7 Crystal Structure

1. Roll No 04
BS (Hons.) Chemistry
2016

2. Triclinic crystal system
An example of the triclinic crystals, microcline
Triclinic (a ≠ b ≠
c and α ≠ β ≠ γ )
In crystallography, the triclinic crystal system is one of
the 7 crystal systems. A crystal system is described by three basis vectors. In the triclinic
system, the crystal is described by vectors of unequal length, as in the orthorhombic system.
In addition, no vector is at right angles (90°) orthogonal to another.
The triclinic lattice is the least symmetric of the 14 three-dimensional Bravais lattices. It has
(itself) the minimum symmetry all lattices have: points of inversion at each lattice point and
at 7 more points for each lattice point: at the midpoints of the edges and the faces, and at the
center points. It is the only lattice type that itself has no mirror planes.
Crystal classes
The triclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin
notation, point groups, International Tables for Crystallography space group number,[1]
orbifold, type, and space groups are listed in the table below. There are a total 2 space groups.
#
Point group
Example Type
Space
group
Class Schönflies Intl orbifold Coxeter
1 Pedial C1 1 11 [ ]+
Tantite
enantiomorphic
polar
P1
2 Pinacoidal Ci (= S2) 1 1× [2+
,2+
] Wollastonite centrosymmetric P1
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3. Monoclinic crystal system
An example of the monoclinic crystal An example Caffeine crystals in monoclinic
In crystallography, the monoclinic crystal system is one of the seven lattice
point groups. A crystal system is described by three vectors. In the monoclinic
system, the crystal is described by vectors of unequal lengths, as in the
orthorhombic system. They form a rectangular prism with a parallelogram as
its base. Hence two vectors are perpendicular (meet at right angles), while
the third vector meets the other two at an angle other than 900.
Bravais lattices and point / space groups
Two monoclinic ravais lattices exist : the primitive monoclinic and the centered
monoclinic lattices, with layers with a rectangular and rhombic lattice, respectively.
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4. Primitiv
Monoclinic Bravais lattice
Pearson s
ymbol mP
Base -centered
mC
Unit cell
3
Name

5. Orthorhombic crystal system
In crystallography, the orthorhombic crystal system is one of the seven lattice point groups.
Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs
by two different factors, resulting in a rectangular prism with a rectangular base (a by b) and
height (c), such that a, b, and c are distinct. All three bases intersect at 90° angles, so the three
lattice vectors remain mutually orthogonal.
Bravais lattices
There are four orthorhombic Bravais lattices: simple orthorhombic, body-centered
orthorhombic, base-centered orthorhombic, and face-centered orthorhombic.
Orthorhombic Bravais lattices
Name
Primitive
(P)
Body-centered
(I)
Base-centered
(A, B or C)
Face-centered
(F)
Pearson
symbol
oP oI oS oF
Unit cell
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6. Tetragonal crystal system
An example of the tetragonal crystals,
wulfenite
In crystallography, the tetragonal
crystal system is one of the 7 lattice
point groups. Tetragonal crystal lattices
result from stretching a cubic lattice
along one of its lattice vectors, so that
the cube becomes a rectangular prism
with a square base (a by a) and height (c, which is different from a).
There are two tetragonal crystal structure types. Bravais lattices: the simple tetragonal (from
stretching the simple-cubic lattice) and the centered tetragonal (from stretching either the
face-centered or the body-centered cubic lattice). One might suppose stretching face-centered
cubic would result in face-centered tetragonal, but face-centered tetragonal is equivalent to
body-centered tetragonal, BCT (with a smaller lattice spacing). BCT is considered more
fundamental, so that is the standard terminology.[1]
Tetragonal Bravais lattices
Name Primitive Body-centered
Pearson symbol tP tI
Unit cell
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7. Trigonal crystal system
In crystallography, the trigonal crystal system is one of the seven crystal systems. A crystal
system is a set of point groups in which the point groups themselves and their corresponding
space groups are associated with a lattice system. The trigonal crystal system consists of
those five point groups that have a single
three-fold rotation axis (see table in
Crystal_system#Crystal_classes).
Sometimes the term rhombohedral
lattice system is used as an exact
synonym, whereas it is more akin to a
subset. Crystals in the rhombohedral
lattice system are always in the trigonal
crystal system, but some crystals such as
alpha-quartz are in the trigonal crystal
system but not in the rhombohedral lattice
system (alpha-quartz is in the hexagonal
lattice system). There are 25 space groups
(143-167) whose corresponding point
groups are one of the five in the trigonal
crystal system, consisting of the seven
space groups associated with the rhombohedral lattice system together with 18 associated
with the hexagonal lattice system. The crystal structures of alpha-quartz in the previous
example are described by two of those 18 space groups (152 and 154) associated with the
hexagonal lattice system.[1]
To distinguish: The rhombohedral lattice system consists of the
rhombohedral lattice, while the trigonal crystal system consists of the five point groups that
have seven corresponding space groups associated with the rhombohedral lattice system (and
18 corresponding space groups associated with the hexagonal lattice system). An additional
source of confusion is that all members of the trigonal crystal system with assigned
rhombohedral lattice system (space groups 146, 148, 155, 160, 161, 166, and 167), can be
represented with an equivalent hexagonal lattice with so called R-centering (rhombohedral-
centering); there is a choice of using a R-centered hexagonal or a primitive rhombohedral
setting for the lattice.[2][3]
Example trigonal
crystals (quartz)
Example trigonal
rhombohedral crystals
(dolomite)
Hexagonal lattice cell
Hexagonal (R-centered)
unit cell
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8. Hexagonal crystal system
In crystallography, the hexagonal
crystal system is one of the 7
crystal systems, the hexagonal
lattice system is one of the 7
lattice systems, and the
hexagonal crystal family is one
of the 6 crystal families. They are
closely related and often
confused with each other, but
they are not the same. The
hexagonal lattice system consists
of just one Bravais lattice type:
the hexagonal one. The
hexagonal crystal system consists
of the 7 point groups such that all
their space groups have the hexagonal lattice as underlying lattice. The hexagonal crystal
family consists of the 12 point groups such that at least one of their space groups has the
hexagonal lattice as underlying lattice, and is the union of the hexagonal crystal system and
the trigonal crystal system. In some cases, it is useful or instructive to redraw a hexagonal
structure with orthohexagonal axes, wherein the b axis is redrawn at 90° to the a and c axes.
Graphite is an example of a crystal that crystallizes in the hexagonal crystal system.
Hexagonal lattice system
The hexagonal lattice system is one of the seven lattice systems, consisting of the hexagonal
Bravais lattice. It is associated with 45 space groups whose underlying lattice has point group
of order 24. It is often confused with the smaller hexagonal crystal system, which consists of
the 27 space groups such that all space groups with the same point group are in the hexagonal
lattice system, or with the larger hexagonal crystal family, consisting of the 52 space groups
in either the hexagonal or rhombohedral lattice systems.
Cubic crystal system
An example of the hexagonal crystals, beryl
Hexagonal Hanksite crystal
Hexagonal lattice cell
(P)
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9. A rock containing three crystals of pyrite
(FeS2). The crystal structure of pyrite is
primitive cubic, and this is reflected in
the cubic symmetry of its natural crystal
facets.
A network model of a primitive cubic system.
In crystallography, the cubic (or isometric)
crystal system is a crystal system where the unit
cell is in the shape of a cube. This is one of the
most common and simplest shapes found in
crystals and minerals.
There are three main varieties of these crystals:
 Primitive cubic (abbreviated cP[1]
and alternatively called simple cubic)
 Body-centered cubic (abbreviated cI[1]
or bcc),
 Face-centered cubic (abbreviated cF[1]
or fcc, and alternatively called cubic close-
packed or ccp)
Each is subdivided into other variants listed below. Note that although the unit cell in these
crystals is conventionally taken to be a cube, the primitive unit cell often is not. This is related
to the fact that in most cubic crystal systems, there is more than one atom per cubic unit cell.
A classic isometric crystal has square or pentagonal faces.
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