Now I'm getting into the dim dark recesses of crystallography.

Converting BCC (Im-3m) to orthorhombic

The twinning plane in BCC is (112), so following [1] (cited by [2]), (and fiddling with the order of axes to maintain right handedness), the orthorhombic basis vectors are defined, in terms of the BCC vectors (2.880 Å), as:

A = a - b (4.073 Å)

B = (1/2) (a + b - c) (2.494 Å)

C = a + b + 2c (7.054 Å)

this gives the c-axis in the faulting direction. This is also triples the volume, so I expect 6 atoms in the unit cell.

I've then manually picked out the atom positions in the new unit cell as

0 0 0

1/2 0 1/2

0 1/3 1/3

1/2 1/3 5/6

0 2/3 2/3

1/2 2/3 1/6

(and it is 6)

By observation, I think it is a B base-centred orthorhombic cell, but I can't get a space group. If I plug it into Topas in P1, the calculated pattern matches BCC, so I'm good there. Platon wants to bring it back to P-3m1. FINDSYM goes back to Im-3m.*

Looking through International Tables, I can't find a SG with the right symmetry. What I think I need is:

B base-centred orthorhombic cell

(0,0,0)+ and (1/2,0,1/2)+

Multiplicity Coords

2 0,0,0 (or equivalent, eg 0,0,z or x,y,z)

2 0,y,y (or equivalent, eg 0,u,z or x,y,z)

Is there such a beast?

*Is there any way to limit the space groups it searches?

[1] Hirsch and Otte (1957) Acta Cryst. 10: 447

[2] Warren "X-Ray Diffraction", p. 305

--

Matthew

This post was edited on 2020-11-13, 03:46 by

rowlesmr.