Dear Researchers,
In XRD analysis, I got the monoclinic phase of CuO for my sample, for this, I need to calculate the Lattice parameter(LP) of monoclinic CuO, herewith I knew the formula for this LP calculation but I don't have any idea to how to solve it. I got only three major peaks from XRD. I have given some details below regarding LP calculation, kindly have a glance and solve it (if it's possible).
2 theta (deg.C) ( h k l )
35.55 -1 1 1
38.69 1 1 1
61.58 -1 1 3
Dear Durai,
although you are able to calculate the distances dhkl of the lattice planes via the Bragg law you have to use for the calculation of your monoclinic lattice parameters (a, b, c, ß) four peaks to solve the equations (please see the formula for d spacings of monoclinic system at the attachement). You have to take an additional one.
Good luck.
Dear Professor Gerhard Martens,
Thank you for your kind reply and answer,
I know the formula whatever you have mentioned in that attachment of formula to calculate Lattice Parameter, here we need to find a, b, c. these three are variables that we know. four peaks to solve the equations means?
from the Bragg's law, I have calculated the d spacing values.
here in this equation what denotes ß value.
Totally I am confused with this.
Yo be frank, I need much clarity for this calculation.
Kindly do the needful.
Please see the attachment.
There the angle ß shows up ( ß is not 90° for monoclinic system), which has to be used to calculate the lattice plane distances according to the d-spacing formula of monoclinic system. ß is the fourth variable which enters the formula via sin²(ß) and cos(ß). Therefore you need 4 equations to solve your set of equations for 4 variables ( a, b, c and ß; see Klug-Alexander table mentioned above)) and therefore you need 4 peaks.
Remark: ß does not show up in the Bragg law [n*lambda=2*d*sin(theta)].
So please take 4 values of dhkl and set up four equations according to the monoclinic d-spacing formula by introducing the appropriate h, k, and l values, which correspond to your d-spacings.
So you will get a system of four equations,
dh1k1l1 = f1(a, b ,c ,ß); (eq. 1)
dh2k2l2 = f2(a, b, c, ß); (eq. 2)
dh3k3l3 = f3(a, b, c, ß); (eq. 3)
dh4k4l4 = f4(a, b, c, ß); (eq. 4),
which you have to solve for a, b, c and ß.
That's it.
http://www.wikiwand.com/en/Monoclinic_crystal_system
Dear Professor Gerhard Martens,
I will do as per your instructions and if I have any clarifications I will discuss with you.
Thank you sir.
Dear Durai,
inverting the above set of equations into
a=..., b=...., c = ... and ß=....
is not an easy job. I do not know whether there is a closed representation existing at all of the solution of the system of equations.
In this case you may solve it numerically. Please google for 'numerical solver of equations'.
Good luck.
Dear Professor Gerhard Martens,
Of course, it is quite difficult to solve......... but I will try my extreme level.
Thanks and Regards
Durai Govindarajan
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