  We report comprehensive x-ray diffraction studies of the crystal structure
and epitaxy of thin films of the topological insulator Bi2Te3 grown on Si (1 1
1). The films are single crystals of high crystalline quality, which strongly
depends on that of their substrates, with in-plane epitaxial relationships of
Bi2Te3 [2 1 -3 0] || Si [1 -1 0] and Bi2Te3 [0 1 -1 0] || Si [1 1 -2] along
which the lattices of 1x3 Bi2Te3 and 2x2 Si supercells are well matched. As the
samples age, we observe loss of crystalline Bi2Te3 film thickness accompanied
with roughening of the crystalline interfaces, formation of new crystalline
phases as well as compositional and structural modification of the Si
substrate, consistent with the diffusion of Te into the Si substrate.
