# Monoclinic Crystal: why is the (100)d-spacing not equal to the lattic cell dimension "a"

• I

## Summary:

Monoclinc primitive crystal, why is (100) d-spacing not equal to lattice cell dimension a.

## Main Question or Discussion Point

Why is it that the d-spacing of the (100) plane is not equal to the lattice cell dimension a.
I can calculate the (010) and (001) d-spacings and they are equal to b & c lattic cell dimensions which is what I expected.

Small bit of background.
My task was to write a small program that calculates the d-spacing for whatever plane the user inputs.
The user inputs the a,b,c & alpha, beta, gamma parameters and use an equation to calculate d-spacings for each of the planes.
The Monoclinc cell has dimensions a=0.52, b=0.54, c=56, alpha=gamma=90deg, beta = 99.18deg.
Any thoughts would be welcome.
Thanks

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anuttarasammyak
Gold Member
d-spacing formula of orthogonal crystals
$$\frac{1}{d_{hkl}^2 }=\frac{h^2}{a^2}+\frac{k^2}{b^2}+\frac{l^2}{c^2}$$
tells (100) d-spacing is a.

Maybe I do not get your situation correctly.

Lord Jestocost
Gold Member
Summary:: Monoclinc primitive crystal, why is (100) d-spacing not equal to lattice cell dimension a.

.....use an equation to calculate d-spacings for each of the planes.
Have a look at the ##1/d^2## equation for the monoclinic crystal system:
http://pd.chem.ucl.ac.uk/pdnn/unit1/unintro.htm

• anuttarasammyak
Thanks for your input. Indeed I used the calculation that you link to http://pd.chem.ucl.ac.uk/pdnn/unit1/unintro.htm
in my program.

I also checked my results with an online calculator at this link https://neutron.ornl.gov/user_data/...tal Plane Spacings and Interplanar Angles.htm
so I am confident that the formula's and calculations are correct.

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I still can't give an explanation in my own words for a reason that the (100) d-spacing is not equal to the lattice parameter for monoclinic whereas the (010) & (001) are equal to their respective lattic parameter.

I compare it to the case of the cubic crystal where it is easy to visualize that the (100) d-spacing is equal to the lattice parameter. However I don't see why this is different for the monoclinic crystal. • 