Crystal Geometry, Structure and its defects

Principal forms of Solids 1. Crystalline 2. Amorphous

Properties of Crystalline structures

Crystal ( Single Crystal & Polycrystalline)

Lattice and lattice Point and Space lattice

Basis

Unit Cell

Objective 18-02-14

Introduction

Solids are materials whose atoms are bonded strongly enough to form

a rigid structure;

others may have a very regular

structure.

Some have a random atomic arrangement with no

particular pattern

A crystal structure is a solid with a unique arrangement of

atoms that results in a pattern.

Which differ significantly in their properties.

Most crystalline solids are made up of millions of tiny single crystals called grains. These grains are oriented randomly with respect to each other. Any single crystal, however, no matter how large, is a single grain.

Crystalline Non-crystalline (amorphous

Solids exist in nature in two principal forms:

The patterns form a lattice, which is an array of points repeating periodically in three dimensions.

In other words, the atoms form points in space that can be connected with geometrical lines to form repeating shapes.

The patterns are recognized and separated as unit cells, which are just boxes surrounding a special arrangement of atoms in order to segment a pattern into its most basic form.

The symmetries within these materials because of the repeating patterns allow us to easily identify some of the properties of special solids.

Properties of Crystalline structures

Amorphous substances have no crystalline structure. Ordinary glass, sulphur, selenium, glycerine and most of the high polymers can exist in the amorphous state.

Amorphous solids have no long-range order. The atoms or molecules in these solids are not periodically located over large distances

• Crystal *Lattice * Basis * Unit Cell• Type of Crystals

Basic Background

What is Crystal ? Crystal

unique arrangement of atoms/molecules/ions in a material

The word crystal is derived from the ancient Greek word krustallos.

CrystalA crystal or crystalline solid is a solid material whose atoms, ions or molecules are arranged in an orderly repeating pattern extending in all three spatial dimensions.

Ionic crystalline solid

"amorphous solid" is a solid in which there is no long-range order of the positions of the atoms.

Amorphous solid

Noncrystalline solid

Single Crystal

Quartz Crystal

A single crystal or monocrystalline solid is a material in which the crystal lattice of the entire sample is continuous.

The periodicity of the pattern exist throughout the solid.

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Most of the materials exist in polycrystalline form, but there are some

materials, which exist in the form of single crystals, e.g. sugar, sodium

chloride (common salt), diamond, etc.

Single crystals represent a material in its ideal condition and are

produced artificially from their vapour or liquid state.

These crystals help us in studying

behavior and defects of the material in

ideal conditions.

Polycrystalline •Large number of small crystals (called grains) with different shape/size are packed with one another along interfaces (grain boundaries).Polycrystalline materials are solids that are composed of many crystallites of varying size and orientation. The variation in direction can be random (called random texture) or directed, possibly due to growth and processing conditions.

Almost all common metals, and many ceramics are polycrystalline.

The atomic arrangement in crystal is called the crystal structure.

In perfect crystal, there is a regular arrangement of atoms.

In a model of a crystal, ions, atoms or molecules can be imagined to be spheres which touch one another and are arranged regularly in different directions.

In a simple model of crystal structure, spheres are replaced by points representing the centres of ions, atoms or molecules.

It is very convenient to imagine points in space about which these atoms, ions or molecules are located. Such points in space are called lattice points. The totality of lattice points forms a crystal lattice or space lattice.

Lattice Points and Space Lattice

Latticelattice is an array of points repeating periodically.

One dimensional lattices: Chains

An infinite array of points in space, in which each point has identical surroundings to all others

Basis

The space lattice---An array of imaginary points which are so arranged in space that each point has identical surroundings.

Crystal structure is always described in terms of atoms rather than points.

We must note

An atom or a group of atoms must be placed on each lattice point in a regular fashion.

Thus in order to obtain a crystal structure

Such an atom or a group of atoms is called the basis and this acts as a building unit or a structural unit for the complete crystal structure.

Obviously, a lattice combined with a basis generates the crystal structure.

Mathematically, one can express it as

Space lattice + Basis------ Crystal Structure

Unit Cell

The atomic order in crystalline solids indicates that the smallest groups of atoms form a repetitive pattern.

In every crystal some fundamental grouping of particles is repeated thus in describing crystal structures, it is often convenient to subdivide the structure into repetitive small repeat units called unit cells.

The unit cell is the basic structural unit or building block of the crystal structure.

The smallest component of the space lattice

Bravais Lattice

7 Crystal Classes with 4 possible unit cell types Symmetry indicates that only 14 3-D lattice types occur

Crystal Structure* A lattice is a regular periodic arrangement of point in space.* When a basis of atoms is attached identically to each lattice point the crystal structure is formed

lattice + basis = crystal

Crystal: Space Lattice & Unit cell

Fig. The constituent particles of a crystalline solid are arranged in a definite fashion in the three dimensional space.

* A regular arrangement of the constituent particles of a crystal in a three dimensional space is called crystal lattice or space lattice.

Crystal: Unit cell

The smallest component of the crystal, which when stacked together with pure translational repetition reproduces the whole crystal

Crystal: Primitive/non primitiveThe smallest three-dimensional portion of a complete space lattice, which when repeated over and again in different directions produces the complete space lattice.

The size and shape of a unit cell is determined by the lengths of the edges of the unit cell (a, b and c) and by the angles.