2
$\begingroup$

For any lattice a good choice of a unit cell is the one that is the most symmetric.

Now if every lattice made by a body centered tetragonal unit cell can be made by a face centered cubic unit cell ,which is more symmetric ,then why keep the body centered tetragonal unit cell as a class of Bravais lattice ? enter image description here

$\endgroup$
1
  • 3
    $\begingroup$ Because not every body centered tetragonal cell is equivalent to a face centered cubic cell. $\endgroup$ – Ivan Neretin Nov 29 '20 at 15:13
5
$\begingroup$

Body-centered tetragonal is face-centered cubic only if $c/a=\sqrt2$. If you try your transformation with a $c/a$ value greater/less than $\sqrt2$, your "cube" will have lateral edges that are longer/shorter (resp.) than the basal edge and so really remains tetragonal.

You can also read this the other way. If you are presented with a body-centered tetragonal lattice and $c/a$ seems to be close to $\sqrt2$, maybe it's really fcc.

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.