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Crystals

Lattices and unit cells, with basis vectors chosen to describe the repeating atomic arrangement in salt and diamond and to count atoms per cell.

Linear Algebra, Crystals

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3 exercises

Exercise 1

How many fundamental regions are there in one face of a speck of salt? (With a ruler, we can estimate that face is a square that is 0.10.1 cm on a side.)

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Exercise 3

Give the locations of the atoms in the diamond cube both in terms of the basis, and in Ångstroms.

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Exercise 4

This illustrates how we could compute the dimensions of a unit cell from the shape in which a substance crystallizes (, p. 462).

  • Recall that there are 6.022×10236.022\times 10^{23} atoms in a mole (this is Avogadro’s number). From that, and the fact that platinum has a mass of 195.08195.08 grams per mole, calculate the mass of each atom.

  • Platinum crystallizes in a face-centered cubic lattice with atoms at each lattice point, that i…

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.

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