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How could these structures be represented in an array or vector while still maintaining the lengths between atoms in C++?

I would like to construct a three dimensional vector to represent the configuration of:

An FCC Lattice. FCC

A BCC Lattice BCC

A HCP Lattice. HCP

A standard three dimensional vector is essentially a SC Lattice: SC

The above are depictions of unit cells, the full lattices look like: Structures And for HCP: HCP structure

The reasons behind it is to more accurately represent the crystal structure of a material using an Ising Model. I would like the lattice to preserve lengths in order to give an accurate calculation of the exchange constant.

NictraSavios
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1 Answers1

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BCC is two SC lattices offset from each other. HCP is an SC lattice skewed.

You'll simply take the crystal structure into account for length calculations. Trying to make indices or memory address correspond to length is an exercise in futility. Just have a mapping function from indices to length.

Ben Voigt
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  • Let me make sure I understand fully, simply take the structures macroscopically as a cube, and account for the lengths through a different value along the x,y and z axis? - Say it was gravity, if x was twice as long as y and z, the force would be cut in one fourth, but otherwise the lattice is taken as cubic? Also, what about FCC? – NictraSavios Dec 15 '13 at 21:41
  • @Nictra: Basically yes. Or when you are doing the HCP, you may need to look at `x`, `y`, and `y-x`, because of the skew. – Ben Voigt Dec 15 '13 at 21:44
  • What would the FCC be in terms of the SC? – NictraSavios Dec 15 '13 at 21:51
  • I think it is four cubic lattices, one with (0,0,0) offset, one with (1/2,1/2,0), one with (0,1/2,1/2), and one with (1/2,0,1/2) – Ben Voigt Dec 15 '13 at 21:52
  • How would I apply those offsets in code? If the variable determining the strength of the interactions is J, how would I modify J_x, J_y, J_z when stepping through a cubic lattice in an Ising-like fashion? – NictraSavios Dec 15 '13 at 22:01