[Ill.u.s.tration: FIG. 71.]

[Ill.u.s.tration: FIG. 72.]

Active dimethyl tartrate melts at 43.3; racemic dimethyl tartrate at 89.4. Active mandelic acid melts at 132.8; the racemic acid at 118.0. In the one case, therefore, the racemic compound has a higher, in the other a lower melting point than the active forms. {219}

In the case of partially racemic compounds (_i.e._ the compound of a racemate with an optically active substance) the type of curve will be the same, but the figure will no longer be symmetrical. Such a curve has been found in the case of the l-menthyl esters of d- and l-mandelic acid (Fig.

72).[300] The freezing point of l-menthyl d-mandelate is 97.2, of l-menthyl l-mandelate 77.6, and of l-menthyl r-mandelate 83.7. It will be observed that the summit of the curve for the partially racemic mandelate is very flat, indicating that the compound is largely dissociated into its components at the temperature of fusion.

III. _The inactive substance is a pseudo-racemic mixed crystal._

In cases where the active components can form mixed crystals, the freezing-point curve will exhibit one of the forms given in Fig. 65. The inactive mixed crystal containing 50 per cent. of the dextro and laevo compound, is known as a pseudo-racemic mixed crystal.[301] So far, only curves of the types I. and II. have been obtained.

Examples.--The two active camphor oximes are of interest from the fact that they form a continuous series of mixed crystals, _all of which have the same melting point_. The curve which is obtained in this case is, therefore, a straight line joining the melting points of the pure active components; the melting point of the active isomerides and of the whole series of mixed crystals being 118.8.

[Ill.u.s.tration: FIG. 73.]

In the case of the carvoximes mixed crystals are also formed, but the equilibrium curve in this case exhibits a maximum (Fig. 73). At this maximum point the composition of the solid and of the liquid solution is the same. Since the curve must be symmetrical, this maximum point must occur in the case of the solution containing 50 per cent. {220} of each component, which will therefore be inactive. Further, this inactive mixed crystal will melt and solidify at the same temperature, and behave, therefore, like a chemical compound (p. 187). The melting point of the active compounds is 72; that of the inactive pseudo-racemic mixed crystal is 91.4

Transformations.--As has already been remarked, the conclusions which can be drawn from the fusion curves regarding the nature of the inactive substances formed hold only for temperatures in the neighbourhood of the melting points. At temperatures below the melting point transformation may occur; _e.g._ a racemate may break up into a _dl_-mixture, or a pseudo-racemic mixed crystal may form a racemic compound. We shall at a later point meet with examples of a racemic compound changing into a _dl_-mixture at a definite transition point; and the pseudo-racemic mixed crystal of camphoroxime is an example of the second transformation.

Although at temperatures in the neighbourhood of the melting point the two active camphoroximes form only mixed crystals but no compound, a racemic compound is formed at temperatures below 103. At this temperature the inactive pseudo-racemic mixed crystal changes into a racemic compound; and in the case of the other mixed crystals transformation to racemate and (excess of) active component also occurs, although at a lower temperature than in the case of the inactive mixed crystal. Although this behaviour is one of considerable importance, this brief reference to it must suffice here.[302]

3. _Alloys._

One of the most important cla.s.ses of substances in the study of which the Phase Rule has been of very considerable importance, is that formed by the mixtures or compounds of metals with one another known as alloys. Although in the investigation of the nature of these bodies various methods are employed, one of the most important is the determination of the character of the freezing-point curve; for from the form of this, valuable information can, as we have already learned, be {221} obtained regarding the nature of the solid substances which separate out from the molten mixture.

Although it is impossible here to discuss fully the experimental results and the oftentimes very complicated relationships which the study of the alloys has brought to light, a brief reference to these bodies will be advisable on account both of the scientific interest and of the industrial importance attaching to them.[303]

We have already seen that there are three chief types of freezing-point curves in systems of two components, viz. those obtained when (1) the pure components crystallize out from the molten ma.s.s; (2) the components form one or more compounds; (3) the components form mixed crystals. In the case of the metals, representatives of these three cla.s.ses are also found.

1. _The components separate out in the pure state._

In this case the freezing-point curve is of the simple type, Fig. 63, I.

Such curves have been obtained in the case of a number of pairs of metals, _e.g._ zinc--cadmium, zinc--aluminium, copper--silver (Heyc.o.c.k and Neville), tin--zinc, bis.m.u.th--lead (Gautier), and in other cases. From molten mixtures represented by one branch of the freezing-point curve one of the metals will be deposited; while from mixtures represented by the other branch, the other metal will separate out. At the eutectic point the molten ma.s.s will solidify to a _heterogeneous mixture_ of the two metals, forming what is known as the _eutectic alloy_. Such an alloy, therefore, will melt at a definite temperature lower than the melting point of either of the pure metals.

{222}

In the following table are given the temperature and the composition of the liquid at the eutectic point, for three pairs of metals:--

-------------------------------------------------------------------

Temperature.

Composition of liquid.

------------------------------------------------------------------- Zinc--cadmium

264.5

73.5 atoms per cent. of cadmium.

Zinc--aluminium

380.5

11 " " aluminium.

Copper--silver

778

40 " " copper.

The melting points of the pure metals are, zinc, 419; cadmium, 322; silver, 960; copper, 1081; aluminium, 650.

2. _The two metals can form one or more compounds._

In this case there will be obtained not only the freezing-point curves of the pure metals, but each compound formed will have its own freezing-point curve, exhibiting a point of maximum temperature, and ending on either side in an eutectic point. The simplest curve of this type will be obtained when only one compound is formed, as is the case with mercury and thallium.[304]

This curve is represented in Fig. 74, where the summit of the intermediate curve corresponds with a composition TlHg_{2}. Similar curves are also given by nickel and tin, by aluminium and silver, and by other metals, the formation of definite compounds between these pairs of metals being thereby indicated.[305]

[Ill.u.s.tration: FIG. 74.]

{223}

A curve belonging to the same type, but more complicated, is obtained with gold and aluminium;[306] in this case, several compounds are formed, some of which have a definite melting point, while others exhibit only a transition point. The chief compound is AuAl_{2}, which has practically the same melting point as pure gold.

3. _The two metals form mixed crystals (solid solutions)._

The simplest case in which the metals crystallize out together is found in silver and gold.[307] The freezing-point curve in this case is an almost straight line joining the freezing points of the pure metals (_cf._ curve I., Fig. 65, p. 210). These two metals, therefore, can form an unbroken series of mixed crystals.

In some cases, however, the two metals do not form an unbroken series of mixed crystals. In the case of zinc and silver,[308] for example, the addition of silver _raises_ the freezing point of the mixture, until a transition point is reached. This corresponds with curve IV., Fig. 65.

Silver and copper, and gold and copper, on the other hand, do not form unbroken series of mixed crystals, but the freezing-point curve exhibits an eutectic point, as in curve V., Fig. 65.

Not only may there be these three different types of curves, but there may also be combinations of these. Thus the two metals may not only form compounds, but one of the metals may not separate out in the pure state at all, but form mixed crystals. In this case the freezing point may rise (as in the case of silver and zinc), and one of the eutectic points will be absent.

Iron-Carbon Alloys.--Of all the different binary alloys, probably the most important are those formed by iron and carbon: alloys consisting not of two metals, but of a metal and a non-metal. On account of the importance of these alloys, an attempt will be made to describe in brief some of the most important relationships met with.

Before proceeding to discuss the applications of the Phase Rule to the study of the iron-carbon alloys, however, the main {224} facts with which we have to deal may be stated very briefly. With regard to the metal itself, it is known to exist in three different allotropic modifications, called [alpha]-, [beta]-, and [gamma]-ferrite respectively. Like the two modifications of sulphur and of tin, these different forms exhibit transition points at which the relative stability of the forms changes.

Thus the transition point for [alpha]- and [beta]-ferrite is about 780; and below this temperature the [alpha]- form, above it the [beta]- form is stable. For [beta]- and [gamma]-ferrite, the transition point is about 870, the [gamma]- form being the stable modification above this temperature.

The different modifications of iron also possess different properties.

Thus, [alpha]-ferrite is magnetic, but does not possess the power of dissolving carbon; [beta]-ferrite is non-magnetic, and likewise does not dissolve carbon; [gamma]-ferrite is also non-magnetic, but possesses the power of dissolving carbon, and of thus giving rise to solid solutions of carbon in iron.

Various alloys of iron and carbon, also, have to be distinguished. First of all, there is _hard steel_, which contains varying amounts of carbon up to 2 per cent. Microscopic examination shows that these mixtures are all h.o.m.ogeneous; and they are therefore to be regarded as solid solutions of carbon in iron ([gamma]-ferrite). To these solutions the name _martensite_ has been given. _Pearlite_ contains about 0.8 per cent. of carbon, and, on microscopic examination, is found to be a heterogeneous mixture. If heated above 670, pearlite becomes h.o.m.ogeneous, and forms martensite. Lastly, there is a definite compound of iron and carbon, iron carbide or _cement.i.te_, having the formula Fe_{3}C.

A short description may now be given of the application of the Phase Rule to the two-component system iron--carbon; and of the diagram showing how the different systems are related, and with the help of which the behaviour of the different mixtures under given conditions can be predicted.

Although, with regard to the main features of this diagram, the different areas to be mapped and the position of the frontier lines, there is general agreement; a final decision has not yet been reached with regard to the interpretation to be put on all the curves.

[Ill.u.s.tration: FIG. 75.]

The chief relationships met with in the case of the {225} iron-carbon alloys are represented graphically in Fig. 75.[309] The curve AC is the freezing-point curve for iron,[310] BC the unknown freezing-point curve for graphite. C is an eutectic point. Suppose, now, that we start with a mixture of iron and carbon, represented by the point _x_. On lowering the temperature, a point, _y_, will be reached at which solid begins to separate out. This solid phase, however, is not pure iron, but a solid solution of carbon in iron, having the composition represented by _y'_ (cf.

p. 185). As the temperature continues to fall, the {226} composition of the liquid phase changes in the direction of _y_C, while the composition of the solid which separates out changes in the direction _y'_D; and, finally, when the composition of the molten ma.s.s is that of the point C (4.3 per cent. of carbon), the whole ma.s.s solidifies to a heterogeneous mixture of two solid solutions, one of which is represented by D (containing 2 per cent. of carbon), while the other will consist practically of pure graphite, and is not shown in the figure. The temperature of the eutectic point is 1130.

Even below the solidification point, however, changes can take place. As has been said, the solid phase which finally separates out from the molten ma.s.s is a solid solution represented by the point D; and the curve DE represents the change in the composition of this solid solution with the temperature. As indicated in the figure, DE forms a part of a curve representing the mutual solubility of graphite in iron and iron in graphite; the latter solutions, however, not being shown, as they would lie far outside the diagram. As the temperature falls below 1130, more and more graphite separates out, until at E, when the temperature is 1000, the solid solution contains only 1.8 per cent. of carbon. At this temperature cement.i.te also begins to be formed, so that as the temperature continues to fall, separation of cement.i.te (represented by the line E'F') occurs, and the composition of the solid solution undergoes alteration, as represented by the curve EF. Below the temperature of the point F (670) the martensite becomes heterogeneous, and forms pearlite.

From the above description, therefore, it follows that if we start with a molten mixture of iron and carbon, the composition of which is represented by any point between D and C (from 2 to 4.3 per cent. of carbon), we shall obtain, on cooling the ma.s.s, first of all solid solutions, the composition of which will be represented by points on the line AD; that then, after the ma.s.s has completely solidified at 1130, further cooling will lead to a separation of graphite and a change in the composition of the martensite (from 2 to 1.8 per cent. of carbon). On cooling below 1000, however, the martensite and graphite will give rise to cement.i.te and solid solutions {227} containing less carbon than before, until, at temperatures below 670, we are left with a mixture of pearlite and cement.i.te.

We have already said that iron consists in three allotropic modifications, the regions of stability of which are separated by definite transition points. The transition point for [alpha]- and [beta]-ferrite (780) is represented in Fig. 75 by the point H; and the transition point for [beta]- and [gamma]-ferrite (870) by the point I. Since neither the [alpha]- nor the [beta]-ferrite dissolves carbon, the transition point will be unaffected by addition of carbon, and we therefore obtain the horizontal transition curve HG. In the case of the [beta]- and [gamma]-ferrite, however, the latter dissolves carbon, and the transition point is consequently affected by the amount of carbon present. This is shown by the line IG.

If a martensite containing less carbon than that represented by the point G is cooled down from a temperature of, say, 900, then when the temperature has fallen to that, represented by a point on the curve IG, [beta]-ferrite will separate out, and, as the temperature falls, the composition of the solid solution will alter as represented by IG. On pa.s.sing below the temperature of HG, the [beta]-ferrite will be converted into [alpha]-ferrite, and, as the temperature falls, the latter will separate out more and more, while the composition of the solid solution alters in the direction GF. On pa.s.sing to still lower temperatures, the solid solution at F (0.8 per cent. of carbon) breaks up into pearlite. If the percentage of carbon in the original solid solution was between that represented by the points G and F, then, on cooling down, no [beta]-ferrite, but only [alpha]-ferrite would separate out.

We see, therefore, that when martensite is allowed to cool _slowly_, it yields a heterogeneous mixture either of ferrite and pearlite (when the original mixture contained up to 0.8 per cent. of carbon), or pearlite and cement.i.te (when the original mixture contained between 0.8 and 2 per cent.

of carbon). These heterogeneous mixtures const.i.tute soft steels, or, when the carbon content is low, wrought iron.

The case, however, is different if the solid solution of carbon in iron is _rapidly_ cooled (quenched) from a temperature above the curve IGFE to a temperature below this {228} curve. In this case, the rapid cooling does not allow time for the various changes which have been described to take place; so that the h.o.m.ogeneous solid solution, on being rapidly cooled, remains h.o.m.ogeneous. In this way hard steel is obtained. By varying the rapidity of cooling, as is done in the tempering of steel, varying degrees of hardness can be obtained.

The interpretation of the curves given above is that due essentially to Roozeboom, who concluded from the experimental data that at temperatures below 1000 the stable systems are martensite and cement.i.te, or ferrite and cement.i.te, graphite being labile. It has, however, been pointed out, more especially by E. Heyn,[311] that this is not in harmony with the facts of metallurgy, which show that graphite is undoubtedly formed on slow cooling, and more especially when small quant.i.ties of silicon are present in the iron.[312] While, therefore, the relationships represented by Fig. 75 are obtained under certain conditions (especially when manganese is present), Heyn considers that all the curves in that figure, except ACB, represent _metastable_ systems--systems, therefore, akin to supercooled liquids.

Rapid cooling will favour the production of the metastable systems containing cement.i.te, and therefore give rise to relationships represented by Fig. 75; whereas slow cooling will lead to the stable system ferrite and graphite. Presence of silicon tends to prevent, presence of manganese tends to a.s.sist, the production of the metastable systems.