By Germain P., Nguyen Q.S., Suquet P.

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17) At the solidiﬁcation temperature Tm , we can postulate ∆hV = −Lf , where Lf is the latent heat of fusion of the material per unit of volume (∆hV is negative) and ∆sV = −Lf /Tm . 19) where ∆Cp is the diﬀerence in speciﬁc heat between the liquid and solid phases. 20) We assumed ∆T = Tm − T , and this quantity is a measure of the degree of supercooling of the liquid. In a ﬁrst approximation, we can hypothesize that ∆Cp = 0. 21) This approximation is totally justiﬁed in the case of metals but is much less justiﬁed for polymers.

15) which is represented by a G(x) diagram, where x is the concentration of one of the constituents. If GA and GB designate the molar free enthalpies of the constituents in the mixture, show that the slope of the tangent at any point in the diagram is given by GB − GA . 4. Fluctuations and Scattering of Light Light scattering is a very widely used technique for studying phase transitions in transparent ﬂuids and solids (Fig. 15). The total scattering intensity at time t corresponding to vector k is: I(k, t) = |E(k, t)|2 where E(k, t) is the electric ﬁeld of the scattered wave, which is associated with ﬂuctuation of the dielectric constant of the hypothetically isotropic medium: E(k, t) ∝ E0 e−iω0 t δ (k, t) 36 1 Thermodynamics and Statistical Mechanics of Phase Transitions ω0 is the frequency of the incident wave, and δ (k, t) is the Fourier transform of ﬂuctuation δ .

The solid in the plastic crystalline phase ﬂows easily because the molecules can rotate freely around one axis and be reoriented. These transitions are ﬁrst-order, but with low latent heat. 2 Transitions with No Change in Structure Phase transitions in which the appearance of a new property is not correlated with any modiﬁcation of the crystal structure of the material are classiﬁed under this heading; it is thus not associated with a change in symmetry. We will study these phase transitions in detail later and will only mention their existence here.