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Bas Nijholt
lectures
Commits
a7a138d7
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a7a138d7
authored
Mar 31, 2018
by
Anton Akhmerov
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more list formatting fixes
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docs/lecture_5.md
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a7a138d7
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@@ 14,36 +14,36 @@ In this lecture we will:

**_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

freedom of translation

multiple lattices with different point densities possible
+
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
+
freedom of translation
+
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
+
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
+
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 $
\r
ightarrow$ no identical points skipped

not always most practical choice
+
smallest possible $
\r
ightarrow$ 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 $
\r
ightarrow$ choose which belongs to unit cell

positions in terms of lattice vectors,
*not*
Cartesian coordinates!
+
only now we care about the contents (i.e. atoms)
+
gives element and position of atoms
+
properly count partial atoms $
\r
ightarrow$ choose which belongs to unit cell
+
positions in terms of lattice vectors,
*not*
Cartesian coordinates!
### Example: graphite
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