How Do Monoclinic to Triclinic Lattice Transformations Occur?

[bebis]

According to the literature, when monoclinic crystal structure transforms to triclinic, the following formulaes, regarding their lattice parameters are valid:

a(T) = 1/2 a(M) - 1/2 b(M)
b(T) = 1/2 a(M) + 1/2 b(M)
c(T) = c(M)

Where T and M stand for Triclinic and Monoclinic, respectively.

Could anyone please inform how do these formulaes come up or any literature source to search further?

Thanks a lot!

 

[Gokul43201]

This looks like it might be a transformation from a face-centered monoclinic to a triclinic. One way to check would be to contruct the lattice on some 3D modeling software (like AutoCAD), and perform the transformations numerically.

What is your source for the relations?

 

[bebis]

The source is 'PRL 99, 247211 (2007)', 'Magnetoelastic Coupling and Symmetry Breaking
in the Frustrated Antiferromagnet
-NaMnO2'. The formulas are presented on the last page, page 4, of this paper.

Any response is kindly welcome.

This looks like it might be a transformation from a face-centered monoclinic to a triclinic. One way to check would be to contruct the lattice on some 3D modeling software (like AutoCAD), and perform the transformations numerically.

What is your source for the relations?