Iron Crystallography

We have already devoted two previous memoirs to this question. In the first we collated and discussed the existing literature on the subject; in the second, we described the crystalline forms obtained by the reduction, at different temperatures, of ferrous chloride by hydrogen or by zinc-vapor. The conclusion from these researches was that the three allotropic states of iron—a, stable below A2; β, stable between A2 and A3; and γ, stable above A3—all crystallize in the cubic system. The differences observed were such as are customarily encountered in the crystallographic records of many minerals of which allotropic varieties or isomerides are not known, and did not conform to the ordinary definition of polymorphism.

It is, however, improbable that allotropic transformations, which are placed beyond doubt by a series of positive facts, do not involve some changes in the intimate structure.

As a matter of fact, the crystals we did obtain were too small to allow of a precise examination, and this might introduce an element of uncertainty in the firm establishment of our conclusions. Professor H. Le Chatelier was even led to think from some of our results that y-iron could very well be a rhombohedron simulating a cube, and not a true cube, and it will be remembered that the crystalline form of bismuth was for a long time incorrectly regarded as cubic.

Allotropy does not, however, necessarily involve such a deduction. Without departing from the cubic system at all, a whole series of variants may be found incompatible among themselves, and yet compatible with the same external forms. But as a study of the latter would scarcely lead to conclusive results concerning the structure of iron, other methods had to be sought to solve the question.

Optical methods are not available, but the morphological and other characters capable of yielding useful information are as follows:

1. Deformation figures:
   Continuous (a). Discontinuous—effaceable: lines of translation and folding (b); not effaceable: mechanical twinning (c).
2. Congenital twinning.
3. Twinning resulting from annealing after deformation.
4. Mechanical properties functional of the crystalline orientation.
5. Corrosion figures.
6. Synchronous crystallization figures.
7. Segregation figures.

Before we describe our experiments and the results of our observations, we shall indicate the principles of these different methods, some of which are but slightly known.

Deformation Figures

In a paper published in collaboration with Mr. Fremont we have expressed the opinion that a crystalline body may in a sense be considered both as cellular and amorphous; the former in so far as it is formed of polyhedral grains, each of which is a crystalline element of definite orientation, and the latter when the deformations are governed only by the direction of the strains and are independent of the crystalline structure.

Whence arise three kinds of deformation, which may be called crystalline, cellular, and banal. In the present work the question of cellular deformation will not arise, as our operations are restricted to isolated crystals. We are chiefly engaged in crystalline deformations. With regard to banal deformations, we shall not study them for their own sake, but only as distinctive characters when we encounter them in course of work.

Every deformation has some sort of general configuration, which may be called its silhouette, and which is the boundary of elementary deformations. It is the area of a previously polished body that loses its polish when the deformation takes place. A silhouette is naturally continuous and closed. Its form on an ordinary metal with cellular structure depends only on the form of the sample and on the nature or direction of the strains; but it ceases to be the same on an isolated crystal, for then its form can be in relation with the crystalline symmetry.

1 (a). Continuous Crystalline Deformations; Silhouettes.—If a sharp conical point is applied to a flat surface of a plastic crystal previously polished, from which all skin-hardening has been removed, a permanent deformation is obtained around the cone of penetration, the silhouette of which is not circular, as it would be on an amorphous or finely grained bed, but presents a definite form characteristic of, firstly, the crystallographic system to which the crystal belongs, and secondly, of the crystallographic orientation of the surface concerned.

These silhouettes can therefore give at least two kinds of information; that is, they can indicate the system of crystallization to which a crystalline body belongs, if that knowledge is required, or if the system is already known they can approximately orient a slice of unknown orientation.

https://www.youtube.com/watch?v=uh4obOPltpw

1 (b and c). Discontinuous Deformations.—Total deformation inclosed in the perimeter of a silhouette is an assemblage of elementary deformations which, in part at least, are discontinuous and in lines. The lines may be straight or curved. In crystalline bodies the straight lines generally have a definite crystallographical orientation. These lines, when obliterated by polishing, may or may not reappear after the re-polished surface is etched by a suitable reagent.

It is generally admitted that a crystalline body is an aggregate of identical molecular polyhedra of the same orientation, and having their centers of gravity at the intersections of a reticulated complex.

Now, it is an acknowledged fact that in a given crystalline body certain definite reticulate planes T Fig. 1, in perspective), called planes of translation, are susceptible to displacement parallel to themselves by sliding the length of one of their ranges, t, and this can take place without causing rupture. The reticulated plane, B, conjugate of T and passing by the range, t, is called the sliding-plane (plan de poussee; in German, Schiebungsebene).

Let us suppose that the plane of translation and the sliding-plane are rectangular, and that the sliding-plane is a plane of symmetry of the system. Let A B C D (Fig. 2) be a mesh of this sliding-plane, A B and C D being parts of two immediately adjoining planes of translation. If a movement of translation takes place, while CD remains fixed, A B could slide on itself.

In this movement two conditions may arise. First, A B moves to A’B’, A’ being any point in the direction A B, and the molecular polyhedra, of which the centers of gravity coincide with the intersections A and B, retain their initial orientation after displacement. There is only a change in the form of the mesh A B C D, which is now in a condition of unstable equilibrium. This would be called a simple translation. Second, A B moves to A” B”, in a position symmetrical with its original position, and, at the same time, the displaced molecular polyhedra also assume the orientation symmetrical with their first orientation, with reference to a plane perpendicular to the direction of translation. In this case mechanical twinning ensues.

The translation, with or without the formation of twins, gives place to the appearance of little straight steps on the exterior faces of the crystal, and these steps are parallel to the lines of the planes of translation. If A B C D (Fig, 8) be a portion of the sliding-plane, let us suppose that, the part C D m n remaining stationary, the plane of translation immediately adjoining m n is displaced for a short distance, involving the upper part of the system. The terminal lines A C, B D will take the profile C m p’A’ (Fig. 4) if the translation is simple, or C m p” A” if there is mechanical twinning.

To distinguish a line of translation from a mechanical twin crystal, the deformed face must be re-polished and etched by a suitable reagent. Lines of translation are not in evidence, because the molecular polyhedra have retained their orientation; the made, on the other hand, shows up—it has a definite thickness, its planes of junction are depresssed, and its corrosion figures are not the same as those of the initial crystal, since the orientation of the molecular polyhedra has been modified.

The notion of translation can easily be generalized. It is, in fact, probable that the so-called planes of translation are only the planes of easiest translation, and that when the faculty of deformation in the direction of these planes is exhausted, others enter into action in their turn. Imagine, then, that the mesh, A B C D (Fig. 2), after having been transformed by simple translation from one parallelogram into another, susceptible of conserving an unstable equilibrium, can, by other movements of translation, change into a quadrilateral—the only condition being that the area remains constant, inasmuch as the density does not change. Ultimately, when all the meshes of a crystalline body are dislocated in this manner, it becomes in a way decrystallized, and this explains the curved deformations (folds, or plissements).

These views on deformation of crystals, still comparatively little known, appear to have originated from the celebrated experiments of Reuscb and Baumhauer, on the mechanical twinning of calcite. Simple translation was introduced into science by a long series of notes due to Prof. Mugge, and published for the most part in the Neues Jahrbueh fur Mineralogie. Prof. Mugge’s researches date back to 1884 at least, but his first work was on minerals, and it was only in 1899 that he took up native metals. The same year Prof. Ewing and Mr. Rosenhain undertook, independently, the study of the industrial metals, and in a remarkable memoir, which has been followed by many more, were developing from their side the idea of translation. In the preceding considerations we have only advanced a tentative personal interpretation, ascribing to a single cause lines of translation, twinning, and folding. If we do not retain, in this instance, the term “ slip-bands ” proposed by Prof. Ewing and Mr. Rosenhain, it is because this term includes both the lines of translation and the folds, between which we consider it useful to make a distinction.

In the case of bodies belonging to the same crystallographical system, the position of the planes of translation and of mechanical twinning, and also the presence or the absence of folds, furnish many very valuable differentiation characters.

Congenital Twinning

We give this name to the twinning which takes place spontaneously during the progress of crystallization, just when the solid molecules are becoming isolated from the liquid medium which holds them in a state of fusion or in solution.

Twinning Resulting from Annealing after Deformation

This twinning results, as the name indicates, from the annealing, for a sufficiently long time and at a sufficiently elevated temperature, of a crystalline solid previously deformed.

This twinning might be susceptible of relation with mechanical twinning and the phenomena of translation. If, for example, translation has moved the point A (Fig. 2) to the vicinity of the symmetrical point A”, but without the molecular polyhedron, which has its center of gravity at A”, having assumed the orientation corresponding to the new position of the system, annealing, when widening the molecular intervals, could render the molecular polyhedron A free to assume the position of twinning equilibrium, which, as a result of the deformation, the system alone had taken, or nearly so. The twinning will only then be consummated. Provided matters actually proceed in this fashion, the annealing simply completes the work of deformation.

Mechanical Properties Functional of the Crystalline Orientation

The possible variations in these properties result from the very definition of the crystalline structure. It has been a known fact for a long time that the cleavage-faces are faces of minimum hardness, and that on the same face the hardness varies with the direction and along the same direction with the sense of the striation.

Synchronous Crystalline Figures

When a body is caused to crystallize on a crystalline face of another body, it occasionally happens that the structure of the latter orients the molecules of the crystallizing body to the extent that, as they separate from the bath, it imposes upon them a pseudosymmetry which does not naturally belong to them. These anomalies can eventually give certain indications concerning the crystallography of the dominant body.

Segregation Figures

When a body, liquid or solid, deposits several successive solid phases, the deposits of the second or third consolidation frequently settle by preference between certain definite crystallographic planes of the deposit from the first consolidation, and in this way show up its structure.

These planes between which the segregation takes place are probably the planes of maximum separation, or, which comes to the same thing, planes of the greatest reticular density.

Experimental Section

Such are the methods we have used or attempted to use.

All of them, of course, have not furnished results which could be used for the end we had in view—that is to say, means of diagnosis applicable to the different varieties of iron. Whether by reason of their inappropriateness, or because we did not know how to make use of them, certain of them have given negative results. This will not deter us from describing any facts observed, whether positive or negative, which could suggest ideas for fresh experiments to other workers.

We must evidently work for each of the allotropic varieties of iron within those limits of temperature where the particular variety is stable.

For α-iron there is no difficulty, since ordinary temperature is within the range of stability.

For β-iron, which cannot be wholly kept in unstable equilibrium, temperatures between 750° and 855° C. (we retain the temperatures indicated in our preceding publications. To take into account the new pyrometric standards, these figures must be raised to about 780° and 890° respectively—that is to say, to the figures given by Roberts-Austen or by Carpenter) are required, as far as possible about the middle of the interval, in the neighborhood of 800°. Besides, a crystal of α-iron heated in the range of β-iron, and cooled to the ordinary temperature, becomes again the same crystal of α-iron—the system persists beyond transformation A2.

This is not the case with the passage of the point A3, provided it has been sufficiently exceeded, and for a sufficiently long time. It is quite possible, if the heating and the cooling down are both done rapidly, to heat a crystal of α-iron up to 900° without destroying it; but if it is maintained at this temperature, the crystal resolves itself into little grains, with the formation of elongated lamellae, which appear to be twin crystals. Fig. 5 is a photomicrograph (100 diameters) of face p(001) of a crystal of iron, after two hours’ heating at about 1,000°; etched, after re-polishing, by alcoholic picric acid; the sides of the photomicrograph are parallel to the sides of the square of the original crystal.

It is therefore preferable for the study of the crystallography of y-iron to resort to the alloys of iron with carbon and manganese, nickel or chromium; naturally selecting from these alloys those that are not magnetic at the ordinary temperature.

In all cases it is expedient to have the crystals as large as possible.

As regards α- and , β-irons, thanks to the generosity of Professor Tschernoff, we had at our disposal a beautiful specimen from an open-hearth furnace, with large cubic cleavages, containing C, 0.05; P, 0.30; Mn, 0.00 per cent.

Another sample, still more remarkable, was procured for us by Mr. Werth, director of the metallurgical works of Denain and Anzin. It consists of the fragments of an old steel rail, which during 15 years had served as a guide to a damper in a furnace-chimney, and of which certain parts had during this long period of time been submitted to conditions favorable to the development of crystals. That is to say, in accordance with Mr. Stead’s excellent work, to a temperature slightly inferior to A2.

Chemical analysis of the sample made in the laboratory at Denain yielded C, 0.06; Si, 0.05; S, 0.02; P, 0.116; Mn, 0.30 per cent. Yet the amount of carbon found must be above the mean, inasmuch as we have encountered no traces of cementite in the numerous sections we have made, and the other oxidizable elements are to a great extent scorified away, so that the metal is almost pure iron, in crystals, of which some attain a magnitude of several cubic centimeters.

For γ-iron we have used a fragment of ordinary cast manganese steel, which Mr. Hadfield kindly had taken from the interior of an ingot, in the region of final consolidation. Another sample came to us from the Imphy Steel Works, and contained C, 0.15; Si, 0.30; P, 0.023; Mn, 0.23; Ni, 24.80; Cr, 2.21 per cent. Although special precautions had been taken to delay the cooling, this sample, which was in the form of a round bar, presented a comparatively fine grain inappropriate for crystallographic researches.

We deformed a piece of it which was afterwards annealed at about 1,300°, and obtained equi-axial grains of a mean diameter of 1 mm. Mr. Hadfield’s manganese steel, on the contrary, showed on fracture distinct crystallites with rectangular branches. It is known that the axes of a crystallite in the cubic system are the quaternary axes of the cube; consequently it was possible to cut sections with a known crystallographical orientation.

Continuous Crystalline Deformation; Silhouettes

The principle of the method has been described above. A sewing-needle served for the tests at the ordinary and at lower temperatures; it was broken, and a point perfectly acute, with an angle of about 60°, was re-made at the hardest part by rubbing on emery-papers of increasing degrees of fineness.

This needle, a (Fig. 6), is fixed by a vise in a socket, D, which can slide along the lever, A B, and be fixed at any point in its length. The lever, A B, is articulated at A on a movable guide along the vertical arm, E F. To obtain a silhouette by the pressure of the point on a polished crystallographical face, the prepared specimen, G, is placed on the support, H, in such a way that the polished face is horizontal. A is moved the length of E F until the lever, A B, is also horizontal and the point just meets the piece G. Then suitable weights are sus-

pended from B so that, taking into consideration the length of the arms of the lever, a desired pressure is brought on a.

Between 200° and 400° C. the ordinary needle would lose its hardness; so it is replaced by a needle made of high-speed steel.

Above 400° C. it is no longer possible to work in the open air; the oxidized film obliterates the silhouettes and the lines. The experiment must be made in hydrogen or nitrogen, and the needle made from cast quartz.

A porcelain tube, A B (Fig. 7), is heated along C D in a Mermet furnace. The extremity, A, is closed by a cork, E, which abuts against a wall, F. Another porcelain tube, G H, with an external diameter rather smaller than the internal diameter of A B, rests against the cork, E, at one end, while at the other end the specimen to be tested, I, is placed, along with two pieces, K, of the same metal, which press between them the end of a Le Chatelier couple.

The pieces, I and K, form together a cylinder which passes into the tube without friction. The quartz needle, L, is set in an iron tube, M, passing with slight friction the cork on the right, N, and resting on a partition, O, of thin sheet-iron diametrically placed. The wires of the couple, P, Q, pass between the tube and the cork, N, and are separated from one another within the tube by a pipe-clay tube.

The holder of the needle serves also as the gas-inlet, and is perforated with a hole, P, for the purpose. To make a test, the apparatus is cleared out by means of pure dry hydrogen, entering at P, and passing out at the tube, S, which penetrates through the cork, E, and is bent at a right angle. When this is done, S is closed, because the play between the handle of the needle and the cork, N, is too great to insure a fast joint, and it is by this passage that the gas now escapes. The furnace is lighted, and the temperature raised very slowly to the desired degree. When this is attained the needle is pushed against the polished surface, I, and pressed against it. With a little practice the pressure is easily regulated, so as to obtain impressions that are neither too large nor too small.

The same set of apparatus could serve for nitrogen were it not that the difficulty of drying nitrogen is greater than in the case of hydrogen; because tubes of sodium, which give off hydrogen as a result of the decomposition of the water-vapor, are not available, and to keep a polished surface of iron intact the desiccation must be perfect. We have therefore modified the apparatus in the following manner :

Two similar iron tubes, A and B (Fig. 8), closed at the lower end, are placed upright side by side in a nickel crucible, C. The test-piece, D, is placed at the bottom of tube, A, and covered with a convex disk, E, of thin sheet-iron, with a small hole in the center, which supports the point of the needle, F. At the bottom of tube, B, there is a piece of iron, G, in which is inserted the end of a Le Chatelier couple, the wires from which, H, I, are separated from one another by a pipe-clay tube, and from the iron tube by a cylinder of mica. In making an experiment the crucible is filled with iron-turnings, which regulate the temperature, while A is filled up between the tube and the holder of the needle with iron which has been reduced by hydrogen at an incipient red heat; the whole is heated over a Meker burner until the desired temperature is attained. This temperature is maintained, and the holder, K, of the needle is pressed. The pressure-figure is made, and there is nothing more to do but to let the test-piece, D, cool before removing it.

The iron should be reduced by hydrogen at a temperature sufficiently high for it not to be pyrophoric, and yet just as low as possible. It then serves to absorb the small quantity of oxygen retained at the bottom of the tube, and also any that may leak in during the progress of the operation. Its use was suggested to us by Mr. Lebeau, and it has succeeded perfectly. The compact iron is less prone to oxidation, and is protected by it. At first we tried copper, which is, in fact, protected by the iron; then we tried Goldschmidt manganese; which arrests the oxidation of iron quite well, but affects its surface, probably on account of the presence of impurities.

According to circumstances, one or other of the three apparatus mentioned has been used.

On α-iron the indenting has been done at the temperature of liquid air, at the ordinary temperature, at blue temper, and at 600° C.

On β-iron at about 800° C.

On γ-iron at 900°, and when employing manganese or nickel steels, at the ordinary temperature.

In every case the silhouettes have the same form on the same crystallographic face, whether the iron was in the state α, the state β, or the γ-state.

On the cube face p(001) it is a cross, of which the arms are parallel to the diagonals of the square, and which has four axes of symmetry parallel respectively to these diagonals and to the sides of the square.

On a rhombododecahedral face b¹(011) the figure may still have four arms, but not rectangular. Most frequently these branches coalesce in pairs, and give a silhouette of two sheets turned towards the faces of the cube which are perpendicular to the section under consideration. The figure has only two axes of symmetry, parallel respectively to the sides of the rectangle.

On an octahedral face a¹(111) there is a figure with three lobes, of which the axes of symmetry are the heights (or bisections) of the equilateral triangle.

To represent these silhouettes, let us imagine a cleavage-cube which has been subject to the truncations b¹ and a¹ apply these truncations to the face of the cube, which they cut at

45°, and project the whole on the plan of the illustration. We shall thus have Fig. 9, upon which the silhouettes that we have just described are drawn.

These results confirm the conclusion that we have drawn from our previous trials—that is to say, that the three allotropic varieties of iron belong to the cubic system. In fact, this is the only system that can give figures with four axes of symmetry on three rectangular faces. The quadratic system could only have these on the bases p(001) parallel with one another, and the cross, with four axes of symmetry, obtained fortuitously on one face, would not be repeated on an adjacent rectangular face, as we have ascertained does happen. In the rhombohedric system the symmetry on one face p(100) is, of course, very poor. Hence, with bismuth, which crystallizes in rhombohedra, simulating cubes, the pressure-figure on a polished natural face is that shown in Fig. 13 (75 diameters). There is only one axis of symmetry, parallel to one of the diagonals of the rhomb. Perpendicular to this axis there are the twin crystals or the lines of translation which have been described by Prof. Mugge.

Of course our conclusions assume that iron remains in the γ-state from the point A3 up to fusion. Should it be demonstrated that the point of Ball and Curie, about 1,300°, corresponds to an allotropic transformation, it would be necessary to split γ-iron into two and to revise matters.

Discontinuous and Effaceable Deformation Figures

Every mode of deformation can be employed to produce these lines. But we have principally resorted to that which has already served us in obtaining the silhouettes described in the preceding section—that is to say, the normal pressure of a needle.

α-Iron.—The crystals are sliced from the cleavage-faces.

We shall first describe as typical the tests made at the ordinary temperature. The results are assembled in Fig. 10. The weight on the needle was 1.6 kilograms.

On face p(001) the branches of the cross are formed of the folds c d e f, which envelop one another. The portions c d, e f are nearly parallel to the diagonals of the square, and might be lines of translation; they are connected together by an approximately semicircular arc. Sometimes, from some unknown cause, this arc is replaced by a line, g h, which is comparatively straight and parallel to one diagonal of the square, and is connected by small arcs to the lines h i, g f.

On the truncation b¹(011) the figure as a whole is still a cross, but its arms, X X, Y Y, are no longer rectangular. The acute angles, X O Y, are turned towards the intersection of the truncation with the face of the cube which is perpendicular to it. The arms are formed of the folds, c d e, roughly elliptical, and enveloping one another. Almost always these folds, instead of closing up, coalesce on the bisection of the acute angles, either after inflection, as represented at f g, or without inflection, as at k i h. No straight line is visible.

On truncation a¹(111), one can observe on each of the three axes of symmetry: firstly, nearly straight lines, c d, which are situated between the point of impact and a summit of the triangle, and parallel to the side opposed to this summit; secondly, curved lines, e f, which part at e from one of the axes of symmetry between the point of impact and the side of the

triangle normal to the axis concerned. These lines, e f, have at their origin the aspect of spirals; they may bend, following g f towards the adjacent axis of symmetry, but more frequently they coalesce, as at h, with the straight lines c d, or again with their neighbors after inflection, as at i, or without inflection.

Other tests have been made on face p(001) at various temperatures. The silhouettes are the same in all cases, but the details may show some variation.

At the temperature of liquid air, under charges of 1.5 to 3 kg., the silhouettes are nearly without details.

At a blue temper beat there were produced many times one or more branches, such as i k l m (Fig. 10; face p)—that is to say, formed exclusively of straight lines; but these could not be reproduced at will.

At about 600° C. in hydrogen, the figure is the same as in the cold, but more subdued, and with little detail.

β-Iron.—It seems that at a red heat in hydrogen the polished iron surface suffers some modification, and that a superficial skin forms which masks the details of the deformation; even after cooling, fresh indentations made at the ordinary temperature show nothing more than the silhouette.

It is true that the details may be made to appear later on, either by spontaneous oxidation in the air (Fig. 14; 150 diameters; face p), or by etching with picric acid; but much sharper results are obtained by working in nitrogen with the apparatus (Fig. 8).

On face p(001) the arms of the cross are exclusively formed of folds which cover or envelop one another; these folds appear to be generally more rounded than those of α-iron.

On face b¹(011) the figure is the same as that for α-iron.
On face a¹(111) the straight lines seen with α-iron are no longer observed. The curved lines similar to the contours of the silhouette alone remain. See Fig. 11.

γ-Iron.—On face p(001) the lines which cover the silhouette of the cross are straight, and parallel to the diagonals of the square.

On face b¹(011) the lines are again straight, and belong to three systems—one is parallel to the intersection of the truncation with the face of the cube which is normal; the other two are symmetrical in relation to the sides of the rectangle, and make with one another, with a very gratifying approximation,

the theoretical angle of the faces of the octahedron—that is, 109° 28′.

In face a¹(111) the lines are always straight, and parallel respectively to the three sides of the equilateral triangle.

The results are arranged on Fig. 12.

We have also made deformation tests on practically pure iron above 900°. Under these conditions, we have seen a single crystal break up into grains; but under the condition of working in hydrogen, there are on these little grains lines of deformation; they are still straight lines—lines of translation.

The curved lines of β-iron and α-iron are therefore not attributable to a question of temperature. (We learn, subsequent to writing this note, that Mr. Rosenhain has made observations on γ-iron which agree with ours, and which were presented at the meeting of the Iron and Steel Institute in May.)

If we compare the three varieties of iron, we see at the start that the lines of deformation are exclusively straight on γ-iron. γ-iron, hence, has planes of easy translation, and according to directions noted, these planes are the planes

a¹(111)—that is to say, parallel to the faces of the octahedron, exactly as in the case of copper, gold, silver (Mugge), and lead (Humphrey).

On β-iron the lines are exclusively curved; there are no planes of translation.

On α-iron there is, at least on faces p, and especially on faces a¹, a mixture of straight and curved lines. The orientation of the straight lines apparently proves the existence of planes of translation parallel with the faces of the octahedron—planes also referred to by Messrs. Ewing and Rosenhain, and of which we had previously disputed the presence in iron. But the curved lines dominate considerably, therefore the translation is difficult, and the greater part of the deformation seems due to another mechanism.

We have employed on α-iron other modes of deformation— tensile tests, compression, bending—and in every case we have found scarcely anything but curved foldings, without any relation to the crystallographic directions either as a whole or in their details. We shall cite only one experiment, which appears to us convincing. We impressed the pressure-figures—that

is to say, the cross of Fig. 10—upon a crystal cut into an elongated rectangular sample, and presenting on two lateral faces the faces of the cube; the figures indicated immediately the crystalline orientation. Then we submitted the bar to gentle bending a little beyond the limit of elasticity. This new deformation produced new lines in the vicinity of the crosses, and on the crosses themselves; Fig. 15 (200 diameters) shows one of the crosses and its surroundings. It will be noticed that the lines produced by the bending are neither parallel to the diagonals of the square (axes of the arms of the cross) nor to the sides of the square, as they ought to be, if they were the lines of translation following the faces of the octahedron or of the cube.

Non-Effaceable Deformation Figures: Mechanical Twinning 

The lines that have just engaged our attention, lines of translation or foldings, if obliterated by re-polishing, do not reappear under the influence of etching. And, to our knowledge, slight static deformations produce no others.

On the other hand, under certain circumstances that we are going to examine, lines are obtained that etching reveals after re-polishing. These are actual lamellae, with very slight but decided thickness; in other words, mechanical twin crystals or macles.

α-Iron.—The lamellae known as Neumann’s lamellae or lines, in honor of the savant who discovered them in 1850, have been recognized for a long time in cubical meteoric iron and in kamacite (nickel ferrite). Their presence in terrestrial iron was noted by Prestel. (For the history of Neumann’s lines we have drawn, to a large extent, on the excellent book of Professor Cohen, MeAeoritenkunde, Stuttgart, 1894.)

Neumann’s lamellae are visible frequently to the naked eye, on a cleavage-face. On these faces they are parallel either to the diagonals of the square or to the lines which join the angles at the center of the opposed edges (Fig. 16).

After polishing to low relief, they appear as slight depressions on the faces of the cube, sometimes as depressions, sometimes in relief upon any other crystallographic section. The best reagents for showing that they have a decided thickness are alcoholic picric acid and nitric acid, the latter very dilute (1 in 500), which gently eats away the planes of junction (Pigs. 17, 250 diameters, and 18, 600 diameters). With reagents susceptible of giving corrosion figures, the interior of the lamellae can assume a different
color from that of the principal crystal which contains them.

The lamellae may be of uniform thickness, like those to be seen parallel to the sides of Fig. 17, or present a more or less regular indentation, probably connected with the formation of another system of lamellae (Fig. 18). Fig. 19 (250 diameters; etched with picric acid) is a good example of indented or jagged lines on a non-oriented section.

If the etching is vigorous—for example, with 10 per cent, nitric acid for half a minute, after a previous etching for four minutes with double chloride of copper and ammonium to show the corrosion figures—Neumann’s lines are then very much enlarged; they become visible like so many fine file teeth, and if they are numerous enough, give the piece a watered aspect.

Seen through the microscope, the line is channeled (Fig. 20; 250 diameters), but these channels, corrosion figures, markings of strong etching, extend really to the edges of the lamellae, and it becomes almost impossible to distinguish the lamella itself from the corrosion figures belonging to it.

Neumann’s lamellae have given rise to numerous works. It is agreed to regard them as twin crystals; but many divergent opinions have been expressed on the nature of these twins, on their position in the principal mass, and on the law of twinning.

Neumann and, later, Tschermak admit that it is a question of fluorspar twinning, which is represented (Fig. 21, 1a and 1b) in elevation and plan; the octahedral face is the plane of

twinning, and the ternary axis the axis of twinning. As there are four ternary axes, the lamellae could belong to four cubic sub-elements imbricated in the dominant cube; and the twenty-four faces of these four sub-elements, identified with the planes of Neumann, would consequently be parallel respectively to the faces of the trioctahedron a½( 122). Fig. 21, 1c, indicates the position corresponding to a lamella on a diametrical plane passing through two edges of the dominant cube; the face of junction is the face of the cube of one of the sub-elements.

Rose, who only studied the direction of etched lines, could not decide whether the lamellae are parallel to a½(122) or to a²(112).

Sadebeck has observed, on a cleavage-face of the dominant cube, that the faces terminal to those of the lamellae, which make an angle of 45° with the sides of the square, make an angle of 144¾° with the plane of the face of the cube. Regarding these terminal faces as the cleavages of the sub-ele-

ments, he concluded that the plan of twinning belonged to a trioctahedron (20.20.9)—the axis of twinning being perpendicular to a face of this trioctahedron. The law of association, represented by Fig. 21, 2, thus would become very simple; for in accordance with this law, and in the case of the two elements twinned, if one considers two faces of the twinned cubes cutting one another in the direction of a common diagonal, the face of one of these cubes is a face of the trapezohedron (112) of the other; moreover, in the same zone, an octahedral face of the dominant cube is the rhombododecahedral face of the secondary cube.

Finally, Linck admits, with Neumann and Tschermak, the law of fluorspar twinning, but the junction faces should be a²(112) and not a½(122). See Fig. 21, 3c. Under these conditions the planes of junction have the same notation for the two unit elements twinned. The planes a²(112) are at the same time planes of translation : the summit d of the mesh a d b c (Fig. 21, 3c) of the dominant cube has only to be transported at d’, parallel to a b, in order to form the twin.

In face of these different opinions, fresh researches would apparently not be useless.

Taking a trihedral cleavage-angle on Professor Tschernoff’s iron, we cut a rectangular parallelopiped measuring about 15 by 15 by 7 mm., consisting mainly of a single crystal. We polished, etched, and photographed the six faces successively, and stuck the photographs on a wooden model of the size desired. The lamellae of Neumann could in this way be followed on two or more faces; they were very numerous in the specimen, and it was certain that they were always parallel to the planes a²(112), which contradicts Tschermak’s law of junction, and confirms that of Sadebeck and of Linck. The law of twinning still remained to be decided. It appeared difficult to decide experimentally between the two which have been proposed: Neumann’s lamellae are far too thin to permit of them taking pressure- figures ; and for the same reason one would not fare better in attempting interpretable corrosion figures. But it may be remarked that Sadebeck’s twin would be unique of its kind. The observation which suggests this—that is to say, the angle of 144¾° made by the fracture-facets of the lamellae with the plane of cleavage of the dominant cube—is easily explained by Linck’s conception : these fracture-facets are just simply the planes (112) of the lamellae; and an experiment made on the principal dominant cube shows actually that the planes of junction (112) of Neumann’s lamellae are also the possible planes of fracture. Therefore Linck’s theory seems to us sufficiently demonstrated.

The question whether Neumann’s lamellae are congenital twin-crystals, as-Tschermak thought, or the result of mechanical twinning, in accordance with the common view of Sadebeck and Linck, remains to be decided. If we have to deal with congenital twinning, or a product formed during solidification, the twin crystals would really belong to γ-iron; but as we do not depart from the cubic system, the system would be maintained throughout the transformations, and a twin of γ-iron remain a twin of α-iron. There is, therefore, no objection on this head. But congenital twins are of the same magnitude as the crystals from which they are derived, since the development of the two elements twinned has been simultaneous. Neumann’s lamellae, on the contrary, are extremely small; moreover, as we have seen (Figs. 18 and 19), they are frequently inflected and thrust aside by meeting lamellae of another system. Linck has also observed in the meteoric iron of Braunau that the delicate lamellae of rhabdite, (Fe, Ni)3P, are broken and thrust aside by the lamellae of Neumann; at least, it is easy to produce these lamellae artificially by deforming, by shock, a fragment of crystal, of which the pre-existing lamellae have been recorded by a photograph. Notably when a crystal of iron is cleaved, Neumann’s lamellae appear in abundance on both sides of the cleavage-face.

Therefore there is no doubt that Neumann’s lamellae are mechanical twins. Up to the present we have only been able to obtain them by shock, and more readily the lower the temperature. The Swedish iron that Mr. Hadfield ruptured by traction at the temperature of liquid air, exhibits many of them in the vicinity of the fracture. At the ordinary temperature, the production of lamellae is still easy, at least by shock, as we have already said. But it does not take place at the temperature of blue temper, nor at higher temperatures.

β-Iron.—In this case there are no known mechanical twins.

γ-Iron.—Slight deformation, without shock, only gives effaceable lines of translation. But more severe deformation furnishes twins as well. On our nickel-chromium steel from Imphy we have impressed marks deeply in the cold; the surface marked in this manner was partly filed, re-polished, and etched with a hydrochloric solution of iron perchloride. The etching shows, in the region of most deformation, parallel double lines, with the space between of different coloration from that of the grains in which they occur—this is therefore a question of twins. To determine the orientation, the etched piece was subjected to slight general deformation; lines of translation appeared, and it was always observed that one of the systems of lines was alongside or parallel with the twins.

If the twins are represented by heavy lines, and the lines of translation by fine ones, the scheme, Fig. 22, is obtained. The octahedral faces are, at the same time, planes of translation, planes of twinning, and planes of junction. The occurrence is frequent in the cubic system.

The same twins are obtained in manganese steel quenched at yellow heat, but they are localized around the lines of fracture, and are due to the tensile stresses which have caused these fractures (Fig. 23, of 200 diameters, and Fig. 24, of 800 diameters, etched with 5-per cent, alcoholic picric acid).

When the same metal is subjected to an alternative series of polishings and etchings, reliefs form around the patches of cementite or other foreign substances which have not been dissolved, and on these reliefs the polishing alone results in the formation of twinned lamellae (Fig. 25; 200 diameters; etched 30 seconds by a solution of ferric chloride, containing, per cent., 10 parts of concentrated chloride and 6 of hydrochloric acid).

Figures 23, 24, and 25 recall martensite exactly, and thus offer an easy explanation of its structure: the partial transformation of γ-iron into α-iron, a transformation which starts below 400° C. in the case of sudden quenching, and causes considerable stresses. These stresses, in their turn, involve a more or less complete formation of an infinity of twins, parallel in each grain to the four pairs of octahedral faces; hence the frequency of square figures and equilateral triangles on a chance section.

The structure of martensite is hence a structure peculiar to γ-iron, although the iron is not present in the γ-state, at least for the most part. Even after tempering, when all the iron has resumed the α-state, if the temperature and duration have been sufficiently controlled to prevent the reconstitution of equiaxial grains which characterize α-iron, the α-iron may be retained pseudomorphic on the martensite structure of γ-iron. The grains are in this way cut up by an infinite number of extremely thin lamellae parallel to four different planes; the continuity of the cleavages p(001) is broken, and the natural fragility of α-iron, due to these cleavages, is evaded. Hence the part played by quenching and tempering in the amelioration of mild steels.

This structure of martensite is that of octahedral meteoric irons on a reduced scale. It is known that these irons are formed of comparatively thick lamellae parallel to the four pairs of regular octahedral faces. Disregarding the taenite (alloy rich in nickel), the schreibersite, (Fe, Hi)3P, and the plessite (mixture of taenite and kamacite), which may be found interspersed among the lamellae, the latter are composed of α-iron containing about 7 per cent, of nickel in solid solution, and have received the petrographic name of kamacite (from Kauaf, beam). This is still a structure of γ-iron; Although the iron has resumed the α-state, this structure is preserved because, in the presence of nickel, the point of transformation A 3 is lowered to such an extent that the α-iron cannot resume its natural structure of equiaxial grains. The position is exactly that of martensite tempered at a moderate temperature. The α-iron remains crystallized on the axes of the γ-iron.

Linck was already convinced that he could affirm octahedral meteoric irons being polysynthetic aggregates of four twinned cubic sub-elements with a dominant cube, following the ordinary law: a¹(111) plane of twinning and plane of junction. We have tried to verify this affirmation on a fragment of a meteorite brought from the neighborhood of Timbuctoo by Mr. Ward. This fragment, taken from near the periphery, was unfortunately a little deformed. For this reason we have not been able to put Linck’s law to the test by the study of Neumann’s lines, on a section parallel to a face of the dominant cube. The directions observed differed too much from the theoretical to allow a verification of the law; but this difference would be explained by the notable deformations manifestly sustained, the least deformation causing the angles to vary rapidly. In fact, the method was too delicate in character. We then turned to a coarser and consequently more appropriate method, that of pressure-figures. If Linck’s theory is true, a face p(001) of the dominant cube cuts the associated four twinned secondary cubes on the planes a½( 122). Every pressure-figure on such a face of the dominant cube ought then to be characteristic either of a plane (001) or of four planes (122) variously oriented, and no other figures ought to be formed. This is what experiment has fully confirmed, verifying again, in this instance, the conclusions to which Linck had been led by other methods.

Let us add that this polysynthetic structure is by no means peculiar to iron. There is a tendency for it to take place whenever allotropic or isomeric changes are produced in the solid state with a change in volume, so that the resulting tensions can effect mechanical twinning. It is in this manner that Mr. Breuil has been able to show martensitic structure in hardened aluminum bronze, a fact which has been confirmed by Dr. Guillet. These are only specific cases of a general phenomenon.

Congenital Twinning

This can only be encountered in γ-iron, which alone crystallizes from the liquid state. But as we have said, in connection with octahedral meteoric irons, these twins of γ-iron could, under favorable circumstances, be preserved in the α-state. It is in this way that Tschermak tried to explain Neumann’s lamellae. But this explanation, although it did not prove reliable in this particular case, is plausible in itself ; and it may yet be asked if adjacent grains of a crude ingot of iron, each of which grains can represent a primitive crystallite or part of one, could not form twinned groups among themselves.

It is this that we have endeavored to investigate on the same crystal of iron of which we have already spoken, and which has served us in studying the crystallographical position of Neumann’s lamellae. The rectangular parallelopiped cut on three cleavage-faces contained, in fact, besides the dominant crystal, fragments of three or four adjacent grains. If a face p(001) is etched by Heyn’s reagent (12-per cent, double chloride

of copper and ammonium) during 30 seconds, then by (1 to 5) nitric acid, to eat out Neumann’s lines, the sections of the foreign grains viewed in vertical light have in general a much deeper tint than that of the faces p(001) of the dominant cube. Moreover, on the latter themselves darker veinings can be seen. Fig. 26 (10 diameters), the sides of the photomicrograph are parallel with the sides of the face of the cube. When these veinings or marblings are studied it is seen that, as regards direction, they are related to the foreign grains. The micrograph reproduced furnishes an example: it shows seven dark bands slightly inclined to the vertical; the middle and longest one is more pronounced than the others, and is not crossed by the Neumann’s lines which meet it; this is a fragment of a foreign crystal, whereas the parallel bands crossed by Neu

mann’s lines form integral parts of the dominant crystal. Under high magnifications of the microscope, while the plain portions show beautiful square corrosion figures (Fig. 27, 1200 diameters, with the sides of the photomicrograph parallel to the diagonals of the square), the dark marblings show much smaller and less decided figures, separated by furrows strongly depressed, where, with the light and focus delicately adjusted, square forms can be recognized (Fig. 28; 1200 diameters). There is no doubt that these marblings represent crystallite branches which arise from one of the neighboring grains after solidification. These branches in course of a very slow cooling were assimilated below the point A3 by the crystal which they penetrate. Only, although the assimilation was crystallographically complete, since Neumann’s lamellae have nothing to do with the marblings, there yet remained some recognizable traces of the difference of origin, which are rendered evident by the copper chloride.

The grains that retained their own orientation different from that of the dominant crystal, are the residues of the primary crystallites. Therefore, from the actual orientation of the foreign grains we can see if these primary crystallites are formed in the position of twins. In that case, the face of the dominant cube will cut the twinned cubes on the planes a½(122), as happens in the octahedral meteoric irons. The experiment made with pressure figures only confirmed this conjecture for one grain in three. But the two other grains may originate from a different group; it would therefore be imprudent to draw a definite conclusion either one way or the other.

Twinning Resulting from Annealing after Reformation

Such twins as these are produced with greatest ease in copper, bronze, brass, etc., as shown by the work of Prof. Heyn, Mr. Charpy, and others.

When a crystal of iron which has suffered partial deformation—by the pressure of a needle on a face of the cube, for example—is annealed either below A2 or between A2 and A3, the region of most deformation—-that is to say, in the case under consideration, a ring round the point of impact—resolves itself into little grains of various crystalline orientation (Fig. 29 ; 60 diameters ; etched with 5-per cent, alcoholic picric acid); but these new grains never show twinned lamellae.

With γ-iron it is not the same. Our sample of nickel-chromium steel, which, as rough cast, contained no twin, developed a large number when cold-deformed and annealed at about 1,300°. It remained to determine these twins, although from our knowledge of meteoric irons it, a priori, was highly
probable that-we-again had to do with a¹ twinning.

The grains were much too small, with a mean diameter of 1 mm., to permit of isolation and slicing, so a chance cut was made. It was probable that on this section, which contained a hundred or so grains, there would be some presenting spontaneously a cube face. To find them, the whole

piece was subjected to slight general deformation in two directions at right angles, so as to show lines of translation in the polished section, and microscopic search was made for grains presenting two systems of rectangular lines and no others. We found one of sufficient size fulfilling these conditions (Fig. 30, above the line A B). This grain is cut precisely by lamellae A a q b, c d e f, g h o B, q p r s, parallel to one of the systems of lines, without having the second: they are twins, and we happen to be on a face p(001) of the dominant cube, or nearly so. To make certain, indentations were made with the needle, and the cross of the cubic faces was obtained in good form, and on one of the twins a different figure. However, on looking closely into the matter, it was observed that the arms of the cross inclined slightly to the vertical lines; that the crosses gave rise to a new system of lines also slightly inclined to the vertical, and that the line a b, boundary of the twin that we have figured perpendicular at A B, is not exactly so. This was therefore not a true p(001) face, hut it did not deviate much from one. To rectify matters, a cut was made perpendicular to the first following A B, and this is represented by the lower part of Fig. 30, after reduction to the plane of the picture.. This section, encounters the twins A a b’, c e d’ f’, g i h’ k’, l m’ B, belonging to two different systems.

If it is a true b'(011) face, and if our conjectures concerning the nature of the twinning are well founded, the lines a b’, c d’, etc., should make an angle of 54° 44′ with AB. In reality, as may be supposed after the remarks made, these conditions were not well fulfilled. But taking the direction of the lamellae for a guide, the first cut was adjusted on a fine grindstone, then the second, and so on progressively. When the work was done, the two rectangular faces ought to be exactly p(001) and b¹(011) respectively; and the lamellae ought to make with AB an angle of 90° on the first and of 54° 44′ on the second. From measurements made on the photographs with a protractor, the angles are respectively 89° and 54½°, which is a satisfactory result, more particularly as the production of lines of translation necessitated a slight deformation. The twinning resulting from annealing γ-iron is then the same as the mechanical twinning, with a¹(111) for plane of twinning and plane of junction; it is possible, as we have already said, that the annealing simply develops the germs of mechanical twins.

Mechanical Properties Functional of Crystalline Orientation

α-Iron.—Two prismatic test-pieces were taken in the same crystal previously annealed at about 800°, and cut in such a way that one of the axes of the figure was in the one case parallel to a quaternary axis of the crystal (lateral faces parallel to p(001), p(001), b¹(011), b²(012)); in the other case to a ternary axis (lateral faces parallel to b¹(011) and a²(112)).

These two test-pieces were submitted to compression, with the following results:

Trials of hardness were also made by Brinell’s method, under a charge of 140 kg., applied during 2 min. with a ball of 5 mm. diameter, with the following results :

The number for the mean hardness of metal annealed at bright cherry red (70) is notably lower than the minimum (76) of Dr. Benedicks for iron also annealed; this is explained by the absence of joints in our sample.

Each of our numbers is the mean of four impressions measured in two rectangular diameters. These impressions are neither so sharp nor so circular as on metals with fine grain, where they affect a large number of grains of varied orientation. Consequently there is some uncertainty in the measurement of the diameters, and as the differences appropriated to different faces do not much exceed the limit of experimental errors, the question may be asked if these differences are quite positive. We do not think, however, that doubt can be cast on them, since we have two simultaneous series concordant among themselves, with the compression tests and with the general law which assigns the minimum hardness to cleavage-faces.

The conclusions are that the mechanical properties of α-iron vary with the crystallographic orientation.

γ-Iron.—For this purpose Mr. Hadfield’s manganese steel was used. The grains were sufficiently large to permit of test being made with the ball.

On face p(001) the impressions are not circular : the diameters parallel to the diagonals are about 10 per cent, longer than the diameters parallel to the sides, by reason of swelling in the direction of the former. Means were taken.

On faces b¹ and a¹ the impressions are circular.

Under a charge of 200 kg., applied during 2 min. with a ball 5 mm. in diameter, the results were:

These numbers indicate a very moderate maximum of hardness on face b¹(011), but the differences between different faces are less than those observed between two adjacent impressions on the same face, γ-iron is hence practically isotropic as far as the mechanical properties are concerned.

Corrosion Figures

The corrosion figures of α-iron on face p(001) have been described by Mr. Stead and Mr. Heyn. It is known that these are squares parallel to the edges of the cube face. We have given above a photograph (Fig. 27). On β-iron we have obtained corrosion or growth figures spontaneously in our previous tests on the crystallization of iron; they are the same as for α-iron.

On γ-iron, still working on face p(001), the lines of corrosion are again parallel to the sides of the square, only they are neither so continuous nor so soft as on α-iron. As reagent, the double chloride of copper and ammonium, or 10 per cent, nitric acid, can be used for the manganese steel, while for nickel-chromium steel, iron perchloride, acidified with hydrochloric acid, is preferable: the etching is irregular, and, even after deformation, followed by annealing at 1,300°, shows the primary crystals very clearly. It is well to polish it lightly again. The appearance Fig. 31 is then obtained, which corresponds to a magnification of about 200 diameters. The drawing shows a face p(001) and an adjacent face b¹(011), with a twinned lamella.

To put it briefly, corrosion figures, up to the present, have not furnished useful distinctive characters.

Synchronous Crystallization Figures

We heated to redness a crystal of iron having a cube face polished in a nickel crucible, beneath a layer of magnesia calcined at a high temperature, which in its turn was covered with a layer of cast-iron shavings.

The polished face oxidized naturally, and displayed square figures strongly resembling corrosion figures (Fig. 32; 400 diameters), the sides of the photo-micrograph being parallel to the edges of the cube face. It seems that the oxidation has been regulated by the structure of the metal. We have tried to repeat the experiment under known conditions of temperature, but without success.

In another test, we introduced a crystal of iron, again having a polished cube face, into a bath of molten boric acid, at about 800° C., the temperature being gauged by the eye. Needles of boric acid congealed at first on the polished surface, and preserved it provisionally from attack in such a way that the silhouette of the needles was imprinted on the iron (Fig. 33; 200 diameters). The interesting point is that the needles of boric acid, instead of arranging themselves on their own account in their natural order, as in Fig. 33, may follow the direction of the system of the iron ; the appearance Fig. 34 (400 diameters) is then obtained, of which the sides are parallel to the edges of the cube face. In this figure some directions parallel to these edges may be seen, and others which seem to be parallel to the directions of Neumann’s lines, These directions are really somewhat uncertain, because the needles of boric acid form fan-shaped groups, and, what is more, the experiment does not always take place in the. way desired. Researches in this direction might, perhaps, merit resumption and following up.

Segregation Figures

Crude cast manganese steel in the vicinity of the pipe presents details of structure that demand studying on their own account. Little hard nuclei are encountered, to which other constituents are attached, and notably lamellae of cementite, crystallographically oriented.

On a cube face the nuclei occupy the summits of a square system. Fig. 35 shows the result of simple polishing at 65 diameters. The lamellae which start from the nuclei, and others which are isolated in the metal, are parallel either to the edges of the cube face or to its diagonals, or to the lines which join the summits to the centers of the opposed edges. These lamellae are too small to permit of their being followed on two adjacent cube faces: hence it is impossible, at least with the sample at our disposal, to determine exactly all the planes of segregation. Only it may be remarked that the lamellae are of two kinds, and of decidedly different scales of magnitude, and that the larger ones are those which follow the diagonals of the square. It is concluded from this that the principal planes of segregation of γ-iron are again the planes a¹(111); but that secondary planes also may exist p(001), b¹(011), b²(012), a²(112), or a½(122), among which we should not know now which to choose. It is the lamellae of cementite which contribute the relative brittleness to crude cast manganese steel, and cause it to break. The fracture then shows brilliant little facets disposed in cups; these are really the lamellae. The quenching

keeps the cementite in solid solution, and so communicates all the characters which distinguish the metal. In the same way, if hypereutectoid carbon steels are cooled from about 1,100° quickly enough, without actual hardening, the cementite is distributed in the planes of segregation of γ-iron.

Rose established that, in the cubic meteoric irons of Braunau and Seelasgen, the rhabdite, (Fe, Ni)3 P, is oriented in accordance with the three cube faces. Tschermak confirms this fact, and adds another possible plane of segregation parallel to Neumann’s lamellae—that is to say a²(112). According to Kunz and Weinschenk, the rhabdite in the Floyd Mountain meteorite is parallel to Neumann’s lamellae. (All these notes relating to meteorites are borrowed from the frequently cited book of Cohen.)

Inasmuch as phosphorus tends to the elimination of point A3, it is possible that the planes of segregation p(001) and a²(112) of rhabdite characterize either β- or α-iron. Systematic experiments on the crystallographic segregation of phosphorus, at known temperatures and on samples of known composition, would therefore probably be interesting. Mr. Stead, who has made such brilliant studies of the relations between iron and phosphorus, would be better fitted than any one else to conduct them, successfully.

Summary

The results of this research are set forth in the following table:

It is very difficult to interpret these results. Two courses suggest themselves.

Firstly, it may be supposed, with some probability, that the planes of translation, of twinning, of cleavage, and of segregation, are planes of the greatest reticular density, something like the walls and floors of a house. Moreover, it is known that there are three varieties of the cubic system: the simple cube, which has intersections only at its summits; the centered cube, which has another intersection at its center; and the cube with centered faces, with an intersection at the center of each of its faces. (These three cubes are represented by Fig. 36, projected on one of their diametrical planes ; the little circles indicate the intersections.) In the simple cube the plane of the greatest reticular density is the plane p(001), and among the truncations on the angles, the plane a¹(111). In the centered cube the number of intersections is doubled on b¹(011) and a²(112), and is not modified on p(001) and a¹(111), so that the reticular density becomes greater on b¹ than on p, greater on a² than on a¹. In the cube with centered faces the number of intersections is doubled on p and b¹, quadrupled on a¹, which becomes the plane of greatest reticular density. If it is now observed that p is a plane of perfect cleavage and minimum hardness for α-iron, and that a¹ plays the part, by far the most prominent part, in the crystallography of γ-iron, one is led to think that if the mesh of β-iron is a simple cube, and that of γ-iron a cube with centered faces, then that of β-iron would be a centered cube. As, on the other hand, the number of intersections is equal to that of the cube meshes for the simple cube, double for the centered cube, and quadruple for the cube with centered faces, each allotropic transformation of iron will be characterized by a division into halves of the molecular polyhedron with rising temperature. This is a very simple view.

However, the plane a²(112) has a greater reticular density than a¹(111) in the centered cube, and not in the simple cube, hence the Neumann lamellae, which demand a²(112) as plane of translation, could not be attributed to α-iron. And one is led to attribute them to β-iron, which should be formed temporarily, under the influence of shock. This is no unreasonable supposition, and may also be arrived at by other considerations, notably by the experiments of Curie and of Morris on the laws of the appearance and disappearance of magnetism.

Secondly, Mr. Wallerant considers the mechanical twinning as a proof of merosymmetry. That is another course to follow.

Really these attempts at interpretation are probably premature in the present state of the crystallography, but they can be used as working hypotheses. The only positive conclusion that we can draw from these researches is, that the three allotropic varieties of iron, although they all crystallize in the cubic system, present well-marked specific characters, and cannot have the same internal structure.

Nickel.—Pressure-figures were made at a temperature above the disappearance of magnetism, on a polished surface of a sample of nickel, containing a little iron and manganese, and previously cold-deformed and annealed at a white-heat. These indentions may be made in the open air, nickel being much less prone to oxidation than iron. Around each point of impact, lines of translation—that is to say, straight ones—were obtained.

Then, under the microscope, a new indention was made in the cold alongside each of the indentions made at the high temperature upon any grain with sufficient surface. In every case, the lines produced in the cold are also straight, and just like those produced on the same grain while hot. α-nickel and β-nickel have the same plane of translation, a¹(111), which is also plane of twinning by annealing for β-nickel. It is true, as Professor Le Chatelier has said, that β-nickel corresponds to γ-iron ; α-nickel corresponds to α-iron, with this difference, that it does not give curved lines of deformation.

We have also made deformation figures on the iron-nickel alloy called “ invar,” of which the coefficient of dilatation is almost nil at the ordinary temperature, and which is in consequence in course of transformation at this temperature. It might be asked if this circumstance would not have some influence on the deformation lines. It has not any. Fig. 37 represents a section of this metal after slight deformation and previous polishing at 200 diameters. This section shows beautiful lines of translation. The twins seen were pre-existing. The deformation has only put them in evidence.