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The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other. The crystalline state of matter is characterized by a distinct structural rigidity and very high resistance to deformation (i.e. changes of shape and/or volume).
Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time ...
Crystal growth provide dramatic examples of autocatalysis: the growth rate depends on the surface area of the growing crystal. The growth of metal films from solution using the technique of electroless plating is autocatalytic. The rate of plating accelerates after some deposition has occurred, i.e., nucleation. Mathematical description
Crystallization. Crystallization is the process by which solids form, where the atoms or molecules are highly organized into a structure known as a crystal. Some ways by which crystals form are precipitating from a solution, freezing, or more rarely deposition directly from a gas. Attributes of the resulting crystal depend largely on factors ...
Exponential decay. A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant ( λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Catalysis. A range of industrial catalysts in pellet form. An air filter that uses a low-temperature oxidation catalyst to convert carbon monoxide to less toxic carbon dioxide at room temperature. It can also remove formaldehyde from the air. Catalysis ( / kəˈtæləsɪs /) is the increase in rate of a chemical reaction due to an added ...
Nucleation is a common mechanism which generates first-order phase transitions, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immediately. Nucleation is often very sensitive to impurities in the system.
Growth of bubbles in a liquid foam via Ostwald ripening. [2] Ostwald ripening is a phenomenon observed in solid solutions and liquid sols that involves the change of an inhomogeneous structure over time, in that small crystals or sol particles first dissolve and then redeposit onto larger crystals or sol particles. [3]