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PHY.K02UF Molecular and Solid State Physics | ||||
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