SOLIDS AND LIQUIDS

§ 3. SOLIDS AND LIQUIDS

The interest of the results to which the researches on the continuity between the liquid and the gaseous states have led is so great, that numbers of scholars have naturally been induced to inquire whether something analogous might not be found in the case of liquids and solids.

We might think that a similar continuity ought to be there met with, that the universal character of the properties of matter forbade all real discontinuity between two different states, and that, in truth, the solid was a prolongation of the liquid state.

To discover whether this supposition is correct, it concerns us to compare the properties of liquids and solids. If we find that all properties are common to the two states we have the right to believe, even if they presented themselves in different degrees, that, by a continuous series of intermediary bodies, the two classes might yet be connected.

If, on the other hand, we discover that there exists in these two classes some quality of a different nature, we must necessarily conclude that there is a discontinuity which nothing can remove.

The distinction established, from the point of view of daily custom, between solids and liquids, proceeds especially from the difficulty that we meet with in the one case, and the facility in the other, when we wish to change their form temporarily or permanently by the action of mechanical force. This distinction only corresponds, however, in reality, to a difference in the value of certain coefficients. It is impossible to discover by this means any absolute characteristic which establishes a separation between the two classes. Modern researches prove this clearly. It is not without use, in order to well understand them, to state precisely the meaning of a few terms generally rather loosely employed.

If a conjunction of forces acting on a homogeneous material mass happens to deform it without compressing or dilating it, two very distinct kinds of reactions may appear which oppose themselves to the effort exercised. During the time of deformation, and during that time only, the first make their influence felt. They depend essentially on the greater or less rapidity of the deformation, they cease with the movement, and could not, in any case, bring the body back to its pristine state of equilibrium. The existence of these reactions leads us to the idea of viscosity or internal friction.

The second kind of reactions are of a different nature. They continue to act when the deformation remains stationary, and, if the external forces happen to disappear, they are capable of causing the body to return to its initial form, provided a certain limit has not been exceeded. These last constitute rigidity.

At first sight a solid body appears to have a finite rigidity and an infinite viscosity; a liquid, on the contrary, presents a certain viscosity, but no rigidity. But if we examine the matter more closely, beginning either with the solids or with the liquids, we see this distinction vanish.

Tresca showed long ago that internal friction is not infinite in a solid; certain bodies can, so to speak, at once flow and be moulded. M.W. Spring has given many examples of such phenomena. On the other hand, viscosity in liquids is never non-existent; for were it so for water, for example, in the celebrated experiment effected by Joule for the determination of the mechanical equivalent of the caloric, the liquid borne along by the floats would slide without friction on the surrounding liquid, and the work done by movement would be the same whether the floats did or did not plunge into the liquid mass.

In certain cases observed long ago with what are called pasty bodies, this viscosity attains a value almost comparable to that observed by M. Spring in some solids. Nor does rigidity allow us to establish a barrier between the two states. Notwithstanding the extreme mobility of their particles, liquids contain, in fact, vestiges of the property which we formerly wished to consider the special characteristic of solids.

Maxwell before succeeded in rendering the existence of this rigidity very probable by examining the optical properties of a deformed layer of liquid. But a Russian physicist, M. Schwedoff, has gone further, and has been able by direct experiments to show that a sheath of liquid set between two solid cylinders tends, when one of the cylinders is subjected to a slight rotation, to return to its original position, and gives a measurable torsion to a thread upholding the cylinder. From the knowledge of this torsion the rigidity can be deduced. In the case of a solution containing 1/2 per cent. of gelatine, it is found that this rigidity, enormous compared with that of water, is still, however, one trillion eight hundred and forty billion times less than that of steel.

This figure, exact within a few billions, proves that the rigidity is very slight, but exists; and that suffices for a characteristic distinction to be founded on this property. In a general way, M. Spring has also established that we meet in solids, in a degree more or less marked, with the properties of liquids. When they are placed in suitable conditions of pressure and time, they flow through orifices, transmit pressure in all directions, diffuse and dissolve one into the other, and react chemically on each other. They may be soldered together by compression; by the same means alloys may be produced; and further, which seems to clearly prove that matter in a solid state is not deprived of all molecular mobility, it is possible to realise suitable limited reactions and equilibria between solid salts, and these equilibria obey the fundamental laws of thermodynamics.

Thus the definition of a solid cannot be drawn from its mechanical properties. It cannot be said, after what we have just seen, that solid bodies retain their form, nor that they have a limited elasticity, for M. Spring has made known a case where the elasticity of solids is without any limit.

It was thought that in the case of a different phenomenon—that of crystallization—we might arrive at a clear distinction, because here we should he dealing with a specific quality; and that crystallized bodies would be the true solids, amorphous bodies being at that time regarded as liquids viscous in the extreme.

But the studies of a German physicist, Professor 0. Lehmann, seem to prove that even this means is not infallible. Professor Lehmann has succeeded, in fact, in obtaining with certain organic compounds—oleate of potassium, for instance—under certain conditions some peculiar states to which he has given the name of semi-fluid and liquid crystals. These singular phenomena can only be observed and studied by means of a microscope, and the Carlsruhe Professor had to devise an ingenious apparatus which enabled him to bring the preparation at the required temperature on to the very plate of the microscope.

It is thus made evident that these bodies act on polarized light in the manner of a crystal. Those that M. Lehmann terms semi-liquid still present traces of polyhedric delimitation, but with the peaks and angles rounded by surface-tension, while the others tend to a strictly spherical form. The optical examination of the first-named bodies is very difficult, because appearances may be produced which are due to the phenomena of refraction and imitate those of polarization. For the other kind, which are often as mobile as water, the fact that they polarize light is absolutely unquestionable.

Unfortunately, all these liquids are turbid, and it may be objected that they are not homogeneous. This want of homogeneity may, according to M. Quincke, be due to the existence of particles suspended in a liquid in contact with another liquid miscible with it and enveloping it as might a membrane, and the phenomena of polarization would thus be quite naturally explained. [12]

M. Tamman is of opinion that it is more a question of an emulsion, and, on this hypothesis, the action on light would actually be that which has been observed. Various experimenters have endeavoured of recent years to elucidate this question. It cannot be considered absolutely settled, but these very curious experiments, pursued with great patience and remarkable ingenuity, allow us to think that there really exist certain intermediary forms between crystals and liquids in which bodies still retain a peculiar structure, and consequently act on light, but nevertheless possess considerable plasticity.

Let us note that the question of the continuity of the liquid and solid states is not quite the same as the question of knowing whether there exist bodies intermediate in all respects between the solids and liquids. These two problems are often wrongly confused. The gap between the two classes of bodies may be filled by certain substances with intermediate properties, such as pasty bodies and bodies liquid but still crystallized, because they have not yet completely lost their peculiar structure. Yet the transition is not necessarily established in a continuous fashion when we are dealing with the passage of one and the same determinate substance from the liquid to the solid form. We conceive that this change may take place by insensible degrees in the case of an amorphous body. But it seems hardly possible to consider the case of a crystal, in which molecular movements must be essentially regular, as a natural sequence to the case of the liquid where we are, on the contrary, in presence of an extremely disordered state of movement.

M. Taminan has demonstrated that amorphous solids may very well, in fact, be regarded as superposed liquids endowed with very great viscosity. But it is no longer the same thing when the solid is once in the crystallized state. There is then a solution of continuity of the various properties of the substance, and the two phases may co-exist.

We might presume also, by analogy with what happens with liquids and gases, that if we followed the curve of transformation of the crystalline into the liquid phase, we might arrive at a kind of critical point at which the discontinuity of their properties would vanish.

Professor Poynting, Planck, and Ostwald supposed this to be the case.

But more recently, M. Tamman has shown that:

• such a point does not exist
• the region of stability of the crystallized state is limited on all sides.

All along the curve of transformation the two states may exist in equilibrium, but we may assert that it is impossible to realize a continuous series of intermediaries between these two states.

There will always be a more or less marked discontinuity in some of the properties.

In the course of his researches M. Tamman has been led to certain very important observations, and has met with fresh allotropic modifications in nearly all substances, which singularly complicate the question.

In the case of water, for instance, he finds that ordinary ice transforms itself, under a given pressure, at the temperature of -80° C. into another crystalline variety which is denser than water.

The statics of solids under high pressure is as yet, therefore, hardly drafted, but it seems to promise results which will not be identical with those obtained for the statics of fluids, though it will present at least an equal interest.

§ 4. THE DEFORMATIONS OF SOLIDS

If the mechanical properties of the bodies intermediate between solids and liquids have only lately been the object of systematic studies, admittedly solid substances have been studied for a long time. Yet, notwithstanding the abundance of researches published on elasticity by theorists and experimenters, numerous questions with regard to them still remain in suspense.

We only propose to briefly indicate here a few problems recently examined, without going into the details of questions which belong more to the domain of mechanics than to that of pure physics.

The deformations produced in solid bodies by increasing efforts arrange themselves in two distinct periods. If the efforts are weak, the deformations produced are also very weak and disappear when the effort ceases. They are then termed elastic. If the efforts exceed a certain value, a part only of these deformations disappear, and a part are permanent.

The purity of the note emitted by a sound has been often invoked as a proof of the perfect isochronism of the oscillation, and, consequently, as a demonstration a posteriori of the correctness of the early law of Hoocke governing elastic deformations. This law has, however, during some years been frequently disputed. Certain mechanicians or physicists freely admit it to be incorrect, especially as regards extremely weak deformations. According to a theory in some favour, especially in Germany, i.e. the theory of Bach, the law which connects the elastic deformations with the efforts would be an exponential one. Recent experiments by Professors Kohlrausch and Gruncisen, executed under varied and precise conditions on brass, cast iron, slate, and wrought iron, do not appear to confirm Bach’s law. Nothing, in point of fact, authorises the rejection of the law of Hoocke, which presents itself as the most natural and most simple approximation to reality.

The phenomena of permanent deformation are very complex, and it certainly seems that they cannot be explained by the older theories which insisted that the molecules only acted along the straight line which joined their centres. It becomes necessary, then, to construct more complete hypotheses, as the MM. Cosserat have done in some excellent memoirs, and we may then succeed in grouping together the facts resulting from new experiments. Among the experiments of which every theory must take account may be mentioned those by which Colonel Hartmann has placed in evidence the importance of the lines which are produced on the surface of metals when the limit of elasticity is exceeded.

It is to questions of the same order that the minute and patient researches of M. Bouasse have been directed. This physicist, as ingenious as he is profound, has pursued for several years experiments on the most delicate points relating to the theory of elasticity, and he has succeeded in defining with a precision not always attained even in the best esteemed works, the deformations to which a body must be subjected in order to obtain comparable experiments. With regard to the slight oscillations of torsion which he has specially studied, M. Bouasse arrives at the conclusion, in an acute discussion, that we hardly know anything more than was proclaimed a hundred years ago by Coulomb. We see, by this example, that admirable as is the progress accomplished in certain regions of physics, there still exist many over-neglected regions which remain in painful darkness. The skill shown by M. Bouasse authorises us to hope that, thanks to his researches, a strong light will some day illumine these unknown corners.

A particularly interesting chapter on elasticity is that relating to the study of crystals; and in the last few years it has been the object of remarkable researches on the part of M. Voigt. These researches have permitted a few controversial questions between theorists and experimenters to be solved: in particular, M. Voigt has verified the consequences of the calculations, taking care not to make, like Cauchy and Poisson, the hypothesis of central forces a mere function of distance, and has recognized a potential which depends on the relative orientation of the molecules. These considerations also apply to quasi-isotropic bodies which are, in fact, networks of crystals.

Certain occasional deformations which are produced and disappear slowly may be considered as intermediate between elastic and permanent deformations. Of these, the thermal deformation of glass which manifests itself by the displacement of the zero of a thermometer is an example. So also the modifications which the phenomena of magnetic hysteresis or the variations of resistivity have just demonstrated.

Many theorists have taken in hand these difficult questions. M. Brillouin endeavours to interpret these various phenomena by the molecular hypothesis. The attempt may seem bold, since these phenomena are, for the most part, essentially irreversible, and seem, consequently, not adaptable to mechanics. But M. Brillouin makes a point of showing that, under certain conditions, irreversible phenomena may be created between two material points, the actions of which depend solely on their distance; and he furnishes striking instances which appear to prove that a great number of irreversible physical and chemical phenomena may be ascribed to the existence of states of unstable equilibria.

M. Duhem has approached the problem from another side, and endeavours to bring it within the range of thermodynamics. Yet ordinary thermodynamics could not account for experimentally realizable states of equilibrium in the phenomena of viscosity and friction, since this science declares them to be impossible. M. Duhem, however, arrives at the idea that the establishment of the equations of thermodynamics presupposes, among other hypotheses, one which is entirely arbitrary, namely: that when the state of the system is given, external actions capable of maintaining it in that state are determined without ambiguity, by equations termed conditions of equilibrium of the system. If we reject this hypothesis, it will then be allowable to introduce into thermodynamics laws previously excluded, and it will be possible to construct, as M. Duhem has done, a much more comprehensive theory.

The ideas of M. Duhem have been illustrated by remarkable experimental work. M. Marchis, for example, guided by these ideas, has studied the permanent modifications produced in glass by an oscillation of temperature. These modifications, which may be called phenomena of the hysteresis of dilatation, may be followed in very appreciable fashion by means of a glass thermometer. The general results are quite in accord with the previsions of M. Duhem. M. Lenoble in researches on the traction of metallic wires, and M. Chevalier in experiments on the permanent variations of the electrical resistance of wires of an alloy of platinum and silver when submitted to periodical variations of temperature, have likewise afforded verifications of the theory propounded by M. Duhem.

In this theory, the representative system is considered dependent on the temperature of one or several other variables, such as, for example, a chemical variable. A similar idea has been developed in a very fine set of memoirs on nickel steel, by M. Ch. Ed. Guillaume. The eminent physicist, who, by his earlier researches, has greatly contributed to the light thrown on the analogous question of the displacement of the zero in thermometers, concludes, from fresh researches, that the residual phenomena are due to chemical variations, and that the return to the primary chemical state causes the variation to disappear. He applies his ideas not only to the phenomena presented by irreversible steels, but also to very different facts; for example, to phosphorescence, certain particularities of which may be interpreted in an analogous manner.

Nickel steels present the most curious properties, and I have already pointed out the paramount importance of one of them, hardly capable of perceptible dilatation, for its application to metrology and chronometry. [13] Others, also discovered by M. Guillaume in the course of studies conducted with rare success and remarkable ingenuity, may render great services, because it is possible to regulate, so to speak, at will their mechanical or magnetic properties.

The study of alloys in general is, moreover, one of those in which the introduction of the methods of physics has produced the greatest effects. By the microscopic examination of a polished surface or of one indented by a reagent, by the determination of the electromotive force of elements of which an alloy forms one of the poles, and by the measurement of the resistivities, the densities, and the differences of potential or contact, the most valuable indications as to their constitution are obtained. M. Le Chatelier, M. Charpy, M. Dumas, M. Osmond, in France; Sir W. Roberts Austen and Mr. Stansfield, in England, have given manifold examples of the fertility of these methods. The question, moreover, has had a new light thrown upon it by the application of the principles of thermodynamics and of the phase rule.

Alloys are generally known in the two states of solid and liquid. Fused alloys consist of one or several solutions of the component metals and of a certain number of definite combinations. Their composition may thus be very complex: but Gibbs’ rule gives us at once important information on the point, since it indicates that there cannot exist, in general, more than two distinct solutions in an alloy of two metals.

Solid alloys may be classed like liquid ones. Two metals or more dissolve one into the other, and form a solid solution quite analogous to the liquid solution. But the study of these solid solutions is rendered singularly difficult by the fact that the equilibrium so rapidly reached in the case of liquids in this case takes days and, in certain cases, perhaps even centuries to become established.