DNA is the premier material for directing nanoscale self-assembly, having been used to produce many complex forms(1-4). Recently, DNA has been used to direct colloids(5,6) and nanoparticles(7,8) into novel crystalline structures, providing a potential route to fabricating meta-materials(9) with unique optical properties. Although theory(10-12) has sought the crystal phases that minimize total free energy, kinetic barriers(13) remain essentially unstudied. Here we study interfacial equilibration in a DNA-directed microsphere self-assembly system(5,6,14) and carry out corresponding detailed simulations. We introduce a single-nucleotide difference in the DNA strands on two mixed microsphere species, which generates a free-energy penalty(5,15,16) for inserting 'impurity' spheres into a 'host' sphere crystal, resulting in a reproducible segregation coefficient. Comparison with simulation reveals that, under our experimental conditions, particles can equilibrate only with a few nearest neighbours before burial by the growth front, posing a potential impediment to the growth of complex structures.