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Hi all,

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?

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?

[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

Thanks

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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