  Recently the supercooled Wahnstrom binary Lennard-Jones mixture was partially
crystallized into ${\rm MgZn_2}$ phase crystals in lengthy Molecular Dynamics
simulations. We present Molecular Dynamics simulations of a modified
Kob-Andersen binary Lennard-Jones mixture that also crystallizes in lengthy
simulations, here however by forming pure fcc crystals of the majority
component. The two findings motivate this paper that gives a general
thermodynamic and kinetic treatment of the stability of supercooled binary
mixtures, emphasizing the importance of negative mixing enthalpy whenever
present. The theory is used to estimate the crystallization time in a
Kob-Andersen mixture from the crystallization time in a series of relared
systems. At T=0.40 we estimate this time to be 5$\times 10^{7}$ time units
($\approx 1. ms$). A new binary Lennard-Jones mixture is proposed that is not
prone to crystallization and faster to simulate than the two standard binary
Lennard-Jones mixtures; this is obtained by removing the like-particle
attractions by switching to Weeks-Chandler-Andersen type potentials, while
maintaining the unlike-particle attraction.
