 ### hmm...

parent a7a138d7
 ... ... @@ -13,7 +13,6 @@ In this lecture we will: ### Crystal classification - **_Lattice_** + periodic pattern of *lattice points*, which all have an identical view + lattice points are not necessarily the same as atom positions + there can be multiple atoms per lattice point ... ... @@ -21,25 +20,21 @@ In this lecture we will: + multiple lattices with different point densities possible - **_Lattice vectors_** + from lattice point to lattice point + \$N\$ vectors for \$N\$ dimensions + multiple combinations possible + not all combinations provide full coverage - **_Unit cell_** + spanned by lattice vectors + has 4 corners in 2D, 8 corners in 3D + check if copying unit cell along lattice vectors gives full lattice - **_Primitive unit cell_** + smallest possible \$\rightarrow\$ no identical points skipped + not always most practical choice - **_Basis_** + only now we care about the contents (i.e. atoms) + gives element and position of atoms + properly count partial atoms \$\rightarrow\$ choose which belongs to unit cell ... ... @@ -52,12 +47,10 @@ In this lecture we will: 1. Choose origin (can be atom, not necessary) 2. Find other lattice points that are identical 3. Choose lattice vectors, either primitive (red) or not primitive (blue) - lengths of lattice vectors and angle(s) between them fully define the crystal lattice - for graphite: \$|{\bf a}_1|=|{\bf a}_2|\$ = 0.246 nm = 2.46 Å, \$\gamma\$ = 60\$^{\circ}\$ 4. Specify basis - using \${\bf a}_1\$ and \${\bf a}_2\$: C\$(0,0)\$, C\$\left(\frac{2}{3},\frac{2}{3}\right)\$ - using \${\bf a}_1\$ and \${\bf a}_{2}'\$: C\$(0,0)\$, C\$\left(0,\frac{1}{3}\right)\$, C\$\left(\frac{1}{2},\frac{1}{2}\right)\$, C\$\left(\frac{1}{2},\frac{5}{6}\right)\$ ... ...
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