Mg-Al-Zn Phase Diagram
Isothermal and Vertical Sections
In a ternary system, composed of three components, we select the state variables T, P, and composition. We assume constant total pressure, high enough to suppress any gas phase formation in all of the following. At constant temperature, say T = 500 °C, only two variables are left to fix the state point of the system. In the Mg-Al-Zn system we may select the contents of Al and Zn, thus fixing [wt.% Mg] = 100 − [wt.% Al] − [wt.% Zn]. The natural way to plot these two variables is in rectangular coordinates as shown in Fig. 7(a). Only the right-angle triangle area highlighted by the colored phase regions corresponds to real alloys; outside that range at least one composition becomes negative. The compositions on the straight line [wt.% Mg] = 0 are in the binary edge system Al-Zn. In order to obtain symmetry among the components the y-axis is tilted to get the equilateral or Gibbs triangle in Fig. 7(b), generally used if the complete composition range is covered. For enlargements of small composition ranges the rectangular diagram is much more useful, the tilted axis is disapproved for partial diagrams. Both figures are true phase diagrams because any point in the triangles corresponds to a fixed state point with unique constitution. That is shown for the intersection of the dotted lines for 30 wt.% Al and 20 wt.% Zn, where the single phase liquid is stable. At 500 °C in the Mg-Al-Zn system five single-phase regions are observed, L, HCP, FCC, τ, and MgZn2, the latter developing as a line compound due to significant solubility of Al in binary MgZn2. The term “line compound” refers to the one-dimensional extension of the single-phase region in the phase diagram section under consideration; it is also used for the phases β and ε in Fig. 4. A compound with no solubility range for any component is denoted as “stoichiometric compound”; the phase ε is an example that will be discussed in Fig. 8.
Coming back to the isothermal section of the Mg-Al-Zn phase diagram at 500 °C in Fig. 7, a number of two-phase regions, such as L + FCC, span between the solubility limits of single phases, marked by series of selected tie lines. For example, the tie line passing through the state point of the Mg10Al70Zn20 (wt.%) alloy indicates the compositions of the equilibrium phases L (50.2 wt.% Al, 33.4 wt.% Zn) and FCC (86.7 wt.% Al, 8.6 wt.% Zn). The lever rule can also be applied here, providing the mass fractions of the two phases, f
Liquid = 0.458 and f
FCC = 0.542. This is easily checked by the materials balance for Al, 50.2 × 0.458 + 86.7 × 0.542 = 70.0 wt.% Al, and analogously for Zn or Mg. Finally, two three-phase regions occur, marked by the red tie triangles. That completes the entire area of the phase diagram with unique constitution at each state point.
The isothermal section at 400 °C is shown in Fig. 8. At this lower temperature the extension of the single-phase liquid region shrinks into two separate patches and three more solid phases become stable, γ, ε, β, and Mg2Zn3. Note that the solid phases at 400 °C may be categorized as follows: HCP and FCC are terminal solid solutions, extending from the pure components; the Zn-rich HCP phase region is very small because we are just below the melting point of Zn at 419.5 °C. Another useful notation for these terminal solid phases is (Mg) and (Zn) for HCP and (Al) for FCC. We have two separate stable patches of the same phase HCP, just as we have two separate patches of L. Next we have γ, β, MgZn2, and Mg2Zn3, binary intermetallic phases with significant ternary solubility; only γ shows also a significant binary solution range, the other three appear as line compounds in the ternary. Next there is ε, a binary intermetallic phase that remains stoichiometric, visible only as a point on the Mg-Al binary edge. Finally there is τ, the only truly ternary solid phase since it does not connect in a continuous single-phase range to any of the binary edges, not even at different temperature. Another ternary solid phase, φ, will form below 387 °C.
Let us have a closer look at the three-phase region FCC + τ + β, marked by one of the red tie triangles in Fig. 8 with one apex at each of these single-phase boundaries. The state point of an example alloy Mg30Al50Zn20 (wt.%), marked by the crosshairs, is located inside this region, indicating that this combination of three phases is the most stable configuration of distribution of atoms on available phases with the absolute minimum of the Gibbs energy of the system. The composition of each phase is fixed and may be read at the corners of the tie triangle, FCC (88.6 wt.% Al, 1.6 wt.% Zn), τ (42.3 wt.% Al, 25.9 wt.% Zn), and β (55.9 wt.% Al, 10.2 wt.% Zn). The mass fractions are f
FCC = 0.104, f
τ = 0.681, and f
β = 0.215, again determined by the lever rule. For any other alloy composition located inside this three-phase region FCC + τ + β the phase compositions remain fixed, only the phase fractions change. The closer the state point moves to a corner of this tie triangle the larger the fraction of this phase becomes.
One may envisage the complete ternary Mg-Al-Zn phase diagram (at constant pressure) as a prismatic 3D model, spanned by the triangular composition base and a vertical temperature axis. Each point inside that prism is a fixed state point with unique constitution: Type(s), composition(s), and fraction(s) of phase(s) are given by the equilibrium condition of Gibbs energy minimum. The isothermal sections in Fig. 7 and 8 form one way to produce a 2D section through the prism for quantitative display of the phase relations. The other way is the vertical section, also called T-x section or isopleth. If the interest is in phase relations along a series of alloys at various temperatures, the 3D prism will be sectioned parallel to the temperature axis along the composition line defined by the series of alloys. The result is a 2D section, such as in Fig. 9 for the example of ternary alloys at constant 20 wt.% Zn. The selected composition line along the alloy range Mg80Zn20-Al80Zn20 (wt.%) is also indicated by the dotted lines in Fig. 7 and 8. Along this line at 500 °C the same phase relations appear in Fig. 7 and 9. The stable regions of the liquid phase, or the FCC phase, are easily discerned in both diagrams.
The important distinction occurs in the two-phase region, such as L + FCC. Figure 7 clearly shows that for the alloy Mg10Al70Zn20 the phase compositions of L and FCC are off the section plane at constant 20 wt.% Zn, thus, the phase compositions cannot be read in Fig. 9. That is generally true for all two- or three-phase regions in a vertical section: Only the type of phases, not the composition of phases can be read from the vertical section. Therefore, the lever rule cannot be applied to determine the phase fractions. The complete constitution information can only be read from the isothermal section because all the tie lines are in the plane of that 2D section, and that is always the case for ternary systems.
In very rare and special cases all the tie lines may also happen to lie inside the plane of the vertical 2D section. In that case it is also necessary that the end points of the composition section are in a single-phase region, α or β, for example of a stoichiometric melting compound or a pure component. Not even that condition is met for the end point Mg80Zn20, that alloy is two-phase HCP + L. If all the tie lines are inside the plane this vertical phase diagram section between the phases α and β is called a pseudobinary system. It may be read like a binary system α-β, and it will provide the full constitution information on type, composition, and fraction of phases. Such pseudobinary systems are sometimes found in systems between stoichiometric oxides, such as Bi2O3-Fe2O3 in the Bi-Fe-O system,[18] or if a complete series of solid solutions exist between congruent melting compounds, such as GdA12-NdA12.[19] In the Mg-Al-Zn system any composition section will cut at least one tie line or tie triangle, thus, no pseudobinary section exists.
For the isothermal or vertical 2D sections, such as in Fig. 8 and 9, the simple rule outlined above is again helpful: If we cross a phase boundary we either gain a phase or loose a phase. Start by reading the phase regions at 400 °C and Al80Zn20 in the single-phase FCC region in Fig. 9. With decreasing Al-content, at constant 20 wt.% Zn, we cross the phase boundary at 79.5 wt.% Al and must enter a two-phase region. From Fig. 8 it is obvious that this is the FCC + MgZn2 region, so we have gained the phase MgZn2, as correctly labeled in Fig. 9. The next boundary is at 75.9 wt.% Al and, according to the rule, it might be single- or three-phase. From Fig. 8 we see that this is the narrow three-phase region FCC + MgZn2 + τ, so we have gained the phase τ. At 75.3 wt.% Al we cross the boundary to the wide region labeled as FCC + τ in Fig. 9, so we have lost the phase MgZn2, in consistency with Fig. 8. Now it becomes obvious that the next phase boundary at 53.7 wt.% Al in Fig. 9, where we gain the phase β, reflects just the cut through the FCC + τ edge of the tie triangle FCC + τ + β in Fig. 8. All phase compositions of FCC, τ, and β, are way off the vertical section. For the example alloy Mg30Al50Zn20 compositions can only be obtained from the isothermal section, as detailed above. One may continue reading the 400 °C line in Fig. 9 and add labels to all phase regions in consistency with Fig. 8 and the “gain/loose-a-phase-rule”.
Invariant Equilibria
Invariant equilibria in the Mg-Al-Zn system generally comprise four phases and occur at a fixed temperature. Five phases may only occur if we include the gas phase at a distinct pressure, but that is not discussed here. In the 3D prism diagram the four-phase region forms a 2D area, spanned by the fixed composition points of the four phases. Precisely four different three-phase triangles merge at this temperature because each of the four phases, at unique composition, is in equilibrium with the three others. This four-phase plane may appear as a tetragon or as a triangle. The latter case is seen if one composition point is inside the largest three-phase triangle. One may see a glimpse of this four-phase plane in the vertical phase diagram section as a line, where the vertical section cuts through this tetragon or triangle.
In Fig. 9 this part of the four-phase region L + FCC + τ + β is seen as the horizontal line at 447.07 °C from 47.3 to 53.4 wt.% Al. That means that any alloy in that composition range will, on cooling from higher temperature, experience this invariant equilibrium. It is associated with a unique invariant reaction, in this case
$$ {\text{L }} = {\text{ FCC}} + \tau + \beta \quad {\text{at 447}}.0 7\,^\circ {\text{C}}, $$
(9)
which is a ternary eutectic reaction. It is emphasized that none of the phase compositions is located on that horizontal line in Fig. 9. The small part of the graph around that line appears misleadingly like a “binary eutectic”. The appearance may differ if the vertical section is selected in a different direction in the 3D prism. In fact, the composition of L is inside the largest three-phase triangle FCC + τ + β, forming the boundary of the four-phase plane. In any ternary eutectic the liquid completely decomposes into three phases. Here the reaction products are FCC + τ + β at 447.07 °C, so there is only one possible exit from this reaction, the FCC + τ + β region in Fig. 9.
The second possible reaction type occurs in the four-phase region L + γ + HCP + φ, seen as the horizontal line at 365.34 °C from 9.2 to 29.5 wt.% Al in Fig. 9. All alloys in that composition range will go through the invariant reaction
$$ {\text{L }} + \gamma = {\text{ HCP }} + \varphi \quad{\text{at 365}}. 3 4\,^\circ {\text{C}}, $$
(10)
which is a ternary transition-type reaction. The liquid reacts with γ to form HCP + φ and, depending on the initial phase fractions of L and γ, there are two possible exits from this reaction, either HCP + φ + L or HCP + φ + γ, because some unreacted excess of an initial phase may remain together with the newly formed phases HCP + φ. If the initial fractions of L + γ are exactly balanced a special exit into the two-phase region HCP + φ is possible, as seen in Fig. 9. It is obvious that the general “gain/loose-a-phase-rule” cannot hold at such special points, here the transition from the phase region L + γ + HCP + φ occurs to HCP + φ. The rule only holds for extended boundaries, not for special points. More examples of special points are presented in the next paragraph. In a transition-type reaction the composition of L must be outside the three-phase triangle of the solid phases, here γ + HCP + φ, and the boundary of the four-phase plane is a tetragon.
The last possible reaction type occurs in the four-phase region L + τ + γ + φ, seen as the horizontal line at 387.37 °C from 30.2 to 31.7 wt.% Al in Fig. 9. Any alloy in that composition range will go through the invariant reaction
$$ {\text{L }} + \tau + \gamma = \varphi \quad{\text{at 387}}. 3 7^\circ {\text{C}}, $$
(11)
which is a ternary peritectic reaction. The three phases L + τ + γ react to form φ. Depending on the initial phase fractions there are three possible three-phase exits from this reaction, either φ + L + τ, or φ + L + γ, or φ + τ + γ. In the peritectic reaction type the composition of the formed phase φ must be inside the three-phase triangle of the reactant phases, here L + τ + γ, and the boundary of the four-phase plane is this triangle.
In Fig. 9, because of the selected composition cut through this four-phase plane, one sees only two of the possible three-phase exits to lower temperature, φ + L + γ, and φ + τ + γ. In between there is the special case that reaction (11) ends with the two-phase equilibrium φ + γ because the initial phase fractions of L and τ are balanced, so they react completely. A very special case, not seen in Fig. 9, occurs if all initial phase fractions are balanced and the reaction ends with complete formation of single-phase φ only. That requires the alloy composition to be exactly identical to the unique composition point of φ at 387.37 °C; this temperature is also the thermal stability limit of φ. Upon heating such an (equilibrated) single-phase alloy it will decompose at 387.37 °C into the three phases given by Eq 11, a process that can be viewed as a reverse eutectic type reaction. A note of warning regarding kinetics should be considered. Similar to the binary peritectic/peritectoid reaction the ternary one in Eq 11, and to some extent also the transition-type reaction, Eq 10, slows itself down because the solid product phase forms a growing diffusion barrier between the reactant phases. As opposed to that, the ternary eutectic reaction is more likely to occur completely even at faster cooling rates due to its decomposition type.
It is emphasized that only three types of invariant reactions may occur in ternary systems: eutectic type (decomposition), transition-type, and peritectic type (formation). Depending on the kind of phases involved one may find special names, such as eutectoid if a solid phase decomposes into three others. The important point is to realize which type of invariant reaction (not which name) occurs because it provides an indication if this reaction is likely to occur under real world cooling conditions.
If all phases involved in a ternary invariant reaction were exactly stoichiometric phases the above discussion reduces to the simple classical chemical reaction equation, such as A2B + B2C = B3C + A2. That highlights the power of the phase diagram approach. Even if only one of these phases, e.g. A2B, is a phase with distinct solution range the classical chemical reaction equation becomes very cumbersome or inapplicable. Moreover, the information about neighboring three- and two-phase relations cannot be given that way. The phase diagram, however, provides the comprehensive information on all equilibrium phase relations and reactions/transformations in a clear, concise and precise manner.
Liquidus Projection
For melting and solidification processes the equilibria of the liquid with solid phases are especially important. The extensions of the liquidus lines from the binary edges form the liquidus surface in the 3D prism and its projection to the composition triangle forms the liquidus projection, shown in Fig. 10. It immediately answers the question which phase crystallizes primary. For any alloy composition in the region marked “HCP” this is the primary phase that may grow freely in the melt, thus forming a typical dendritic or globulitic microstructure. In the adjacent primary γ region this intermetallic will form first from the melt. At the intersection line the liquid phase compositions are in equilibrium with both HCP and γ; the liquid is double saturated. This intersection line displays the projection of the monovariant three-phase equilibrium L + HCP + γ. It emerges from the Mg-Al edge were it starts as the binary invariant eutectic reaction L = HCP + γ at 436.3 °C, proceeding to lower temperature into the ternary. At 400 °C it is seen as the tie triangle L + HCP + γ in Fig. 8. The triangular shape tells that it is monovariant, at a given temperature all three phase compositions are fixed. Only the trace of the apex at phase L is plotted in the projection in Fig. 10, the solid compositions would make that graph too busy. Each primary phase region is confined by such monovariant lines of double saturated liquid, or by the binary edges.
At an intersection point of different monovariant lines we have a contact point of three primary phase regions, such as FCC, τ, and β. That unique liquid composition is (triple) saturated with all three phases, thus forming the four-phase equilibrium L + FCC + τ+β. That is exactly the invariant reaction of Eq 9, associated with the unique temperature of 447.07 °C in the projection. Therefore, Fig. 10 reveals all the liquid compositions involved in invariant equilibria. One simply reads the types of the three adjoining primary regions, e.g. τ, γ, and φ to see the composition of L in the invariant L + τ + γ = φ at (34.7 wt.% Zn, 14.7 wt.% Al) and 387.37 °C, discussed in Eq 11.
In total there are 12 different invariant four-phase reactions in the Mg-Al-Zn system corresponding to the intersection points in Fig. 10. The closing of the tiny primary field of Mg5Zn2, at 52 wt.% Zn, 0.1 wt.% Al and 338.9 °C, produces the 12th point, which cannot be discerned on the graph. These invariant reactions are connected by the network of monovariant three-phase equilibria, some of them ending in the binary edges, some just occur in the ternary, such as L + τ + MgZn2. This line offers a special case, the maximum at 530.1 °C with liquid composition (13.4 wt.% Al, 64.4 wt.% Zn). The maximum occurs because the tie triangle L + τ + MgZn2 degenerates to a line and at exactly this point the three-phase equilibrium becomes a unique and invariant three-phase reaction,
$$ {\text{L }} = \tau + {\text{ MgZn}}_{ 2} \quad {\text{at 53}}0. 1\,^\circ {\text{C}}. $$
(12)
This reaction is of the eutectic type because the liquid composition is located exactly in between the τ + MgZn2 tie line. Therefore, the liquid may decompose into these two solid phases without any composition shift. That explains why this reaction is invariant, similar to the binary eutectic. Other double saturated lines show a monotonous temperature variation only, such as L + MgZn2 + FCC from 475.9 °C down to 355.4 °C at the Zn-rich end. One should be careful in assigning a reaction type because it may change within the monovariant range and the transition from eutectic to peritectic type may be hard to detect especially if significant solid solubilities are involved.[2] The safest way, also for multicomponent alloys, is to calculate the phase fractions with a small decreasing temperature step for a given alloy composition and temperature. The shrinking phases go to the left hand side and the growing phases to the right hand side of the reaction equation, valid only at that state point. It can be shown that even within a given tie triangle the transition from eutectic (α = β + γ) to peritectic (α + β = γ) type may occur by just changing the alloy composition at fixed temperature. Therefore, one should generally denote just the three-phase equilibrium (α + β + γ) unless it degenerates to an invariant reaction at a minimum or maximum temperature, such as in Eq 12.
A 2D graphical display of the network of monovariant three-phase equilibria, connecting the invariant reactions of the binary edge system with those in the ternary system, can be given by the “Scheil Reaction Scheme”.[20] It may be used to prove the consistency of the phase diagram; for example the number of three-phase equilibria meeting at a four-phase reaction must be four, and so on. An established notation for invariant equilibria and liquidus projections is developed[21] that covers also more complex cases, such as liquid miscibility gaps intersecting primary crystallization fields in a liquidus surface.
A particularity of the primary regions of φ and τ in Fig. 10 is that they do not touch the binary edges. That may be seen as another indication that φ and τ are true ternary solid phases, however, the decisive distinction is that their solid solution ranges do not touch the binary edges at any temperature. As additional information the projections of selected isothermal liquidus lines are plotted in Fig. 10. These contour lines give a better impression on the shape of the liquidus surface in the 3D prism phase diagram. Moreover they are used to read, or interpolate, the liquidus temperature of a given alloy in addition to the type of primary phase that starts crystallizing at that temperature.
Phase Diagram Applications Exemplified with Mg-Al-Zn
For melting processes the completely molten (single-phase liquid) region needs to be identified and that is obviously done from Fig. 7 to 10. For solution heat treatment the single-phase solid regions must be known, given in Fig. 7 to 9. Similarly the constitution of a ternary multiphase material is read from these diagrams to answer the question if the observed phase assembly is a stable one, or which assembly may be expected after equilibration. For solidification applications the important information on liquidus temperatures and primary crystallizing phase has been discussed above. The equilibrium melting/freezing range may be read from vertical sections, such as in Fig. 9.
A very powerful tool is the calculation of phase fractions (and compositions) of a fixed alloy composition of interest, such as shown in Fig. 5 and 6 for the binary example. That will be demonstrated in detail in the section on Scheil and equilibrium solidification simulation. In principle the equilibrium phase fractions could be read from a series of isothermal sections using the lever rule. That is only simple if the solid phases are all stoichiometric, in that special case even the liquidus projection and knowledge of the stoichiometries is sufficient. In a real world alloy system, with significant solid solubilities, the tie lines and their directions change with temperature, making this a very tedious manual task even if many isothermal sections in small temperature steps are available. The thermodynamic calculation using a software package and a reliable database is highly recommended for that application.
Another very important application is materials compatibility, applied in interface reactions, joining, durability of refractory crucibles for alloy melting, attack of slag, and so on. Initially two materials A and B are brought in contact and heated. For example, if the alloy plate composed of Mg80Zn20 is clamped to another one, Al80Zn20 (wt.%), the phase diagram in Fig. 9 reveals that in the temperature range 300-400 °C various product phases may form between the materials, and also partial melting may occur. At 400 °C more details are seen from Fig. 8, the dotted line at 20 wt.% Zn indicates all possible overall compositions of the clamped material system. All the phase regions crossed by that line indicate potential temporary product phases and the state point, calculated from the overall composition of the two plates, gives the final equilibrium state.
As another example, consider a thin film layer of an alloy Mg60Zn40 (wt.%) deposited on a disk of pure Al and then heating the coated disk at 400 °C. We apply the same technique as in section 3.2, the Cu-Ni example. In a first step we plot the initial composition of materials into Fig. 8, one point at pure Al the other at alloy Mg60Zn40. 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, which must be on the straight line between the starting points. For a very thin film our state point will be in the single-phase FCC region, thus, after equilibration all the Mg and Zn atoms from the film will be dissolved in the (Al) disk. The disk converts to a solid solution that is eventually homogenized by solid state diffusion. Temporarily a partial melting of the film may occur, because that point is in the L + HCP region. After some Al from the disk went into the layer even a temporary complete liquid layer might form on the disk. Subsequently a number of reactions may occur, involving the phases τ, γ, and β, until the equilibrium state, dictated by the state point, is reached. With growing film thickness the state point may be located beyond the (Al) solvus in the adjacent two-phase region FCC + τ, and the τ phase is expected as final secondary phase on the saturated (Al) solution phase. With even larger film thickness, say total mass 5 g film on a thin Al disk of 5 g, the state point is located at Mg30Al50Zn20 (wt.%) and the three-phase equilibrium phase assembly FCC + τ + β, well discussed above, constitutes the final state of the reaction.