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Lattice vectors
Consider a lattice (2D) like the one shown.
We can construct vectors between any two lattice points,
These vectors are known as lattice vectors.
We can construct vectors between any two lattice points,
These vectors are known as lattice vectors.
Now lattice vectors a
& b have been constructed.
As this is a 2D lattice two basis vectors are required to describe all lattice vectors that may be constructed.
These vectors are known as lattice vectors.
As this is a 2D lattice two basis vectors are required to describe all lattice vectors that may be constructed.
These vectors are known as lattice vectors.
If a
and b are such basis
vectors any other vector, t, may be wriiten in terms of a
& b, the basis vectors."
i.e. t= Ua + Vb where U and V are constants.
This is given the shorthand notation of t = [UV]
Note: this extends to 3D also, e.g. t= [UVW]
i.e. t= Ua + Vb where U and V are constants.
This is given the shorthand notation of t = [UV]
Note: this extends to 3D also, e.g. t= [UVW]
For example consider the vector t shown.
How would we write this in terms of the basis vectors a & b?
How would we write this in terms of the basis vectors a & b?
As can be seen t can be written as 2a
+ b or in shorthand
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