Crystal Structure in Solid State Chemistry

Lecture on Crystal Structure Solid State Chemistry Dr Gunvant H. Sonawane M.Sc. Ph. D. Vice Principal Head, Department of Chemistry KVPS Kisan Arts Commerce and Science College, Parola Dist Jalgaon 1

UNIT-4. Crystal Structure (L-11, M-15) Forms of solids, Symmetry elements, Unit cells, Crystal systems, Bravais lattice types and Identification of lattice planes. Laws of Crystallography - Law of constancy of interfacial angles, Law of rational indices. Miller indices. X–Ray diffraction by crystals, Bragg’s law and Bragg’s method. Structures of NaCl, KCl and CsCl (qualitative treatment only). Defects, in crystals: Shottkey and Frenkel defects. Liquid Crystal, Types and Applications. Related numerical 2

Introduction,- States of Matter  Gases are compressible fluids. Their molecules are widely separated.  Liquids are relatively incompressible fluids. Their molecules are more tightly packed.  Solids are nearly incompressible and rigid. Their molecules or ions are in close contact and do not move. 3

Solids • Definite Shape, Size, Volume, Rigidity, Hardness, Non compressibility and Mechanical strength • In solids, atoms ions held together by strong chemical forces • They have fix position, they can vibrate at equbilibrium but does not move • Geometrical stability of solids is due to fix position of structural unit within crytal 4

Solids 1) Crystalline Solid: whose constituents are arranged in an orderly manner. 2) Amorphous Solid: whose constituents are not arranged in orderly manner. Property Crystalline Solid Amorphous Solid 1. Geometry Definite & Regular geometry strong intermolecular forces of attraction Dose not have regular pattern and geometry 2. Melting Point Sharp Melting point Dose not have sharp melting point 3. Physical properties Anisotropic Eg Diamond, Graphite, NaCl, KNO3, Isotropic Eg Rubber, Plastics, Glass, Organic polymers, Carbon Soot 5

Anisotropic and Isotropic Properties Anisotropy: Due to regular arrangement of constituent particles, the different particles are fall in different ways of a crystalline solid. The values of properties like electrical conductivity and thermal expansion not remains same in all the direction this is called anisotropy. Isotropy: In the amorphous solids there is no regular arrangement of particles thus the properties like electrical conductivity, thermal expansion are identical in all the direction. This property is called isotropy. 6

Crystalline and Amorphous Solid 9

Crystallography: Study of properties, structure, crystal growth and geometry of crystal • Crystal: A small portion of matter in solid state composed of small structural units called unit cells. • Crystal Lattice: A regular arrangement of points (representing atom, ion, molecule) in three dimension. 11

Lattice Points- The points that represents the position of constituent particles in crystal lattice called lattice points. Lattice points have identical environment. Position of lattice points are shown by Lattice vector Space Lattice- Array of points showing how constituents are arranged in three dimensional space. Each point in a space lattice is atom or molecule is Fig- Two dimensional Lattice 14

Space Lattice: An array of points showing how atoms, ions, molecules are arranged at different sites in a three dimensional space. Unit Cell: Smallest repeating unit in the space lattice which when repeated over and over again results in a crystal. 1) Simple or Primitive cube 2) Body Centred Cube 3) Face Centred Cube 4) End Centred Cube 16

Unit Cell • Unit Cell is the smallest, 3D,fundamental, repeating unit of a crystal structure representative of its: • atomic structure • chemical composition • crystal symmetry • It represents all the features of crystal • Unit Cell is a regularly ordered arrangement of atoms with a fixed geometry relative to one another • The atoms are arranged in a ‘box’ with parallel sides, the unit cell, which is repeated by simple translations to make up the crystal • It is macroscopic crystal • Unit cell dimensions measured in angstroms • 1A = 10-10m 17

TEM image of Cordierite (Mg2Al4Si5O18) showing ordered structure typical of crystalline structures Macrocrystals of Cordierite showing well developed flat crystal faces that characterise crystals in their macro form 20

Symmetry in Crystal  Symmetry Operation: is an operation performed around a line, plane, or point on a body so that it yields same or similar appearance of body.  Symmetry Elements: elements by which symmetry operation is performed. 1) Plane of Symmetry: an imaginary plane which divides crystal in two equal parts such that one is mirror image of other. 21

2) Axis of Symmetry: an imaginary line about which crystal is rotated such that it gives similar appearance more than once during complete rotation. 3- fold axis 2- fold axis 4- fold axis 3) Centre of Symmetry: it is a point that any line drawn through it intersects the surface of crystal at equal distance in both directions. 23

Bravais Lattices - lattices, 230 possible arrangements called space groups in three dimensions 7 Systems, 14 Bravais 26

Seven Basic Crystal system Crystal System Intercepts Crystal Angles ===90° 1. Cubic a=b=c ==90° 2. Rhombohedral a=b=c a=bc ===90° 3. Tetragonal a=bc ==90°, =120° 4. Hexagonal abc ===90° 5. Orthorhombic abc ==90°,   90° 6. Monoclinic abc     90° 7. Triclinic 28

Seven Basic Crystal system 29

Unit cell dimensions of the seven crystal systems • CUBIC a = = b = = c; α = = β = = γ = 90 TETRAGONAL a = = b   c; α = = β = = γ = 90 ORTHORHOMBIC a   b   c; α = = β = = γ = 90 MONOCLINIC a   b   c; α = = γ = 90 TRICLINIC a   b   c; α   β   γ   90 HEXAGONAL a = = b   c; α = = β = 90; TRIGONAL – Hexagonal a = = b   c; α = = β = 90; = 90; γ =120 TRIGONAL – Rhombohedral a = = b = = c; α = = β = = γ   90 < 120 90 < 120 = 90 • = 90 • = 90 • = 90 β > 90 > 90 • 90 • = 90; γ =120 =120 • =120 • Where a, b, and c are the unit cell axes dimensions and α, β, and γ are the inclination angles of the axes in the unit cell. 30

1. Miller indices are used to specify direction and planes. 2. These directions and planes could be in a lattices or in crystal. 3. The number of indices will match with the dimension of the lattice or the crystal. Eg in 1 D there will be 1 index and 2D there will be 2 indices etc 4. (hkl) represents a plane 31

Indexing: Method of naming the planes Weiss Indices: An integer to indicate the plane by considering the intercept made by the plane on the axis Or An integer designate the plane in terms of cuts made by the plane on axes in terms of unit intercept. 33

• Miller Indices: Miller indices is defined as the reciprocals of the intercepts made by the plane on the three axes. 35

Eg: Miller indices of plane ABC Plane ABC has intercepts of 2 units along X-axis, 3 units along Y-axis and 2 units along Z-axis. 36

DETERMINATION OF ‘MILLER INDICES’ Step 1:The intercepts are 2,3 and 2 on the three axes. Step 2:The reciprocals are 1/2, 1/3 and 1/2. Step 3:The least common denominator is ‘6’. Multiplying each reciprocal by lcd, we get, 3,2 and 3. Step 4:Hence Miller indices for the plane ABC is (3 2 3) 37

IMPORTANT FEATURES OF MILLER INDICES For the cubic crystal: especially, the important features of Miller indices are, A plane which is parallel to any one of the co-ordinate axes has an intercept of infinity (). Therefore the Miller index for that axis is zero; i.e. for an intercept at infinity, the corresponding index is zero. Plane parallel to Y and Z axes ( 1 0 0 ) plane 38

In the above plane, the intercept along X axis is 1 unit. The plane is parallel to Y and Z axes. So, the intercepts along Y and Z axes are ‘’. Now the intercepts are 1,  and . The reciprocals of the intercepts are = 1/1, 1/ and 1/. Therefore the Miller indices for the above plane is (1 0 0). 39

Miller indices for planes : Procedure- 1. Identify the plane, intercepts on X, Y and Z axis. 2. Specify intercepts in fractional coordinates. 3. Take the reciprocals of the fractional intercepts. 42

Crystal Structure in Solid State Chemistry