What is allotropy
Many metals can exist in more than one crystalline form, depending on pressure and temperature.. This phenomenon is called allotropy..
Iron undergoes a series of allotropic transformations during heating and cooling, as shown in the picture 1. Note, that allotropic transformations are transformations of solid phases and therefore occur at a constant temperature during both heating, and cooling.
Picture 1 - Allotropic transformations in pure iron 
Allotropic transformations in iron
- Under equilibrium cooling conditions, solidification of pure iron from a liquid occurs at a temperature 1540 ºС and forms then, what is called delta iron (dFe), which has a body-centered cubic structure (ock-structure) (picture 2).
- Delta iron is then stable upon further cooling, until it reaches temperature 1395 ºS, when it undergoes transformation into a face-centered cubic structure (hcc structure) (picture 3), which is called gamma iron (cFe).
- Upon further cooling to 900 ºС gamma-iron undergoes another phase transformation with a transition from the fcc structure) back to the OCK structure. This structure is called alpha iron or ferrite. (aFe), to distinguish it from high temperature delta iron.
- This last transformation γFe → αFe is extremely important, as it creates the basis for hardening steel. Note, that the transformation γFe → αFe occurs at temperature 900 ºС during cooling and somewhere below temperature 910 ºС when heating. This temperature difference is known as allotropic phase transformation hysteresis..
- Temperatures (denoted by the letter A), which are related to heating, contain subscript "c", and temperature, which are related to cooling - subscript "a". The letter "c" comes from the French word "chauffage", which means "heating", a letter «a» – from the French word "refroiddissement", which means "cooling".
Picture 2 - Body-centered cubic structure 
Picture 3 - Face-centered cubic structure 
Allotropy in metals and non-metals
Many other metals, like some non-metals, also exhibit allotropic transformations. for instance, titanium, zirconium and hafnium exhibit a transition from a hexagonal close-packed structure upon heating (hcp structures) k ock-structure. Note, that in each case the close-packed structure is stable at room temperature, whereas less dense structures are stable at elevated temperatures. Although this does not always happen, this rule is an empirical fact for many metals.
1. Elements of Metallurgy and Engineering Alloys / Ed. F.C. Campbell – ASM International, 2008