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What do the Greek letters (α, β, γ...) convey when they are prefixed to a crystalline substance?

For example: β-potassium zirconate

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    $\begingroup$ Interesting question! (upvotes) I came across this (α, β prefixes) when I was reading up on tin the other day. Apparently, it refers to crystal structure (that's as far as I could deduce). en.wikipedia.org/wiki/Tin#Physical_properties $\endgroup$ Jan 28, 2017 at 9:09
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    $\begingroup$ They mean "the first one", "the other one", and "hey, there's a third one" respectively. $\endgroup$ Sep 14, 2022 at 19:07

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They signify one polymorph (the beta polymorph) of barium zirconate.

Allotropy is the property of some chemical elements or compounds to exist in two or more different forms in the same physical state at different temperatures. Technically, they are the same element or compound but have other crystal structures at changing temperatures. To name them, the greek letters alpha, beta, gamma, etc. are used in the prefixes to depict them as the allotropes formed at different temperature phases. That helps in their differentiation.

E.g. iron has 5 allotropes, namely:

  • ferrite (α-iron): the ferromagnetic form at T < 770 °C (the Curie point, TC); body-centered cubic (BCC) crystal structure
  • β-iron: T = 770 – 912 °C; the paramagnetic form of α-iron; same structure as α
  • austenite (γ-iron): 912 – 1,394 °C; face-centered cubic (FCC) crystal structure
  • δ-iron: 1,394 – 1,538 °C; forms from cooling down molten iron; same structure as α
  • ε-iron (also called hexaferrum): forms at high pressures; hexagonal close-packed (HCP) crystal structure

There are several more examples of such types of nomenclature of elements that can be found in the wikipedia article of allotrope(see table).

Also, not only elements form allotropes. Compounds also form allotropes but have a different name, i.e., polymorphs. Generally, binary metal oxides are polymorphs. Polymorphs have different temperature phases in which one form of crystal structure exists. These phases are depicted by giving a greek alphabet letter at the prefixes like α-phase, β-phase, etc. Polymorphs or allotropes of compounds are given that greek alphabet prefixes according to that phase in which one form of that compound exists.

For e.g. iron oxide $\ce{Fe2O3}$ has 4 phases.

  • α-phase: at ambient conditions: has Corundum-type Rhombohedral (R3c) like structure
  • β-phase: below 773 K: has body-centered cubic (Ia3) like structure
  • γ-phase: up to 933 K: has cubic spinel structure (Fd3m) like structure
  • ε-phase: has Rhombic (Pna21) like structure

So, iron oxide $\ce{Fe2O3}$ has 4 polymorphs : $\ce{\alpha-Fe2O3, \beta-Fe2O3, \gamma-Fe2O3, \epsilon-Fe2O3}$.

For more information, you can check this question(asked by myself) or this question, which describes how polymorphs are formed.

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    $\begingroup$ Got a comment: Allotrope is generally understood as limited to elements. While polymorph is more general term for different structural forms. $\endgroup$
    – ankit7540
    Jan 28, 2017 at 10:24
  • $\begingroup$ @ankit7540 Yes, allotrope is for elements but polymorphs is generally for compounds. $\endgroup$ Jan 28, 2017 at 10:29
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Some inorganic crystals show the property of structural polymorphism where two or more crystal polymorphs exist. These polymorphs may differ either by position of metal ion or ligand (or other ion species) within the crystal or by different crystal packing. Usually polymorphs have different space groups.

Several of these forms or polymorphs have different physical properties and some may exist only at some temperatures and pressures (stability as a reason). Read more here: Crysal polymorphism - Wikipedia.

With respect to barium zirconate, it has cubic type pervoskite crystal structure where the barium atom is at the center of the cube while the zirconate ion is present on all of 8 edges.

For the β-form mentioned in your question, I do not find any reference for polymorphic barium zirconate, however when the crystal is doped with other atoms (like yttrium replacing barium) then polymorphism occurs (Yoshihiro Yamazaki, Raul Hernandez-Sanchez, and Sossina M. Haile. J. Mater. Chem. 2010, 20, 8158-8166.).

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