interplanar spacing.pptx

derivation of inter-planar spacing by mathematical method is used

1. DERIVATION OF INTER-PLANAR SPACING AND EXPRESSIONS FOR INTER-PLANAR SPACING FOR VARIOUS CRYSTAL STRUCTURES GERUGANTI SUDHAKAR PHD(MATERIAL’S ENGINEERING) UNIVERSITY OF HYDERABAD

2. Useful concept for crystallography & diffraction Lattice planes Think of sets of planes in lattice - each plane in set parallel to all others in set. All planes in set equidistant from one another Infinite number of sets of planes in lattice d d - interplanar spacing

3. The interplanar distance dhkl is defined to be the distance from the origin of the unit cell to the ( hkl ) plane nearest the origin along the normal to the plane, i.e. the perpendicular distance from the origin to the plane.

4. Equation of plane in intercept form is: (x/a)+(y/b)+(z/c) = 1 ………….(I) Where a,b,c are x-,y-,z-intercepts respectively. In the present case, PLANE is touching x-axis=a/h, y-axis=b/k, z-axis=c/l Substituting THIS INTERCEPTS in equation (I); we have [x/(a/h)]+[y/(b/k)]+[z/(c/l)] = 1;

5. On simplying we have, ( hx /a)+( ky /b)+( lz /c) = 1 ………(II) PERPENDICULAR DISTANCE FROM ORIGIN TO ABOVE PLANE (II) IS “INTER-PLANAR SPACING: d” Therefore,1/√[(h/a)^2+(k/b)^2+(z/c)^2] = d  d^2= 1/[(h/a)^2+(k/b)^2+(z/c)^2]

6. FOR: TETRAGONAL a = b ≠ c; ORTHO-RHOMBIC a ≠b ≠c. Substituting the above in “INTER-PLANAR SPACING : d” We get expression for THOSE crystal structures