How Changes Occur in the Crystal Structure of Metals?

Many materials such as iron, tin, zinc, nickel, cobalt, etc. undergo crystalline transformation in the solid state when there is a change in their temperature. They exist in one lattice form over a certain range of temperature, but at a somewhat higher or lower temperature, the lattice form changes to another lattice form, which is stable in that temperature range.

Allotropy or Polymorphy

An element that occurs in more than one crystallographic or lattice form is called allotropy or polymorphy, and the material in which such changes occur are known as allotropic. The process in which the crystal lattice is changed in accordance with the temperature is called allotropic or polymorphic transformations of the material. Diamond and graphite are two allotropic forms of the element carbon. The allotropic forms in which a metal exists are called its modifications. The different modifications of the same metal are designated by the Greek letter alpha (α), beta (β), gamma (γ), delta (δ), etc. Pure iron (Fe) is body centred cubic in structure at all temperature up to 910˚ C. It is then called α iron. Between 910˚c and 1390˚C the structure is face centred cubic and this form is called γ iron. And from1390˚C to 1537˚C it returns to body centred cubic in structure and called delta (δ) iron.
Allotropic Forms of Iron at Different Temperature

Another example is elemental tin (Sn), which is malleable near ambient temperatures but is brittle when cooled. This change in mechanical properties due to existence of its two major allotropes, α- and β-tin. The two allotropes that are available at normal pressure and temperature, α-tin and β-tin, are more commonly known as gray tin and white tin respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C and pressures above several GPa (Giga Pascal).

Anisotropy and Isotropy

In a single crystal, the physical and mechanical properties often differ with orientation. If a crystalline solid has a lattice structure whose atoms are arranged or spaced differently when viewed in any or all of the 3 planes, that crystal is called anisotropic. Also it can be defined as a difference, when measured along different axis, in a material's physical property (absorbance, refractive index, density, strength, etc.). Some materials, such as wood and fiber-reinforced composites are very anisotropic, being much stronger along the grain/fiber than across it. Wood is a naturally anisotropic material. Its properties vary widely when measured with the growth grain or against it. Wood's strength and hardness will be different for the same sample if measured in different orientation.
Grain Direction in Wood
Alternately, when the properties of a material are same in all directions, the material is said to be isotropic. For many polycrystalline materials the grain orientations are random before any working (deformation) of the material is done. Therefore, even if the individual grains are anisotropic, the property differences tend to average out and, overall, the material is isotropic. The examples of isotropic materials are aluminium, steel etc, in standard wrought forms. They typically have the same stiffness regardless of the directional orientation of the applied forces. 
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