Q.10. Define crystal structure, crystal
lattice and Bravais lattice. (AKTU. 2015 - 16)
Ans. Crystal Structure: -
In crystallography, crystal structure is a description of the ordered
arrangement of atoms, ions or molecules in a crystalline material. Ordered
structures occur from the intrinsic nature of the constituent particles to form
symmetric patterns that repeat along the principal directions of
three-dimensional space in matter.
The smallest group of particles in the material that
constitutes the repeating pattern is the unit cell of the structure. The unit
cell completely defines the symmetry and structure of the entire crystal
lattice, which is built up by repetitive translation of the unit cell along its
principal axes. The repeating patterns are said to be located at the points of
the Bravais lattice.
The lengths of the principal axes, or edges, of the
unit cell and the angles between them are the lattice constants, also called
lattice parameters. The symmetry properties of the crystal are described by the
concept of space groups. All possible symmetric arrangements of particles in
three-dimensional space may be described by the 230 space groups.
The crystal structure and symmetry play a critical
role in determining many physical properties, such as cleavage, electronic band
structure, and optical transparency.
Crystal Lattice: -
Crystals
are a type of solid material composed of atoms or groups of atoms that are
arranged in a three-dimensional pattern that is very ordered. In a crystal, the
groups of atoms are repetitive at evenly spaced intervals, all maintaining
their orientation to one another. In other words, the geometric shape of a
crystal is highly symmetrical. When you see the word 'symmetrical,' think about
the perfect proportion and balance of these atoms in a crystal. Now that we
know what a crystal is, and that is can be found inside our table salt and a
sparkly diamond, let's look at crystal lattices.
A crystal lattice is the arrangement of these atoms,
or groups of atoms, in a crystal. These atoms or groups of atoms are commonly
referred to as points within a crystal lattice site. Thus, think of a crystal
lattice site as containing a series of points arranged in a specific pattern
with high symmetry. Note that these points don't tell you the position of an
atom in a crystal. They are simply points 'in space' oriented in such a way to
build a lattice structure.
Bravais Lattice: -
In geometry and crystallography, a
Bravais lattice, studied by Auguste Bravais (1850), is an infinite array of
discrete points in three dimensional space generated by a set of discrete
translation operations described by:
R = n1a1 + n2a2 + n3a3
where ni are any
integers and ai are known as the primitive vectors which lie
in different directions and span the lattice. This discrete set of vectors must
be closed under vector addition and subtraction. For any choice of position
vector R, the lattice looks exactly the same.
When the discrete points are atoms, ions, or polymer
strings of solid matter, the Bravais lattice concept is used to formally define
a crystalline arrangement and its (finite) frontiers. A crystal is made up of a
periodic arrangement of one or more atoms (the basis) repeated at each lattice
point. Consequently, the crystal looks the same when viewed from any equivalent
lattice point, namely those separated by the translation of one unit cell (the
motif).
Two Bravais lattices are often considered equivalent
if they have isomorphic symmetry groups. In this sense, there are 14 possible
Bravais lattices in three-dimensional space. The 14 possible symmetry groups of
Bravais lattices are 14 of the 230 space groups.
Q.11. Explain lattice planes in crystal. (AKTU. 2015 - 16)
Ans. Lattice Plane: -
In crystallography, a lattice plane
of a given Bravais lattice is a plane (or family of parallel planes) whose
intersections with the lattice (or any crystalline structure of that lattice)
are periodic (i.e. are described by 2d Bravais lattices) and intersect the
Bravais lattice; equivalently, a lattice plane is any plane containing at least
three noncollinear Bravais lattice points. All lattice planes can be described
by a set of integer Miller indices, and vice versa (all integer Miller indices
define lattice planes).
