texture
In a polycrystal every grain is a little crystal pointing some way. If the grains point every which way at random, the material has no texture — like a bucket of dice thrown in with no arrangement. But if processing has nudged many grains to share a preferred crystal orientation — most of them pointing roughly the same way, like dice mostly showing six up — the material has texture, also called preferred orientation. Texture is the answer to: are the grains' crystal directions random, or do they line up?
Texture arises from directional processing. Rolling a metal sheet shears and rotates grains until certain crystal planes and directions align with the rolling and sheet-normal directions (a rolling texture); drawing a wire aligns a crystal direction along the wire axis (a fibre texture); solidification against a mould aligns grains with the heat-flow direction. Texture is described quantitatively by pole figures, inverse pole figures, and most completely by the orientation distribution function, which gives the density of grain orientations in orientation space — measured as multiples of the random (untextured) density, so a value of 1 everywhere means no texture.
Texture matters because it makes a polycrystal anisotropic. A single crystal is anisotropic — stiffer and stronger along some directions than others — and a randomly oriented polycrystal averages this away to near-isotropy; but a textured polycrystal keeps some of the single-crystal directionality, so its strength, stiffness, magnetic response and formability differ with direction. This is often exploited: the cube-on-edge (Goss) texture in transformer steel aligns the easy magnetization direction with the working direction to cut energy losses. Honest note: texture is about orientation, not shape — grains can be perfectly equiaxed yet strongly textured, and it is the shared orientation, not the shape, that causes the anisotropy.
A rolled aluminium sheet with a strong rolling texture shows earing when deep-drawn into a cup — the rim rises into ears at particular angles to the rolling direction because the textured sheet yields unequally around the circle, whereas a near-random sheet draws an even rim.
Shared grain orientations (texture) survive averaging and make the sheet respond differently in different directions — visible here as drawing ears.
Texture is orientation, not shape. Equiaxed grains can be sharply textured; it is the shared crystal orientation, not grain shape, that makes the polycrystal anisotropic. A random texture (isotropic) is the special case, not the norm after processing.