Here is an argument that looks sound: “Base-centred tetragonal is not a new lattice

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Symmetry and the classification of crystals

Problem

Here is an argument that looks sound: “Base-centred tetragonal is not a new lattice. Rotate the square base by

45^\circ

and the corner and base-centre points trace out a smaller primitive tetragonal cell. The same

45^\circ

construction applied to a base-centred orthorhombic cell also gives a smaller primitive cell, so base-centred orthorhombic is not a separate Bravais lattice either.” ((a)) For a base-centred tetragonal cell with

a=4.00\ \text{\AA}

and

c=6.00\ \text{\AA}

, find the edge

a'

of the smaller primitive cell and the volume per lattice point in each description. ((b)) For a base-centred orthorhombic cell with

a=4.00\ \text{\AA}

and

b=5.00\ \text{\AA}

, centred on the faces containing

a

and

b

, find the length of each of the in-plane edges

\tfrac12(\mathbf a+\mathbf b)

and

\tfrac12(-\mathbf a+\mathbf b)

of the smaller cell, and the angle between them. ((c)) Find the error in the argument.

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