Question

How to calculate lattice constant from miller indices of an unknown?

Answer 1

By using Bragg's law 2*d*sin@= n*lemda ........ (1)

now we first figure out interplanner displacment 'd' rearrange eq.(1) for d we can get

d= lemda/2sin@ .................... (2)

now here, we know lemda = 0.154 nm/2* sin (20)/2 = 0.3546 nm (roughly)

Now if you know about the geometry of your sample like whether it is FCC, BCC and hexagonal for example it if FCC then the unit cell diminision is

d = a/sqrt(h2+k2+l2) ......................(3)

and for FCC the unit cell volume is a = 2*r sqrt(2)

............................(4)

and 'a' is gives as a = 0.128 nm

Now put this value in equation (3) we can

sqrt(h2+k2+l2) = a/d = 0.3546/0.209 (approximately)

= 1.732

h+k+l = 3.0

For FCC

the pricilpal planes are those whose indices are odd or even such as (111), (200), (220). This is the posssible planes to the corresponding peaks positions. Now among these which are even or odd gives (hkl) 3.0. so the only possibiliy here is 111 such as h=k=l 1 which when we add gives us 3 not less nor higher. hence, the diffraction peaks at 20 theta is the one whose (hkl) = (111).

Hope it wl help you to figure out all these in such a way

Answer 2

Explanation:

Calculate the Lattice Constant

Calculate the Lattice ConstantIf the space lattice is FCC, the lattice constant is given by the formula [4 x r / (2)1/2] and if the space lattice is BCC, then the lattice constant is given by the formula a = [4 x r / (3)1/2].