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discussion of the allotropes of sulfur in Melting point of sulfur and comments below reminded me of Napoleon's buttons, cf. Tin pest; Allotropic transformation. That section in its entirety reads:

At 13.2 °C (55.8 °F) and below, pure tin transforms from the silvery, ductile metallic allotrope of β-form white tin to the brittle, nonmetallic, α-form grey tin with a diamond cubic structure. The transformation is slow to initiate due to a high activation energy but the presence of germanium (or crystal structures of similar form and size) or very low temperatures of roughly −30 °C aids the initiation. There is also a large volume increase of about 27% associated with the phase change to the nonmetallic low temperature allotrope. This frequently makes tin objects (like buttons) decompose into powder during the transformation, hence the name tin pest. The decomposition will catalyze itself, which is why the reaction accelerates once it starts. The mere presence of tin pest leads to more tin pest. Tin objects at low temperatures will simply disintegrate.

Is this really catalysis proper? Is the acceleration of the already thermodynamically favorable conversion of a pure element from one allotrope to another by the presence of some of the final allotrope

  1. a chemical reaction?
  2. at least auto-catalysis?

Is there even general agreement on the answers to those?

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  • $\begingroup$ Let's rephrase. My point is this matter is inherently arguable. One could say it's not a reaction, or that it is and both answers would be OK. Similarly one could argue that it's autocatalysis, or just catalysis, or no catalysis at all, and none of these answers would be necessarily incorrect. $\endgroup$
    – Mithoron
    Commented May 17 at 17:20
  • $\begingroup$ Questions like this hardly lead to anything conclusive, eg. chemistry.stackexchange.com/questions/33278/… chemistry.stackexchange.com/questions/2686/… chemistry.stackexchange.com/questions/1293/… $\endgroup$
    – Mithoron
    Commented May 17 at 17:34
  • $\begingroup$ @Mithoron and yet I've already received a well-reasoned and thorough answer, drawing directly from IUPAC definitions. $\endgroup$
    – uhoh
    Commented May 17 at 23:50
  • $\begingroup$ This also apply to other state changes, e.g., supercooled water or sodium thiosulfate. Drop in a seed crystal (ice or solid sodium thiosulfate), and the whole mass turns to solid in seconds. Is a seed crystal a catalyst? A matter of definition. $\endgroup$ Commented May 31 at 3:46
  • $\begingroup$ @DrMoishePippik "A matter of definition" My thinking is that in modern day chemistry there are generally accepted and agreed-upon definitions, so a fairly clear, unambiguous answer here should be possible (and it seems has happened). Also, what you are describing is a phase change from a disordered liquid to an ordered solid. I think that the transition from one ordered solid to another is different enough that those are not in the same category, but they are close, which makes me wonder, is the crystal transition a "phase change"? Hmm... Maybe so! $\endgroup$
    – uhoh
    Commented May 31 at 4:59

1 Answer 1

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There are elements of catalysis present.

Let's presume $\ce{A -> P}$ proceeds by a single elementary step. The two states of $\ce{A}$ and of $\ce{P}$ can be compared with each other by a change of overall Gibbs Free enthalpy, $\Delta{}G^\circ{} = \Delta{}H^\circ -T \Delta{}S^\circ$. Simultaneously accounting for enthalpic and entropic contribution, the balance governs if a reaction at all were favorable, or not, regardless of the mechanism actually engaged. Second, for a reaction to happen, an activation is necessary; itself described by $\Delta{}G^\ddagger$ and connected to the kinetics of a specific reaction path,* by the Eyring equation

$$k = \frac{\kappa k_B T}{h} \exp\left(-\frac{\Delta{}G^\ddagger}{RT} \right)$$

This now relates the kinetic rate of a reaction ($k$) with a transmission coefficient ($\kappa$), Boltzman constant ($k_B$), the thermodynamic temperature ($T$), Planck constant ($h$), Gibbs' free energy of activation ($\Delta{}G^\ddagger$) and universal gas constant ($R$). Hence the energetic advance (or trajectory) of a reaction can be depicted in (simplified) projections of energy surfaces, e.g.

enter image description here

(Robert Grossman, p. 20)

Catalysis now alters the relevant reaction trajectory; the activation energy $E_a$ between the starting point of the reaction and the highest energy in the course of the reaction is lowered, too:

enter image description here

(image credit Д.Ильин, used by Wikipedia)

typically provided by heat, or radiation. In other words, less energy is required to pass across this barrier to reach the reaction product(s), or (equivalent) the reaction (already) occurs at a lower temperature.

The transformation of $\beta$ Sn to $\alpha$ Sn occurs at $\pu{13.2 ^\circ{}C}$, and yet

There seems to be general agreement in the literature that the maximum rate of tin pest formation occurs at $\pu{−30 ^\circ{}C}$ to $\pu{−40 ^\circ{}C}$. [...] Tin can spend anywhere from months to years in cold storage before developing observable signs of tin pest. Following nucleation, growth is relatively rapid, with 100% transformation to α‑tin observed to occur in as little as 30 days.

(James Clark)

are in line with said acceleration catalysis provides.

  1. Is it a chemical reaction? In $\alpha$ Sn, the lattice is best described as face centered diamond cubic (property box, English edition of Wikipedia) where each Sn is in a centre of a tetrahedron which is not the case for $\beta$ Sn (body centred tetragonal). The different environment of Sn then arguably affects the (electronic) band structure. Because IUPAC Gold book defines

    chemical reaction: A process that results in the interconversion of chemical species. [...] (ref)

    and

    chemical species: An ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on the time scale of the experiment. The term is applied equally to a set of chemically identical atomic or molecular structural units in a solid array. [...] (ref)

    I reason yes it does qualify as a chemical reaction even if there are no directed covalent bonds broken/established to interconvert between the allotropes as for instance $\ce{O2} \text{ vs. } \ce{O3}$, or diamond vs. graphite.

  2. Is it an example of autocatalysis? By the established difference between $\alpha$ and $\beta$ form I think no, it would not be an autocatalysis.

* This then explains the formation of a thermodynamic vs. a kinetically preferred reaction product e.g., the selectivity for endo vs. exo product of a Diels-Alder reaction.


Grossman, R. The Art of Writing Reasonable Organic Reaction Mechanisms. 2nd edition (2003), Springer, New-York, ISBN 0-387-95468-6

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