Crystal Geometry, Structure and its defects

1. Crystal Geometry, Structure and its defects

2. Objective 18-02-14 • 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

3. Introduction Solids are materials whose atoms are bonded strongly enough to form a rigid structure; Some have a random atomic arrangement with no particular pattern others may have a very regular structure. A crystal structure is a solid with a unique arrangement of atoms that results in a pattern.

4. Solids exist in nature in two principal forms: Crystalline Non-crystalline (amorphous 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.

6. Properties of Crystalline structures 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.

7. 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

8. Basic Background • Crystal *Lattice * Basis * Unit Cell • Type of Crystals

9. What is Crystal ? Crystal unique arrangement of atoms/molecules/ions in a material The word crystal is derived from the ancient Greek word krustallos.

10. Crystal A crystal or crystalline solidis a solid material whose atoms, ions or molecules are arranged in an orderly repeating pattern extending in all three spatial dimensions. Ionic crystalline solid Noncrystalline solid "amorphous solid" is a solid in which there is no long-range order of the positions of the atoms. Amorphous solid

11. Single Crystal A single crystal or monocrystalline solid is a material in which the crystal lattice of the entire sample is continuous. ????????? Quartz Crystal The periodicity of the pattern exist throughout the solid.

12. 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.

13. 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.

14. Lattice Points and Space Lattice 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.

15. Lattice lattice is an array of points repeating periodically. An infinite array of points in space, in which each point has identical surroundings to all others One dimensional lattices: Chains

16. Basis The space lattice---An array of imaginary points which are so arranged in space that each point has identical surroundings. We must note Crystal structure is always described in terms of atoms rather than points. Thus in order to obtain a crystal structure An atom or a group of atoms must be placed on each lattice point in a regular fashion. 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.

17. Obviously, a lattice combined with a basis generates the crystal structure. Mathematically, one can express it as Space lattice + Basis------ Crystal Structure

18. Unit Cell The smallest component of the space lattice 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.

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

21. 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

22. Crystal: Space Lattice & Unit cell * A regular arrangement of the constituent particles of a crystal in a three dimensional space is called crystal lattice or space lattice. Fig. The constituent particles of a crystalline solid are arranged in a definite fashion in the three dimensional space.

23. Crystal: Unit cell The smallest component of the crystal, which when stacked together with pure translational repetition reproduces the whole crystal

24. Crystal: Primitive/non primitive The 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.

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