MÜGE BAŞARAN 030090704 WEEK 10 (1)

(1) NONEQUILIBRIUM SOLIDIFICATION

Group: material | transformations

There is no old definition

NEW DEFINITION

Nonequilibrium conditions vary widely from process to process, from manufacturer to manufacturer for a given process, and from day-to-day (and batch to batch within a day) for a specific process performed by a specific manufacturer. There are literally an infinite number of ways in which conditions can differ from equilibrium. and only one way there can be equilibrium. To take into account the effects of nonequilibrium is not simple, and the best that can be done is to model some cases as boundary (or bounding) conditions. Because, as engineers, you will spend much of your working life dealing with nonequilibrium, we will look at one example of how nonequilibrium results in different microstructure during the solidification of a single-phase alloy now.

So, let us reconsider the case of nonequilibrium solidification of a single-phase alloy in an isomorphous binary system to see how the microstructure that develops differs from equilibrium. 

Figure 13.18. Cooling from the melt will occur too fast for equilibrium to prevail during the process of solidification. The boundary conditions that will be imposed (because nonequilibrium always requires some statement or assumption about the bounding conditions) are:

(1)  complete mechanical stirring of the liquid will assure uniform composition throughout the volume of liquid present (i.e., we are not relying on diffusion of atoms in the liquid to keep the composition uniform) and

(2)  there will be no time for any diffusion in the solid state, so the composition of solid at every stage of its formation will remain unchanged. In many references on solidification in general, and welding in particular, this set of boundary conditions is known as Case 2 (with equilibrium solidification being known as Case 1).

·         Above the equilibrium liquidus temperature. T_liquidus entire volume of material is liquid L of composition C_o for an alloy of composition C_o.

·         Upon reaching T1, just below T_liquidus, the first equiaxed particles (or grains) of solid of composition C_s, begin to form randomly throughout the volume of liquid I. under homogeneous nucleation. Because not all of the solute B dissolved in the L at C_o can be accommodated in the new solid (i.e., C_s, < C₀), the excess solute B rejected into the liquid at the S–L interface is assumed (here) to be immediately mechanically mixed through the entire liquid, raising its composition slightly above C_o to C_L1.

·         As the temperatures continues to fall farther below T_liquidus say to T₂ the new solid that forms on the outside of all of the original particles of solid, along with some additional new particles of solid, has composition C_s2’ which is higher in solute B than C_s, as the result of it having been formed from liquid containing more solute B than C_o. Because there is assumed to be no diffusion in the solid state, this new layer of C_s: forms over the earlier particles of C_s1. resulting in a cored structure. Rejection of solute B as this new layer of solid forms raises the composition of the liquid L to C_L2—everywhere due to instantaneous mechanical stirring.

·         The average composition of particles or grains of the solid formed to this point (i.e., between T_liquidus and T₂} is not C_s2 however, because the cores of the particles or grains contain less solute R than C_s2, (i.e., C_s1 in this case). Hence, the average solute composition of all of the solid formed to this point lies somewhere between C_s1 and C_s2 depending on the slopes of the liquidus and solidus lines and on the relative volume fractions of each in the particles or grains. indicated here by an X.

·         Upon reaching the equilibrium solidus temperature. T_liquidus, at which solidification would be completed under equilibrium, here called T3, the new solid forming from liquid (as an outer layer on all previously formed grains, as well as forming some new grains by further nucleation) with the composition C_L3, has the composition C_s, = C_o. Once again, the average composition of all of the solid formed to this point (i.e., to T3) lies between C_s2 and C_s, = C_o, here shown by the X at T₃

·         Because the total composition of all of the solid formed has not reached C₀ (the composition of the starting liquid L), the material or mass balance is not correct and, thus, solidification cannot actually be completed. For solidification to be completed, the average composition of the solid (grains) must be C_o.

·         By extending the average solid composition line (shown bold and dashed) until it crosses the composition line at C_o, it can be seen that solidification under these nonequilibrium conditions is not actually completed until the temperature reaches T4. At T4, the composition of the last solid layer formed is C_s4 having formed from highly solute-enriched C_L4.

The consequences of such nonequilibrium solidification of an alloy are: ( I) resulting grain structure (actually, dendritic structure in real castings or welds) will be cored, with varying composition (and, thus, properties) from solute-lean regions near the grain centers to highly solute-enriched at grain boundaries, often with weak or brittle grain boundary regions; (2) solidification well below the equilibrium solidus tem-perature, typically 50 to a couple of hundred degrees C (90 to several hundred degrees F) for real alloys, depending on their melting ranges: and (3) unexpected remelting (upon reheating in service, for example) at grain boundaries. Unfortunately, such microsegregation of solute during nonequilibrium solidification is a natural consequence of solute redistribution and is largely unavoidable. There are, in fact, additional complications with nonequilibrium, because deviation from equilibrium shifts transformation temperatures (i.e., phase boundary lines) on equilibrium phase diagrams. Nonequi-librium heating shifts transformation temperatures upward, more for faster heating rates, whereas nonequilibrium cooling shifts transformations downward, more for faster cooling rates. The effects of cooling are generally greater than the effects of heating, because it is easier to cool rapidly than to heat rapidly. Shifting phase transformations require phase boundary lines to change in slope and extend into the normally adjoin-ing phase region, thereby shifting the compositions of the phases that form also. In rare cases, extreme nonequilibrium solidification can result in nonequilibrium metastable phase formation, but this is rare. Not so during nonequilibritun solid-state transformations, however.

(Robert W. Messler, The Essence of Materials for Engineers, pg.391-393)