Stability of α, β, γ allotropes at different temperatures

Question

While reading about elements or compounds I often come across allotropes (or forms) being referred to as α, β, γ forms.

Examples:

• Sulfur has two allotropes: α rhombic and β monoclinic. Out of these two α is considered more stable at ordinary temperatures.
• $\ce{SO3}$ has three forms out of which again α is considered more stable.
• α-Form of iron is considered the most stable at ordinary temperatures.

Based on this small data, it makes me think whether α forms are always in general the more stable ones? Is it true? How does this nomenclature signify stability at different temperatures?

Answer 1

A German speaking mineral atlas states:

«Man unterscheidet die verschiedenen polymorphen Modifikationen durch Voranstellen der griechischen Buchstaben alpha, beta, gamma usw. Die Buchstaben entsprechen im Wesentlichen der Erhöhung oder Erniedrigung der Umwandlungstemperatur.»

which may be translated into

«One discerns the different polymorphs by Greek letters $\alpha$, $\beta$, $\gamma$, etc. The letters mainly correspond to an increase or decrease of the [solid-solid] phase transition.»

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To extend the answer by @ĐỨc Lê Hồng (+1):

Eilhard Mitscherlich may be credited to extend Steno's angle law about crystals of one and the same compound to isomorphism (different chemical compounds may yield crystals of at least very similar shape) and eventually allotropes (about elements) / polymorphism (the term equally applicable for compounds) that the same chemical compound may form crystals of distinct different shape and symmetry.

Back around 1825, the experimentally accessible space in terms of temperature and especially pressure was much more constraint, than today. Thus, the phases were sort in ascending order of the temperature of the corresponding phase transition by Greek letters.

This is the reason why e.g., while the stable form of tin observed at room temperature is labeled by $\beta$, and the one at lower temperatures by $\alpha$. Staying with elements, cyclic $\ce{S8}$ sulfur is known in the $\alpha$ form stable below $\ce{95.3 ^\circ{}C}$, but by the $\beta$ and $\gamma$ form above this temperature. Without counting the other allotropes of sulfur. (reference).

Iron is an example suitable to to show early limitations of this nomenclature. The phase diagram of pure iron still is simple for its $\alpha$, $\gamma$, and $\delta$ form.

(credit)

(There equally is a $\beta$ form of Fe, but this is of much lesser significance, seen in the binary phase diagram Fe-C.)

Today's convention to count polymorphs by roman numbers (if there is more than one) has the advantage that these may reflect the sequence of their discovery, regardless if researchers explore the variation of temperature, pressure, or the combination of the two. An example for this may be water:

(figure 7 from here, figure 2 from here, both open access)

On occasion, you encounter binary phase diagrams reflecting both approaches, e.g., Fe-C:

(credit)

describing ledeburite I (a micro structure of austenit + $\ce{Fe3C}$) and ledeburite II (a microstructure of Perlit + $\ce{Fe3C}$).

Answer 2

I think most of the time, they sort according to the order which temperature the allotrope/polymorph is more stable. Let's say element Z has two allotropes A and B. A is stable below 100 °C and B is stable above 100 °C. Thus allotrope A would be denoted alpha-Z and allotrope B would be denoted beta-Z.

Gray tin (alpha-tin) and white tin (beta-tin) is an example. Gray tin is stable only below 13.2 °C and white tin is stable above this point. So that's why gray tin is called alpha-tin because it is stable at a lower temperature, and ditto with white tin. As you can see in this case the beta allotrope would be the one stable at room temperature one.

Quartz (a crystalline form of silicon dioxide) is another example. See this from Wikipedia:

Quartz exists in two forms, the normal α-quartz and the high-temperature β->quartz, both of which are chiral. The transformation from α-quartz to β-quartz >takes place abruptly at 573 °C (846 K; 1,063 °F).