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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

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

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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