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begins and the cooling slows down ; at a certain point the liquid is all crystallized and the mixture, now a solid mass of crystals, will go on cooling uniformly. The change of slope in the curve of cooling accordingly corresponds to the passage of the substance from S to E in temperature (or from the purely liquid to the purely solid areas). The physical condition of the substance at any given temperature can also be ascertained by the method of chilling. If the charge be taken from the furnace and plunged in water (or in some cases mer- cury) the mixture consolidates almost immediately, and any parts which were liquid will assume the form of a glass, or a very finely crystalline aggregate. This is especially the case with silicates, many of which crystallize with difficulty. Microscopic investigation will enable us to determine the nature and relative proportions of the crystals which were present. The results obtained can be checked by experiments on mixtures having a different composition, and in this way a complete diagram built up on a sound experi- mental basis. The case outlined .above is the simplest known. Many complications may appear, requiring special precautions and elaborate investigation. Thus the liquid may not begin to crystallize at the proper point on the upper curve, as some substances crystallize with difficulty and the liquid becomes " undercooled." A heating-up experiment may be tried to check the cooling experiments; the same phenomena should appear in the reverse order if no complications are present. Many silicates crystallize with great difficulty in or- dinary crucible experiments (such as the felspars, albite and ortho- clase). Again, it may be impossible to melt the mixture we desire to investigate in any furnace which is suitable for experiments of this kind. Magnesia, alumina, and lime are examples of substances which cannot be fused at temperatures such as 1600 to 1700 C., which are the limits of accurate work in our laboratories at present ; part of the diagram accordingly will be incomplete when substances like these are studied, but an approximate solution can generally be made by extrapolation. Another frequent complication is the ap- pearance of transformations in the solid state. The first mineral to crystallize becomes unstable as the temperature falls and changes spontaneously into another crystalline form of the same substance. The change will be attended by an alteration in the slope of the cool- ing curve, for in such cases heat is either liberated or absorbed, and successful chilling tests can often be made by which the mineral transformation can be clearly demonstrated. Silica, for example, appears in three minerals, cristobalite, tridymite and quartz, the transition temperatures being 1470 and 870. Each of these min- erals occurs in two forms. Carbonate of lime has a high-tem- perature and a low-temperature form. Below 1190 calcium meta- silicate crystallizes as wollastonite; above that temperature it forms another mineral, pseudo-wollastonite. Many of these " high- temperature " forms are not known as natural minerals, and as a rule they are very rare in rocks, probably because rock cooling is essentially a slow process, and the most stable forms at low tem- peratures are the only ones likely to be present when the mass has completely cooled. Some very interesting results have been obtained in this field of research ; for example, it is known that quartz has two

TEMP.

15% B

60% B

TIME

FlG. 2.

modifications, one above 575", the other below that temperature, and it has been proposed to use quartz as a geological thermometer to show at what temperature it crystallizea in a rock mass. If above 575 it would appear as quartz and on cooling would pass inta o-quartz ; and by various indications, such as crystalline form, cracks, etc., a record of this transformation may be obtained.

Very interesting modifications of the process of crystallization occur when two or more of the minerals formed are members of an isomorphous series and can in consequence form mixed crystals. This is very common among the minerals of igneous rocks, of which the felspars, pyroxenes, olivine (and probably also hornblende, mica, nepheline and the felspathoids) all belong to isomorphous series. If we have, for example, two components such as albite and anorthite, they will tend to form mixed crystals (known generally as plagioclase felspars). Anorthite has the higher melting-point (about 1550 C.); albite crystallizes in crucibles only with great reluctance at a temperature about nooC. A mixture containing equal proportions of anorthite and albite will melt at about 1450, and on cooling will begin to form crystals at that temperature.

These crystals will contain about 60% anorthite that is to say, they are enriched in the less fusible component. As crystallization proceeds, the felspar that separates becomes gradually less rich in anorthite. The composition of the liquid also alters, because the crystallization is abstracting anorthite molecules more rapidly than albite molecules. This process may go on till the felspar has all crystallized, the last deposited being near albite in composition, and the crystals, examined microscopically, will show zones, of which the internal are rich in anorthite and the external are progressively richer and richer in albite. But if sufficient time is allowed, a reaction sets in between the crystals and the liquid ; in other words, the fel- spars crystallized are not in equilibrium with the magma except at the moment of crystallization, and as the magma becomes richer in albite it will attack the early plagioclase, replacing it by a variety containing more albite. These phenomena are well known to petrologists as zonal structure of plagioclase felspars; and corrosion of the cores and internal zones of the crystals is almost universal in such rocks as basalt and andesite. Rocks of similar composition which have cooled very slowly, such as gabbro and norite, as a rule do not contain zoned plagioclase crystals, no doubt because equilibrium has been attained and homogeneous crystals formed by the process above described.

FIG. 3.

This may be illustrated by fig. 3. The horizontal line represents composition, the vertical temperature. A is 100% albite, B is 100% anorthite. The upper curve is the liquidus above which there is only liquid; the lower is the solidus below which all is crystallized : between these lines is a space representing stages in which crystalliza- tion is going on but still incomplete. Each point on the solidus has a corresponding point on the liquidus, which is found by drawing a horizontal line across the intervening space. A mixture of any composition, say a at ab, is completely liquid. As the temperature falls it begins to crystallize at b. The crystals formed have the composition c. Further cooling results in the formation of crystals at b the composition being c'. At b* all is crystallized, the last crys- tals being d. If resorption is completely accomplished the final crystals have the composition x, but they are usually more rich in albite: this will depend on the rate of cooling, the number and size of the crystals formed, and on a variety of other factors.

The theoretical investigations of Roozeboom and Gibbs have shown that five types of crystallization of isomorphous substances may occur, in some of which the mutual solubility of the two com- ponents is unlimited, while in others it is limited so that only mixed crystals of certain types may occur. Several of these have been identified in rock-forming minerals, and others are suspected though not yet proved.

Ternary Magmas. Magmas of three components (ternary) are much more complicated than binary .magmas. To represent their behaviour a triangular diagram is necessary. Usually an equilateral triangle is employed and the distance from any point to the three sides of the triangle is made to represent the three components of any mixture in their true proportions; the sum of these three per- pendiculars is constant and equal to the height of the triangle: if lines be drawn through the point, parallel to the sides of the triangle, they will cut the sides at distances which will represent the relative proportions of the components. Any mixture of three components can be represented by one point in this triangle. To represent tem- perature another coordinate is required which is perpendicular to the plane of the triangular diagram : and a solid model must be made, resembling a triangular prism with flat base and an irregular surface representing the consolidation temperatures as the top of the prism. Each of the three vertical surfaces of the prism represents the be- haviour of the mixture of two of the components.

To enable us to construct such a model a very large number of experiments must be made, first with binary mixtures and then with mixtures of the three substances. Their exact temperature of first crystallization must be ascertained in each case and also the nature of the mineral which crystallizes. Simultaneous crystallization of two minerals will follow, and the temperature at which the second mineral appears is to be determined. Three minerals will ultimately