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I would say that every solid has a non-zero vapour pressure at room temperature and so could vaporize; even Iron, for example. How much vaporizes, it's another story. For a solid like Iron, the speed would be ridiculosly low.--lightarrow
At room temperature (300 K), I calculate 1 out of 10122 atoms in a diamond lattice could leave the solid for vapor phase (assuming they are all at the surface). This means that any reasonable sample size (say less than an Earth mass) would actually exert 0 vapor pressure at room temperature... Under sunlight radiation there would be a higher pressure of ejected electrons!
Yes diamond. A counter-example to the claim that every solid has a non-zero vapor pressure.