PHY.K02UF Molecular and Solid State Physics

Cesium chloride (CsCl)

Cesium chloride (CsCl) is a crystal structure with a simple cubic Bravais lattice and two atoms in the basis.

Crystal structure: CsCl
Bravais lattice: Simple cubic
Space group: 221 ($Pm\overline{3}m$),   Strukturbericht: B2,   Pearson symbol: cP2
Point group: m3m (Oh)   six 2-fold rotations, four 3-fold rotations, three 4-fold rotations, nine mirror planes, inversion


The lattice parameters of the conventional unit cell are:

\[ \begin{equation} a = b = c, \hspace{0.5cm} \alpha = 90^{\circ} , \,\beta = 90^{\circ} ,\,\gamma = 90^{\circ} . \end{equation} \]

The primitive unit cell is the same as the conventional unit cell. The primitive lattice vectors are,

$\vec{a}_1=a\hat{x}$,   $\vec{a}_2=a\hat{y}$,   $\vec{a}_3=a\hat{z}$.

There are two atoms in asymmetric unit and in the basis. In fractional coordinates of the conventional unit, the positions of the two atoms are,

Cl=(0,0,0),   Cs=(0.5,0,0).

Space group: 221 ($Pm\overline{3}m$)
48 symmetry operations:

1	x,y,z	identity
2	-x,-y,z	C2 axis
3	-x,y,-z	C2 axis
4	x,-y,-z	C2 axis
5	z,x,y	C3 axis
6	z,-x,-y	C3 axis
7	-z,-x,y	C3 axis
8	-z,x,-y	C3 axis
9	y,z,x	C3 axis
10	-y,z,-x	C3 axis
11	y,-z,-x	C3 axis
12	-y,-z,x	C3 axis
13	y,x,-z	C2 axis
14	-y,-x,-z	C2 axis
15	y,-x,z	C4 axis
16	-y,x,z	C4 axis
17	x,z,-y	C4 axis
18	-x,z,y	C2 axis
19	-x,-z,-y	C2 axis
20	x,-z,y	C4 axis
21	z,y,-x	C4 axis
22	z,-y,x	C2 axis
23	-z,y,x	C4 axis
24	-z,-y,-x	C2 axis
25	-x,-y,-z	Ci: 0 0 0
26	x,y,-z	mirror plane
27	x,-y,z	mirror plane
28	-x,y,z	mirror plane
29	-z,-x,-y	3-bar axis|inversion center at 0 0 0
30	-z,x,y	3-bar axis|inversion center at 0 0 0
31	z,x,-y	3-bar axis|inversion center at 0 0 0
32	z,-x,y	3-bar axis|inversion center at 0 0 0
33	-y,-z,-x	3-bar axis|inversion center at 0 0 0
34	y,-z,x	3-bar axis|inversion center at 0 0 0
35	-y,z,x	3-bar axis|inversion center at 0 0 0
36	y,z,-x	3-bar axis|inversion center at 0 0 0
37	-y,-x,z	mirror plane
38	y,x,z	mirror plane
39	-y,x,-z	4-bar axis|inversion center at 0 0 0
40	y,-x,-z	4-bar axis|inversion center at 0 0 0
41	-x,-z,y	4-bar axis|inversion center at 0 0 0
42	x,-z,-y	mirror plane
43	x,z,y	mirror plane
44	-x,z,-y	4-bar axis|inversion center at 0 0 0
45	-z,-y,x	4-bar axis|inversion center at 0 0 0
46	-z,y,-x	mirror plane
47	z,-y,-x	4-bar axis|inversion center at 0 0 0
48	z,y,x	mirror plane