The Growth of an Initial Sphere

One of the simplest cases to analyze is that of a growing sphere. If the temperature is held at just the right value, a spherical crystal can be maintained. It is an unstable equilibrium: If the temperature is lowered slightly, it will grow--slowly at first, but then more rapidly as the sphere becomes larger and the interface becomes flatter. Similarly, if the temperature is raised slightly, it will shrink, slowly at first, but then accelerating.

A single, nearly spherical crystal of NH4Cl growing in an aqueous solution

By deliberately oscillating the temparture around the equilibrium value, we can cause the crystal to grow and shrink. This provides us with a way to measure the surface energy for this material. A movie of the experiment is available here.

We then measure the temperature of the sample and radius of the crystal as a function of time, and fit them to a theoretical model to determine the capillary length d₀.

Fit for the radius vs. time for a crystal subject to an oscillating temperature.

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