Figure 1: Two examples of microstructures formed from the solidification of oxide melts (slags). Both images are Back scattered electron mode SEM images. The left image shows a melt quenched to a glass with prominent round bubbles but virtually no internal crystallisation. The right image shows a fully crystallised slag, with three main solidification phases (A, B, C), and only a small amount of interstitial residual material (marked with labels).

Fig. 1 illustrates the importance of the rate of change by comparing microstructures from the solidification of melts formed under two very different cooling rates. Depending on the cooling rate, a melt can either be quenched completely into a glass as shown in the right case, which is a silicate (i. e. oxide, slag) melt rapidly quenched from about 1500 °C, cooled so fast that it reached the glass transition temperature without any significant nucleation and growth of equilibrium crystalline phases. The material is as homogeneous as the original melt was, showing only a set of large bubbles as structure. In contrast, the left image also shows an oxide melt – also a slag, just with a somewhat different composition. Yet this slag cooled slowly from similar temperatures, and then was held at a temperature close to its solidification point for an extended time. As a result, it has nearly completely crystallised into three solid phases that have different brightness on this SEM BSE image and are marked as phases A, B, and C. None of the phases shows any preferred morphology given by its inner crystallography. Irrespective of phase, there is a space filling assembly of grains which tend to have rounded or even polygonal shapes (in microstructural terms, such grain shapes are called xenomorphic, stating that their shape is not internally determined). Neither by shape, nor by distribution, grain size or any other arrangement can an argument be made which of these phases crystallised first and which later, even though the overall composition of the material is such that the phases must have had a sequential order of crystallization. There is only a small amount of interstitial material of a fourth kind that shows a fine-grained intergrowth (see marking) which could be interpreted as possible eutectic structure, indicating that the holding temperature of the entire material may have in fact been just above its solidus. The entire field of view approaches what is called a batch equilibrium case, in which the material reaches a full equilibrium state at the given set of conditions, both chemically but also in terms of its microstructure (minimization of surface energies, which ends in polygonal microstructures best known from tempered metals). In fact, the right image of a quenched glass could also be called a batch equilibrium case, but there it is metastable – preserved by rapid quenching, the material still shows the (absence of) structure it has as a self equilibrated liquid at high temperature.

This comparison shows how important all three basic parameters are that influence the development of microstrcutures: thermochemistry determining the (successive) phase assemblages; transport properties at every successive set of conditions that determine the scale over which structures can develop; and the rate of change of conditions that can allow of suppress structure formation or obliteration (overprinting) of earlier structures in the history of conditions the material experiences. The observed microstructure of any material is the result of these parameters interacting and must be explained in their terms. In turn, information about each of these three parameters is preserved within the observable structure.

The thermochemistry of phase equilibria in multicomponent systems sets the frame in which the microstructures of a solidifying melt develops. Practically all melts encountered are multicomponent solution phases – whether it is an alloyed metal being cast or salted water on the road to prevent freezing. The rules of crystallisation in such multicomponent systems are the same in any type of material – whether it is water, ceramics or metals. This is shown by the following set of phase diagrams.

Fig. 2 – Ternary liquidus phase diagrams for multicomponent melts. Left – system Al2O3 – CaO – MgO (source : Slag Atlas); right – System Cu-Sn-Ti (Li et al 2018, J. of Alloys and Compounds 735:1374, modified).

Each of these is a ternary liquidus phase diagram of a three component system : The system ACM (ceramic shorthand for Al2O3-CaO-MgO) in the left case, the system Cu-Sn-Ti as a metal alloy case in the right diagram. Each shows which solid phase is the first to crystallize from a melt of the given composition, the so called ‘liquidus phase fields’, separated by cotectics leading to eutectic points. The system ACM (left) is contoured by isotherms showing the temperature at which the liquidus phase starts to crystallise from let at the given composition in the ternary. The right diagram has spared these isotherms for clarity as the system contains very many mixed intermetallics setting up a lot of cotectics (note that the triangle shown is just a fraction of the whole system, centered on the Cu corner). The comparison is meant to illustrate that there is really no difference between ceramic and metallic materials, their structure forming principles are just the same, only the specific material properties differ. Phase diagrams such as this are required and must be understood to be able to deduce the sequence of crystallization that a multicomponent liquid undergoes. A small example is given in the ceramic system: The solid blue circle lies in the MgO primary liquidus field, so crystallises MgO first at the temperature indicated by the isotherm it sits on (2100 ³C here). This depletes the remaining liquid of MgO, so that the composition of the remaining melt shifts away from MgO (blue tie line) until it encounters the cotectic (open blue circle). At this point and temperature it begins to crystallise another phase additionally – here, spinel (MgAl2O4, or MA in ceramic notation).

Fig. 3: The system Al2O3-CaO-MgO (Slag Atlas), with an illustration of the successive types of crystal-melt equilibria during crystallisation of a multicomponent melt, given by the colored points for a starting composition in the spinel liquidus field. The equilibria at the points are named and described at the right side. See text for discussion.

Since the sequence of events in a cooling and crystallizing solution liquid is similar regardless of specific material put in, a terminologic system has evolved in thermodynamics to name and characterize the successive phase transitions, and this is applicable to all. The following illustration explains this, using the above ACM system as example. Following through a composition situated in a random field – here in the spinel primary liquidus phase field, red dot – the system goes through the following set of phase transitions; each marked by where on the side of the reactions the liquid and solid phases are situated. L denotes Liquid, X denotes solid (X1, X2 … are different solid phases):

• L0 → X1 + L1 Liquidus phase crystallization. By removal of solid X1, liquid changes its composition from L0 to L1.

• L0 → X1 + X2 (+ L1) Cotectic crystallization. Two species of solids now crystallize together form a liquid (of which a changed composition remains as L1). Either of X1 or X2 may already have been crystallising previously, but both are now and remain stable.

• L0 + X1 → X2 (+ L1) Peritectic reaction. Liquid reacts with an already-formed crystal X1, to form a new species X2, consuming X1 and liquid (some of which may remain as changed L1).

• L0 → X1 + X2 + X3 … (But no remaining L1)  Eutectic crystallization. Liquid transforms entirely, with all its composition, to a set of solid phases, as much as is needed to entirely comprise its composition. No remaining liquid is left : This is the lowest temperature point of crystallization in its region of a phase diagram.

These types of transformation in the solidifying liquid must be distinguished, each leads to particular microstructures that should be recognized in a material. However, before we can discuss their examples, we must separate the influence of the third factor influencing microstructure – the rate of change. Namely, in solidification, the rate of change (cooling rate, in competition with transport rates) determines to what extent a system remains a single system trying to set up its equilibrium. For example, in the above list of types of reaction, if a material always completely reaches equilibrium with itself in all its parts, then an early formed crystal that later encounters a peritectic reaction, would at a lower temperature, react completely away, and the lower temperature state might not show any hint of the prior existence of this phase. Alternatively, if cooling is rapid and transport is slow, it might survive. This is shown in the following simple sketch.

Fig. 4: Sketch contrasting the microstructure development of crystals growing from melt in a batch equilibirum case, vs a fractional crystallisation case. A simple phase diagram is given on the left side and a sketch of the crystal development is at right.

Consider a simple binary system as shown above, in which there is perfect solubility between the compounds A and B in the solid, as is there also in the liquid. This sets up a solidification along a simple binary, as shown (the famous “banana” type of phase diagram): a liquid with the composition corresponding to the red line, cools, then hits the liquid phase crystallization at temperature T1. A solid solution with a composition on the solid line is formed (indicated by the symbol T1). At the right side of the sketch is shown how this looks like as structure.

As the system cools, two possibilities arise from the contrast between cooling rates and transport rates. Within the solid, diffusion is the means to mass transport. (This is nearly always the limiting factor as within melts, diffusion is more rapid plus there is the mass transport by advection which cannot occur in a solid). So, on cooling, the phase diagram suggests that liquid and melt both change their composition – the melt continually keeps growing new layers of the growing solid, but as it becomes progressively depleted in component A, so does the newly formed layers of solid become progressively depleted in component A. If conditions of batch equilibrium prevail, always all parts of the whole system, including the solid, equilibrate with each other.

This means that transport within the crystal has to be rapid enough to redistribute elements so that the changing increments of solid composition always get homogenized throughout the solid. In this case, the solid always retains a homogeneous composition – as shown in the batch equilibrium case of the sketch – it simply grows, is richer in B at T2, and at some temperature the crystal composition reaches the composition that the liquid initially had – at which time the entire liquid has solidified and no liquid is left. However, if diffusion in the solid is so slow, that the changing increments of solid deposition from the liquid cannot be rehomogenized into the crystal, then the crystal becomes zoned. It becomes heterogeneous in compositition – with a core richer in A, and successive growth zones progressively richer in B. This process is termed fractional crystallization and is shown in the lower set of sketches at right. This condition however means, the crystal is no longer in equilibrium with itself at a given temperature, and the inner parts of the crystal, which cannot chemically communicate anymore with the outside melt, are effectively removed from the overall system composition that governs further solidification. Effectively, the “solidifying system composition” approaches the composition of the fractional melt at each temperature, as each deposited layer of crystal is removed. In that case, the melt can successively deposit fractions bay fractions of always B-richer solid, but there is always some fractional melt left, until the last batch of melt reaches essentially pure B, which solidifies as a terminal layer of pure B around a complex zoned crystal.

Thus, even in the simplest case of L1(solution) → X1(solution), the microstructure that results is governed not just by the phase relations (which set up the bounds) but by the conditions and their rate of change, that is, the history, of the material. This needs to be kept in mind if we will now discuss the microstructures of the above-defined types of liquid crystallization.

Fig. 5: Examples of liquidus phase crystallisation: phenocrysts in a silicate melt (left), morphologically similar dendrite networks in oxide slag and iron melt (right)

The above example shows the structures typical for single-phase liquidus phase crystallization from a multicomponent melt. (They all have been shock-frozen, quenched, at a later stage, which allowed preservation of these structures). The images above are mainly showing ceramic (oxide melt) examples, although the right one shows the same in a metal also.

The most characteristic feature of this type of crystallization is that the liquidus phase forms suspended in a liquid, in which it is the only solid around, that means, its growth is not hindered in any direction by the impingement on other solids or other structures. Therefore, it is free to develop the growth shapes that result from its internal structure (crystallographic symmetry, and the specific free surface energies of the surfaces developed in its habitus). Therefore, phases that grow as liquidus phases tend to grow in ideal shapes. The microstructural term for this is idiomorphic (indicating a shape controlled by its own internal crystallographic habitus). This growth is further modified by the fact that the growth rates of crystals vary over their surfaces. As the exposed crystal structure is different on different crystallographical faces, the energetics of crystal growth varies and therefore the growth rates. Further, the multicomponent melt must remove compounds that are not incorporated into the crystal, which is controlled by diffusion/advection in the melt. It is more difficult to do this along a planar growing surface than along a growing crystal edge; thus, crystal growth is typically fastest at edges compared over surfaces. This leads to the feature that edges can outpace flat surfaces in growth, so that surfaces remain as hollow areas, over which the eges of crystals can then grow back, largely enclosing pools of liquid in the then complex shaped (but idiomorphic) crystal. This is called hopper crystallization and is characteristic for rapid growth. The left image above gives an example of this, where a calcium fluorosilicate grows as liquidus phase (bright) from a fluorinated silicate melt. While all the crystals are idiomorphic it can be seen that they tend to include enclosed areas of melt, indicating fast edge growth and back-growth over slower surfaces. (Note also the visible slight brightness zonation based on varying composition, which confirms the fractional crystallization character of this case). The right case shows a metal droplet (bright, at right) embedded in a silicate liquid (at left) – this is a case of two liquids, where both of them underwent their own liquidus phase crystallization. Only, in the silicate case, CaS (a sulfide) was the liquidus phase, and grew in the visible, dendritic star-shaped mid-grey crystal network. The metal is in this case a Fe-C melt, in which, as is well known, a grafite microstructure results at eventual solidification. However in this case, as the C content of the melt was not very elevated, the melt has an iron phase (austenite) and not a carbon phase as its liquidus phase, and the first-formed austenite crystals in dendritic habitus are visible as bright shapes, set apart from the later formed, grafite containing matrix.

Fig. 6: Examples of liquidus phase crystallisation in metallic melts. Left: a solder alloy (same as in Fig. 2, Li et al op. cit.). Right: as Cast Al-Si alloy, M. C. Flemings 1991.

The above image shows more examples of the morphology developed in liquidus phase crystallization, taken from published literature: a Cu25Sn alloy at left, where the first formed alpha-phase phenocrysts are clearly set apart from the (later solifiied eutectic) matrix, by their size and their idiomorphic shapes. The term phenocryst, originating from the geosciences, denotes such a crystal – a crystal that corresponds to a crystal that was formed from the melt, in the surrounding where it is observed and more or less in equilibrium with it. It most often is also idiomorphic, since as discussed above, free growth in a melt favored the development of idiomorphic shapes. However, solid phases sometimes have only very small differences in growth energetics between different crystallographic faces or edges. This is most often the case in the relatively simple cubic structures of metallic or intermetallic phases (simple compared to the spatial arrangements of polymerized compex anions in some silicates). Then, strict idiomorphy is often not observed as in the case of the Al-Si alloy shown in the lower right image. There, the dendritic growth still gives away the first-formed bright liquidus phase, however one observed the rounded, non-idiomorphic shapes characteristic of many growing metal systems.

The strong influence that the conditions, but also the specific history of conditions can have over the mircostructures associated with even such a simple process as liquidus phase crystallization, are shown by the following example.

Fig. 7: Liquidus phase crystallisation of a steel during continuous casting. At the sidewall, delta-ferrite forms, traced out by tiny Al2O3 particles carried in the liquid. See text. Karnasiewicz (2017)

This case is taken from an industrial steel production (Karnasiewicz 2017 thesis). Here, a relatively simple steel melt that was largely pure Fe (a microallyed cast) was passed through an intermediate vessel (the tundish) into the eventual mould. The image shows the side of the liquid steel volume within the tundish, where it adjoins the refractory that makes up the build of the vessel (lower image edge, the irregular dark areas). As can be expected, this surface is a cooling surface – the passing liquid steel loses some heat to its sides. As the crystallization interval of a microalloyed steel is very tight, often only a few tens of degrees, only a little bit of thermal loss already forces the steel to undergo liquid phase crystallization. In its composition however, iron (delta-ferrite) is the liquidus phase. In samples taken from solidifying steel, which are all cooled and solidified completely when studied under the microscope, it is usually not possible to identify iron liquidus crystals set in a matrix of an interstitial liquid that also crystallises to Fe (etching techniques can sometimes help, but often enough the structure is obliterated by later tempering and processing). In the case shown here however, there was a second phase present in the steel – a small amount of non-metallic inclusions (alumina in this case) , such as they are present in ppm-range amounts in most steel casts. In the present case, which is an optical microscopy image, these alumina grains appear as the tiny dark inclusions visible along the steel sidewall. As they are solid while floating in the steel, when the steel begins to form delta ferrite liquidus phase crystals, these non metallic inclusions are confined to the interstitial spaces between the delta ferrites. Thus, by their distribution, they negatively trace the shape of delta ferrites already formed at this location. The location of some of these ghost-like traced delta ferrites is indicated. They have rounded, bulbous, not very idiomorphic forms, but the shapes correspond to the development iof microstructure in slurry casting (semi solid casting) as described in literature (sketch at left, from MC Flemings 1991). In that sketch it can be seen how the shape of such liquidus phase iron crystals in iron melt varies with residence time close to liquidus temperature in an environment under competing shear and cooling.

Fig. 8: Cotectic crystallisation. System Al2O3-CaO-MgO at right. At left, a SEM BSE image of a calciumaluminate falling on a cotectic in this system.

Cotectic crystallization refers to the state when the solidifying remaining melt, which has been crystallizing its first formed liquidus phase for a while, eventually encounters a cotectic in the phase diagram and starts to crystallise a second phase, along with the first. The above image shows both an example at left, and at right the phase diagram actually applicable for this case. The melt here was a ceramic (oxide) melt in the system ACM, which crystallized spinel first – the dark phase in the SEM BSE image. The second phase crystallizing here is CA2, the mid-grey phase which occurs as elongated but idiomorphic crystals. As with liquidus phase crystals, the cotect CA2 here can crystallize freely in a melt, and develops idiomorphic shapes consistent with its own preferred crystal habitus. The groundmass (matrix) corresponds to the remaining melt in the three-phase state nowdeveloped (L+X1+X2). Both CA2 as well as spinel (MA) are relatively high-alumina phases compared to the remaining melt, so the combined further crystallization of both removes alumina from the remaining liquid, which will develop along the cotectic to progressively lower-Al2O3 compositions, until eventually more phases become stable (peritectic, or eutectic).

Cotectic crystallization is furnamentally similar to liquidus phase crystallization, in the controls of morphology shapg the freely cgrowing crystals. It can be hard to establish from a microstructure whether the two observed crystal phases in the melt are truly cotectic, or which of them was the earlier liquidus phase. Ideally, the earlier phase should be available for the second cotectic phase to overgrow, thus the earlier phase should be morefrequently found as inclusions within the later formed phase. (see the image above, where clusters of spinel occur within the CA2 plates). However, in true cotectic crystalisation, both phases continue to grow, and therefore the opposite inclusion relationship can also occur.

Fig. 9: Cotectic crystallisation in a metallic melt (solder alloy). The phase diagram is at left, the SEM image of the microstructure at right. From Chen et al 2014 J. of Alloys and Compounds, 722:499.

The above image shows a case of cotectic crystallization fom a metallic system (in this case an alloy of Bi, Te and In). The rough phase compositions of the phases seen in the SEM BSE image at right are shown in the phase diagram at right – the two solids are in dark red, the matrix approximating the liquid phase as orange dot. In this case the two solid phases are the dark In4Te3 together with the cotectic grown Bi crystals (bright, as this is a very heavy metal even in this alloy). Comparison to the above ceramic example shows the similarity of structures between the ceramic and the metal case. To establish that this is a true cotectic requires that there is no indication of a reaction between the two solids: here, where Bi overgrows the In4Te3 dendrites, there should be no indication that the dendrites change shape or diminish in size compared tp the non overgrown ones, which is roughly the case.

Fig. 10: Peritectic Crystallisation in carbon steel. Fe-C phase diagram at left. Confocal Scanning Laser Microscopy image of the growth front in a solidification at right (see text). 

Peritectic crystallization is famous in metallurgy as it defines an entire class of materials in the steel range, the peritectic grades. As discussed above, peritectic crystallsiation simply means that a once-formed crystal back-reacts with the fractional liquid to form a new crystal, consuming both the older crystal and a bit of the fractional liquid (leaving behind a changed remaining liquid). As thi case is famous in steel metallurgy, an example is given here of steel – see above. The phase diagram at left is the well known Fe-C binary T-X section, in which the peritectic reaction occurs between delta ferrite and L at about 1492 C (depending on alloy). The right is a series of photo stills from a video (Griesser et al Acta Materiala 81:111) observing this reaction in a CSLM (Confocal Laser Scanning Microscope) in which it can be observed in situ. Gamma phase (Austenite) can be observed to nucleate at the delta surface at a given carbon content, and grow both inside replacing the delta ferrite, but also outside into the liquid, both of which it consumes. This can best be observed in the leftmost column where the eventual Gamma layer incorporated the end point of an earlier delta grain boundary at some depth, which was the position of the liquid-solid interface at the time of Gamma nucleation. The back-reaction into the earlier crystal which is being replaced can be dendritic (middle column) or massive (right column); this is in fact already an example of a solid-solid transformation.

Even though the peritectic reaction is famous in metallurgy, it is hard to observe it in bulk materials when it has either run to completion or is otherwise obscured by later structure development. A rare case where it was possible to see it occurring in a ceramic case is shown in the following illustration.

Fig. 11: Peritectic crystallisation in an oxide (slag) melt. At left an overview image (SEM BSE mode). The yellow box is magnified out at right, showing a detail of the microstructure. A dark layer (CNA2) forms by reaction between the CA2 phenocrysts and the interstitial melt (now solidified to melilite C2AS).

The above set of SEM BSE images (the right one is a magnification of a spot in the left one) shows a silicate melt that cooled and solidified atop some substrate (seen at bottom). The primarly liquidus phase in the layer of ceramic melt over the substrate was CA2, which formed a network of lath or platelet shaped crystals sometimes with dendritic development. The intervening residual melt eventually crystallised into two phases, namely C2AS (a melilite) and a small amount of ZrO2 making up a very finely intergrown eutectic in between the CA2 laths as shown in the right image. However it can there be seen that a thin layer of a darker phase covers a lot of the CA2 surfaces (but not all of them), in places mimicking the CA2 outlines but having irregular non-idiomorphic contacts with the CA2 below. This phase was found by analysis to be CNA2 (CaNa2Al4O8). The phase is otherwise not present in the interlath eutect. What happened here was that the melt was contaminated by a sodium rich agent just before crystallization. The pulse of sodia mixed into the crystallizing melt briefly turned the system from quasi ternary (ACS) into the ACNS quaternary, in which the preexisting CA2 liquidus phase was replaced by CNA2, enforcing a peritectic replacement reaction. However this was a short pulse, quickly fixing the sodium addition as a layer of CNA2 atop the CA2 after which the rapid solidification with the melilite eutect followed, preserving the CNA2 layer.

It can be hard to distinguish peritectic reactions from sequential crystallization, especially when the later microstructural development obscures some of the earlier formed structures. However, it is important to be aware of them and to recognize them where present since they contain an important element of the reaction history of a sample.

Fig. 12: Eutectic crystallisation. Two examples of phase diagrams with an eutectic point highlighted as orange dots. At left a metallic case, at right an oxidic case, the already often used system ACM.

Eutectic crystallization is conceptually simple.As defined above it is characterized my a melt turning completely – without surviving remaining liquid – into an assemblage of solid phases that together reproduce the composition of the eutectic melt. As such it represents the lowest temperature of crystallization in a region of a phase diagram (multicomponent systems can have multiple eutects in various parts of their compositional space). Conceptually simple, phase diagram examples are shown above for a metallic system (at left – Al Si Nio alloys) and for a ceramic system at right (ACM system, as used before). The eutectic point is marked in each. It is the point to which the system of cotectics separating the liquidus phase fields lead, going down temperature.

As the eutect transforms a liquid into an assembly of solids, it is most often marked by cooperative crsyatllisation: the multiple types of crystals grow in a concerted fashion. The previously uniform melt must split up and its compents must become “unmixed” to supply the crystals in the right amounts at their growing locations. This means, that at a scale dictated by the transport properties of the melt at the given T, there results a systematic spatial arrangement (intergrowth) of phases. Such intergowths are called eutectic intergrowths and are of large importance in both metal casting and ceramic materials sciences.

Fig. 13: Examples of eutectic crystallisation in metal systems. At left, a eutectic in the Al-Si alloy system. Note the uniform size and uniform spacing of the Al (darker) and Si crystals in the matris. At right, am example of a complex alloyed steel melt, where phenocrysts can be distinguished from a ground mass which on magnification is found to consist of a similar eutectic phase intergrowth.

The above image gives examp,les for eutectic intergrowths from solidified metallic liquids. The left example is an Al-Si alloy (SEM BSE) : the ground mass structure of evenly spaced dark Al laths with Si mantles is evident. The left example shows a solidified droplet of a complex Fe-C-Si-B alloy droplet, which has a large prominent phenocryst of Fe2B. The enlargement shows that it is embedded in a matrix ion which rounded blobs of a leter crystal generation – FeSi – can be made out, themselves embedded in a very fine grained but systematically structured intergrowth of about Fe2Si composition. This is the corresponding eutect in the Fe-Si system. The necessity to redistribute the elements spatially to provide for the growth of all the crystals taking part in the eutect creates the ordered arrangement, which by itself again often imparts bulk properties to the eutectic intergrowth that differ substantially from the individual properties of the involved phases.

Eutectics in a ceramic melt function just like this. That is shown in the following image.

Fig. 14: Eutectic crystallisation in an oxide (silicate) slag melt. In this case the melt composition was changing locally due to assimilation and formed different separate eutectic structures in response to the locally (strongly) changing melt properties. See text for discussion. 

In this case, there are multiple eutectic microstructures visible. The image at left is an overview (SEM BSE) which shows a ceramic melt (at the bottom) that was adjoining to a (porous) refractory sidewall (at the top). The border of the (at high temperature solid) refractory sidewall to the fully molten material is shown by a blue line. The ceramic melt by itself crystallized to an eutect visible at the lower edge of the image – an organized intergrowth of a bright and a dark phase together completely making up the volume of the original liquid (The phases are a calcium fluorosilicate called cuspidine, and a sodium alumosilicate called Nepheline, as marked in yellow in the enlargement). However, at and before crystallization, the refractory was melting into the contacting ceramic melt (note that the blue line does not trace idiomorphic refractory crystals but rounded dissolution shapes). This dissolution of the refractory material created a compositional gradient in the adjoining melt. The compositional gradient by itself changed properties in the melt that are fundamental for structure development, namely the transport properties responsible for the scale over which the eutectic development happens. As can be seen in the image the structure reacted sensitively to the change. While the phases remained constant throughout (Nepheline and cuspidine; no change in eutectic assemblage) the scale length of the intergrowth reacted to the addition of elelemnts by the refractory. This example demonstrates that even a microstructure that arises in a ‘simple’ way as a consequence of a phase diagram, carries significantly more information than only those phase relationships.

Fig. 15: Eutectoid microstructure in a rapidly crystallised oxide (slag) melt. Crystallisation forms a porous void volume around cooperatively crystallising eutectic phases in the right image. In the left image, a minimum phase is seen filling the corrsponding phase. This is an example of the ' shrinkage porosity' formation caused by the volume loss during solidification. See text for discussion. 

A final example of a semi-eutectic microstructure is shown here, and relates to the volume effect of eutectic crystallization. As noted above the crystals make up the same bulk composition as the preceding melt. However, the solid phases as a rule are denser than the liquid. Often therefore, the combined volume of the eutectic phases is less than the volume the melt occupied efore. If there is no means of adjusting sample volume either in bulk, or by material displacement (liquid flow) internally to a sample, then a shrinkage porosity must result. Such shrinkage porosity can be an important element of the microstructure formed, especially in metallurgy where it often is a highly unwanted feature of a metal cast. The above image shows similar issues arising in the solidification of a ceramic melt. In this case, it is an oxidic melt that eventually solidifies into a three-phase quasi-eutect made of the three phases that have the ceramic shorthand notations C2S, MW, and C2(A,F). (A dicalcium silicate, a magnesio wuestite, and a calcium ferrite). This solidification is a quasi-eutect as in detail it is still having a crystallization sequence, especially between C2S and MW on one hand which grow cooperatively in a first step, and the calcium ferrite on the other hand which incorporates the last liquid (thereby being a minimum phase and not a true eutect as the transformation is L → X only). As the solid phases are comparatively dense, the volume effect is significant. In most cases it is made up by internal displacement of the last liquid fraction comprising later calcium ferrite, leading to a dense structure as in the left example, where a network of C2(A.F) can be seen to surround the ‘bushels’ of cooperatively grown calcium silicate and magnesiowuestite. The right image – from the sample larger sample – gives the corresponding opposite case – here the calcium ferrite liquid drained away, leaving the calcium silicate and magnesiowuestite bushels exposed, with nothing but void in between (a tiny fraction of calcium ferrite is still present). In net effect , this mechanism concentrates the overall volume loss incurred over the entire sample, to a special region (pictured at right) where the amount of void is far larger than would have been expected just from this location alone. Similar processes happen in many metal casts, where shrinkage porosity is found to occur not distributed throughout but concentrated in some parts of the sample. This is not only a concern to the mechanical properties of such a sample. The underlying cast-internal melt flow also leads to the development of chemical heterogeneity, which can be very hard to completely remove in later process steps and can doom the quality of a product. (In the above ceramic example, the displacement of calcium ferrite from a region like the right one, onto one like the left one, naturally means that elements enriched in calcium ferrite become heterogeneously distributed.) 

Fig. 16: An example of a crystallised oxide (slag) melt in which all the major steps of sequential crystallisation are visible in one location. The area is a sort of melt pod enclosed between early formed phenocrysts (liquidus phase crystals), in which the entire sequence played out in a little subsystem. See text for discussion.    

Instead of a summary repeating all the points made above, the above image is meant to be a sort of recapitulation of the features of microstrcutures formed from the solidification of melt. The image, is taken (SEM BSE) from a ceramic melt of an industrial process. In a single image, it contains most of the features explained above, which all can be identified, and can be understood to result in a coherent pricture of the development of this samples solidification. The column at left summarizes the various steps. Very generally, one can see that this sia ‘patch’ embedded in a region of blocky, idiomorphic, slightly zoned crystals, called “A”, which can be identified as the stable solid crystal in a first phase when all the rest was liquid. The phase is idiomorphic, but not specially dendritic or hopper shaped, indicating that this was likely an extended high-temperature period, not already part of a rapid cooling sequence. This then is followed by a rapid sequence of nucleation and growth of other phases (B, then C) that together lead to complete solidification of the patch, while all the while the same phase A also continues to crystallise (which why its early formed idiomorphic grains are only ghostly visible). The sudden change in morphology from blocky-equant to dendritic in phase B indicates that this later stage (leading to solidification of the patch) was a rapid cooling stage. In agreement with this, phases A and B form a sometimes very fine grained ordered intergrowth and phase C has a tendency to occur interstitially to these intergrowths (which thereby can be seen not to represent an actual eutectic). Phase C is the eventual minimum crystallising phase representing the last liquid part. Important in correctly deciphering a microstructure such as this is the recognition that it is shaped by two very different stages – a high temperature stage which was in comparatively static equilibrium (blocky phase A with L) and a rapid-cooling stage where all the rest formed. As this is a sample from an industrial process, the first of these can be taken to represent the industrial process of interest. This means, that the composition of the actual liquid present in the industrial process can be reconstructed from this image: it is represented by all the phases B and C and that part of the phase A that takes part in the solidification intergrowths in the solidified patch. This distinction within phase A – that it has a fraction which was already present at the industrial process and a fraction that formed only on cooling can be made on microstructural criteria in this image. It is necessary for the reconstruction of the in-process melt, but, once done, it allows measuring the composition of this in-process melt – a melt of which no actual traces remain. This can include elusive things, such as the distribution of P between melt and crystals during industrial production, which can decide about the success of operations. It is hoped this examples serves to show the usefulness of the analysis of microstructures by microscopy, to read out information that otherwise is hard (sometimes impossible) to obtain.