lattice planes Brajmohan kushwah

lattice planes Brajmohan kushwah

1. SEPARATION BETWEEN LATTICE PLANES 2/10/2016 RAI SAHEB BHANWAR SINGH COLLEGE NASRULLAGANJ 1

2. NAME : BRAJMOHAN KUSHWAH CLASS : BSC VI SEM (C.S) COLLEGE : RAI SAHEB BHANWAR SINGH COLLEGE NASRULLAGANJ SUBMITTED TO : GYANRAO DHOTE SIR 2/10/2016 RAI SAHEB BHANWAR SINGH COLLEGE NASRULLAGANJ 2 Presented BY

3. 2/10/2016 RAI SAHEB BHANWAR SINGH COLLEGE NASRULLAGANJ 3 WEL COME

4. PH 0101 UNIT 4 LECTURE 2 4 SEPARATION BETWEEN LATTICE PLANES Consider a cubic crystal of side ‘a’, and a plane ABC. This plane belongs to a family of planes whose Miller indices are (h k l) because Miller indices represent a set of planes . Let ON =d, be the perpendicular distance of the plane A B C from the origin.

5. PH 0101 UNIT 4 LECTURE 2 5 SEPARATION BETWEEN LATTICE PLANES

6. PH 0101 UNIT 4 LECTURE 2 6 SEPARATION BETWEEN LATTICE PLANES Let  1 ,  1 and  1 (different from the interfacial angles  ,  and  ) be the angles between co- ordinate axes X,Y,Z and ON respectively. The intercepts of the plane on the three axes are, (1)

7. PH 0101 UNIT 4 LECTURE 2 7 SEPARATION BETWEEN LATTICE PLANES From the figure, 4.14(a), we have, (2) From the property of direction of cosines, (3) Using equation 1 in 2, we get,

8. PH 0101 UNIT 4 LECTURE 2 8 SEPARATION BETWEEN LATTICE PLANES Using equation 1 in 2, we get, (4) Substituting equation (4) in (3), we get,

9. PH 0101 UNIT 4 LECTURE 2 9 i.e. (5) i.e. the perpendicular distance between the origin and the 1st plane ABC is,

10. PH 0101 UNIT 4 LECTURE 2 10 Now, let us consider the next parallel plane. Let OM=d 2 be the perpendicular distance of this plane from the origin. The intercepts of this plane along the three axes are

11. PH 0101 UNIT 4 LECTURE 2 11 Therefore, the interplanar spacing between two adjacent parallel planes of Miller indices (h k l ) is given by, NM = OM – ON i.e.Interplanar spacing (6) SEPARATION BETWEEN LATTICE PLANES

12. PH 0101 UNIT 4 LECTURE 2 12 Worked Example The lattice constant for a unit cell of aluminum is 4.031Å Calculate the interplanar space of (2 1 1) plane. a = 4.031 Å (h k l) = (2 1 1) Interplanar spacing  d = 1.6456 Å PROBLEMS

13. PH 0101 UNIT 4 LECTURE 2 13 PROBLEMS Worked Example : Find the perpendicular distance between the two planes indicated by the Miller indices (1 2 1) and (2 1 2) in a unit cell of a cubic lattice with a lattice constant parameter ‘a’. We know the perpendicular distance between the origin and the plane is (1 2 1) and the perpendicular distance between the origin and the plane (2 1 2),

14. PH 0101 UNIT 4 LECTURE 2 14 PROBLEMS The perpendicular distance between the planes (1 2 1) and (2 1 2) are, d = d 1 – d 2 = (or) d = 0.0749 a.

15. PH 0101 UNIT 4 LECTURE 2 15 Physics is hopefully simple but Physicists are not

16. THANK YOU 2/10/2016 RAI SAHEB BHANWAR SINGH COLLEGE NASRULLAGANJ 16