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I have a lattice with Lattice Vectors $(\vec{t}_1,\vec{t}_2,\vec{t}_3)$ which are NOT orthogonal in general.
How can I identify the atoms/unit cells that belong to a plane - that is normal to a given direction.
I do recognise that the lattice might not be periodic in ANY direction - only specific ones.

I worked out a way to calculate the periodicity of the lattice planes:

1. Given the direction $\vec{t}$, construct the corresponding reciprocal lattice vector G.
2. Project $\vec{G}$ in the direction of $\vec{t}$ and take the inverse of the length of the projected vector.
   i.e. Distance between lattice planes normal to the direction $\vec{d} = \vec{G}\cdot \frac{\vec{t}}{\vert\vec{t}\vert}$

My question, once again, is to find an algorithm that identifies the atoms in the crystal planes thus formed.

I have a lattice with Lattice Vectors $(\vec{t}_1,\vec{t}_2,\vec{t}_3)$ which are NOT orthogonal in general.
How can I identify the atoms/unit cells that belong to a plane - that is normal to a given direction.
I do recognise that the lattice might not be periodic in ANY direction - only specific ones.

I worked out a way to calculate the periodicity of the lattice planes:

1. Given the direction $\vec{t}$, construct the corresponding reciprocal lattice vector G.
2. Project $\vec{G}$ in the direction of $\vec{t}$ and take the inverse of the length of the projected vector.
   i.e. Distance between lattice planes normal to the direction $d = \vec{G}\cdot \frac{\vec{t}}{\vert\vec{t}\vert}$

My question, once again, is to find an algorithm that identifies the atoms in the crystal planes thus formed.

I have a lattice with Lattice Vectors $(\vec{t}_1,\vec{t}_2,\vec{t}_3)$ which are NOT orthogonal in general.
How can I identify the atoms/unit cells that belong to a plane - that is normal to a given direction.
I do recognise that the lattice might not be periodic in ANY direction - only specific ones.

I worked out a way to calculate the periodicity of the lattice planes:

1. Given the direction $\vec{t}$, construct the corresponding reciprocal lattice vector G.
2. Project $\vec{G}$ in the direction of $\vec{t}$ and take the inverse of the length of the projected vector.
   i.e. Distance between lattice planes normal to the direction $\vec{t} = \vec{G}\cdot \frac{\vec{t}}{\vert\vec{t}\vert}$

My question, once again, is to find an algorithm that identifies the atoms in the crystal planes thus formed.

I have a lattice with Lattice Vectors $(\vec{t}_1,\vec{t}_2,\vec{t}_3)$ which are NOT orthogonal in general.
How can I identify the atoms/unit cells that belong to a plane - that is normal to a given direction.
I do recognise that the lattice might not be periodic in ANY direction - only specific ones.

I worked out a way to calculate the periodicity of the lattice planes:

1. Given the direction $\vec{t}$, construct the corresponding reciprocal lattice vector G.
2. Project $\vec{G}$ in the direction of $\vec{t}$ and take the inverse of the length of the projected vector.
   i.e. Distance between lattice planes normal to the direction $\vec{d} = \vec{G}\cdot \frac{\vec{t}}{\vert\vec{t}\vert}$

My question, once again, is to find an algorithm that identifies the atoms in the crystal planes thus formed.