inter planar spacing

1. INTER-PLANAR SPACING AND IT’S
DERIVATION,EXPRESSIONS FOR VARIOUS CRSTAL
SYSTEMS

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. 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.

5. 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);

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