while examining two different x-ray pattern of copper and aluminium, I have above doubt. can anyone explain me this effect.
As you pointed out this question for Cu and Al, First I will say that as both of them are having FCC crystal structure so both materials will show the same (hkl) set. i.e (111), (200), (220), (311)...so on. This you already know.
Now the main thing, as both the material Al and Cu are having different size of crystal structure i.e different lattice parameter (a), so the interplaner spacing (d) is also different, which cause the peaks of same (hkl) to come at different 2 theta values.
as you know we have
2dSin(theta)= lamda, where d is the interplaner spacing
and
d=a/(h2+k2+l2)-1/2
as 'd' depends on 'a', and thata depends on 'd', for larger 'a' you will observe same (hkl) to come at lower 2 theta position. 'a' is larger for Al so you observe it at lower 2theta.
it is just bcoz of the different crystal structure size. which will give different lattice parameter and interplaner spacing is also. that results the same peaks at different 2 theta values.
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