Solid state (2)

1,549 views
1,269 views

Published on

Published in: Education
0 Comments
5 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
1,549
On SlideShare
0
From Embeds
0
Number of Embeds
25
Actions
Shares
0
Downloads
0
Comments
0
Likes
5
Embeds 0
No embeds

No notes for slide

Solid state (2)

  1. 1. States Of Matter <ul><li>Gaseous State </li></ul><ul><li>Liquid State </li></ul><ul><li>Solid State </li></ul>
  2. 2. Solid State <ul><li>Form of matter that has a definite shape and volume and is rigid. </li></ul><ul><li>Low compressibility </li></ul><ul><li>High density </li></ul><ul><li>Very slow diffusion </li></ul><ul><li>Low vapour pressure </li></ul>
  3. 3. Classification of Solids <ul><li>Crystalline Solids </li></ul><ul><li>Building entities are arranged in regular geometric pattern </li></ul><ul><li>Sharp melting point </li></ul><ul><li>Definite geometrical shape </li></ul><ul><li>Possess cleavage planes </li></ul><ul><li>Exhibit anisotropy </li></ul><ul><li>Possess crystal symmetry </li></ul>
  4. 4. Classification of Solids <ul><li>Amorphous Solids </li></ul><ul><li>Shapeless </li></ul><ul><li>Building entities are randomly present </li></ul><ul><li>No definite MP </li></ul><ul><li>No cleavage planes </li></ul><ul><li>Exhibit isotropy </li></ul><ul><li>No symmetry </li></ul>
  5. 5. Crystal Lattice/ Space Lattice <ul><li>The regular repeating arrangement of points representing the constituent particles in three dimensional space </li></ul><ul><li>Each point in a lattice represents a constituent particle-atom/ion/molecule </li></ul><ul><li>Such point is called lattice point/lattice site </li></ul>
  6. 6. <ul><li>Three dimensional crystal lattice </li></ul>
  7. 7. UNIT CELL unit cell Lattice
  8. 8. Unit Cell <ul><li>Fundamental building block of space lattice </li></ul><ul><li>Smallest 3-d portion of a complete space lattice which when repeated in different directions produces the whole space lattice </li></ul>
  9. 9. Parameters of unit cell <ul><li>Edge </li></ul><ul><li>angle </li></ul>
  10. 10. Types of unit cells <ul><li>1.Primitive Unit Cells/ simple unit cells </li></ul><ul><li>- Particles are present only at the corners </li></ul><ul><li>2. Non primitive/ Centred unit cells </li></ul><ul><li>- Particles are present at corners as well as at other positions within the unit cell </li></ul>
  11. 11. Primitive Unit Cell <ul><li>Simple cubic crystal </li></ul>
  12. 12. Types of non primitive unit cells <ul><li>Body Centred unit cells (BCC) </li></ul>
  13. 13. Types of non primitive unit cells <ul><li>Face Centred Unit Cell (FCC) </li></ul>
  14. 14. <ul><li>Atom shared between two unit cells in FCC </li></ul><ul><li>Atom shared between 8 unit cells in SCC </li></ul>
  15. 15. Calculation of contribution of particles per unit cell <ul><li>An atom at a corner is shared by eight unit cells. </li></ul><ul><li>Contribution of an atom per unit cell </li></ul><ul><li>= 1/8 </li></ul><ul><li>An atom at a face is shared by two unit cells. </li></ul><ul><li>Contribution of an atom per unit cell </li></ul><ul><li>= ½ </li></ul><ul><li>An atom at the centre of body of unit cell is not shared by any other atom </li></ul><ul><li>Contribution of an atom per unit cell </li></ul><ul><li>= 1 </li></ul>
  16. 16. Calculation of number of atoms per unit cell <ul><li>Primitive unit cell </li></ul><ul><li>- 8 corners </li></ul><ul><li>- 1 atom at each corner </li></ul><ul><li>- total 8 atoms on 8 corners </li></ul><ul><li>- contribution of each atom=1/8 </li></ul><ul><li>- no of atoms per unit cell= 1/8 X 8=1 </li></ul>
  17. 17. Calculation of number of atoms per unit cell <ul><li>BCC </li></ul><ul><li>Contribution by each atom on corner=1/8 </li></ul><ul><li>Contribution by 8 atoms = 1/8 X 8= 1 </li></ul><ul><li>Contribution by atom within the body = 1 </li></ul><ul><li>No of atoms in a unit cell </li></ul><ul><li>= 1+1=2 </li></ul>
  18. 18. Calculation of number of atoms per unit cell <ul><li>FCC </li></ul><ul><li>Contribution by each atom </li></ul><ul><li>on corner =1/8 </li></ul><ul><li>Contribution by 8 atoms 1/8 X 8= 1 </li></ul><ul><li>Contribution by atoms </li></ul><ul><li>on the faces 1/2X6= 3 </li></ul><ul><li>No of atoms in a unit cell 1+3=4 </li></ul>
  19. 19. Packing Fraction/Efficiency <ul><li>Fraction of total volume of the unit cell occupied by the atoms present in it-Pck Fraction </li></ul><ul><li>Percentage of total space filled by particles- Pck Efficiency </li></ul>
  20. 20. Packing efficiency in simple cubic cell r r a
  21. 21. Packing efficiency in simple cubic cell <ul><li>No of particles per unit cell = 1 </li></ul><ul><li>Vol of particle =4/3 π r 3 </li></ul><ul><li>Vol of cube =a 3 </li></ul><ul><li>=(2r) 3 </li></ul><ul><li>=8r 3 </li></ul><ul><li>Packing fraction = 4/3 π r 3 ÷8r 3 = π /6 </li></ul><ul><li>=0.524 </li></ul><ul><li>Packing efficiency =52.4% </li></ul>
  22. 22. Nearest Neighbour Distance (d) <ul><li>d=a=edge length </li></ul>a
  23. 23. Packing efficiency in FCC B A C r r 2r
  24. 24. Packing efficiency in FCC <ul><li>AC=4r </li></ul><ul><li>AC= √AB 2 + BC 2 </li></ul><ul><li>AC=√a 2 + a 2 </li></ul><ul><li>AC=a√2 </li></ul><ul><li>a√2=4r </li></ul><ul><li>a=4r/√2 </li></ul>B A C r r 2r
  25. 25. Packing efficiency in FCC <ul><li>Vol of unit cell = a 3 = 3 </li></ul><ul><li>4r/√2 </li></ul><ul><li>= 32r 3 /√2 </li></ul>
  26. 26. <ul><li>No of spheres in the unit cell =4 </li></ul><ul><li>Vol of 4 spheres =4X4/3 π r 3 </li></ul><ul><li>=16/3 π r 3 </li></ul><ul><li>Packing fraction </li></ul><ul><li>=16/3 π r 3 ÷32r 3 /√2 </li></ul><ul><li>= π √2/6 </li></ul><ul><li>=0.74 </li></ul><ul><li>Packing efficiency= 74% </li></ul>Packing efficiency in FCC
  27. 27. Nearest Neighbour Distance (d) <ul><li>a=4r/√2 </li></ul><ul><li>a√2/4=r; r=0.3535a </li></ul><ul><li>d=2r </li></ul><ul><li>d=2X0.3535a </li></ul><ul><li>d=0.707a </li></ul>a
  28. 28. Packing efficiency in BCC <ul><li>BD 2 =CD 2 +BC 2 </li></ul><ul><li>but BC 2 =AB 2 +AC 2 </li></ul><ul><li>BD 2 =CD 2 +AB 2 +AC 2 </li></ul><ul><li>(4r) 2 =a 2 +a 2 +a 2 </li></ul><ul><li>16r 2 =3a 2 </li></ul>D B C A
  29. 29. Packing efficiency in BCC <ul><li>16r 2 =3a 2 </li></ul><ul><li>a=(16r 2 /3) 1/2 </li></ul><ul><li>a=4r/ √3 </li></ul><ul><li>Vol of cube=a 3 </li></ul><ul><li>Vol of unit cell=( 4r/ √3) 3 </li></ul><ul><li>No of spheres in BCC=2 </li></ul><ul><li>Vol of one sphere= 4/3 π r 3 </li></ul><ul><li>Vol of two spheres= 8 /3 π r 3 </li></ul><ul><li>Packing fraction=8 /3 π r 3 ÷64r 3 /3√3 </li></ul><ul><li>= 0.68 </li></ul><ul><li>= 68% </li></ul>
  30. 30. Nearest Neighbour Distance (d) <ul><li>a=4r/ √3 </li></ul><ul><li>r= a √3/4 </li></ul><ul><li>r=0.433a </li></ul><ul><li>d=2r </li></ul><ul><li>d=0.866a </li></ul>
  31. 31. Density Of A Crystal <ul><li>Density of cubic crystal of elements </li></ul><ul><li>ρ =mass of unit cell÷vol of unit cell </li></ul><ul><li>ρ = Z X M÷N A a 3 g/cm 3 </li></ul><ul><li>Z= No of atoms per unit cell </li></ul><ul><li>M= atomic mass of the element </li></ul><ul><li>convert pm to cm using- 1pm=10 -10 cm </li></ul>
  32. 32. Packing in crystal lattices <ul><li>Close packing in 2d </li></ul><ul><li>Square close packing </li></ul><ul><li>Hexagonal close packing </li></ul><ul><li>Close packing in 3d </li></ul><ul><li>- cubic close packing (ccp) </li></ul><ul><li>- hexagonal close packing (hcp) </li></ul>
  33. 33. Close Packing in Two Dimensions <ul><li>Square Close Packing </li></ul><ul><li>CN=4 </li></ul><ul><li>Packing Efficiency=52.4% </li></ul>
  34. 34. Close Packing in Two Dimensions <ul><li>Hexagonal Close Packing </li></ul><ul><li>CN=6 </li></ul><ul><li>Packing Efficiency=60.4% </li></ul>
  35. 35. <ul><li>Base layer A </li></ul><ul><li>void a </li></ul><ul><li>void b </li></ul><ul><li>voids a and b are triangular </li></ul>Close Packing in 3 d
  36. 36. Second Layer <ul><li>Second layer on voids a, voids b open </li></ul><ul><li>Voids made by layer B- voids c (octahedral) are above voids b, voids d(tetrahedral) </li></ul>Voids c Voids d
  37. 37. Third layer <ul><li>Depending on the arrangement of the third layer, packing may be </li></ul><ul><li>Hexagonal close packing </li></ul><ul><li>spheres of the third layer fit into voids d made by layer B ie exactly in line with spheres of layer A </li></ul><ul><li>ABABAB…. </li></ul><ul><li>Coordination No-12 (six of same layer, 3 from upper layer,3 from lower layer) </li></ul>
  38. 38. 3D hexagonal close packing
  39. 39. Cubic close packing <ul><li>Third layer C –spheres occupy voids c </li></ul><ul><li>Spheres are neither aligned with layer A nor with B </li></ul><ul><li>Spheres of fourth layer are aligned with layer A </li></ul><ul><li>Unit cell of such lattice is FCC </li></ul><ul><li>CN no=12, 6 in one plane,3 each in planes above and below. </li></ul>
  40. 40. Cubic close packing
  41. 41. HCP and CCP <ul><li>Packing efficiency=74% </li></ul><ul><li>Ex- HCP-crystals of Mo,Mg,Be,Cd,Zn,Ti </li></ul><ul><li>Ex-CCP-crystals of Fe,Ni,Ag,Au,Al </li></ul>
  42. 42. Voids/Interstices <ul><li>Tetrahedral void Octahedral void </li></ul>
  43. 43. Voids/Interstices <ul><li>The unoccupied/vacant space present in the lattice of a crystal </li></ul><ul><li>Types- </li></ul><ul><li>Tetrahedral-vacant space surrounded by four nearest neighbours in tetrahedral position </li></ul><ul><li>Every void is surrounded by 4 particles </li></ul><ul><li>8 voids are present around each particle. </li></ul><ul><li>Hence, no. of tetrahedral voids is twice the number of constituent particles </li></ul>
  44. 44. Voids/Interstices <ul><li>-Octahedral voids- </li></ul><ul><li>Vacant space surrounded by six nearest neighbours in octahedral arrangement </li></ul><ul><li>Each oct void is surrounded by 6 particles </li></ul><ul><li>6 voids around each particle </li></ul><ul><li>No of oct voids=no of constituent particles </li></ul>
  45. 45. Radius Ratio of voids <ul><li>The ratio of radius of a void to that of a particle </li></ul><ul><li>For a tetrahedral void- </li></ul><ul><li>r/R=0.225 </li></ul><ul><li>Limiting radius- a tetrahedral void can accommodate a particle of radius less than 0.225 only </li></ul>
  46. 46. Voids/Interstices <ul><li>Octahedral void- </li></ul><ul><li>r/R=0.414 </li></ul><ul><li>Limiting radius=0.414 </li></ul>
  47. 47. Defects/Imperfections in crystals <ul><li>Ideal Crystal- same unit cell containing same lattice points throughout the lattice </li></ul><ul><li>Difficult to obtain above 0 K </li></ul><ul><li>Deviation from an ordered arrangement- </li></ul><ul><li>Defect </li></ul>
  48. 48. Atomic Defects/Point Defects <ul><li>Due to irregularity in arrangement of atoms </li></ul><ul><li>Atoms are missing </li></ul><ul><li>OR </li></ul><ul><li>Atoms are dislocated </li></ul>
  49. 49. Atomic Defects/Point Defects <ul><li>Stoichiometric Defects- ratio between cations and anions remains undisturbed </li></ul><ul><li>Non stoichiometric Defects- ratio of cation and anion differs from the chemical formula </li></ul><ul><li>Impurity Defects </li></ul>
  50. 50. Stoichiometric defects <ul><li>Types- </li></ul><ul><li>Schottky defect </li></ul><ul><li>Frenkel defect (dislocation defect) </li></ul>
  51. 51. Schottky Defect <ul><li>Pair of cation and anion missing from the crystal </li></ul><ul><li>Ex-NaCl, KCl,KBr </li></ul>A + A + A + A + A + A + A + B - B - B - B - B - B - B -
  52. 52. Frenkel Defect <ul><li>Dislocation of cation into a vacancy </li></ul><ul><li>Ex- ZnS, AgBr, AgCl </li></ul>A + A + A + A + A + A + A + B - B - B - B - B - B - B - A + B -
  53. 53. Non Stoichiometric Defects <ul><li>Types- </li></ul><ul><li>Metal excess defect due to anion vacancies (F-centre or farbe centre defect) </li></ul><ul><li>Ex- LiCl, KCl </li></ul><ul><li>paramagnetic </li></ul><ul><li>coloured </li></ul>A + A + A + A + A + A + A + A + B - B - B - B - B - B - B - e -
  54. 54. Non Stoichiometric Defects <ul><li>Metal excess due to interstitial cation </li></ul><ul><li>Ex-ZnO </li></ul>e - A + A + A + A + A + A + A + A + A + B - B - B - B - B - B - B - B -
  55. 55. Non Stoichiometric Defects <ul><li>Metal deficiency due to cation vacancy </li></ul><ul><li>Ex-FeS, FeO, NiO </li></ul>A + A 2+ A + A + A + A + A + B - B - B - B - B - B - B - B -

×