Converting between Crystallographic Notations: A Simple Guide

[zeta]

Hi Folks;
Trying to run an ewald summation to create a crystal field for a Gaussian98 calculation. Problem is the input file wants crystal translation vectors, but my structure data is in terms of a,b,c alpha beta gamma. It's been a while, how does one go between the two notations? Are the alpha beta gamma the direction cosines?
sorry if this is a stupid question

 

[Gokul43201]

I believe you need to convert a, b, c, alpha, beta, gamma into Cartesian components: a_x, a_y, a_z, b_x,...c_z (9 numbers).

Alpha, beta, gamma are not the direction cosines, they are actual angles. What are your values of a, b, c, alpha, beta, gamma?

 

[zeta]

yes sorry, angles. but they are for the direction cosines, yes?

there are a number of compounds I'm doing NMR EFG and chemical shift tensor calculations on, including kaolinite where a b c alpha beta gamma are 5.1535 8.9419 7.3906 91.926 105.046 89.797

thanks for the interest/help

 

[Gokul43201]

First you need to orient your unit cell along the xyz axes. The standard approach is to put a along x and b in the xy plane. For the above monoclinic unit cell, this gives:
a_x=a
a_y=a_z=0
b_x=b*cos(gamma)
b_y=b*sin(gamma)
b_z=0
c_x=c*cos(beta)
...etc...
it gets tricky from there, but if you draw the picture and do the trig carefully, you can find the other components.

The thing to know is that alpha, beta, gamma are angles between (b,c), (c,a) and (a,b). If the trig proves tricky, use a 3d modeler like autocad to figure out the components.

PS: Don't take this much more than an educated guess. I haven't seen this stuff in ages.

 

[zeta]

hey thanks that's awesome :)

 

[xamnidar]

Here's the final results of gokul's approach:

a_x=a
a_y=a_z=0

b_x=b*cos(gamma)
b_y=b*sin(gamma)
b_z=0

c_x=c*cos(beta)
c_y=c*[cos(alpha)-cos(gamma)*cos(beta)]/sin(gamma)
c_z=sqrt(c^2-c_x^2-c_y^2)