Anisotropy in the hardness of single crystals

Abstract

The results of this work, and those published by other researchers who have used Knoop indentation measurements, confirm that the nature of anisotropy in hardness is essentially determined by the crystal structure and the primary slip systems which accommodate dislocation motion during indentation. Materials belonging to the same class of crystal structure and having common slip systems possess similar anisotropic properties. The varying extent of work-hardening or fracture, associated with indentations, does not appear to influence the anisotropy— although twinning on the basal planes of hexagonal closepacked metals may have a significant effect. An analysis of the indentation process is presented which establishes a clear relationship between the ‘effective resolved shear stress’ (t 0 '), in the bulk of the crystal beneath the indenter, and the observed hardness. Directions which correspond to the minimum values of t' e , on specific crystallographic surfaces, are those of maximum hardness and conversely. The analysis is shown to be equally applicable to a wide range of crystalline solids including nonmetallic materials, of various crystal structure, and typical f.c.c., b.c.c. and c.p.h. metals. Finally, anisotropy in hardness can be used to identify active slip systems in those crystals where it is possible for dislocations to move on more than one system.

The temperature dependence of microhardness of the transition-metal carbides

“…Hannink et al [21] have shown, by measuring the anisotropy in hardness (i.e., the dependence of hardness on the orientation of the long axis of a Knoop indenter) and by employing the analysis of Brookes et al [23], that the active slip system in TiC undergoes a change near 200~ In their analysis of the resolved shear stresses under an indenter on the active, crystallographic slip systems, Brookes et al formulated an equation which relates the effective resolved shear stress to hardness anisotropy and correctly predicts the active slip systems of more than twenty crystals of six different crystal structures. Application of this analysis to hardness-anisotropy data at several temperatures for TiC, shows that in the low temperature regime (T < 200~ the {110} (110)system is active, in the intermediate regime (200 ~< T ~< 600~ both the {110} (li0) and the {111} (110) systems are active, and in the high temperature regime (T < 600~ the {1 1 1} ( 1 i0 ) system is active.…”

Micro-scale deformation of gypsum during micro-indentation loading

“…Gypsum is moderately water soluble ( $ 2.0-2.5 g/L at 25 1C) and gypsum crystals are found to contain anion water, making it an important indicator of water in ancient evaporitic lake beds on, for example, the surface of Mars [20]. Experimenting on single crystals is important for engineering applications and in material science research because crystal structure and orientation are closely related to strength properties of the mineral [21]. Further, deformation and fracture characteristics are simplified and measurements are more repeatable for single-crystal measurements [22], enabling a more detailed understanding of the mineral's behaviour under controlled experimental conditions.…”

Study of Knoop microhardness anisotropy on the (001) face of potassium bichromate single crystals

“…Brookes et al [1] concluded that materials having the same crystal structure and common slip systems have similar hardness anisotropy. Later works [2e7] revealed that Knoop hardness anisotropy may be used to investigate active slip systems in a wide variety of materials.…”

“…The aim of the present work was two-fold: (1) to determine the Knoop hardness and its planar anisotropy on the (001) face of potassium bichromate single crystal taken as an example of triclinic crystal, and (2) to explain the results of microhardness anisotropy in terms of shear stress on the possible slip systems of this crystal. Potassium bichromate crystal (K 2 Cr 2 O 7 ; abbreviated as KBC) is an interesting material for the study of the microhardness and its anisotropy for several reasons:…”