Sep 23rd, 2015

Diamond Crystallography – Cube Analysis

Diamonds crystallize in the tetrahedral system which is a sub system to the main cubic system. To better understand the crystal structure of diamonds I am going to start by analyzing the cube. So let us put the cube through its mathematical paces. Here is a standard 100 mm cube that we are going to use in this experiment.

 

Next let us bisect the cube diagonally as in the following image

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Following are the dimensions of the bisected plane, calculated as follows:

100 ÷45 sin = 141.4213562373095.

 

 

Now, let us look at the bisected plane facing us and do some more calculations.ө = 100 ÷ 141.42 inv tan = 35.26438968275465°.

 

Now we are able to do some deductions. If ϴ is 35.26438968275465°, then the obtuse angle of the bottom triangle would be 180° – (2 x 35.26438968275465°)  = 109.4712206344907° rounded to 109.47°. This is exactly the angle of any three adjoining diamond atoms. The view below is of the 110 orientation as we bisected the cube on the 110 plane.

Next, let us take the second triangle with its apex on the top center of our rectangle then we can deduce the following: 180° – 109.47° = 70.53°

 

 

The two base angles of this triangle are 180° – 70.53 ÷ 2 = 54.735. Also, by extension still within the same rectangle we can deduce the following:

 

Conclusion.

The angles of crystal faces of a diamond in relation to each other are perfectly demonstrated as per the analysis of the cube we have just completed above.