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Strictly speaking, we have to divide ΔV(Ω) into a part that is consistent with the crystallographic symmetry and one that is not consistent with it, in order to define the two order parameters in a more unambiguous way: For example, this can be done by decomposing ΔV(Ω) into a spherical harmonic functions (see our paper I). Unfortunately, there is not a straight-forward way to pick up only such a part of ΔV(Ω); for simplicity, thus, we assume in this paper that all the parts of ΔV(Ω) are not consistent with the crystallographic symmetry.
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It should be noted that in this paper we do not consider the growth kinetics of nucleated crystals, which was discussed by Turnbull and Cohen (Ref. 9) in detail, since we are interested only in ideal glass formation without any nuclei in a liquid. Thus, the criteria described here should also be regarded as those for ideal vitrification.
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A subtle problem relating to this prediction will be discussed later.
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