We study the time evolution of the surface composition and the atomic sputter yields when a multicomponent alloy is bombarded with a broad ion beam. For a binary or a ternary alloy, the sputter yields approach steady-state values exponentially with time if the sputter yield of each atomic species is proportional to its surface concentration. There may be two distinct stable steady-state solutions to the equations of motion for the sputtering of a binary alloy if the sputter yield of one of the atomic species is amplified. In the case of a ternary alloy, we give a hypothetical example that satisfies the minimal physical requirements and that yields long-lived oscillations in the sputter yields of the three atomic species.
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