How were the crystal lattices of elements determined to perfection ? (Ex:- That of a copper is a cubic lattice ) [duplicate]

Question

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How can crystal structures be determined using X-ray diffraction?

Are there any simple means in order to verify the nature of complex lattices like that of Triclinic , Orthorhombic etc...

Answer 1

Simple, no, except for very specific cases. I recall that ionic lattices are fairly simple to predict on purely geometric constraints: for a two atom ionic lattice, only the ratio of the radii matter. In general, the standard approach is to pick a sufficiently powerful method, such as Density Functional Theory (there are many others!), guess a structure, and evaluate the free energy. After you try out all the lattice structures you want to (e.g., triclinic, simple, etc.), the one with the lowest free energy is right. Or it should be, if you calculated it correctly.

I'm sure there are many groups that do this, but as a student at Berkeley, I'm most familiar with the Cohen and Louie groups. They have a very long history of ab initio studies in solid state. The plots in Pseudopotential Calculations of Structural Properties of Solids tell some of the story, e.g. Fig. 3 shows a calculation of the silicon energy for many lattices, and very accurately predicts the correct lattice, lattice constant, cohesive energy, etc. This is another reference I remember from a class with Louie.