The isotopic mass and lattice parameter of diamond; a path-integral simulation

The dependence of the lattice parameter of diamond upon the isotopic mass has been studied by path-integral Monte Carlo simulations in the isothermal-isobaric ensemble. This computational method provides us with a quantitative and nonperturbative procedure for analysing such anharmonic effects. Atomic nuclei were treated as quantum particles interacting via a Tersoff-type potential. At 300 K, the difference ha between the lattice parameter of isotopically pure crystals of C-12 and C-13 is found to be 6.1 x 10(-4) Angstrom, in good-agreement with experimental results. This difference decreases under an applied external pressure, and for 4000 kbar we obtain Deltaa = 2.4 x 10(-4) Angstrom.