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I am trying to compare the band structure of a slab and the bulk phase, just like the example on the VASP wiki. In the example of VASP, it calculates the band structure of the slab of Ni metal.
A slab is basically a crystal that has a new kind of symmetry, but the example doesn't generate K-points from the slab, it uses the K points extracted from the Brillouin zone of the bulk primitive cell. I am not sure if this is appropriate.
And I should follow the way in the example, why should I choose K points from the one facet of the Brillouin Zone of bulk phase?

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the example doesn't generate K-points from the slab, it uses the K points extracted from the Brillouin zone of the bulk primitive cell.

Not sure you're reading the figure correctly.

The bottom of the figure shows the three-dimensional Brillouin zone of the primitive cell, but the top of the figure (which the G-M-X-G path refers to) shows the two-dimensional Brillouin zone of the slab.

You are right that the relation between the Brillouin zone of the primitive cell and a slab may not be straightforward and certainly depends on how the slab is constructed. In this particular instance, the authors indicate a relation between the W point of the lower BZ and the G-M midpoint in the upper BZ.

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