The lower limiting crystallite size and internal strains in some cold-worked metals

Abstract

In recent X-ray work on the structure of a metal after cold-working (Wood 1935), and similarly after fatigue stressing (Gough and Wood 1936), it was shown that when a metal consisting of annealed perfect grains received any permanent deformation, then the grains were dispersed into crystallites with orientations departing widely from the crystallographic orientations of the parent grains. It is possible to set an upper limit to the size of the crystallites in the following manner. With the back-reflexion technique as used in the work, the X-ray photograph of a stationary annealed specimen shows isolated clear-cut reflexion spots which lie on the diffraction rings corresponding to the Bragg reflexion angles. Deformation of the metal causes the spots to extend into continuous arcs owing to the increase in number of independently reflecting units produced with various orientations in the reflecting volume. It can be shown, by calibrating for known grain sizes, that the formation of a continuous line by multiplication and coalescence of the reflexion spots in this way requires an increase in number which can only be brought about by a decrease in size of the units to about 10 -4 cm. The continuity of the diffraction arc indicates therefore that the crystallites must be less than about 10 -4 cm. It is then possible to set a lower limit to the crystallite size from consideration of the Scherrer effect by which the radial breadth of the continuous diffraction arc depends on the particle size according to a formula of the type δB = 0.9 λ/t cos θ , where δB is the increase in breadth due to the fine-grain effect, t the linear particle size, and θ the reflexion angle. The effect becomes appreciable only when the particle size is less than 10 -4 cm.; thus in the present experiments a barely noticeable increase in width of 0.1 mm. on the photographic plate would occur in the (420) ring of aluminium, using cobalt K -radiation, if the crystallite size decreased to 0.8 x 10 -4 cm.; but the breadth would increase by about 1 mm. at 10 -5 cm. and by 1 cm. at 10 -6 crystallite size, thus constituting a sensitive indication of any reduction in size below the value of 10 -4 cm. fixed as upper limit. It is found, however, that the broadening of the diffraction line produced by the breakdown of the grains under progressive deformation of a metal never exceeds a definite maximum. On these grounds, the author has pointed out that the limited broadening, whether due to the fine-grain effect or the alternative possibility of lattice distortion or any other cause, automatically sets a lower limit to the size of the crystallites formed on deformation; also, that the striking contrast on the one hand between the ease with which the grains are dispersed into crystallites immediately after deformation and, on the other, the subsequent impossibility, even after the most severe deformation, of breaking them down below about 10 -5 cm., the value corresponding to the order of maximum line-broadening observed, indicates that the crystallite must be regarded as a fundamental unit of the metallic grain.