(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

given the following position vector:

R = (10n1 + 9n2 + 19n3)(a/10)x+ 6(n2+n3)(a/5)y+ 2(n3)az

where n1, n2 and n3 are integers

Find the primitive lattice vectors.

2. Relevant equations

any position vector of a lattice point is of the type

R= c1 a1 + c2 a2 + c3 a3;

and a position vector like the one showed above is a linear combination of the primitive lattice vectors a1, a2 and a3.

3. The attempt at a solution

I think I solved the question correctly, but my intuition tells me its wrong:

we can do the following:

a1 = a/10X

a2 = a/5Y

a3 = aZ

In our case, since n1,n2 and n3 are just integers:

c1 = 10n1 + 9n2 + 19n3

c2 = 6(n2 + n3)

c3 = 2n3

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# Deduce primitive lattice vectors from position vector.

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