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I just realized that there is a gap somewhere in my understanding of K vectors and reciprocal space.

My question is how can we talk about K vectors "living" in the first Brillouin Zone, when these vectors cannot be expressed on the vector form of reciprocal space (r*=ha*kb*+lc*, where h,k,l integers)? First Brillouin Zone as I understand it, extends until half the length of the first neighboring lattice point of the reciprocal space.

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# K vector in first brillouin zone

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