  We give an explicit, nonnegative formula for the expansion of nonsymmetric
Macdonald polynomials specialized at $t=0$ in terms of Demazure characters. Our
formula results from constructing Demazure crystals whose characters are the
nonsymmetric Macdonald polynomials, which also gives a new proof that these
specialized nonsymmetric Macdonald polynomials are positive graded sums of
Demazure characters. Demazure crystals are certain truncations of classical
crystals that give a combinatorial skeleton for Demazure modules. To prove our
construction, we develop further properties of Demazure crystals, including an
efficient algorithm for computing their characters from highest weight
elements. As a corollary, we obtain a new formula for the Schur expansion of
Hall--Littlewood polynomials in terms of a simple statistic on highest weight
elements of our crystals.
