Yes, I agree with Tapan: f you have a tetragonal cell with base centering, then you can choose a primitive (tetragonal cell ) having the area corresponding to one half of the centered one. This means that centering operation does not produce (in this case ) something new. A completely different situation sets up when centering the base C of the monoclinic lattice; as a matter of fact, if one obtains a primitive cell from the monoclinic C , an oblique rhombic prism is obtained (which is no longer monoclinic).
All the best
Dino
If you have a tetragonal cell with base centering then then you can easily choose smaller primitive tetragonal cell. This is illustrated in Fig. 2.4 (p. 37) in the text book of B.D. Cullity, Elements of X-ray Diffraction, Addison-Wesley (1978).
Yes, I agree with Tapan: f you have a tetragonal cell with base centering, then you can choose a primitive (tetragonal cell ) having the area corresponding to one half of the centered one. This means that centering operation does not produce (in this case ) something new. A completely different situation sets up when centering the base C of the monoclinic lattice; as a matter of fact, if one obtains a primitive cell from the monoclinic C , an oblique rhombic prism is obtained (which is no longer monoclinic).
All the best
Dino
https://www.quora.com/Why-is-a-face-centered-tetragonal-not-possible
A tetragonal crystal system has a defining symmetry of a single four-fold rotation axis.
A face-centered tetragonal (FCT) lattice does have this symmetry. So it must belong to the tetragonal crystal system. But there is no FCT Bravais lattice in the tetragonal system. We then explore to find a smaller body-centered tetragonal (BCT) unit cell as shown in the figure of the answer given by Jeanne Paquette.
Focussing only on the size of a possible smaller unit cell can lead to wrong conclusions. For example, a smaller BCT unit cell is also possible in a face-centered cubic (FCC) lattice. This can be seen using a figure similar to that shown by Paquette. But we cannot replace FCC by BCT because FCC has a higher symmetry (four three-fold axes along the body diagonals) which the BCT does not have. So although a smaller unit cell is possible in this case also we do not go for it. We retain the larger FCC unit cell in the interest of symmetry.
In fact why BCT unit cell, although smaller, cannot be used as a description of FCC lattice is a classic example of the priority of symmetry over unit cell size and shape.
Bravais lattice is based on the symmetry of the unit cell and not the shapes of unit cell.
Symmetry for tetragonal is single four fold axis, which means we can get the same lattice if we rotate the unit cell by 90 degree along C-axis.
In case of face centred tetragonal, symmetry number is greater and this symmetry is not considered for tetragonal crystal system.
So only FCT does not exists
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