Zpf-110 Manual

[Nga Sagastume]

Phasediagrams are the perfect road map to understand the conditions for phase formation or transformation in any material system caused by variation of temperature, composition, pressure or any other viable state variable. That is why one can use phase diagrams as the starting point for materials design and process optimization by manipulating composition and processing variables to achieve the desired microstructures. That applies to all sorts of materials, such as alloys, ceramics, semiconductors, cement, concrete etc., and to a multitude of processes, such as melting, casting, crystal growth, joining, solid-state reaction, heat treatment/phase transformation, oxidation, vapor deposition, and so on.

Starting from the very basics of phase diagrams and phase equilibria we will go through reading unary, binary and ternary phase diagrams, including liquidus projections, isothermal and vertical phase diagram sections. Application examples are directly derived from these phase diagrams of Fe, Cu-Ni, Mg-Al, and Mg-Al-Zn. The use of stable and metastable phase diagrams and appropriate choices of state variables are explained for the relevant Fe-C system. The most useful zero-phase fraction lines in phase diagram sections of multicomponent systems are made clear by coming back to the Cu-Ni and Mg-Al-Zn systems. Finally, thermodynamic solidification simulation using the Scheil approximation in comparison to the equilibrium case is covered in context of multicomponent multiphase solidification. In many of the embedded application examples, explicitly demonstrated on real material systems and various materials processes, the path from initial off-equilibrium state towards equilibrium is emphasized.

This work is written in the context of state-of-the-art thermodynamic software packages for phase diagram calculation, such as Pandat,[5] Thermocalc[6] or Factsage,[7] which are all based on the Calphad method.[8] The intention is to assist in the proper interpretation of results obtained from such calculations, not in the operation of such calculations. In fact, all diagrams presented in this work are produced by thermodynamic calculations using the Pandat software package[5] and the quantitative thermodynamic database for Mg-alloys, PanMg,[9] unless noted differently. The examples shown are for metallic systems and related alloys, just to keep this work concise. The basic approach outlined here is directly applicable for all inorganic materials, as indicated above. Examples of binary phase diagrams are found even for organic[10] and polymeric[11] materials, however, not as widespread as for inorganic materials. The only condition for the applicability of phase diagrams as a powerful tool in materials science and engineering is that the concept of phase, as defined above, is viable for the material under consideration.

The most important distinction in this field is the one between property diagram and phase diagram. Figure 1 shows the enthalpy of pure iron as function of temperature at constant pressure of 1 bar. It is a property diagram; the areas in that diagram have no meaning. Only the curve has a meaning. It is labeled with the different phases associated with the three different continuous parts of the enthalpy curve, BCC (α), FCC (γ), and BCC (δ), where BCC and FCC are a shorthand for the different crystal structures, body centered cubic and face centered cubic, respectively. Figure 1 is not a phase diagram.

The industrial importance of steel basically originates from a peculiarity of the phase diagram in Fig. 2, the occurrence of two separate regions of BCC, one at high temperature BCC (δ), and one at low temperature, BCC (α). Normally the more densely packed FCC crystals should be stable down to room temperature. However, the less densely packed BCC iron crystals undergo magnetic ordering, which significantly decreases the values of G BCC (T), making the BCC phase stable again at lower temperature. That results in the occurrence of the γ/α phase transition of iron, which may be modified and tailored by addition of carbon and other alloying elements in steel. Properly designing this γ/α solid-state phase transition forms the basis for controlling the variety of microstructures in steel, from the as-cast structure through heat treatment or thermo-mechanical processing. Without the FCC (γ)/BCC (α) transition in Fig. 2 at ambient pressure man could not produce steel.

All other unary, or one-component, P-T phase diagrams can be understood following the example of iron. The rules and the resulting topology are identical if the component is an element or a pure substance, defined as a compound that cannot change composition. A prominent example is the phase diagram of pure H2O, shown in many textbooks with the phase regions of vapor, water, ice and, at high pressure, the various crystalline ice phases. However, it is quite a special case because all the phase transitions of H2O (e.g. melting, evaporation) are congruent ones, where at any two-phase equilibrium the compositions of both phases are identical. That is clearly fulfilled for all phases of H2O.

Therefore, the compound SiC does not form a unary P-T phase diagram, in contrast to the compound H2O. In order for the simple topology of Fig. 1, observed for any element, to prevail also for a compound it is necessary that this compound exists in all phases under all conditions (at all state points) as stable single phase, making all phase transitions congruent. Otherwise the topology of the P-T phase diagram will be more complex. The important distinction between property and phase diagram, however, is generally valid and must be kept in mind also for multicomponent systems.

One might think that FCC with its lower, more negative, value of G is stable. However, an even lower value of G system is achieved if one part of the atoms is distributed on a Ni-poor Liquid phase and the rest on a Ni-rich FCC phase. Under the constraint of materials balance 0.428 mol of Liquid with 52.6 at.% Ni and 0.572 mol of FCC with 65.6 at.% Ni may form, maintaining the overall 60 at.% Ni of the system. For the individual phases we get

The total Gibbs energy of this two-phase system at 1320 C with overall 60 at.% Ni and total amount of 1 mol of atoms equals the sum of the Gibbs energies of all present phases multiplied by their phase amount:

In addition the phase fractions may be easily calculated by the lever rule, derived from the materials balance. The closer the state point is located to one end of the tie line the larger the fraction of this phase is. In our example the phase fractions, f phase, are calculated from the compositions of system and phases as follows:

Another very useful application of the phase diagram is materials compatibility and materials bonding. Assume we drop a piece of solid nickel, preheated to 1320 C, into pure liquid copper kept in a furnace at constant 1320 C. In a first step we plot the initial status of materials into Fig. 3, one point at pure Cu the other at pure Ni, both at 1320 C. The phase diagram tells us that there is no tie line between these points, thus, there is no equilibrium and therefore a reaction is expected. In a second step we calculate or estimate the overall composition of this (closed) system. Assume the piece of nickel is small, amounting to only 10 at.% Ni in our Cu-Ni experiment. This defines the state point at 1320 C and 10 at.% Ni, which is in the single-phase liquid region in Fig. 3. That is the direction into which the reaction between the initial materials is expected to go and also the final state of the system; the solid piece of Ni will completely dissolve in the melt.

If our experiment is performed the other way around, pouring liquid copper in a nickel crucible at 1320 C, the first two steps in applying the phase diagram are done in the same way. If we have a thin Ni crucible, amounting to a total of 10 at.% Ni in the system (as before), the dissolution will produce a hole in the crucible and a mess in the furnace. With a thick Ni crucible and, say, total 85 at.% Ni of the system, that state point is in the single-phase FCC region in Fig. 3. Now, in a third step, we use this knowledge to assess a realistic reaction path. Ni from the crucible will dissolve in the liquid Cu, shifting its composition towards the liquidus point. Concurrently, some Cu will dissolve in the FCC-Ni, shifting its composition in the direction of the solidus point, in a much slower solid state diffusion process. During that process the amount of liquid decreases because Cu is taken out of the liquid. A composition gradient builds up in the crucible, and at the Liquid/FCC interface a local equilibrium is attained with the composition of the two phases given by the tie line in Fig. 3. Eventually, the amount of liquid goes to zero, with the last drop of liquid at 52.6 at.% Ni and the FCC at 65.6 at.% Ni at the last contact point. Now the system is isothermally solidified. The composition gradient in the single-phase (not yet homogeneous!) FCC crucible is eventually leveled out by solid state diffusion until the equilibrium dictated by the state point at 85 at.% Ni and 1320 C is attained in the homogeneous FCC.

The region where the three phases HCP + L + γ are in equilibrium at 436.3 C is marked by the line, with dots indicating the phase compositions. This is the intersection of three two-phase equilibria, HCP + L, HCP + γ, and L + γ, which may also be seen as the overlap of these three tie lines. This three-phase equilibrium region is a true line (1D), while all the two-phase and single-phase regions are areas (2D), remembering that even the β and ε regions will extend under sufficiently high magnification. That is why the three-phase equilibrium is an invariant equilibrium, temperature and all phase compositions are fixed. All other three-phase equilibria in Fig. 4 follow the same rules.

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