We have that for a crystal the lattice parameters

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SUMMARY

The discussion focuses on calculating the lattice vector components for a crystal with lattice parameters of 10.5 Å and angles of 109.5°. The solution provided by the user includes the components for vectors a, b, and c, calculated using trigonometric functions. The resulting matrix of vector components is presented, and a query is raised regarding the correctness of two different matrix representations, emphasizing the importance of vector ordering for accurate atom positioning.

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Eduard1
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Homework Statement



We have that for a crystal the lattice parameters (in angstrom and degree) are:

a b c (in Angstrom)
10.5 10.5 10.5

\alpha β γ (in degree)
109.5 109.5 109.5


Find the lattice vectors components.


Homework Equations




The Attempt at a Solution



The way I solved the problem:

a_1 (first component of the vector a) = 0
a_2 = sin (109.5) * 10.5 = 9.8977356555
a_3 = cos (109.5) * 10.5 = -3.5049720195

b_1 = sin (109.5) * 10.5 = 9.8977356555
b_2 = 0
b_3 = cos (109.5) * 10.5 = -3.5049720195

c_1 = sin (109.5) * 10.5 = 9.8977356555
c_2 = cos (109.5) * 10.5 = -3.5049720195
c_3 = 0


The matrix with the vectors' components is then:

0.0000000000 9.8977356555 -3.5049720195
9.8977356555 0.0000000000 -3.5049720195
9.8977356555 -3.5049720195 0.0000000000


Is this correct ?

One could also write this matrix as:

0.0000000000 -3.5049720195 9.8977356555
9.8977356555 0.0000000000 -3.5049720195
9.8977356555 -3.5049720195 0.0000000000

(notice the interchange in the the first vector components). Which matrix is correct ? The ordering will be definitelly important for the atom positions.

Thank you very much for any help.
Eduard
 
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Check if those vectors really enclose 109.5° angle.

ehild
 

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