= Solution
The metallic conventional cell has four tin atoms, whereas the conventional <diamond cubic structure> cell has eight. Therefore the volume per atom is
$$
v_\beta=\frac{(0.5831)^2(0.3182)}4
=0.0270474\,\mathrm{nm^3},
\qquad
v_\alpha=\frac{(0.6489)^3}{8}
=0.0341541\,\mathrm{nm^3}.
$$
The fractional change for metallic to nonmetallic tin is
$$
\boxed{\frac{v_\alpha-v_\beta}{v_\beta}\simeq0.2627,
\qquad\text{about }26.3\%\text{ expansion}.}
$$
The atom count is unchanged, so this is also the unconstrained bulk volume change for complete transformation under the model. If it were macroscopically isotropic, the corresponding free linear expansion would be $(1.2627)^{1/3}-1\simeq8.1\%$.
Such a large transformation <strain> creates stresses where transformed and untransformed regions constrain one another. Cracking, loss of mechanical integrity and disintegration can follow: the phenomenon is <tin pest>. The calculation establishes the volume mismatch, not the transformation rate; <temperature>, nucleation and impurities affect when a real specimen changes.
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