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Volume 42, 1909
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Art. XXXI.—An Apparent Relation between some of the Physical Properties of Solids.

[Read before the Philosophical Institute of Canterbury, 1st December, 1909.]

The usual conception of the mechanical structure of solids is that the finite particles or molecules composing them are held together by forces of mutual attraction called “cohesion.” In rigid solids these forces are such that very little change can occur in the relative position of the particles. The greater the force of cohesion, the greater must be the counter-force necessary to separate the particles, the greater the resistance to breaking-down of the solid.

This breaking-down of the solid can take place in several ways, of which the following are the chief: (1) Mechanical rupture, crushing, &c.; (2) solution in a liquid solvent; (3) volatilisation, with or without fusion as a step in the process.

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The energy required to break down and completely overcome the cohesion of a given mass of solid should be the same in amount whether that breaking-down be accomplished by crushing, by solution, or by fusion and volatilisation.

Measurements are made of these three kinds of change in solids in various ways, the more important of which are as follows:—

Case 1: Mechanical Rupture.—This is measured by—(a) tensile strength; (b) crushing strength; (c) hardness, &c.

In isotropic solids the force to be overcome is the same for all of these methods, and the results expressed in suitable terms should be comparable. But most solids are not isotropic; mica, selenite, and asbestos may be cited as extreme cases where the strength in different directions is totally different. In all such cases different methods of measurment may give quite different values for the mechanical strength. For present purposes the determination of hardness, although by no means precise or exact, is perhaps the most useful. It is very easy to measure roughly, so that where the hardness differs much in different directions the maximum value is easily found.

Case 2: Solution in a Solvent.—This method of breaking down a solid is measured usually in terms of the weight of solid which dissolves in a given weigth of solvent at a definite temperature. In a given solvent at a given temperature the solubility depends upon two principal factors—first, the attractive force or adhesion between solid and solvent; and, second, the cohesion of the solid. Assuming the first to be nearly constant, the solubility should increase as the cohesion and the mechanical strength become less.

Case 3: Fusion and Volatilisation.—This, the third method given for separating molecules, is a question of two opposing forces—molecular cohesion versus molecular velocity. When the average kinetic energy of the moving molecules is greater than the energy of cohesion, the molecules escape from each other and volatilise. With any given solid the energy of the moving molecule increases with the temperature proportionately, while the cohesion remains the same. Hence the greater the cohesion and mechanical strength, the higher the temperature required for volatilisation, or fusion and volatilisation.

In the absence of suitable quantitative measurements, which, as already seen, are particularly difficult to get in the case of mechanical strengths, no exact correspondence can at present be shown between strength, solubility, and volatility or fusibility in solids, but evidence enough is available to show distinctly that some such correspondence exists.

In a chemical laboratory hundreds of artificially prepared pure solids are met with. Owing to the limitations of manufacturing processes, these are almost entirely confined to compounds readily soluble, or fusible, or volatile, and in every case the crystals are mechanically soft and weak—in fact, softness and weakness are the most striking characteristics of artificially prepared crystals. Quite recently the high temperatures of the electric arc have come into commercial use, and one of the most notable results is the formation of new and difficulty fusible crystals, such as carborundum, which is little short of a diamond in hardness.

A few more definite examples may be given. If we arrange six of the more common salts of calcium in order of increasing hardness, thus—chloride, carbonate, sulphate, phosphate, fluoride, silicate—it will be found that this is also the order of increasing insolubility.

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In the closely related compounds, sugar, starch, and cellulose, the insolubility and strength increase together very clearly, sugar being freely soluble and weak, starch semi-soluble and comparatively strong, cellulose insoluble and very strong.

In the numerous commercial glasses, all those easily fusible are soft; hardness and infusibility increase together. Very much the same is true of the resins.

All the solid hydrocarbons are very easily melted, and all are very soft and weak.

Ordinary phosphorus is readily fusible, soluble, and very soft, while the change which converts it into red phosphorus makes it difficultly fusible, and at the same time insoluble and relatively hard.

There are a few prominent cases which appear at first sight to be exceptions to the general rule. All the forms of carbon are highly infusible and insoluble, but some are quite soft. The explanation appears to be that the soft forms are not compact; the particles are not close enough for cohesion to have full play. Any process which makes the carbon more dense and compact increases very largely its strength and hardness. This is very well seen in the manufacture of the glow-lamp filament. Ordinary charcoal does not seem a promising material to make into a strong, hard, elastic wire; yet by simply increasing its compactness, bringing a greater proportion of the molecular particles within reach of each other, the required strength and elasticity result. Similarly, retort carbon is hard and strong. The softness of charcoal is due to its spongy, open character. Alumina and its important compound clay are very insoluble and difficultly fusible, and yet both are soft and unctuous to the touch. That this also is due to the loose, open structure, to the molecules being too far away to hold each other firmly, is pretty clear. Clay, when strongly heated, shrinks very much, the particles come within closer reach of each other, and the mass becomes both hard and strong. The change is well seen in the manufacture of bricks and pottery. If the heating be very prolonged, the clay may actually crystallize, as in the mineral andalusite, which is harder even than quartz. Alumina can be melted in the electric arc, and then forms a compact solid, with the strength and hardness of the ruby.

Quartz is much more infusible than any glass, and after fusion is proportionately stronger—so strong that thin crucibles of quartz can be plunged into cold water while red-hot without injury.

In practically every case, then, with resistance to solution, or fusion, or volatilisation comes resistance to mechanical rupture. Hence strength and hardness may be to a great extent foretold in compact solids if the solubility or fusibility be known, and vice versâ.

The matter has been brought before the Institute in order to make a little more clear and definite a relation long felt more or less vaguely, and utilised more or less consciously by many practical men.