Consider an FCC structure. Are all the 1st nearest neighbours (NN) always at a distance of lattice parameter/sqrt(2)?
What about disordered random solid solutions?
The crystal structure describes the average, both spatial and over time. Thus in an FCC structure, the average position of next neighbors is always the same - or it would not be FCC, but a different structure. Locally this might be different. Depending on the experimental method, one sees one aspect of the structure or the other.
Think about the question you are asking. "Do all nearest neighbors have the same distance from the lattice point?" "... nearest neighbors...?" If you are tempted to think they might have different distances, they are not nearest neighbors. By definition, the nearest neighbors must always have the same distance (on average, when thermal vibration is considered) from the lattice point. If you have some at greater distance, they are not nearest neighbors. For many things, second nearest and more distance neighbors are important, but those are not nearest neighbors.
The above responses are sufficient. Without the average equidistance positions, the crystal of interest would not exist and hence can best be described as amorphous.
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