. Thereafter the mechanisms of adsorption of impurities on growing crystal surfaces are briefly presented, and some typical experimental data on the kinetics of crystal growth in the presence of impurities and the tapering of KDP-type crystals are discussed in terms of the proposed mechanisms. The general features of growth hillocks at isolated and composite dislocation sources are then described and discussed in relation to the morphological importance of as-grown faces and growth conditions. The latest results on the bunching of elementary steps and the formation and stability of macrosteps are subsequently presented and discussed in the light of the existing theories of bunch formation. Finally, observations of dislocation hollow cores and decoration of growth steps on the as-grown surfaces of crystals during their extraction from supersaturated solution through an immiscible solvent layer placed above the solution are described.

Analysis of the indentation size effect in the microhardness measurement of some cobalt-based alloys

The load dependence of the Vickers microhardness of some cobalt-based alloys subjected to heat treatment at different temperatures for various duration has been investigated using Hanemann’s method and a PMT-3 hardness tester. It is found that even for the same sample Hanemann’s method shows a decrease in microhardness with applied load (i.e., normal indentation size effect) while the PMT-3 hardness testing exhibits a reverse effect. The experimental data were analysed using Meyer’s law, Hays–Kendall’s model, the elastic/plastic deformation model of Bull et al., the proportional specimen resistance model of Li and Bradt and the energy balance approach of Buckle. The analysis of the experimental data revealed that: (1) the Meyer hardness index n decreases linearly with logarithm of the so-called standardised hardness constant A, (2) within the limits of experimental errors, the load-independent microhardness of a given sample predicted by the other models used is constant, (3) the quantities contributing to the load dependence of hardness are inversely related with the constants describing the load-independent hardness, (4) the quantities contributing to the load dependence of hardness are related with the Meyer hardness index n and (5) the constants of the energy balance approach are mutually related but the load-independent microhardness predicted by this approach is erratic with respect to that obtained by the other models.

Etching of MgO crystals in acids: kinetics and mechanism of dissolution

Kinetics of etching of MgO crystals have been studied in H2SO4, HNO3 and HCl. The effects of etching time, acid concentration and temperature on the growth of hillocks, on the selective etch rate and on the rate of overall dissolution are demonstrated. It is observed that etch rates are independent of time, but are determined by the temperature and concentration of the acid. The etch rate-concentration curves show maxima which are characteristic of an acid. The values of activation energy for the processes of dissolution, selective etching and hillock growth and the corresponding frequency factors are computed. It is established that the process of dissolution in concentrated H2SO4 is diffusion controlled, while in H2SO4 with concentrations below 18 N and in HNO3 and HCl it is reaction rate controlled. The pre-exponential factor is found to be a function of acid concentration. The results are discussed from the standpoint of chemistry. A comment on the data published on MgO by previous workers is made.

Effect of impurities on the processes of crystal growth

Abstract The influence of impurities inherently present in growth media and deliberately added to them on crystal growth is manifested during the process of crystallization in a number of ways. Impurities change growth rates, shape and thickness of growth layers and growth habit, and are trapped as impurity striations and large clusters of impurities and inhomogeneities. Some of these effects of impurities are reviewed for growth of bulk single crystals.

Nature of multilayer steps on the {100} cleavage planes of MgO single crystals

Abstract The results of an AFM study of the nature of multilayer steps on the {100} cleavage faces of MgO crystals is described and discussed. The results show that (i) multilayer cleavage steps of a width between 55 and 590 nm and of a slope between about 1 and 8° are stable, (ii) the terminal planes of multilayer steps are composed of high-index vicinal faces with indices (7 0 1), (42 0 1) and (77 0 1) for the 〈010〉 steps with respect to the (100) cleavage, which do not correspond to the low-index planes of the equilibrium form of MgO crystals, and (iii) that the curved parts of the profile of a multilayer cleavage step in its upper and lower regions extend to a distance equal to the width of the step.

Effect of impurities on the growth of KDP crystals: On the mechanism of adsorption on {100} faces from tapering data

The results of the dependence of the tapering angle θ and the micromorphology of tapered faces on the concentration of Fe 3+ and Cr 3+ impurities at various supersaturations are presented and discussed. The kinetic data on tapering angle are analysed by considering the adsorption of impurity species at kinks and steps on a surface and calculating the corresponding energy of adsorption. The analysis suggests that adsorption of both Fe 3+ and Cr 3+ impurities takes place at kink sites on {100} faces.

Effect of impurities on the growth of KDP crystals: Mechanism of adsorption on (101) faces

Abstract The results of the dependence of growth rate, R001, along 〈001〉 directions of KDP crystals in aqueous solutions at 30°C on the concentration ci, up to 4.0×10-6 mol/mol, of Fe3+ and Cr3+ impurities in aqueous solutions at different supersaturations are presented and discussed. It is observed that with an increase in ci, in the case of Fe3+ impurity R001 first increases and then decreases at 4.2% supersaturation. For Fe3+ impurity at 6.3% supersaturation and for Cr3+ impurity at 6.3% and 8.55% supersaturations, R001 regularly decreases with an increase in ci. At 13% supersaturation, R001 increases with an increase i n the concentration of both Fe3+ and Cr3+ impurities. The effect of impurities on growth rates at 4.2%, 6.3% and 8.5% supersaturations is discussed in terms of changes in the thermodynamic and kinetic parameters involved in the crystal growth theories. The increase in R001 at 13% supersaturation is, however, explained by considering the formation of three-dimensional impurity nuclei on the pyramidal faces. The analysis suggests that adsorption of both Fe3+ and Cr3+ impurity takes place at kink sites on (100) and (101) faces.