Crystal lattice 1 CeCu 2 Si 2 NaCl SmRu 14 P 12 periodic array of - - PowerPoint PPT Presentation

Crystal lattice

NaCl (Ba,K)FeAs CeCu2Si2 SmRu14P12 K-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-x

periodic array

• f atoms

complex sub-structures

1

Crystal lattice

unit cell lattice vectors primitive lattice vectors Wigner-Seitz cell

basis set

2

Crystal lattice - Space Group

general symmetry operations in a crystal lattice

~ r 0 = g~ r + ~ a = {g|~ a}~ r

{g|~ a} space group element

~ r g~ r

~ r 0 ~ a

{E|~ a}

~ a

point group element lattice vector basic translations

{g|~ 0}

rotations, reflections, inversions screw axis, glide plane

basic elements

+

~ a 0

{g0|~ a0} g0

60o rotation around z-axis not a lattice vector not a basic point group element

screw axis

g ∈ P

3

Crystal lattice - Space Group

space group is a group

R

{E|~ 0} {g|~ a}{g0|~ a0} = {gg0|g~ a0 + ~ a}

multiplication unit element

{E|~ 0}{g|~ a} = {Eg|E~ a +~ 0} = {g|~ a}

inverse

{g|~ a}−1 = {g−1| − g−1~ a}

{g|~ a}−1{g|~ a} = {g−1| − g−1~ a}{g|~ a} = {g−1g|g−1~ a − g−1~ a} = {E|~ 0}

associative

space groups with screw axes and glide planes

non-symmorphic

230 space groups = 73 symmorphic + 157 non-symmorphic

symmorphic non-symmorphic

4