  The whole Al-Li phase diagram is predicted from first principles calculations
and statistical mechanics including the effect of configurational and
vibrational entropy. The formation enthalpy of different configurations at
different temperatures was accurately predicted by means of cluster expansions
that were fitted from first principles calculations. The vibrational entropic
contribution of each configuration was determined from the bond length vs. bond
stiffness relationships for each type of bond and the Gibbs free energy of the
different phases was obtained as a function of temperature from Monte Carlo
simulations. The predicted phase diagram was in excellent agreement with the
currently accepted experimental one in terms of the stable (AlLi, Al2Li3,
AlLi2, Al4Li9) and metastable (Al3Li) phases, of the phase boundaries between
them and of the maximum stability temperature of line compounds. In addition,
it provided accurate information about the gap between Al3Li and AlLi solvus
lines. Finally, the influence of the vibrational entropy on the correct
prediction of the phase diagram is discussed. Overall, the methodology shows
that accurate phase diagrams of alloys of technological interest can be
predicted from first principles calculations.
