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My background in solid-state chemistry isn't much, so I apologize in advance if there arises the need to raise a basic fact while answering my question. I've been learning mostly from the web, with my main text resource 'Band Theory of Solids: An Introduction from the point of view of symmetry.' by Simon L. Altmann.

From what I understand, Brillouin zones are areas (or volumes in 3-D) in reciprocal space where you use to describe the energy levels with respect to the k-vectors. Thus typically in band structure plots the k-vectors range from the origin Γ along some straight path which contains points like Δ, K etc.

So far the common examples I've seen for a Brillouin zone are for just a 'pure' elements (Si, Cu etc.) where you have the atoms in a crystal formation, which you obtain direct lattice pattern, and then the reciprocal space, and finally the Brillouin zone polyhedron.

What I'm really curious about is, if I have a material that I know the Brillouin zone (like a graphite sheet), and this material reacts with another molecule (like a dopant), how would the Brillouin zone change? A scenario would be performing structural relaxation of a carbon nanotube with some dopants, and the nanotube deforms slightly (with the dopants moving to an equilibrium configuration). In this case even if I know the Brillouin zone of a pure (undoped) carbon nanotube, with the deformation, how should I determine which are the k-vector points then?

My background in solid-state chemistry isn't much, so I apologize in advance if there arises the need to raise a basic fact while answering my question. I've been learning mostly from the web, with my main text resource 'Band Theory of Solids: An Introduction from the point of view of symmetry.' by Simon L. Altmann.

From what I understand, Brillouin zones are areas (or volumes in 3-D) in reciprocal space where you use to describe the energy levels with respect to the k-vectors. Thus typically in band structure plots the k-vectors range from the origin Γ along some straight path which contains points like Δ, K etc.

So far the common examples I've seen for a Brillouin zone are for just a 'pure' elements (Si, Cu etc.) where you have the atoms in a crystal formation, which you obtain direct lattice pattern, and then the reciprocal space, and finally the Brillouin zone polyhedron.

What I'm really curious about is, if I have a material that I know the Brillouin zone (like a graphite sheet), and this material reacts with another molecule (like a dopant), how would the Brillouin zone change? A scenario would be performing structural relaxation of a carbon nanotube with some dopants, and the nanotube deforms slightly (with the dopants moving to an equilibrium configuration). In this case even if I know the Brillouin zone of a pure (undoped) carbon nanotube, with the deformation, how should I determine which are the k-vector points then?

My background in solid-state chemistry isn't much, so I apologize in advance if there arises the need to raise a basic fact while answering my question. I've been learning mostly from the web, with my main text resource 'Band Theory of Solids: An Introduction from the point of view of symmetry.' by Simon L. Altmann.

From what I understand, Brillouin zones are areas (or volumes in 3-D) in reciprocal space where you use to describe the energy levels with respect to the k-vectors. Thus typically in band structure plots the k-vectors range from the origin Γ along some straight path which contains points like Δ, K etc.

So far the common examples I've seen for a Brillouin zone are for 'pure' elements (Si, Cu etc.) where you have the atoms in a crystal formation, which you obtain direct lattice pattern, and then the reciprocal space, and finally the Brillouin zone polyhedron.

What I'm really curious about is, if I have a material that I know the Brillouin zone (like a graphite sheet), and this material reacts with another molecule (like a dopant), how would the Brillouin zone change? A scenario would be performing structural relaxation of a carbon nanotube with some dopants, and the nanotube deforms slightly (with the dopants moving to an equilibrium configuration). In this case even if I know the Brillouin zone of a pure (undoped) carbon nanotube, with the deformation, how should I determine which are the k-vector points then?

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# Brillouin zones of a compound after structural relaxation

My background in solid-state chemistry isn't much, so I apologize in advance if there arises the need to raise a basic fact while answering my question. I've been learning mostly from the web, with my main text resource 'Band Theory of Solids: An Introduction from the point of view of symmetry.' by Simon L. Altmann.

From what I understand, Brillouin zones are areas (or volumes in 3-D) in reciprocal space where you use to describe the energy levels with respect to the k-vectors. Thus typically in band structure plots the k-vectors range from the origin Γ along some straight path which contains points like Δ, K etc.

So far the common examples I've seen for a Brillouin zone are for just a 'pure' elements (Si, Cu etc.) where you have the atoms in a crystal formation, which you obtain direct lattice pattern, and then the reciprocal space, and finally the Brillouin zone polyhedron.

What I'm really curious about is, if I have a material that I know the Brillouin zone (like a graphite sheet), and this material reacts with another molecule (like a dopant), how would the Brillouin zone change? A scenario would be performing structural relaxation of a carbon nanotube with some dopants, and the nanotube deforms slightly (with the dopants moving to an equilibrium configuration). In this case even if I know the Brillouin zone of a pure (undoped) carbon nanotube, with the deformation, how should I determine which are the k-vector points then?