Is Changing between Allotropic forms a Physical or Chemical Process? When a substance changes its alloptropic form, is this considered a physical change or a chemical change?

Right now, I am thinking that it would depend on what the change was. For example, if graphite was changed to diamond under high pressure, I would say it is a chemical change since new bonds are formed. However the change of iron from a body-centred cubic structure (ferrite) to a face-centred cubic structure (austenite) at high temperatures would be a physical change because only the arrangement of the atoms are changed.

Am I correct?
Well, it's a matter of choice and tradition. We traditionally classify phase transitions (such as melting of ice or evaporation of water) as physical changes. The conversion of ferrite into austenite is a phase transition, so it should formally be classified as a physical change. But yes, it's hair splitting indeed, especially when you consider the phase change from diamond (giant covalent lattice, sigma-bonds only) to fullerene (simple molecular lattice, sigma plus delocalised pi-bonds), which clearly shows some characteristics of a chemical transformation (the change in the bonding nature). Still, even such changes are formally "physical". The traditions do not go easily!