Some Applications of X-Rays*

J. J. Trillat, Paris

Study of Metals. Applications in Inorganic Chemistry

A. Study of Metals

This article deals with the application of X-rays to the study of metals—an application based on the phenomena of X-ray diffraction in crystals. Other applications, which are no less important—for example, radiographic methods—are described by us elsewhere.

X-ray spectroscopy in the field of metal research is of enormous importance both from a purely scientific point of view and from the point of view of applications in industry. The results obtained up to the present time are, generally speaking, fairly easy to interpret and, thanks to this, lead to a whole series of data of enormous interest for metallurgy.

The principal applications discussed below may be listed as follows: 1) determination of the atomic structure of metals and alloys, 2) determination of the magnitude of the “grain,” 3) study of internal stresses, 4) orientation phenomena; the influence of physical or mechanical treatment, 5) practical applications in metallurgy.

1. Determination of the Atomic Structure of Metals and Alloys.

a) Pure metals. Determination of the structure of metal—

* Chapter from the book by J. J. Trillat, Les applications des Rayons X. See Advances in the Physical Sciences, vol. XI, no. 3, p. 493, and no. 4, p. 595.

metals and alloys has been the subject of many very important works. Here we shall give a brief summary of these works, indicating only those results that are of essential significance.

Metals usually present themselves as aggregates consisting of a large number of microcrystals, or sometimes—as crystals of sufficiently large dimensions. In the first, more general case, the Debye–Scherrer method is used for the study of metals. In the second case, the Laue method is suitable for this investigation. Without dwelling on the technique of the work itself, nor on the subsequent course of interpreting the diagrams, we shall confine ourselves

Fig. 1. Visual diagram of the spectra of powders of the cubic system (according to Clark).

only to pointing out that, in the general case of applying the Debye–Scherrer method, the law of the relative positions of the lines makes it possible to determine the type of lattice, and the exact measure of the absolute position of a given line—the absolute magnitude of the elementary cell of the crystal. Fig. 1 gives a general idea of the distribution of lines in the case of cubic lattices. In the case of more complex crystalline systems there also exists a method of graphical representation, which was proposed by Hull and Davey.

The results obtained with the aid of these methods may be checked in the following way. To each type of space lattice there corresponds a definite number of atoms in the elementary cell. This number is determined on the basis of the results of X-ray analysis. On the other hand, if by \(\rho\) we denote the density of the metal, by \(d\) the length of the edge of the cell, and by \(M\) the atomic weight, de-

divided by Avogadro’s number \((N = 6.07 \cdot 10^{23})\), then this number of atoms in the cell can be calculated from the relation:

\[ n=\frac{\rho d^3}{M}, \]

which also makes it possible to calculate \(d\), if \(n\) is known. This result, based on the hypothesis, is always found to be in excellent agreement with the results of X-ray analysis.

The following table gives the dimensions and types of crystal cells of the most important pure metals.

Cubic system with centered faces.

Atomic number	Metal	\(a\)	Atomic number	Metal	\(a\)
13	Al	4.043	45	Rh	3.820
26	Fe(\(\gamma\))	3.63	47	Ag	4.079
27	Co	3.554	78	Pt	3.913
28	Ni	3.540	79	Au	4.075
29	Cu	3.603	82	Pb	4.920

Cubic centered system.

Atomic number	Metal	\(a\)	Atomic number	Metal	\(a\)
11	Na	4.30	42	Mo	3.143
24	Cr	2.875	73	Ta	3.272
26	Fe(\(\alpha\))	2.855	74	Tu	3.155

Hexagonal compact system.

Atomic number	Metal	\(a\)	\(c/a\)	Atomic number	Metal	\(a\)	\(c/a\)
12	Mg	3.22	1.624	30	Zn	2.657	1.86
22	Ti	2.92	1.59	40	Zr	3.23	1.57
24	Cr	2.714	1.625	48	Cd	2.960	1.89
27	Co	2.514	1.633	76	Os	2.714	1.59

Some metals possess a special lattice, for example indium and manganese \((\gamma)\) (a tetragonal prism with centered faces).

Spectrographic investigation of metals also makes it possible to study the various allotropic forms of solids. As an example one may cite the investigations

By Vestrgren and Fragmen1 on the various allotropic modifications of iron. Using a thread of diameter 0.3 mm and various temperatures, these authors obtained good diagrams, which are shown in Fig. 2. The upper diagram was obtained at a temperature of 20°; this is the region of ferromagnetic $\alpha$-iron (ferrite), which crystallizes in the body-centered cubic system ($a = 2.87\ \text{Å}$). The second diagram, obtained at 800°, corresponds to nonmagnetic $\beta$-iron; here the lines are arranged in the same way as in the first case; the slight displacement is due to expansion caused by the high temperature ($a = 2.90\ \text{Å}$). The third diagram, obtained at 1100°, refers to the case of $\gamma$-iron (austenite); it is easy to see that here the lattice is completely changed, but it also belongs to the cubic system with centered faces ($a = 3.63\ \text{Å}$). Finally, at 1450° we pass into the region of $\delta$-iron, which cannot be detected by means of microphotography, but whose existence is proved by magnetic measurements. Here the lattice turns out to be similar to the first two lattices (centered cube, $a = 2.93\ \text{Å}$), so that one may quite properly speak of a repetition of the $\alpha$-modification.

In a similar way other modifications of iron have also been successfully studied, for example martensite, which has a lattice with centered faces and which consists of extremely small crystals (the effect of quenching).

b) Alloys. The study of alloys and their structure is of great interest, since it makes it possible not only to establish the crystalline system and the dimensions of the elementary cell, but also to observe phase modification from changes in the diagrams, the formation of eutectics, solid solutions, etc. These investigations were carried out chiefly by Bain2, Vestrgren3, Fratmen, Owen, Preston4, Hull5, Schmid, Teler, Zakson and others.

Alloys may consist either of several phases (several kinds of crystals), or of one phase (crystals of a definite—

of definite composition and solid solutions). Obviously, in the first case, where one has to deal with a mixture of crystals, the spectrograms will be formed by the superposition of lines corresponding to each crystalline system; precisely such a picture is obtained, for example, in the case when two finely crystalline powders are mixed. This case is not of special interest from the theoretical point of view, since the diagrams obtained in this way are, naturally, very complex and almost inaccessible to interpretation. In practice, however, they are of great interest, since it is usually sufficient to compare them with the spectrograms of the corresponding specimens in order to see directly whether they correspond to the type taken for comparison, whether impurities are present (new lines), whether they crystallize just as well, etc. Thus this method is purely qualitative and is suitable only for observations by comparison, although in some cases it is also very useful. In any case, it is impossible here to obtain data concerning the lattice and atomic structure of each of the phases.

For this reason the second case (alloys with one phase) is of the greatest interest. Here one should make a subdivision into two categories: crystals of definite composition and solid solutions, which possess the property that they exist in the state of a single phase for a whole series of compositions taken within given limits. Crystals with a definite composition give characteristic diagrams that can easily be interpreted by the usual methods; solid solutions, on the contrary, have a structure that is more difficult to establish, and our knowledge of them is still somewhat uncertain.

Eutectics. In 1921, Bёnom² established, although this had been known earlier as well, that eutectics consist of a mechanical mixture of two phases.

Study of binary alloys. The study of binary alloys that give continuous solid solutions when the concentration of two selected metals is varied has given rise to investigations of very great importance.

Let us take, for example, alloys of copper \((a = 3.60\ \text{Å})\) and nickel \((a = 3.54\ \text{Å})\). These two metals always crystallize in a cubic lattice with centered faces, and their elementary cells have dimensions very close to one another. The study of various X-ray photographs obtained for different concentrations shows that these two metals mix in all proportions, giving a whole series of mixed crystals, where one element penetrates into the other; the spectra correspond to the same space lattice as in the pure metals, with only the difference that the dimensions of the cell have an intermediate character. The resulting lines are located between the lines of copper and nickel, and their position can be calculated in advance on the basis of a simple rule of proportions. Usually the lines are very fine, which is evidence that the lattice is constructed uniformly and quite regularly.

The same kind of picture is obtained also for the alloys Ag—Pd and Ag—Au. But if the cells of the two initial metals have sufficiently different dimensions (for example Cu \(a = 3.60\ \text{Å}\) and Au \(a = 4.075\ \text{Å}\)), then a somewhat different picture is obtained: a rapid change of the lattice is observed only in the case of intermediate concentrations, whereas in the case of weak concentrations of one or the other metal the lattice changes hardly at all. Thus up to \(25\%\) of the copper atoms can be replaced by gold atoms without any noticeable changes being observed.

In what way, then, can one imagine the structure of mixed crystals, for example Cu—Ni alloys? The fact of obtaining fine and perfectly definite diagrams leads inevitably to the conclusion that we are dealing with a very perfect and uniform mixture and that the crystalline structure is single. This structure consists of cubes with centered faces, in which the nodes are occupied by atoms of the two metals; for example, copper atoms can be replaced by nickel atoms without changing the general structure. It is highly probable that for certain concentra-

TABLE I

Fig. 2. Above—diagrams of the $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-iron. Below—diffraction spectra of $\alpha$-iron (cf. line width).

Fig. 4. Left—Cu—Al alloys (Debye–Scherrer method).
Right—Cu—Sn alloys (Westrgren and Fragneau).

Transactions of the Physical Sciences, vol. XI, issue 5.
To the article by Zh. Zh. Trillat.

these two compositions the atoms are distributed not in an arbitrary way, but with a certain regularity.

Alloys Ni—Cr, Ni—Fe, Cu—Mn. In these alloys one of the metals has a body-centered cubic lattice (Fe-α, Cr, Mn), the other—a face-centered cubic lattice (Ni, Cu); the alloys obtained, as shown by microphotographs and thermal analysis, are continuous solid solutions of one metal in the other.

In studying these special cases, Bain, McKeehan, and Miss Endres found that the addition to one metal of a small amount of another metal does not appreciably change the lattice of the metal serving as the solvent. Thus, for example, in the case of the Fe—Ni alloy the structure of iron remains the same up to a 25% replacement of iron atoms by nickel atoms; in this case the length of the edge of the cell increases from 2.872 Å only to 2.89 Å. The same is obtained also in the case when, in nickel, 30% of its atoms are replaced by iron; here the edge increases from 3.51 Å to 3.60 Å. Conversely, in the intermediate region diagrams are obtained with lines corresponding to two different lattices; this serves as proof that the alloy contains two kinds of crystals, which at present cannot be detected by means of microphotography.

If in this special case Fe—Ni the alloy is heated above 900° (the transformation point of α-iron into γ-iron, cubic with centered faces), then such a mixture of two constituent parts is no longer observed. Here both lattices consist of face-centered cubes, and the diagram shows only lines corresponding to such a lattice. In this case the concentration at which the mixture of two lattices appears proves to depend on the quenching condition of the specimen.

Alloys Cu—Zn. These alloys, first studied by Bain and his pupils, then by Owen and Preston (l. c.), and finally by Westgren and Phragmén, consist of a metal possessing a cubic lattice with centered—

...with face-centered lattices (Cu), and a metal crystallizing in a compact hexagonal system (Zn). The results obtained, as well as the thermal diagrams (Fig. 3), make it possible to draw the following conclusions.

For 100% copper, the diagram consists only of lines corresponding to a cubic lattice with centered faces. Up to 32% zinc the lattice does not change, although a known number of copper atoms is replaced by zinc atoms. These two elements, having a rather close atomic number, do not show any appreciable difference in diffraction intensity, and the cell edge changes very little.

Fig. 3. Alloys of zinc with copper (thermal diagram).

Beginning with 44% zinc, a new lattice is obtained, which as yet only weakly resembles the structure of β brass.

At 47% zinc, pure β brass is obtained, which is characterized by a centered cube containing copper atoms at each node and a zinc atom in the center.

At 56% zinc, alongside the β-brass lattice there appears a new lattice belonging to the γ-brass modification. The abundance of lines indicates the complexity of the new elementary cube, which contains 52 atoms.

At 73% zinc, alongside the γ modification there appears the ε modification, especially clearly noticeable at 80–86% zinc.

Finally, at 95% zinc, alongside the ε modification, pure solders’ zinc begins to appear, and at higher concentrations the lattice passes into the lattice of pure zinc (hexagonal compact).

Now the question arises: how should one understand the fact that in certain limiting solid solutions (aluminum bronze, α-brass) the spectrum obtained is of the same nature as that of the pure metal, and that the cell dimensions change ...

only to a slight degree? To explain this, two hypotheses could be put forward: either the aluminum or zinc atoms are introduced between the copper atoms in the intervals of the lattice, or they occupy the places of copper atoms in the lattice. The latter hypothesis is confirmed by density measurements, both by the direct method and with the aid of X-rays.

Cu—Al alloys. After the first investigations of Owen and Preston there appeared the excellent works of Jette, Fratmen, and Westgren[^7], which are based on Stockdale’s thermal diagrams. The photographs obtained by these authors are reproduced in Fig. 4. It is easy to see that, in the transition from one phase to another, some lines are sometimes preserved (the transition from \(\gamma\) to \(\gamma'\)); moreover, alloys with two phases give spectra in which one can see the superposition of the component phases.

In the case of these crystals, Fratmen and Westgren established that the alloy \(\mathrm{Cu—Al_2}\) possesses a square-centered system with a cell containing 4 molecules of \(\mathrm{CuAl_2}\). The solid solution (from 16 to 25%) has a cubic cell containing 50 atoms, which do not obey the law of simple substitution mentioned earlier. Here, apparently, two Al atoms replace three Cu atoms, and the number of atoms contained in the cell changes from 52 to 49.

Other alloys. The structure of a very large number of other alloys has also begun to be investigated successfully. Among the most important investigations, one should mention the studies of Fe—C alloys, discussed above, which are of great interest in the metallurgy of steel, where the complexity of the thermal diagrams, caused by the allotropic forms of iron, is the source of many contradictory opinions concerning the composition of the various phases. X-rays have made it possible to obtain many valuable results in this field. With suitable research technique, with well-defined specimens, and especially with good thermal diagrams, X-ray analysis makes it possible to solve many metallurgical problems, especially if these investigations are accompanied by metallomicroscopic studies.

These works make it possible to foresee those deep relations which connect the two limiting cases: a perfectly definite compound and a perfect solid solution. In the first case, atoms cannot mutually replace one another and play, to a certain extent, a specific role. In the second case, atoms can be substituted indeterminately in the various cells of the lattice. The existence of intermediate cases is also possible, where groups or complexes of atoms may replace one another. It is easy to understand from this what broad horizons alloy spectrography by means of X-rays opens up for the metallurgist. In addition to these results of a scientific order, one should also not neglect the obtaining of diagrams, sometimes very complex and difficult to interpret (the case of special steels with Ni, Cu, Tu, Va), thanks to which the metallurgist can be informed of the identity of a given product with a specimen possessing certain mechanical or physical characteristics.

2. Determination of Grain Size

Knowledge of the grain size of a metal or, if one likes, of the average number of small crystals in a given volume, is of primary importance in metallurgy. Even the study of micrographic polished sections makes it possible to obtain an idea of the order of this magnitude, especially in the case where the number of crystals is small for the given polished surface. The application of X-rays makes it possible to extend this investigation further and offers, moreover, the advantage that only a small quantity of substance is required here, and it needs no treatment whatsoever. At the same time, the radiographic method is suitable for the investigation not only of metals, but also of all microcrystalline and even colloidal substances (on this, see, for example, the article on cellulose, etc.).*

* Cf. Uspekhi fizicheskikh nauk, II, issues 3 and 4, 1931.

Determination of the grain size of metals can be carried out in two different ways, namely by using mixed radiation (the Laue method) or monochromatic radiation (the Debye–Scherrer method).

a) Laue method. If, by means of a tube with a tungsten anticathode, operating for example at 80–100 kV, a single crystal is irradiated, then so-called characteristic spots are obtained on the photographic plate. If, however, two crystals instead of one are penetrated by the same beam of X-rays, then two Laue images are obtained on the plate, the spots of which reflect the relative arrangement of both crystals. The greater the number of crystals penetrated by the given beam of rays, the more Laue spots will appear, so that comparison of the images makes it possible, with a certain accuracy, to determine the number of crystals in an element of volume, whence the size of these crystals is also determined.

Chokralski8 carried out very interesting investigations of the number of crystals contained in a given volume of various metals, chiefly in aluminum. Fig. 5 (Table II) reproduces the obtained radiographs alongside micrographic polished sections sufficiently well, so that the method leaves almost nothing to be desired.

G. Clark* used this method for the purpose of studying the influence of grain size on the magnetic properties of steel (hysteresis), used for transformers. It is known that the most important factor here is the size of the particles, but this determination is made exclusively by means of empirical methods based on hysteresis losses. The X-ray method, applied to silicon steel subjected to various heat treatments, gives diagrams with the most varied number of Laue spots. Clark found the following empirical relation for the number \(P\) of these spots and the hysteresis loss \(W\) at \(с^{1.15}\):

\[ W = 112 \sqrt{P} + 400, \]

* G. Clark, Applied X-Rays, see bibliography.

which proves to be valid for induction values up to 60 thousand gauss and for a frequency of 60 periods. The radiographs obtained show that as the diffraction spots develop and become more and more rare, the hysteresis losses decrease; the best magnetic properties are obtained in the ideal case of a metal consisting of a single crystal.

b) The Debye–Scherrer method. If monochromatic radiation is used, valuable data can also be obtained on the composition of the crystallites forming the grain of the metal or of the substance under investigation. For this it is enough to place a small piece of the metal or of the substance under investigation at the end of the collimator or in the middle of the round Debye–Scherrer camera. Rings or lines are then obtained, the structure of which may serve as an indication of the average grain size. To solve the problem it is sufficient to have several typical radiographs corresponding to known grain sizes; then, by simple comparison, the dimensions of the specimen under investigation can be determined with sufficient approximation. In various places we shall point out different applications of this method (see, for example, Figs. 2, 18, and 19). As an example we give Böhm’s table,^10 in which the sizes of iron-oxide grains are listed in connection with the character of the interference lines.

Böhm’s table

Character of the lines	Grain size
Lines consisting of large dots	Crystals \(> 0.1\) mm
Lines consisting of small dots	Crystals about \(0.1\) mm
Continuous sharp lines	From \(0.01\) to \(0.007\) mm
Broad blurred lines	Colloidal sizes \(10^{-4}\) mm

From this table it is evident that, as the grain sizes decrease, the lines obtained become more and more clear and homogeneous; when these sizes are further reduced, the lines broaden and become more blurred. This occurs when the particle size reaches colloidal dimensions.

This latter circumstance brings us to the very interesting problem of determining the size of colloidal particles by means of X-rays. This question, which is of enormous importance from both the scientific and the industrial point of view, has also been studied by various other methods, of which I cannot speak here. Scherrer^11 and Laue^11a, on the basis of measurements of the width of interference lines, were in many cases able to determine the size of colloidal particles, chiefly in colloidal metals, various oxides, etc.

Scherrer established the following relation for a crystal of the cubic system:

\[ B = 2 \sqrt{\frac{\lg_e 2}{\pi} \cdot \frac{\lambda}{D} \cdot \frac{1}{\cos \frac{\theta}{2}}} + b. \]

Here \(B\) denotes the angular width of the line or ring between two points where the intensity is equal to one half of the maximum intensity (this corresponds to half the width of the line), \(\theta\) denotes the diffraction angle for wavelength \(\lambda\), \(D\)—the thickness of the crystal in the direction parallel to the face of the cube, \(b\)—the constant of the apparatus (the minimum width given by the apparatus).

With the aid of this method Debye and Scherrer were able to determine the sizes of particles of colloidal gold down to \(18.6 \,\text{\AA}\), a size corresponding to a particle in which, in each direction, 4–5 elementary cubes are fitted. Thus we see that metals in the colloidal state, even with very great dispersion, still possess a crystalline structure.

It should be noted that so far this formula is applied only to the case of elements crystallizing in the cubic system. Nevertheless, it can be extended to other cases as well, and then its application will be more general.

The method of determining grain size has become the subject of many new studies, among which we shall point to the works

Mark and Hengstenberg[^36], Patterson[^37], Brill[^38], Möller and Reis[^39], and Mark[^40]; from these important works it follows that there is a noticeable influence of the absorption of X-rays by the specimen being studied on the width of the diffraction lines. Therefore, when carrying out measurements of this kind, it is necessary to take very great precautions.

Fig. 6. Catalytic nickel (after Clark).

As another example of the application of the X-ray method to the study of metals, one may cite the very interesting work of Clark, Asbury, and Wick[^12], concerning the investigation of the particle size of nickel and its catalytic activity. Making photometric determinations of the width of the diffraction lines of nickel prepared under various conditions and possessing different activities, these authors obtained curves (Fig. 6), from which they find that the increase in the activity of the catalyst does not proceed in parallel with a decrease in the magnitude

PLATE II

Labels in the figure: f, e, d; a, b, c.

Fig. 5. a—1 Al crystal; b—2 crystals; c—5 crystals; d—120 crystals; e—2 thousand crystals; f—1 million crystals (after Chokralsky).

Fig. 7. Asterism effect in a gypsum crystal (Chokralsky).

Advances in the Physical Sciences, vol. XI, issue 6.
To the article by J. J. Trillat.

particles, as one would have expected. Here even the reverse course of these quantities is observed, at least within certain definite limits. Other investigations, described in the works of Clark and Eborn^12 and of Levin and Haardt^13 and concerning platinum (a catalyst in the manufacture of sulfuric acid by the contact process), have shown that there exist optimal particle sizes. It is easy to understand what interest these investigations have for those branches of industry in which catalysts are used.

Other interesting applications of this method relate to the study of the state of metallic surfaces. It is sometimes very useful to know whether the surface of a specimen consists of fine grains (polished metal), and to what distance inward from this surface this structure extends. For this purpose Clark and Broutman^14 made use of the reflection method, the specimen being placed so that it was possible to obtain X-ray beams at an angle \(\theta\), which could be varied at will. The photographic plate is placed at an inclination of angle \(2\theta\) with respect to the direction of the incident rays. In this way it is possible to study the more or less fine structure of the grains as a function of the penetration of the rays; for example, one specimen of duralumin from an American dirigible, at a very small angle of incidence, showed the presence of exceedingly fine grain, which is characterized by very broad lines overlapping one another; this occurs under the influence of rolling, which breaks the whole into particles. In the case of larger angles, i.e. for layers situated at a distance of several atomic layers from the surface, sharper rings appear, characteristic of the ordinary structure of the metal.

In conclusion, mention should be made of some investigations of colloidal solutions of carbon in \(\alpha\)-iron. Martensite gives broad diffraction lines corresponding to the cubic body-centered lattice of \(\alpha\)-iron (particles of the order of \(10^{-6}—10^{-7}\) cm). The effect of heat treatment increases the grain sizes and, at \(625^\circ\), gives a spectrum analogous to the spectrum of cementite \(\mathrm{Fe_3C}\) (Fig. 2).

An extraordinarily important group of applications of this method is the study of annealing and its influence on grain size and recrystallization. Annealing, generally speaking, leads to an increase in the crystals, clearly visible on the diagrams. We shall discuss this question later.

3. Study of Internal Stresses in Metals

If a crystal undergoes deformation exceeding its elastic limit, then the resulting Laue spots, initially elliptical, become considerably elongated, and the diagram assumes an entirely distinctive appearance (Fig. 7, Table II). The spots take the form of long traces or bands, which are called “asterism bands.” What, then, are the causes which, in a crystal deformed in this way, lead to the appearance of such a picture? As a result of many investigations it is now believed that external or thermal stresses lead to the slip of various lattice planes and at the same time to distortion or curvature around certain crystallographic directions. In such a case the reflection of X-rays occurs not from planes, but from cylindrical surfaces, whence arise the elongation of the spots and the production of radial bands of this kind. If, instead of a single crystal, an entire group of microcrystals—for example, an entire metal sheet—is subjected to such mechanical deformations or thermal treatments, then the resulting effect will be the sum of elementary effects, and by means of the Laue method it will be possible to obtain diagrams in which many radial bands appear, characterizing internal stresses. Thus the phenomenon of asterism constitutes proof of the existence of residual internal stresses in the metal under study.

Very good radiographs were published by Clark in connection with his investigations of internal stresses, which play such an important role from the point of view

of metallurgy. For these investigations it is best to use the Laue method, employing a continuous spectrum of X-rays.

According to the indications of the same author, it is also possible to study the influence of heat treatment on the disappearance of internal stresses. Generally speaking, radiograms show in a remarkable way the favorable influence of sufficiently strong heating. In practice it is very difficult to estimate quantitatively the magnitude of internal tensions, but it is very easy, on the other hand, by comparing different radiograms, to trace the gradual disappearance of these tensions, which gives this method very great interest. As a direct application, Clark (Applied X-Rays, p. 223) carried out a graphical determination of the distribution of equivalent zones of internal stresses in various metallic specimens, as well as of the disappearance of weak spots. In this way it is possible to foresee fracture lines and, consequently, through systematic investigations, to achieve an improvement in the technique of metal fabrication. The same author also succeeded in studying various methods of welding in air and in hydrogen and in determining the grain size and internal stresses in each individual case; such investigations have brought enormous benefit to the development of these methods.

Trillat, in his investigations on the hardening of steel tips for tools, also discovered changes in grain size at various points of the specimen, as well as the existence of more or less pronounced internal stresses, and gave a graphical representation of their localization. Let us also point to the many works of Sachs devoted to the study of analogous questions (see the bibliography).

In conclusion it should be noted that deformations of crystal lattices are usually not the sole result of microstresses; generally speaking, they are accompanied by an increase in the size of the crystals or by the appearance of new phases; in addition, deformations due to mechanical working are the cause of the emergence of pre-

possessing directions. On the basis of radiographs these phenomena can receive a correct explanation.

4. Orientation phenomena. The influence of physical or mechanical treatment

General remarks. This field of the study of metals has developed extraordinarily in recent years, and metallurgy has been enriched with a very large amount of new information thanks to X-ray spectrography. It may be said that the first to open the way in this direction was M. de Broglie¹⁴, who was the first to study the diffraction pattern obtained when a beam of X-rays passes through a metallic foil.

A large number of theoretical investigations, published chiefly by Polanyi and his collaborators, served as the starting point for these works; the theory of “fiber diagrams,” established by Polanyi, served as a firm foundation for all subsequent work along this path. Here we confine ourselves to presenting the various applications that follow from this theory.

The study of deformations of metals by means of X-rays is of very great interest; the information obtained in this way proves to be far more abundant than that obtained by any other method; moreover, it is very important that only small quantities of material are required for the investigation, which entails no inconvenience whatsoever; further, here there is absolutely no need to resort to any precise preparations, as is done in metallography, and finally the diagrams show the complete internal structure of the specimen, even in its deep layers, and not only the appearance of the polished-section surface.

The advantages of this method become clear at once if one recalls that the quality of a metal, even after heat treatment, often depends on the mechanical treatment, which produces a fibrous structure, and that in most forged metals defects must be attributed to mechani-

chanical treatment and incomplete annealing, which destroys the properties inherent in the fibrous state. Interpretation of the diagrams makes it possible to determine these different structures quantitatively and to derive from this the mechanism of deformation of metals. Various physical properties, especially those that have to do with resistance or hardness, are closely connected with the more or less fibrous structure of the metal; hence the interest of such a method is understandable, since it makes it possible not only to carry out a certain control, but sometimes also to predict certain properties and to influence thermal or mechanical treatment with a view to obtaining the desired quality.

In what follows it seems difficult to us, in each individual case, to delimit completely what relates to the phenomena of orientation and deformation in the proper sense of the word and to the phenomena that accompany an increase in temperature. Therefore, in describing certain investigations, we shall speak at one and the same time of both processes, dwelling as necessary on details concerning one or the other process.

Experimental method. For these investigations the Debye–Scherrer method is suitable, which consists in attaching to the end of the collimator a small particle of the metal under study and placing a photographic plate behind it; all precautions are reduced only to avoiding harmful effects, for example secondary rays, the central spot, etc. Here one may work with a tube with tungsten or molybdenum anticathodes at voltages of 40–60 kV or even higher, depending on the thickness of the specimen, which may reach 2–3 mm; however, it would be more advantageous to use thinner specimens, namely 0.1 to 0.2 mm thick, and to employ a tube either with a molybdenum or with a copper anticathode. The desired thickness is obtained, for example, by dissolving part of the metal in acid, which does not change the internal structure of the metal; one may also grind off part of the metal, taking care only that it does not become heated and stratified, which sometimes occurs very easily.

The specimen must be fixed on a rotating support with circular graduations, so that it can be studied at various angles of incidence.

Study of stretching. The effect of stretching of metals very often occurs in practice, chiefly in those cases where the metal has to withstand a strong tension during operation. It is therefore of great interest to obtain knowledge about the internal phenomena that occur in such cases in the metal.

We shall give here several examples of the most important results obtained along this path.

Tension of aluminum single-crystal specimens. After their experiments on obtaining giant aluminum crystals and stretching them, Taylor, Müller, Carpenter, and Elam^17 investigated by means of X-rays whether the slip planes, observed by the purely geometrical method, were connected with the orientation of the crystal lattice relative to the axis of the bar.

The method was as follows. A single-crystal bar was placed vertically, so that one of its generators passed through the axis of rotation of the spectrograph. A series of radiographs was taken on the same plate while the bar was rotated about the vertical axis through various angles. The reflection spots obtained in this way can easily be assigned to definite planes of the aluminum lattice. Working with specimens that had undergone various degrees of elongation, it is possible to establish changes in the orientation of the various planes under the influence of stretching. Müller was thus able to prove that the slip plane is the plane (111), and that the direction of slip in this plane is the direction (101). Further, stretching also produces a distortion of the lattice planes, which is manifested in the broadening of the diffraction spots. This partial degradation begins at small elongations; it is impossible to combat it by annealing, even if the elongation does not exceed 7% at 600°. Conversely, if this limit is crossed, then one obtains

complete recrystallization of the bar into one or several crystals, depending on the degree of deformation, and the diffraction spots become perfectly sharp. Then there is no longer any connection between the orientation of the old crystal, the orientation of the lattices of these new crystals, and the direction of the applied force.

The method described makes it possible to establish that the principal cause of the increase in strength is due to this initial fragmentation of the crystal. It is probably in this also that lies the cause of the well-known hardening of metals observed during the cold working of metals.

Study of monocrystalline and ordinary wires. The first series of investigations, carried out by Polanyi, Mark, and Schmid^18 in 1922, showed that deformations of wires of drawn monocrystalline zinc take place by sliding along one of the planes, depending on the direction of drawing. Zinc has a hexagonal lattice, and sliding occurs in the plane of the base of the prism; at the same time a new orientation gradually arises, which tends to bring the direction of sliding in these planes closer to the axis of the wire, i.e., to the direction of tension. Fig. 8 is a schematic representation explaining how deformation proceeds under tension (the case of zinc).

Fig. 8. Deformation of zinc crystals.

The study of questions of drawing or wire-drawing was undertaken by Mark, Polanyi, and Weissenberg^19. One may expect a priori that, when metal passes through the die of a wire-drawing machine, the microcrystals making up the metal should acquire a certain predominant orientation; and indeed, certain directions have a tendency to orient themselves during deformation, owing to sliding along the axis of drawing. With the aid of the phase-diagram method it is possible to achieve a quantitative study of all phenomena associated both with drawing and with rolling.

Thus Polanyi and his collaborators arrived at the following results: wires of Cu, Al, Pd (face-centered cubic lattice) are oriented parallel to the drawing axis in the direction (111) (or the cube diagonal), sometimes in the direction (100) (or the cube edge). For wires of Tu, Fe, Mo, which have face-centered cubic lattices, orientation in this way occurs along the direction (101) (or the face diagonal). These directions of orientation are not perfectly strict and form a cone with a semi-angle of up to \(10^\circ\). Fig. 9 (Table III) shows a very good diagram of a strongly drawn aluminum wire.

Fig. 10. Theoretical diagram of drawn aluminum.

As we have already said above, the theory developed by Polanyi makes it possible to discover the directions of orientation and the planes of slip; conversely, it makes it possible to establish in advance what diagram should result for an aggregate of microcrystals having some predominant direction of orientation. If we take, for example, the case of aluminum (face-centered cubic), then on the basis of the theory there should result the diagram shown in Fig. 10, if we assume that the (111) axis is parallel to the axis of the wire. It is obvious that this scheme very much resembles the diagram of Fig. 13 (Table III), obtained experimentally.

These experiments enabled Polanyi to prove that during drawing the axis of symmetry is the more readily arranged along the direction of the wire, the smaller the acute angle which this axis makes with one of the slip directions.

The most recent investigations of Tanaka\(^{20}\) have shown that in the case of drawn aluminum the (210) axis is most readily ori-

TABLE III

98%

92%

50%

0%

Fig. 13. Structure of cold-drawn aluminum as a function of the degree of flattening.

Fig. 9. Aluminum wire, cold-drawn (Zeeman and Schiebold).

On the right:
Fig. 15. Flattening of a copper sheet.
At top—in one direction; in the middle—in two directions perpendicular to one another; at bottom—in many directions.

Uspekhi Fizicheskikh Nauk, vol. XI, issue 6.
To the article by Zh. Zh. Trillat.

...is oriented along the axis of the wire. This result does not quite agree with what was said above. Further, it is possible that there exists not one, but two directions of the predominant orientation, as was shown by Schmid and Wassermann. For metals of the cubic system with centered faces (Al, Cu, Ag, Au, Pd), there may exist two fiber axes, namely along the diagonal of the cube and along the edge of the cube; the relative proportion of these two systems is different for different metals.

One may now ask how the orientation changes as a function of the thickness of the wire being drawn? In other words, are the crystals aligned better at the center or at the periphery of the wire?

This question is answered by Becker’s work.^21 If one works with a drawn tungsten filament (single-crystalline) and gradually reduces its diameter by means of iron-cyanide alkali, then it can be shown very clearly that the orientation is expressed considerably more strongly in the inner layers than in the outer ones. In the present case the inner layers consist of a single crystal, whereas the outer layers tend to give a powder diagram (microcrystals).

Fig. 11.

Related to these investigations are the works of the General Electric Co laboratory (1924) with a tungsten filament treated in such a way that the crystals of the metal occupy the entire cross-section of the filament. If this filament is subjected to a tensile force, then among the other crystals one is spontaneously selected whose deformation proceeds along two series of slip planes. Fracture occurs along a wedge according to the scheme of Fig. 11. X-ray investigations make it possible to determine the slip planes; the crystals slip along the planes (112) in the direction (111). The distortions occur at the same time at angles from 10 to 20°. The mechanism of deformation by wedge is easily explained if one notes that slip along the planes (112) occurs most easily when the direction of tension goes approximately at an angle of 40°. Indeed, the axis of the wire...

forms an angle of about 35° with each plane (112); consequently the angle with one of the two planes is always closer to 40° than with the other. Slip begins along this plane; during drawing, the other plane, owing to the distortion, in turn becomes closer to 40°, and slip then continues along the latter, and so on. It is easy to verify that the bisector of the planes (112), which represents the direction (110), always coincides with the axis of the wire; this result confirms Polanyi’s views, discussed above. Fig. 11 shows the mechanism of deformation and fracture along a wedge in a tungsten wire.

Study of rolling. The rolling of metallic sheets is explained, as in the case of drawing, by the alignment of microcrystals along several predominant directions. However, the phenomena observed in the two cases are not identical, especially from the standpoint of the planes that arise in the process. Moreover, rolling may proceed in different directions, whence follows the possibility of more detailed investigations.

The method of investigation here is the same as in the case of drawn wires: a small piece of metal, previously provided with marks in accordance with the directions of rolling, is illuminated by a monochromatic beam of X-rays. For a sufficiently complete study it is necessary to work in such a way that the metal sheet, if possible, is illuminated in three mutually perpendicular directions. Indeed, if the orientation axis lies in a plane normal to the direction of the incident beam, then a fiber diagram arises; conversely, if this axis is parallel to the direction of the X-rays, then only complete Debye–Scherrer rings are observed. It is likewise very useful to study the diffraction pattern obtained when the metallic plate is inclined at various angles with respect to the X-ray beam.

Many studies have been published on rolling, chiefly in Germany, England, and the United States.

states. There is no possibility here of giving a detailed account of all these works, and we shall confine ourselves to only the briefest survey.

As we have already said above, the beginning of these investigations was apparently undertaken by M. de Broglie \(^{16}\) in connection with the question of the structure of rolled sheets; the first authors who studied these phenomena in sufficient detail were Polanyi, Mark, and Weissenberg (1923) \(^{22}\).

It was established by these authors that, for rolled metals of the cubic system with centered faces (Ag, Au, Cu, Pt, Al), two orientations may be obtained: one with the direction \((112)\) along the rolling axis, the plane \((101)\) being situated along the axis of the sheet; the other, rarer, with the direction \((100)\) along the rolling axis and the plane \((100)\), or cube face, in the plane of the sheet. As a result of these data Polanyi came to the conclusion that the bisectors which make with the slip directions the angle as acute as possible and less than or equal to \(45^\circ\) are oriented along the rolling axis. In addition, the secant planes which make with the slip directions an angle as acute as possible and less than or equal to \(45^\circ\) are oriented in the plane of the sheet.

Fig. 12. Rolling of an aluminum sheet. Perspective view of the orientation of the cube and octahedron in aluminum rolled specimens (Wever).

Later Wever \(^{23}\) arrived at a somewhat different conclusion. Studying sheets of aluminum and iron rolled to various thicknesses (from 0 to 99%), this author showed that aluminum crystals flattened by 99% are arranged symmetrically with respect to the normal plane passing through the flattening axis \(W\) (Figs. 12 and 13). This flattening axis coincides with the directions \((111)\) of the lattice; the directions \((110)\) are oriented in the plane of the sheet perpendicular to the flattening axis, and the directions \((112)\)—normal to the sheet.

On the contrary, for plates rolled less strongly (50%), Wever obtains results that are in agreement with those obtained by Polanyi. For iron (cubic body-centered lattice) he finds that even weak flattening gives rise to a considerable orientation. These results agree with Polanyi’s experiments. The structure of rolled sheet iron may be represented in the form of the orientation of a rhombic dodecahedron, shown in Fig. 14.

Fig. 14. Perspective view of the orientation of a rhombic dodecahedron in sheets of rolled iron.

Generally speaking, it may be said that, in the case of ideal rolling, perpendicular to the direction of flattening there are arranged the lattice planes most densely occupied by atoms. For metals of the cubic system with centered faces these planes are the (111) planes, then the (100) planes, and for the centered cubic system—the (110) planes. Thus there exists an important relation between the effect of mechanical deformations and the position of these planes, as was also found for drawing. In practice this ideal position of the crystals is somewhat disturbed owing to the dispersion of the crystals. In the case of aluminum this consists in the crystallites being grouped in pairs with respect to the plane of flattening, regarded as a plane of symmetry, on one side and the other of this plane; the crystallites tend to shift, by rotation about the vertical, into the ideal position, and also by rotation about the direction of flattening, this latter rotation being much less pronounced. In iron the crystallites tend to rotate chiefly about the direction of flattening.

The results obtained by Wever have been fully confirmed by Owen and Preston^24 with the aid of an ionization spectrometer. Among other important works on this question, mention should be made of the work of Tammann and Heindl^25 with the rolling of aluminum ingots. Tammann and Heindl calculated the relative proportions of the various orientations

depending on the treatment (degree of absorption, annealing, more or less rapid cooling, etc.); obviously, these investigations are of great practical interest.

Finally, Sachs and his collaborators^26, and also Glocker^27, undertook an important series of investigations on various metals rolled to different degrees; these remarkable works are illustrated with excellent radiograms.

The investigations consisted in observing the sheet at various angles of incidence, which made it possible to determine precisely the position of the orientation in space occupied by the crystals. In addition, when observing rolling in different directions it was established that the structure, at first very fibrous, becomes more and more isotropic and approaches the structure of a metal composed of unoriented grains (Fig. 15). Thus it proves possible to control quantitatively the rolling and its influence, which is of great technical interest.

Various mechanical deformations. In addition to drawing and rolling, many other investigations carried out by means of X-rays concerned the mechanical deformation of crystals. It may be said that at the present time it is possible to study qualitatively, and sometimes even quantitatively, the effects produced by torsion, forging, bending, stamping, etc. It is known, for example, that impacts bring metals of the cubic system with face-centered lattices into such an orientation that the diagonals of the face (110) are arranged in the direction of the pressure. For metals with body-centered cubes (iron), parallel to the direction of pressure there are chiefly the diagonals of the cube (111). As a result of torsion, the structure of metals of the first group is expressed by the orientation of the cube diagonal along the axis; for metals of the second group, along the fiber axis lies the diagonal of the face (110), whereas the direction (121) is arranged in the direction of the weak pressure.

Stamping, whose influence is more complex, was studied by J. J. Trillat^15 (1928), who showed,

that it is quite possible to determine the influence of the orientation caused in the case of such treatment. In the case of sheets of mild steel, treatment of the tips causes an alignment of the microcrystals of the metal, and one of the crystallographic directions becomes the axis of the fiber; this axis coincides with the direction (110), i.e. with the diagonal of the face of the cube, which is placed parallel to the direction of the deformed mean fiber (Fig. 16). This orientation effect is especially strong in the region of greatest curvature and is accompanied by changes in the sizes of the grains; these various phenomena cease at a small distance from the forging region (Fig. 17).

Fig. 16.

— · — · — some of the planes deformed during forging and hardening.
— — — — direction of the orientation axis.

Influence of annealing. Recrystallization. Crystals subjected to cold working undergo changes during heating, which restores to them the properties of untreated metals (annealing) and leads to recrystallization.

The study of annealing and recrystallization is one of the most fruitful, from the point of view of the results obtained by means of X-ray analysis. Indeed, it is quite possible, on the one hand, to obtain information on the average size of the crystallites (see above, determination of grain size), and, on the other hand, to trace changes in these sizes as a result of thermal or

mechanical working, as well as the phenomena of “deorientation” or recrystallization that arise during such working.

Generally speaking, simple partial annealing is explained by an increase in grain size and by reversible change in their position. For the case of a drawn metallic wire, for example an aluminum one, which very well represents the phenomena

Fig. 17. The regions under study are outlined with a dotted line. Lines with arrows indicate the direction of orientation. They are larger the more distinctly the structure is oriented.

of orientation as a result of cold working, Sachs and Teler^28, and also Schmid, Wassermann^29, Glocker and Widmann^30 showed that complete recrystallization is obtained in all grades of aluminum upon heating above 250°. Special 99.9% aluminum assumes a structure of large crystals above 400°; commercial aluminum—only above 600°. In addition, all the intermediate stages were recorded on X-ray photographs (Fig. 18, Table IV), which make it possible to trace and study these phenomena after drawing and heating, simultaneously with the study of mechanical properties.

Annealed metals usually show a more or less good general orientation; even in the case of metals of related structure, such as aluminum, silver, and copper, the observed orientation texture is entirely dif-

face-centered. The structure most often obtained is a disorderly arrangement of large crystals, as, for example, is seen in Fig. 18. In some cases, however, a genuine recrystallization texture with new orientations is obtained. Glocker[^27] showed that, on annealing a sheet of refined silver ($99.7\%$ Ag, $0.2\%$ Cu), a recrystallization structure appears which is clearly distinguished from the arrangement of crystals in the rolled sheet: between 200 and $212^\circ$ the direction (112) is located parallel to the rolling direction, while the direction (113) is perpendicular to the rolling plane. Above $750^\circ$ there is a return to the disordered state.

On a copper sheet Sachs[^31] likewise showed the existence of a considerably more pronounced recrystallization structure, in which the cubic crystals are arranged with one edge of the cube in the rolling direction and with the other edge perpendicular to the rolling plane. From the work of Sachs and Heller it follows that there is a high sensitivity of the recrystallization arrangement depending on differences in the rolling process and on the percentage of impurities. The duration of annealing, the temperature, and the rate of heating exert their effect on the size of the grains and on the diminution of their orientation. If one works with copper wire instead of a copper sheet, it may be verified that after annealing at $1000^\circ$ the crystals are arranged with their direction (112) along the axis of the wire.

X-ray spectrography also makes it possible to study changes in the structure of drawn tungsten and to show that a spiral made from a thin wire obtained by drawing compressed powder is transformed at high temperature into a single crystal of larger dimensions, which explains the brittleness of fired filaments.

The existence or disappearance of the fibrous structure obtained by one or another kind of mechanical working can likewise be studied by means of X-ray analysis, as the preceding examples show. In doing so it is possible to trace all the internal changes that accompany annealing. From a practical point of view, these

new applications to the study and control of heat treatment are of considerable value. They showed (see the following paragraph) that the chief reason for failures in metallurgy lies in the imperfection of annealing.

5. Arrangement of Crystals and Mechanical Properties

It is now appropriate to pose the following important question: is there a connection between the crystalline structure and the arrangement that can be detected on radiographs, and the various physical and mechanical properties of metals?

Excellent investigations on this question were carried out by Backsoff[^31], who studied mechanical properties in parallel with radiographs.

In most metals there is a close connection between recrystallization and the loss of mechanical resistance. In some cases, where the grain size increases as recrystallization proceeds, it seems possible to obtain a direct conclusion about the properties of cohesion. But in other cases the decrease of mechanical cohesion (“decohesion”) and recrystallization do not proceed parallel to one another. This case is observed especially when there is a slow transformation of crystals of zinc and tin by stretching. Then an almost complete destruction of resistance is observed, not accompanied by recrystallization. In the case of microcrystalline aggregates, which constitute the majority of metals, there apparently exists a much greater connection between orientation effects observed on fiber diagrams and tensile resistance in different directions. We have already pointed out that X-rays represent here, in a certain sense, a method of quantitative investigation applicable not only to metals, but also to many other substances (fibers, colloids, etc.). On the contrary, there is not always a simple connection between mechanical decohesion and recrystallization. For example, in the case.

of commercially available aluminum, studied by Sachs, some individual points on the curves of the relation between temperature and tensile strength (after annealing) do not coincide with the changes in the X-ray photographs. This result shows that the causes of these changes in properties must be sought elsewhere. The results obtained do not have the same origin. For example, an aluminum specimen annealed at 150° has a greatly reduced strength. However, X-ray analysis, as well as micrography, shows no sign of recrystallization. Further, at 250°, i.e., at the temperature at which the specimen loses all cohesion (the strength being greatly weakened), the diagrams show only very imperfect recrystallization, and only beginning with 300° can full recrystallization actually be observed. A comparison of these results shows that a very strong decrease in cohesion may occur even without any appreciable changes in the X-ray photographs.

In many cases, however, Glocker, Kaupp, and Widmann^30 were able to show that the mechanical properties remain connected with the changes observed on the X-ray photographs. Furthermore, Geler and Sachs, in investigations of the properties of rolled and annealed copper sheet, likewise arrived at very interesting results. In this connection we may refer to the work of Glocker’s laboratory in Stuttgart. Finally, it should be noted that not only mechanical properties, but also physical or chemical properties, must depend on the structure of crystalline aggregates—for example, corrosion, thermal expansion, evaporation rate, etc.

Be that as it may, it apparently still requires a great deal of work along this path, which opens attractive prospects.

6. Various practical applications

The various results of which we have spoken in the preceding paragraphs show the interest that

represents the application of X-rays to the investigation of the structure of metals and their deformations. In metallurgy these methods are widely used, and at the present time, not only in research institutes but also in large factories, there exist well-equipped X-ray laboratories. These laboratories have as their aim, on the one hand, scientific investigations and, on the other, the control of materials; but they strive chiefly toward the development of production techniques under which it would be possible to obtain metals with the desired structure. Clark is following this path in the United States, and it may now be said that such investigations constitute a firm basis for continuous progress in this field.

To characterize the industrial applications of X-ray analysis, we consider it sufficient to summarize some of Clark’s investigations, described in his book Applied X-Rays:

The influence of the treatment of metals. It is very important to know how the various effects of metal treatment are to be explained. Various methods of investigation make it easy to answer this question. Sometimes there is no need whatever to resort to theoretical explanations or to complicated calculations. Usually, the study of X-ray diagrams alone is sufficient to explain a phenomenon qualitatively.

Clark and his collaborators have in this way carried out work on steels that is very important for industry. The diagrams show with great clarity how little homogeneous the mass is after melting. Ordinary heat treatment is still insufficient to bring the metal into a state of uniform distribution. One of the successes of this method consists precisely in determining what the heat treatment should be in order to bring it to an ideal structure, i.e., to the existence of only small crystals arranged according to the law of chance, without internal stresses; in this state the mechanical characteristics are excellent.

As we have already indicated, Clark determined in samples of cast steel regions of internal stresses (lines of identical stresses), so that it was possible to predict weak points in a piece and in this way modify the treatment. The last traces of austenite are very difficult to make disappear, and for this purpose, during annealing, very considerable intervals of time are sometimes required. The effects of more or less rapid cooling, the effects of hardening, etc., can likewise easily be studied.

To this same range of questions also belong the author’s investigations of the influence of drawing on the structure of sheet steel (p. 874).

Clark also dealt with questions of arc and hydrogen welding, checking the results obtained by him with the aid of microphotography and tensile tests, thanks to which it was possible to achieve improvements in this technique.

Factory products. It would be very important to be able to determine, by means of some practical method, what the condition of the metal will be during factory production; very often investigations are required for the absence of guiding properties, and also for the absence of internal stresses. These properties cannot be detected with sufficient clarity either by means of mechanical tests or by means of microphotography. As an example of this, the diagrams in Fig. 20 (Table IV), borrowed from Clark, represent good sheet steel (below) and poor sheet steel (above). The second of them contains ruptures that occurred during working, whereas the microphotographs for both samples come out completely identical. Various steels (soft, hardness 1/4, hardness 1/2, hard) likewise give completely different diagrams with respect to physical properties.

The cause of the rupture of steel wires during drawing was also established by Clark. It lies in the residual moist condition of the wire being drawn. Further, Clark also studied steel rails containing transverse cracks, with the aim of determining the orig—

propagation of these cracks. It should be pointed out here once again to the works of the same author concerning the influence of grain size on magnetic properties, of silicon steels (see above, 857), and also on the practical study of stamped steel (J. J. Trillat).

The investigation of the structure of electrolytic deposits has also been made the subject of many works, chiefly by Glocker, Kaupp^32, Bozorth^33, Clark, Brugmann, Aborn, Frölich^34 and Trillat^35. The influence of current density, concentration, temperature, $p_{\mathrm{H}}$ and stirring on the structure of the deposit has also been studied in great detail. In this way it is possible to discover the best method for obtaining the most homogeneous and strongest layers. These works have shown the existence of a “tree-like” structure in certain deposits, the orientation of particles on the electrode (perpendicular to the surface of the cathode), changes in grain size under certain conditions, etc. Thus, for example, Trillat and Marie^35, working with deposits of electrolytic copper obtained in the presence or in the absence of a small quantity of gelatin, showed that this agent has a considerable influence on reducing the grain size, as well as on the presence of residual internal stresses. In exactly the same way Clark, Frölich and Aborn^34 arrived at analogous results for electrolytic deposits of lead.

In a similar manner one may consider many other applications which concern all branches of industry where metals or their alloys are used, so that it may be said that these applications can be varied almost without limit, depending on the peculiarities of the problems arising in each individual case. Methods based on the application of X-ray analysis promise to give an impetus to a considerable development of industry, and it must be supposed that in the very near future every factory of any importance, in addition to its laboratories for macrophotography and mechanical testing, will also have an X-ray laboratory intended—

valuable both for research and for improving production and for control.

The reader will find at the end of this article a list of works published up to 1929, in which all the questions summarized above are set forth in detail.

B. Various Applications of X-ray Spectrography in Inorganic Chemistry

Above we considered the application of X-ray spectrography only to the case of metals. There exists, however, a whole series of other applications that are of interest for various fields of human activity. Examples of these applications we give in the following lines.

1. The study of lime, cements, clays, porcelain, etc. The Debye–Scherrer method is very convenient for the practical study of powdery or fine-crystalline substances, for example sand, lime, cements, marble, porcelain, etc. In this way it is not difficult to trace the appearance of various structures during firing; it is known, for example, that at \(550^\circ\) metakaolin shows no signs of crystallization, while at \(1000^\circ\) crystals of mullite, tridymite, and cristobalite clearly appear, arising as a result of the transformation of the former. Wyckoff, Grieg, and Bowen\(^1\), as well as Clark and Farnsworth\(^2\), studied a whole series of clays with varying degrees of plasticity; some of them give diagrams corresponding to pure calcium oxide hydrate in lime, giving plastic hydrate; others give more complex diagrams, showing the lines of \(Ca(OH)_2\), \(CaCO_3\), etc. Abbie studied the course of calcination, and the practical results obtained by him make it possible to place very great hopes in this method.

Various clays and kaolins used in ceramics, as well as bodies with different degrees of firing, were investigated by Trillat, who found that spectrographic study makes it possible to follow the gradual transformation

microcrystalline mass into amorphous products, and also to differentiate clays and kaolins according to the degree of their purity and especially according to grain fineness, which for ceramics plays an extremely important role. When certain crystalline, poorly ground particles are present in the mass, on the diagrams one can see more or less expanded spots corresponding to Laue spots. Portland cements in various states were studied in the same way at the Bureau of Standards.

Paris gypsum shows a decrease in tensile strength after recalcination. According to Farnsworth’s indications, this depends on the size of the particles, which can be reduced by adding 25% alumina.

On the basis of these new results one may suppose that, with the aid of somewhat more complex methods, it is possible to study the plasticity of clays, as well as the influence of various methods of treatment on the structure and various physical properties of the resulting products.

2. Study of pigments and paints in painting.
As we have already indicated above, Scherrer’s formula makes it possible to determine the order of magnitude of colloidal particles. The fineness of pigments, as is known, is of enormous importance in painting. Therefore attempts were made, with the aid of X-ray analysis, to study the particle sizes of pigments, paints, enamels, etc. These investigations concerned various pigments, for example carbon black paint, titanium white, lithophone, etc.

Thus, for example, tin oxide, \( \mathrm{SnO_2} \), in the form of cassiterite, metastannic acid, or artificially prepared oxide, gives characteristic spectra of a tetragonal lattice similar to the lattice of rutile, \( \mathrm{TiO_2} \). Fig. 19 (Table IV) shows on the left spectra obtained with samples of \( \mathrm{SnO_2} \) containing particles of size \(10^{-8}—10^{-5}\) cm (when working with \( \mathrm{KaMo} \)). The middle figure represents the spectrum of a sample containing still smaller particles and showing broadening of the lines (order of magnitude \(2 \times 10^{-6}\) cm); here the particle width is approximately 50 times greater than the elementary prism. Finally, the right-hand figure corresponds to still

smaller particles, barely detectable with the aid of X-rays. Here the lines are strongly broadened; only about four of them can be observed in all. Measurements show that here we are dealing with a \(D\) of the order of \(5 \cdot 10^{-7}\) cm (the particle width is approximately equal to 10 times the size of the elementary cell). In this way we reach the extreme degree of colloidal dispersion. The interest of these studies is easy to understand if one recalls that the opacity and covering power of a paint change extremely strongly with changes in particle size. Generally speaking, it is known that there exist certain optimal particle sizes connected with opacity and covering power.

Naturally, these measurements are not limited to pigments alone; it is possible in the same way to study various mineral paints that enter into the composition of diverse products, such as rubber, synthetic resins, etc., chiefly from the point of view of the influence that their structure and their dimensions may have on the physical properties of the final products.

3. Study of asbestos. Asbestos, or mountain flax, as is known, is a hydrated magnesium silicate. Asbestos fibers are capable of giving excellent diagrams, as was shown by Clark, Eborn, and Brugman\(^5\). From these diagrams it is possible to study the different types of fibers, as well as their modifications under chemical treatment (acids, heating, etc.) and to determine the qualities that would be most suitable for the use of asbestos as a material for impregnating it with catalysts (Fig. 21, Table V).

J. J. Trillat also studied the modifications undergone by asbestos during its weaving under various conditions. He also succeeded in tracing the influence of various mechanical treatments.

4. Study of photographic emulsions. Photographic emulsions consist of silver bromide in gelatin and sometimes also contain a small amount of silver chloride and iodide. It proves quite

TABLE IV

Fig. 18. Recrystallization of an aluminum sheet at various temperatures.

Fig. 19. Spectra of SiO₂, showing the effect of line broadening as a function of decreasing grain size (after Clark).

Fig. 20. Diagram of steel (after Clark).

Advances in the Physical Sciences, vol. XI, issue 6.
To the article by J. L. Trillat.

TABLE V

Fig. 21. Diagrams of various kinds of asbestos (after Clark).

Fig. 22. Above—natural pearls (circular halos or pseudo-hexagonal structure); below—artificial pearls (after Rinne and Hamburg).

Advances in the Physical Sciences, vol. XI, issue 6, to the article by J. J. Trillat.

possible to study the structure of silver bromide grains, to obtain an idea of their sizes, and, by means of X-ray spectrography, to follow various processes of development and fixing. Such experiments were undertaken in order to test certain hypotheses concerning the photographic action (Wilsey,^6 Devi,^7 Bobrovna^8).

1. Study of catalysts and adsorption. We have already indicated above those applications which Clark^9 and his collaborators made of the study, by means of X-rays, of nickel as a catalyst. The same authors, as well as Debye and Scherrer,^10 Ruff, Schmidt and Olbrich,^11 also studied the structure of charcoal powder in adsorption phenomena as a function of the thermal treatment of this powder. Quite clear changes in the X-ray photographs give evidence of the existence of intermediate states between the crystalline form (graphite) and the amorphous state. Some of these carbons correspond to a very high degree of adsorption activity.

Finally, recently Damianovich and Trillat^16 found that powdered platinum, prepared under certain conditions, is capable of adsorbing and even chemically combining with helium.

These results point to the great interest presented by the application of X-rays to the study of these still little-known phenomena, such as catalysis and adsorption. In this respect the method holds out very great hopes.

1. Recognition of natural and artificial pearls. Dauvillier^12 devised an extremely elegant method for recognizing natural and artificial pearls. The latter, obtained by introducing a bead of mother-of-pearl into an oyster, appears to be a true pearl, possessing all the external characteristics of a natural pearl. However, with regard to this “purity” the opinions of eminent zoologists and the best-informed specialists differ. The problem of the pearl comes down, po-

apparently, to the question of the presence of a nucleus of enlarged dimensions, thanks to which artificial pearl loses much of its hardness. And there still does not exist a reliable method that would make it possible to distinguish artificial pearl from natural pearl, which is very favorable to swindlers.

The substance of pearl and mother-of-pearl, identical in their nature, and also very close to each other in density and elasticity—all this does not allow this difference to be established by means of transmission with X-rays. But the difference, which lies only in structure, enabled Dauvillier to show that, for this purpose, analysis of the crystals by means of X-rays is quite suitable.

The apparatus used for this purpose consists of a quartz tube with a replaceable anticathode and of a round spectrograph, allowing up to 16 diagrams to be obtained simultaneously. As was to be expected, only mother-of-pearl gives a pattern analogous to the Laue pattern, although it arises not from a continuous spectrum. The symmetry of the spots is hexagonal when the rays propagate normally to the lamellae, and square in the perpendicular direction. Conversely, pure pearls give a system of rings, sometimes without a single spot, whereas pearls with a nucleus of mother-of-pearl give both rings and spots simultaneously, which indicates a structure of two kinds (Fig. 22, Table V). Comparison of the intensities of both figures makes it possible, without doubt, to establish the thickness of the pearly layer and consequently to determine the true value of the pearl.

Further investigations by Ilexbya showed that calcium carbonate exists in pearl in the form of aragonite; the latter is found in the form of hollow crystals of a pseudohexagonal system, resembling the cells of a honeycomb, with hexagonal symmetry. This lattice is constructed in the form of an optical staircase and therefore gives rise to interference phenomena, on account of which the hue of these substances is called pearly.

Recent studies by Riwiger and Galiburg^14 made it possible for them to improve this method of investigating pearls and to introduce it into practical use.

7. Various applications. The applications that can be foreseen for spectrography are almost innumerable. Therefore we confine ourselves to the examples described above. Here we shall only point out that in this way one can distinguish pyrites and marcasites (T. Frébold), study fossil bones from the standpoint of their history, the formation and decomposition of zinc ferrite (Schwarz and Krauskopf^15), the structure of teeth, etc.

It is obvious that a whole series of other theoretical and practical applications is possible: crystalline structure, the microcrystalline state, phenomena of orientation as a consequence of various treatments, particle sizes, purity, the state of a chemical compound, identification of mixtures; types of lattices, internal stresses, etc.—all this can likewise be studied successfully in an enormous number of cases. Thus these methods should find an increasingly honorable place in research and industrial laboratories.

LITERATURE

A) Study of metals and their compounds

1. Westgren and Phragmen, Iron and Steel, 1, 241, 1922; 1, 160, 1924; Institute of Metals, 31, 193, 1924; Phil. Mag., 1925; Journ. of Iron and Steel Inst., 105, 241, 1922; Zeit. f. phys. Chem., 88, 181, 1921; 102, 1, 1922.

2. Bain, Trans. Am. Inst. Min. Met. Eng., Feb. 1922; Chem. Met. Eng. 28, 21, 65, 1923; 24, 779, 1921; 26, 543, 1922; Trans. Am. Soc. Stell. Treating, 3, 14, 1925.

3. Westgren and Phragmen, Ergänzungsband der Kolloid Zeit., 36, p. 86; Structural analogies of alloys, Arch. för Matem., Astronomi och Fysik, 19 B, No. 12, p. 1; X-ray analysis of the chromium–carbon system. Kundl. Svenska—Vetenskapesakade-mjes handlingor, 2, No. 5; X-ray analysis of the tungsten– and molybdenum–carbon system, Zeit. f. anorg. und allgem. Chemie, 156, 27; Composition of ferrotitanium

alloys, Iron and Steel Inst., (2), 397, 1926; Regularities in the structure of alloys, Metallwirtschaft, No. 25, 700, 1928;

1. Owen and Preston, Proc. Phys. Soc., 36, 49, 1924; 35, 101, Phil. Mag., 2, 1266, 1926.

2. Hull, The crystalline structure of iron, Phys. Rev., 9, 84, 1917; The crystalline structure of aluminum and silicon, Phys. Rev., 9, 564, 1917; X-ray structural analysis of thirty ordinary metals, Phys. Rev., 17, 571, 1921.

3. MacKeehan, Phys. Rev., 21, 402, 1923.

4. Jette, Phragmen, Westgreen, J. Inst. Metals, 31, 193; 1924.

5. Czochralski, Moderne Metallkunde, J. Springer, Berlin, 1924.

6. Clark, Applied X-Rays, New York, p. 237, 1927.

7. Böhm, Koll. Zeits., p. 276, 1927.

8. Shearer, Zsigmondy, “Kolloidchemie,” Appendix, 1920.

11a. Laue, Zeit. f. Krist., 64—115, 1926.

1. Clark, Asbury, Wick, J. Am. Chem. Soc., 47, 2861, 1925; Clark, Aborn, Clark, “Applied X-Rays,” p. 180.

2. Levi und Haardt, Atti. Accad. Lincei, (6), 3, 91, 1926.

3. Clark, Brugmann, Clark “Applied X-Rays,” p. 183.

4. J. J. Trillat, Chemie et Industrie, oct. 1928.

5. M. de Broglie, C. R. Acad. Sciences, 158, 833, 1914.

6. Taylor and Müller, Carpenter and Elam, Proc. Roy Soc. A, 102, 643, 1923; 105, 500, 1924; 107, 171, 1925.

7. Mark, Polanyi und Schmid, Phenomena during the expansion of zinc crystals, Zeits. f. Phys., 12, 58, 78, 111, 1922.

8. Mark, Polanyi, Weissenberg, Zeits. f. Phys., 12, 58; 13; 7, 149, 181; 10, 44; 14, 328; 16, 314; 18, 42.

9. Tanaka, Brit. Chem. Abst., A, p. 1012, 1927.

10. Becker, Zeit. f. Phys., 42, 226, 1927.

11. Mark und Weissenberg, X-ray determination of the structure of rolled metallic foil, Zeits. f. Phys., 14, 328, 1923; 16, 1, 341, 1923.

Polanyi, Naturw., 2, 288, 1921.

1. F. Weyer, Zeits. f. Phys., 28, 68, 1924.

2. Owen and Preston, Proc. Phys. Soc., 38, 132, 1926.

3. Tamman und Heinzel, Zeits. f. Metallkunde, 19, 338, 1927.

4. Sachs und Göler, Structure during recrystallization of metals with face-centered lattices, Zeits. f. Phys., 41, 873, 1927.

Sachs und Schiebold, Recrystallization in the X-ray image, Zeits. f. Metallkunde, p. 400, Dec. 1925.

1. Glocker, Rolled sheets of silver, Zeits. f. Phys., 31, 388, 1925.

2. Sachs und Göler, Structure and hardness of very pure aluminum, Zeits. f. Metallkunde, p. 90, 1927.

3. Schmidt und Wassermann, On the recrystallization of very thin aluminum wire, Zeits. f. techn. Phys., 3, 108, 1928.

1. Glocker und Widmann, Studies on the phenomena of recrystallization in Ag, Cu, Al, Zeits. f. Metallkunde, 18, 41, 1927.
   Widmann, Studies on the recrystallization of silver and copper, Zeits. f. Phys., 45, 200, 1927.

2. Sachs, Straightening of crystals by recrystallization, p. 258, 1928.

3. Glocker und Kaupp, Zeits. f. Phys., 24, 121, 1924.

4. Bozorth, Phys. Rev., 26, 390, 1925.

5. Clark, Brugmann and Heath, Ind. Eng. Chem., 17, 1142, 1925.
   Clark und Frölich, Zeit. Elektroch., 31, 655, 1925. Clark, Frölich and Aborn, Am. Electrochem. Soc., 1926.

6. J. J. Trillat et Marie, Study of the structure of electrolytic copper by means of X-rays, Rev. Metallurgie, 25, 286, 1928.

7. Mark und Hengstenberg, On the form and size of micelles in cellulose and rubber, Zeit. f. Krist., 69, 271, 1928.

8. Patterson, On measuring the size of crystalline particles by means of X-radiation, Zeits. f. Krist., 66, 637, 1928.

9. Brill, Determination of particle size by means of X-rays, Zeits. f. Krist., 68, 387, 1928.

10. Möller und Reis, Zeits. f. Phys. Chem., 139, 425, 1928.

11. Mark, Determination of particle size, Transact. Faraday, March 1928, Londres.

Other bibliographic references on the question of the study of metals by means of X-rays.

Nishikawa and Osahara, Some data on the question of the study of metals by X-rays, Phys. Rev., 15, 88, 1920.

Polanyi, On structural changes in metals during cold working, Zeits. f. Phys., 17, 1923.

Ettisch, Polanyi und Weissenberg, On the fibrous structure in metals, Zeits. f. Phys., 7, 181, 1921.

X-ray studies on metals, Phys. Zeits., 22, 646, 1921.

Fibrous structure of cold-drawn metallic wires, Zeits. f. Phys. Chem., 99, 332, 1921.

Schiebold, Zeits. f. Metallkunde, 16, 462, 1924 (121 references).

Uspenski und Konobiejewski, Diffraction of X-rays in microcrystalline structures, Zeits. f. Phys., 16, 215, 1923.

Glocker, Materialprüfung mit Röntgenstrahlen, Berlin, 1927.

Sachs, Plastische Verformung, Handbuch der Experimentalphysik, Leipzig, 1928.

Grundbegriffe der mechanischen Technologie der Metalle, Leipzig,

1. Technological properties of aluminum crystals, Zeits. des Ver. deutsch. Ing., p. 577, 1923.

Schmidt und Wassermann, X-ray investigations of duralumin, Zeits. f. Metallkunde, 19, 1927.

Hägg, Study of sodium oleate by means of X-rays, Nature, 119, 1928.

Dehlinger, Broadening of Debye lines and calculation of the magnitude of lattice distortions, Zeits. f. Kristallographie, 65, 162, 1927.

Weiss, Spectrography by means of X-rays and metallurgy, Rev. Metallurgie, 27, 459, 1925.

On the spectrography of alloys by means of X-rays, Bull. de la Société chim. de France, p. 607, 1923; Proc. Roy. Soc., 108 A, 843, 1925.

Bain, Amer. Inst. Min. and Metallurg. Eng., No. 1657, 1927.

Bain and Griffiths, Id. No. 1850, 1927.

Bradley and Thewlis, Proc. Roy. Soc., 112 A, 678, 1926.

Fink and Campbell, Trans. Am. Soc. Steel Treating, 9, 717, 1926.

Anderson J. Frankl. Inst., 201, 465, 1926.

Lange, Ann. Physik, 76, 476, 1925.

Jeffries and Bain, Chem. Met. Eng., 24, 779, 1921.

Andrews, Phys. Rev., 15, 245, 1921.

Mathieu, Metallography by means of X-rays, Le Génie Civil, Jan. 1930.

Zornig, Army Ordnance, 4, 77, 1923.

Heindlhofer, Phys. Rev., 24, 246, 1924; Trans. Am. Soc. Steel Treating, 7, 34, 1925.

Williams, Carnegie Scholarship Memoirs, 13, 175, 1924.

Campbell and Fink, Trans. Am. Soc. Steel Treating, 9, 717, 1926.

Ono, Mem. Col. Eng. Kyushu Imp. Univ., 2, 241, 1922.

Seemann und Schiebold, Z. f. Metallkunde, 17, 400, 1925.

Zester and Aborn, Army Ordnance, 6, 120, 200, 282, 363, 1925—1926.

Göhler und Sachs, Internal stresses in X-ray monochromators, Zeits. f. Metallkunde, 10 Okt. 1927.

Sachs und Bauer, The effect of tension on the properties of brass, II. 7, p. 154, 1927.

Jeffries und Archer, Science of metals, p. 185.

Baas und Schmid, On the twinning of cadmium crystals, Zeits. f. Phys., 54, 1929.

Masima und Sachs, Zeits. f. Phys., 51, 1928.

Kargop und Sachs, Experiments with recrystallization of metals, Zeits. f. Phys., 52, 1928.

Göler und Sachs, Stretching of copper crystals and X-ray structures, Zeits. f. Phys., 55, 1929.

Brill und Mark, X-ray study of the structure of complex ferricyanides, Zeits. f. Phys. Chem., 133, 1928.

Kurdjumow, X-ray investigations of the structure of hardened steel, Zeits. f. Phys., 55, 1929.

Burgers und Basart, Recrystallization of aluminum crystals, Zeits. f. Phys., 54, 1929.

Leroux, Silver, its alloys and their preparation, Metallwirts., Apr. 1928.

Müller, Preparation and properties of thin metallic sheets and their properties, Metallwirts., Apr. 1928.

Ewald, The crystalline structure of nonferrous metals, Metallwirts., Apr. 1928.

Röhrig, On the technology of aluminum and its alloys, Metallwirts., Apr. 1928.

Nowack, White gold, Metallwirts., Apr. 1928.

Schmied und Wassermann, On the mechanical formation of twins in zinc crystals, Zeits. f. Phys., 48, H. 5/6, 1928.

Laute und Sachs, What is fatigue? Zeits. des Ver. Deutsch. Ing., 72, No. 34, 1928.

Schmied und Wassermann, Experiments in connection with the problem of duralumin, Metallwirts., 14 Dec. 1920.

Kuntze und Sachs, On the question of the ultimate tensile elongation of steel, Zeits. des Ver. Deutsch. Ing., 1928.

Sachs und Sieglerschmidt, Testing of wire rods for tension and bending, Metallwirts., 8 Febr. 1929.

Göhler und Sachs, Structure of metals with centered faces during rolling and recrystallization, Zeits. f. Phys., 55, 477 495, 1925; Investigations of copper and brass, Zeits. f. Metallkunde, H. 6, 1928.

Karnop und Sachs, Flow of metallic crystals under torsion, Zeits. f. Phys., 53, H. 9/10, 1929.

Göler und Sachs, Refining of aluminum alloys, Metallwirts., 12 Juli, 1929.

Schmid, Fatigue from the point of view of phenomena in single crystals, Zeits. f. Metallkunde, Febr. 1928.

Brill, Crystal structure of FeAl, Zeits. f. Krist., 68, H. 4/5, 1928.

Glocker, Materialprüfung mit Röntgenstrahlen, Berlin, Springer, 1927.

Works of a general character on the question of the study of metals with the aid of X-rays

The reader can find many references in the following works

V. Laue, Zeit. f. Krist., 64, 115, 1926.

Clark, Applied X-Rays, Mc Graw Hill Book Co, New York, 1927.

Study of materials in industry by means of X-rays, Proc., Am. Soc. for Testing Materials, Philadelphia, 27, 1927.

Mark, The Application of X-Rays in Chemistry and Technology, G. Bredig, Handbuch der angewandten physikalischen Chemie, B. 14.

Sachs, The Application of X-Rays to the Study of Materials, Zeits. des Ver. Deutsch. Ing., No. 49, p. 1634, 1926.

Berthold, What Do X-Ray Investigations Give to Practice? Zeits. f. Metallkunde, H. 10, 1928. Investigation of Fine Structure by Means of X-Rays, Id. H. 10, 1928. Application and Technique of the Investigation of Fine Structure by Means of X-Rays, Siemens Reiniger Veifa, Berlin.

J. J. Trillat, The Application of X-Rays in Industry, Chimie et Industrie, No. 6, juni 1927.

The Application of X-Rays in Metallurgy, Rev. de Metallurgie, No. 11, nov. 1926.

Laborde, The Application of X-Rays in Laboratories and in Industry, Conférence parue dans Bulletin Ass. anc. élèves Ecole Phys. et Chim., 1927.

Maugin, La structure des cristaux, Conférence-Rapport, 1924.

Dauvillier, La technique des Rayons X, Conférence-Rapport, 1924.

The Application of X-Rays to the Study of Various Substances, Bull. de la Soc. fr. des électriciens, 5, No. 43, 1925.

De Broglie, Les Rayons X, Conférence-Rapport, 1922.

B) Various Applications of X-Ray Spectrography in Mineral Chemistry

1. Wyckoff, Grieg, Bowen, Amer. Journ. of Sci., 11, 459, 1926; 12, 419, 1926.

2. Farnsworth, Ind. and Eng. Chemistry, 19, 714, 1927.

3. Azbe, Id., 19, 600, 1927.

4. Bureau of Standards (U. S. A.), Amer. Journ. of Sciences, 13, 467, 1927.

5. Clark, Aborn, Brugmann, Jour. Soc. of Automotive Engn., 20, 291, 1927.

6. Wilsey, Phil. Mag., 42, 262, 1921; 46, 487, 1923.

7. Davey, Phys. Rev., 19, 248, 1922.

8. I. Bohrovna, Study of Photographic Emulsions by Means of X-Rays, C. R. Soc. Polonaise de Physique, 3, 1927.

9. Clark, Asbury, Wick, J. Am. Chem. Soc., 47, 2661, 1925.

10. Debye und Sherrer, Amorphous Carbon, Phys. Zeit., 18, 291, 1917.

11. Ruff, Schmid, Olbrick, Zeits. anorg. allg. Chem. 148, 313, 1925.

Clark, Applied X-Rays, p. 177, loc. cit.

1. Dauvillier, C. R. Acad. Sciences, 179, 819, 1924; Rev. scientifique, No. 2, 23 janv., 1926.

1. Shaxby, Study of the diffraction of X-rays in onyx and perlamutr, C. R. Acad. Sc., 179, 1601, déc. 1924; Phil. Mag., 65, 1201, 1925.

2. Ryziger et Galibourg, C. R. Acad. Sciences, 1926.

3. Schwartz und Krauskopf, inst. of metals, Classe D, No. 17, Dec. 1927.

4. H. Damianowich et J. J. Trillat, C. R. Acad. Sc., 8 Apr. 1929, p. 991.

General works on the various applications of X-ray spectrography

Clark, Applied X-Rays, loc. cit. (see above).

Mark, Die Verwendung der Röntgenstrahlen in Chemie und Technik, loc. cit.

Berthold, Die Einrichtungen der Feinstrukturuntersuchung mit Röntgenstrahlen, loc. cit. Anwendung und Technik der Feinstrukturuntersuchung mit Röntgenstrahlen, loc. cit.

J. J. Trillat, Applications des Rayons X dans l’industrie, loc. cit.

Laborde, Les applications des Rayons X dans les laboratoires et dans l’industrie, loc. cit.

Dauvillier, Applications des Rayons X à l’étude de diverses substances, loc. cit.

Ehrenberg, Ewald, Mark, Studies on the crystal optics of X-rays, Zeits. f. Krist., 66, 547, 1928.

Coster, Spektroskopie der Röntgenstrahlen, Sonderdruck aus Müller—Pouillet, Bd. II, 3, 11. Aufl., p. 2025—2096, 1929.

1. Vestrgren and Fragmen. ↩

2. Bain. ↩

3. Vestrgren. ↩

4. Preston. ↩

5. Hull. ↩