The Fascination of Crystals and Symmetry · combination of a hexahedron (cube) and a rhombic...
Transcript of The Fascination of Crystals and Symmetry · combination of a hexahedron (cube) and a rhombic...
The Fascination of Crystals and Symmetry
Unit 2.3
by Frank Hoffmann & Michael Sartor
Miller Indices
(100)
(110)
combination of a hexahedron (cube) and a rhombic dodecahedron
Miller indices are used to name the crystal
faces in a systematic manner, and are also
used to denominate lattice planes.
Miller Indices
William Hallowes Miller
(1801 – 1880)
René Just Haüy
(1743 – 1822)
Hauynite
hauyne / hauynite
Na3Ca(Si3Al3)O12(SO4)
tecto(alumo)silicate
René Just Haüy
(1743 – 1822)
Lattice Planes
lattice planes are a family of parallel planes
which intersects the Bravais lattice and are
periodic
these crystallographic planes are
fictitious planes linking nodes, i.e. lattice points
b
a
unit cell
Lattice Planes
lattice planes are a family of parallel planes
which intersects the Bravais lattice and are
periodic
these crystallographic planes are
fictitious planes linking nodes, i.e. lattice points
b
a
in principle there is an infinite number of
plane families (all parallel planes of a
particular type)
Miller indices form a notation system for
such planes and are expressed by three
integers: (h k l)
Determining Miller Indices
In how many fractions do the planes
intersect the respective lattice constants
a, b, (and c)?
If one of the indices is zero, it
means that the planes do not
intersect that axis (the intercept is
"at infinity")
b
a
(010)
(120)
d spacings
(120)
(010)d010
d120
the lower the indices the higher
the density of lattice points onto
this plane
the lower the indices the larger
the distance d between two
adjacent planes of a plane family
Negative Miller Indices
(120)
if the intercepts are on the negative side
of the coordinate system the indices get
a bar above the number (= minus)
(120)
b
a
Excercise – Determining Miller Indices
A: ?
B: ?
C: ?
D: ?
E: ?
b
a
Miller Indices in 3D
d
(1 0 0)
a
b
c
Miller Indices in 3D
a
b
c
d
(0 1 0)
Miller Indices in 3D
a
b
c
(1 1 1)
Miller Indices of Faces
(100)
(110)
combination of a hexahedron (cube) anda rhombic dodecahedron
the outermost planes of a crystal
build the faces!
Miller Indices of Faces
(100)
(110)
combination of a hexahedron (cube) anda rhombic dodecahedron
the outermost planes of a crystal
build the faces!
110
-110-1-10
1-10
+a
+b
100
-100
0-10 010
-a
-b
Miller Indices of Faces
(100)
(110)
combination of a hexahedron (cube) anda rhombic dodecahedron
the outermost planes of a crystal
build the faces!
Crystal Shapes with VESTA
Picture Credits
If not otherwise stated pictures, images, sketches, clip arts are
• self-taken/self-drawn or
• public domain
This work has been released into the public domain by its author, Lucien Cluzaud.
http://www.mindat.org/photo-151799.html