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# Gibbs-Thomson effect

The Gibbs-Thomson effect (also called the Gibbs-Kelvin effect or Kelvin effect) relates surface curvature to vapor pressure and chemical potential. It is named after Josiah Willard Gibbs and William Thomson, 1st Baron Kelvin. (It is not to be confused with the thermoelectric Thomson effect.)

It leads to the fact that small liquid droplets (i.e. particles with a high surface curvature) exhibit a higher effective vapor pressure, since the surface is larger in comparison to the volume. The Gibbs-Thomson effect can cause strong depression of the freezing point of liquids dispersed within fine porous materials.

Another notable example of the Gibbs-Thomson effect is Ostwald ripening, in which concentration gradients cause small precipitates to dissolve and larger ones to grow.

The Gibbs-Thomson equation for a precipitate with radius $R$ is:

$frac\left\{p\right\}\left\{p_\left\{eq\right\}\right\} = exp\left\{left\left(frac\left\{R_\left\{critical\right\}\right\}\left\{R\right\}right\right)\right\}$

$R_\left\{critical\right\} = frac\left\{2 cdot gamma cdot V_\left\{Atom\right\}\right\}\left\{k_B cdot T\right\}$

$V_\left\{Atom\right\}$ : Atomic volume
$k_B$ : Boltzmann constant
$gamma$ : Surface tension (J $cdot$ m$^\left\{-2\right\}$)
$p_\left\{eq\right\}$ : Equilibrium partial pressure (or chemical potential or concentration)
$p$ : Partial pressure (or chemical potential or concentration)
$T$ : Absolute temperature

Ostwald ripening is thought to occur in the formation of orthoclase megacrysts in granites as a consequence of subsolidus growth. See rock microstructure for more.

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