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Metastable Fe100-xAlx alloys have been formed by ball milling of elemental Fe and Al powders: supersaturated body-centered-cubic solid solutions for x less than or equal to 70, and an amorphous phase for x > 70. Quantitative x-ray-diffraction measurements show that the total root-mean-square displacement (rms) and the static rms in the Fe100-xAlx solid solutions increase significantly with increasing Al content, The total rms at the instability point, however, reaches only 6.8% of the nearest-neighbor distance and is far below the critical value predicted by the Lindemann melting criterion, suggesting that the Lindemann melting criterion is not applicable for the solid-state amorphization. Instead. the Debye temperature of the supersaturated Fe100-xAlx alloys was observed to drop by similar to 22% at the point of amorphization, implying a corresponding softening in the average shear modulus of similar to 40%, which agrees with the microhardness measurements. These results strongly support the empirical elastic instability criterion For the solid-state amorphization process.