Introduction to weld solidification
Of all phase transformations, few have been more widely observed and studied than the transformation of a liquid to a solid (that is, solidification). No activation energy or undercooling is required to add atoms onto an existing substrate. This is the situation that develops when a liquid solidifies on a substrate of the same material or one that is similar in composition and structure, as in the solidification of a weld.
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The process of solidification is the same in all cases, whether it is the freezing of water on a windshield or in a freezer, or the solidification of metal in a casting or in the weld that joins two solids.Weld solidification:
- The process is controlled by the free energy of the liquid phase, Gl, relative to that of the solid, Gs. This is depicted in Fig.1, which shows the behavior of a pure (single component) material. Above the freezing temperature, Tf, the liquid phase has the lower free energy and is therefore stable, but below Tf, the solid is the stable phase. At Tf, both phases are in equilibrium, that is,
Gl = Gs
- In the transition from one phase to another, the change in free energy, ΔG, is the difference in free energy of the product and the reactant. This free energy change can be expressed in terms of the enthalpy and the entropy changes, that is, for the transformation of a liquid to a solid during freezing:
Fig1. : TEMPERATURE DEPENDENCE OF BULK FREE ENERGY OF THE LIQUID AND SOLID PHASES IN SINGLECOMPONENT SYSTEM, THE SOLID LINE PORTION AND THE DASHED LINE PORTION OF EACH GL, AND GS CURVE INDICATE THE STABLE AND UNSTABLE PHASES, RESPECTIVELY, OF THE FREE ENERGY ON EITHER SIDE OF TF
- At the freezing temperature, Tf, ΔG = Gs – Gl = 0, because the free energy of the two phases is the same, and ΔH = TfΔS, It is necessary to cool below Tf for solidification, because at Tf both the solid and liquid phases are present and in equilibrium. Below Tf, ΔG is not equal to zero (Fig. 1 shows that Gs < Gl) and is given by Eq 1 with T = T‘, where T‘ < Tf.
- Because the ΔH and ΔS are not strong functions of temperatures, they can be assumed to be temperature independent.
- Therefore, at any temperature, ΔH = ΔHf and ΔS = ΔSf, where ΔHf and ΔSf are the values of the enthalpy and the entropy changes for the equilibrium reactions at Tf (that is, the latent heat of fusion and the entropy change on fusion, respectively). Combining these enthalpy and entropy expressions, the fact that ΔH = Tf ΔS, then at T‘, one obtains:
Where ΔHf, the latent heat of fusion, is negative, hence, in agreement with Fig. 1, ΔG is negative. The greater the amount of undercooling (super cooling) below Tf (Tf – T‘), then the greater the thermodynamic driving force for solidification.
FREE ENERGY OF FORMATION OF A NUCLEUS AS FUNCTION OF ITS RADIUS:
- There are three ways in which a solid can form: homogeneous nucleation, heterogeneous nucleation, and epitaxial growth.
- Homogeneous nucleation occurs when there is no foreign body (mold wall, solid particle in the melt, etc.) on which to form the solid.
- Figure shows the balance of the surface tension and the bulk free energy per unit volume, ΔGv, as a function of the size of the nucleus that forms during homogeneous nucleation.
- The ΔGv, value is just ΔG divided by the molar volume of the solid, Vs