# SiC surface reconstruction

I know how to cleave surfaces with integer Miller indices, however I wonder how I could cleave a $$(\sqrt{3} \times \sqrt{3}) R30$$ reconstruction of $$(001)\,\, 4H-SiC$$.

I have found a nice link to O-lattice theory here, https://www.tf.uni-kiel.de/matwis/amat/def_en/kap_7/backbone/r7_3_1.html but I thought there might be a script out there for this purpose.

I am currently trying my chances with VESTA!

Thank you for your help, Roozbeh

The reconstructed $$(\sqrt{3} \times \sqrt{3})R30$$ surface unit cell can be obtained by first applying the rotation matrix
$$\begin{pmatrix} 1.0 & 2.0 & 0.0 \\ -1.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{pmatrix}$$
to the primitive bulk unit cell, and then the reconstructed $$(001)$$ surface can be cleaved from this unit cell, or the other way around.