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I’m brushing up my skills on solid state physics and I have a few questions about crystal lattices:

1. What’s the spacing between allowed kx, ky, and kz states for a lattice of dimensions La x Lb x Lc?

My attempt:

The spacing is kx, ky, and kz:

[tex]k_x = \frac{2\pi}{L_a}, \qquad k_y = \frac{2\pi}{L_b} , \qquad k_z = \frac{2\pi}{L_c}[/tex]

Assuming Born–von Karman periodic boundary conditions.

2. How many electrons fit in the first Brillouin zone?

My attempt:

[tex]N_a = \frac{L_a}{a},\qquad N_b = \frac{L_b}{b},\qquad N_c= \frac{L_c}{c}[/tex]

for an orthorhombic lattice of primitive direct lattice constants a, b, and c.

So, the total number of electrons is N = Na x Nb x Nc

Is this right?

Thanks

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# A Basic questions on crystal lattice: k-vectors and Brillouin

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