Crystal Systems

Crystal types and details about crystal system

1. CRYSTAL SYSTEM 1 CRYSTAL SYSTEM 1 Welcome To MY Presentation On CRYSTAL SYSTEMS Representator: MD. MOHYMENUL ISLAM ID: PH 12004 3 rd YEAR 1 st SEMESTER DEPT. OF PHYSICS MBSTU

2. Cry s tal Translational Vector Crystal Structure Crystal Lattice Unit cell Lattice Constant Symmetry Operation Packing Factor Miller Indices Inter-planar Spacing LEARNING OBJECTS CRYSTAL SYSTEM 2

3. CRYSTAL SYSTEM 3 A crystal is a solid in which atoms are arranged in some regular repetition pattern in all directions. Cry s tal Crystals (at a given temperature, pressure, and volume) have stronger bonds between molecules and atoms than liquids . It’s require more energy to break the bonds.

4. Crystalline material is a material comprised of one or many crystals. Ex:Diamond,quartz,mica etc. Amorphous have order only within a few atomic or molecular dimensions. Ex: Glass,plastics,rubbers . Polycrystallne is a material made up of an aggregate of many small single crystals (also called crystallites or grains). Ex:Metals and ceramics. CRYSTAL SYSTEM 4 Crystal Types Single Pyrite Crystal Amorphous Solid Polycrystalline Pyrite form (Grain)

5. CRYSTAL SYSTEM 5 Difference between crystalline & non-crystalline 1 .Long range order. 2.Fixed melting point. 3.Atoms or molecules are periodically arranged. 1.Short range order. 2.No fixed melting point. 3.Atoms or molecules are randomly arranged. Crystalline Non-crystalline CRYSTAL SYSTEM 5

6. CRYSTAL SYSTEM 6 Translational Lattice Vectors A lattice translation operation is defined by the displacement of a crystal by a crystal translation vector. R n = n 1 a + n 2 b This is translational symmetry . The vectors a , b are known as lattice vectors and (n 1 , n 2 ) is a pair of integers whose values depend on the lattice point. P Point D(n1, n2) = ( ,2)

7. CRYSTAL SYSTEM 7 Crystal Structure A CRYSTAL STRUCTURE is a periodic arrangement of atoms in the crystal that can be described by a LATTICE Lattice: A 3D translationally periodic arrangement of points in space. Basis: A group of atoms associated with each lattice point to represent crystal structure.

8. CRYSTAL SYSTEM 8 Bravais Lattice Non-Bravais Lattice

9. Unit Cell The smallest component of the crystal which when stacked together with pure translational repetition reproduces the whole crystal. CRYSTAL SYSTEM 9 Unit Cell S a b 2D-Crystal S S S S S S S S S S S S S S 3D-Crystal

10. Three common Unit Cell in 3D CRYSTAL SYSTEM 10 Primitive (P) unit cells contain only a single lattice point . Internal (I) unit cell contains an atom in the body center . Face (F) unit cell contains atoms in the all faces of the planes composing the cell .

11. CRYSTAL SYSTEM 11 CRYSTAL SYSTEM 11 Crystal Structure 11 Unit cell exist in only seven shapes

12. T he numbers a,b,c specifying the size of a unit cell (in fact, conventional unit cell) are called its lattice constant For cubic lattice, the lattice constant, 12 LATTICE CONSTANT Where, ρ =density of the lattice n= number of particles M= molecular weight of the crystal N A = Avogadro number a=( nM / N A ρ ) 1/3

13. CRYSTAL SYSTEM 13 Symmetry Operation: A symmetry operations is one which leaves the crystal unchanged such as translation, rotation, reflection or inversion. 5-fold symmetry: Symmetry Operations N-fold axes with n=5 or n>6 does not occur in crystals Adjacent spaces must be completely filled (no gaps, no overlaps).

14. CRYSTAL SYSTEM 14 Atomic Packing Factor Atomic Packing Factor (APF) is defined as the volume of atoms in the unit cell divided by the volume of the unit cell.

15. Simple Cubic Structure (SC) Close-packed directions are cube edges. • Coordination = 6 (nearest neighbors) a = 2r, r = a/2 Atomic Radius, r= 0.5a a

16. Atomic Packing Factor (APF):SC • APF = 0.52 , That means the percentage of packing is 52% APF = a 3 4 3 p (0.5 a ) 3 1 atoms unit cell atom volume unit cell volume APF = Volume of atoms in unit cell* Volume of unit cell *assume hard spheres close-packed directions a R =0.5 a Number of lattice point 8 x 1/8 = 1 atom/unit cell

17. Body Centered Cubic Structure (BCC) • Coordination # = 8 • Atoms touch each other along cube diagonals. Ex : Cr, Fe , Molybdenum 2 atoms/unit cell: 1 center + 8 corners x 1/8 Atomic Radius ,r = a x (3) 1/2 /4

18. Atomic Packing Factor: BCC a APF = 4 3 p ( 3 a /4 ) 3 2 atoms unit cell atom volume a 3 unit cell volume length = 4 R = Close-packed directions : 3 a a R a 2 a 3 • APF for a body-centered cubic structure = 0.68

19. Face Centered Cubic Structure (FCC) • Coordination = 12 • Atoms touch each other along face diagonals. Ex : Al, Cu, Ni,Ag 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8 Atomic Radius ,r = a x (2) 1/2 /4

20. Atomic Packing Factor: FCC APF = 4 3 p ( 2 a /4 ) 3 4 atoms unit cell atom volume a 3 unit cell volume Close-packed directions: length = 4 R = 2 a Number of lattice point : 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell a 2 a • APF for a face-centered cubic structure = 0.74

21. Miller Indices • Miller Indices is a group of smallest integers which represent a direction or a plane. To determine Miller indices of a plane, take the following steps : 1) Determine the intercepts of the plane along each of the three crystallographic directions 2) Take the reciprocals of the intercepts 3) If fractions result, multiply each by the denominator of the smallest fraction.

22. CRYSTAL SYSTEM 22 (233)

23. CRYSTAL SYSTEM 23 Inter-planar Spacing For orthorhombic, tetragonal and cubic unit cells (the axes are all mutually perpendicular), the inter-planar spacing is given by: h, k, l = Miller indices a, b, c = unit cell dimensions For cube a = b = c than

24. REFERENCES Source www.Google.com http://en.wikipedia.org Solid State Physics & Electronics By R.K. PURI ” Solid State Physics ” By R.L . SINGHAL Seventh Revised & Enlarged Edition-2003 CRYSTAL SYSTEM 24

25. CRYSTAL SYSTEM 25