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I am trying to calculate lattice parameter of ZnO (wurtzite). I have found out the formula for calculating lattice parameter of this system from a research article.

$\frac{1}{^{d^{2}}}=\frac{H ^{2}+ K^{2}}{a^{2}}+\frac{L^{2}}{c^{2}}$

I have this jcpds data of ZnO for carrying out calculations

a (Å):    3.2489 
b (Å):    3.2489 
c (Å):    5.2062

No.    h    k    l      d [A]     2Theta[deg] I [%]   
  1    1    0    0      2.81000    31.820      80.0
  2    0    0    2      2.60000    34.467      70.0
  3    1    0    1      2.48000    36.191     100.0
  4    1    0    2      1.91000    47.569      70.0
  5    1    1    0      1.62000    56.783      80.0
  6    1    0    3      1.48000    62.728      80.0
  7    2    0    0      1.41000    66.229      50.0
  8    1    1    2      1.38000    67.861      80.0

what i have done so far

for calculating parameter c i used this formula

$c=l*d$

for 002 plane of above data i got a c of 5.198 which is in accordence with jcpds c=5.2062

But while calculating parameter a i am facing some difficulty. i used below formula to calculate a lattice parameter (hk0)

$a=\sqrt{H^{2}+K^{2}}*d$

for 110 of the above data i got a lattice parameter a=2.29 but in jcpds data a=3.2489

Have i done some thing wrong in my calculations?!!

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