Abstract
The principal result of all experiments relating to electron diffraction is the complete confirmation of de Broglie’s hypothesis, i.e., the experimental establishment of the wave nature of moving particles of matter. Over the past year, new material on this question has accumulated, and its presentation constitutes the subject of the present review.
Full Text
NEW DATA ON ELECTRON DIFFRACTION1
G. Mark and R. Wierl, Ludwigshafen am Rhein
The principal result of all experiments concerning electron diffraction is the complete confirmation of the de Broglie hypothesis, i.e., the experimental establishment of the fact of the wave nature of moving particles of matter. During the past year new material on this question has accumulated, and its presentation constitutes the subject of the present review.2
The further development of this field of research has proceeded along several different lines.
On the one hand, the scattering of electrons by material bodies, analogous to the scattering of X-rays, has been used to study the basic properties of the electrons themselves. On the other hand, since cathode rays constitute a convenient means for investigating the structure of matter, attempts have been made with their aid to determine the distribution of charges within the atom, and also the arrangement of atoms in the molecule. Furthermore, observations on slow electrons, whose diffraction occurs chiefly at the surface of a solid body, have provided new material for studying the properties of thin surface layers. In the following lines we shall attempt to give a brief survey of what has been achieved along these lines of investigation.
1. Polarization of Matter Waves
According to de Broglie, to every beam of corpuscles consisting of identical particles of mass \(m\), moving
uniformly and rectilinearly with velocity \(v\), there corresponds a certain wave process, filling all space, by the existence of which the phenomena of interference of these moving particles are explained. The de Broglie relation
\[ \lambda=\frac{h}{mv}, \tag{1} \]
makes it possible, knowing the mass and velocity of the particle, to determine one of the quantities characterizing its wave field, namely—the wavelength. The oscillating quantity itself is characterized at each point of space by a certain complex expression, the square of whose modulus is equal to the density of electricity at the given point. The integral of this density over all space is equal, for each electron, to the elementary charge.
As is known, for a complete explanation of the properties of spectra it is not sufficient to ascribe to the optical electron only a single electric charge. As Goudsmit and Uhlenbeck first pointed out, each optical electron undergoes a gyroscopic rotation, by virtue of which it acquires a certain mechanical moment, whose quantization is also necessary for the interpretation of spectra. Since a rotating electron represents a current, there arises, alongside the mechanical one, a magnetic moment, equal in magnitude to
\[ j=\frac{eh}{4\pi me}. \]
Experiments on the diffraction of cathode rays by material bodies suggested the possibility, by analogy with experiments on the polarization of X-rays, of obtaining direct experimental proof of the fact of the existence of electron “spin.”1 After the question of the character of the expected effect had been discussed by a number of authors, in experiments of the Nerrenberg or Stern–Gerlach type, Mott2 carried out a detailed investigation of the phenomenon—
tions accompanying the scattering of fast electrons by an atom at rest. In his work he started from Dirac’s equations, which, in contrast to Schrödinger’s equation, are relativistically invariant and also describe the electron’s intrinsic spin. Considering the motion of an electron beam thus characterized in the deflecting force field of an atom, Mott obtained, for a beam of electrons scattered through some angle \(\vartheta\), an expression possessing the following remarkable property: if this scattered beam is, in turn, subjected to the action of a deflecting force field, then the number of electrons scattered through an angle \(\vartheta\) to the same side as the original beam (Fig. 1 b) will be greater than the number of electrons scattered through an angle \(\vartheta\) to the opposite side (Fig. 1 a).
Fig. 1. Diagram of the experiment for proving the intrinsic spin of the electron (after Mott)
In the figure, the primary beam of electrons incident on the first mirror is denoted by \(SS_1\). It is deflected through an angle \(\vartheta\), then falls on the second mirror and is again scattered by the latter through an angle \(\vartheta\). This second mirror may be placed either parallel to the first, as shown in Fig. 1,a (parallel arrangement), or as shown in Fig. 1,b, i.e., so that reflection takes place in the same plane and to the same side as the original one (inclined arrangement). In these two limiting positions the azimuth \(\varphi\), which determines the direction of the secondary reflection, is respectively equal to \(0^\circ\) and \(180^\circ\). Mott’s calculations show that the dependence of the intensity of the secondary scattered beam on this azimuth is expressed by a formula of the form:
\[ J = 1 + \delta \cos \varphi, \tag{2} \]
where \(\delta\) is a function of \(Z\) and \(v\), owing to which the effect increases with increasing atomic number and with increasing
electron velocity. Such behavior can be qualitatively explained by considering the interaction of the atom with an electron endowed with a magnetic moment. The greater the charge of the atomic nucleus and the faster the electron moves, the greater the magnetic deflecting action experienced by it. Furthermore, this action increases as the electron approaches the nucleus, i.e., as the angle of deflection increases. For small angles of deflection, as well as for light atoms and slow electrons, the expected effect could not be detected.
Fig. 2. Dependence of doubly scattered electrons on the azimuth angle (according to Rupp).
Experiments to investigate this effect were carried out by C. T. Chase1 and E. Rupp.2 Chase found, in the double reflection of cathode rays of medium velocity \((\vartheta = -45^\circ)\), an asymmetry of intensities lying within the limits of measurement error. Rupp, however, who investigated the double reflection of very fast electrons on metallic surfaces \((\vartheta \sim 10^\circ)\), succeeded in finding a noticeable asymmetry, increasing with increasing \(Z\) and \(v\), as shown in Fig. 2. However, in contradiction to Mott’s theory, the maximum intensity of reflection is obtained for the “parallel” arrangement. Thus, the magnitude and sign of the found
The angle of asymmetry has not yet received a theoretical interpretation. The situation that has arisen may be characterized as follows: although, in the double reflection of fast cathode rays, an asymmetry of intensity has been found, its connection with the fact of the existence of the electron “spin” has not yet been established.
Experiments proposed by Fues and Hellmann¹ for establishing the intrinsic rotation of free electrons are based on an entirely different principle. Here a polarized beam of electrons is obtained by scattering an ordinary beam of cathode rays on a permanent magnet; moreover, electrons belonging to magnetized atoms, with a definite orientation of their “spins,” exchange places (Austausch) with the electrons of the incident beam. In this way, in the cathode beam the number of electrons oriented in a definite manner increases, i.e., this beam becomes polarized, which can be detected by secondary reflection. The experiments undertaken to carry out this scheme have not yet led to final results.
In polarization experiments with double reflection, the greatest difficulty and the source of possible errors lie in the correct setting of the second mirror. This difficulty can be eliminated by causing the beam to be reflected twice from thin sheets; then, owing to the complete randomness in the arrangement of the crystals, a uniform reflection in all directions is obtained. The distribution of intensity in the Debye–Scherrer pattern obtained as a result of the second reflection determines the desired degree of polarization.
2. STUDY OF THE DISTRIBUTION OF INTRA-ATOMIC CHARGES
As early as 1912, Laue pointed out that, when X-rays are scattered by crystals, the dimensions of each atom must exert a substantial influence on the distribution of inten-
¹ E. Fues u. H. Hellmann, Phys. Z. 31, 465, 1930.
intensities in the scattered beam. Consequently, knowing this distribution, one can draw definite conclusions concerning the internal structure of the scattering atoms.
This effect plays an essential role in the X-ray analysis of the crystal lattice. Indeed, data on the arrangement of atoms in a lattice are obtained on the basis of a quantitative evaluation of the scattered intensities. Therefore, if the intensity depends on the shape of the scattering atom, the latter must somehow be taken into account in determining the arrangement of the atoms. In other words, the intensity of the scattered light is determined by a number of factors, in particular by the coordinates of the atom in the lattice cell (“structure factor” \(S\)) and by the distribution of charges in each individual atom (“atomic factor” \(F\)). Other factors—thermal motion, polarization of X-rays, etc.—we may here leave out of consideration.
If we are dealing, for example, with a crystal of diamond or zinc blende, where the coordinates of the atoms or ions can be established with certainty on the basis of simple symmetry considerations, i.e. where the factor \(S\) is specified in advance, then the possibility opens up for an experimental investigation of the factor \(F\). This investigation for several atoms and ions was carried out in a series of careful studies by W. L. Bragg and his collaborators. In this way, for some cases, purely empirical data were obtained on the distribution of intensity in scattering by each individual atom. One such curve is shown in Fig. 3. It represents the distribution of intensity on a single aluminum atom. The radius vector of each point of this curve is proportional to the intensity scattered at the corresponding azimuth. As is seen from the drawing, scattering at small angles is appreciably more intense than at large ones, since at a large deviation of the ray, rays originating from different parts of the atom may mutually cancel by interference. In the direction of the incident ray, however, they are all in phase and therefore mutually reinforce one another.
NEW DATA ON ELECTRON DIFFRACTION
The first attempts to give a quantitative explanation of this intra-atomic interference belong to Debye. Subsequently they were expanded and developed by a number of investigators on the basis of Bohr’s model of the atom, and also—here one must mention chiefly the work of Hartree—on the basis of quantum mechanics. In all these calculations the matter reduces to determining the interaction of two volume elements charged with a definite density in the atom; the result found must then be integrated over the entire volume. The simplest case of this kind is a thin, uniformly charged spherical layer. If the radius of this layer is equal to \(a\), and we consider the scattering of radiation of wavelength \(\lambda\), then for the scattering intensity as a function of \(\lambda\), \(a\), and \(\vartheta\) \((2\vartheta=\) the angle of deflection) one obtains the expression
\[ I=\frac{\sin x}{x}, \tag{3} \]
where
\[ x=\frac{4\pi a}{\lambda}\sin\vartheta . \tag{3a} \]
Fig. 3. Theoretical value \(F\) as a function of the angle of deflection, for X-rays scattered by aluminum \((\lambda=0.71\,\text{\AA})\): \(\times\)—experimental points of James, Brindley and Wood (James, Brindley and Wood. Proc. Roy. Soc., A, 125, 401, 1929).
Equation (3a) shows that the intensity depends only on the magnitude
\[ \frac{\sin\vartheta}{\lambda}, \tag{4} \]
which is therefore convenient to take as the abscissa in a graphical representation. If, as is the case in wave mechanics, we have a charge continuously distributed in space, then expression (3) must be multiplied by the density of electricity and integrated over the entire space occupied by the charge. Then we arrive at the expression
\[ F=\int_{0}^{[[unclear: upper limit]]} U(r)\frac{\sin(kr)}{(kr)}\,dr, \]
where \(U(r)\) is a function characterizing the dependence of the electron density on the distance from the nucleus \(r\).
Thus, knowing the function \(U(r)\), one can determine the influence of the shape of the atom on the intensity of the scattered light. An example of this kind of curve is curve 6 in Fig. 5 (the experimental points from Fig. 4 have also been transferred to this same figure). Starting from this curve, one can, in principle, determine the charge distribution in the aluminum atom.
Fig. 4. Charge distribution \(U(r)\) for aluminum \((Al^{+++})\) (after Hartree).
Fig. 5. Curves \(F^2\theta\)—for x-ray beams on aluminum (corrected for thermal motion and extinction), 4, 5 and 8 for 36 kV electrons on foils of Au, Ag and Al, 7—theoretical scattering curve (after Reznikoff). (\(Z.\) Physik. 60, 741, 1930).
Methods for determining \(U(r)\) are provided by the quantum theory of atomic structure. Considering the electrons surrounding the nucleus as a degenerate gas obeying Fermi statistics, one can obtain theoretical curves for the electron density in atoms with large atomic numbers, similar to that shown in Fig. 4 for the aluminum ion. From Fig. 5 it is seen that the measured points, corresponding to various reflecting planes—
crystal, are laid in the immediate vicinity of the theoretical curve. Thus, the expression \(H(r)\), entering into the formula for \(F\), receives experimental confirmation.
Electron diffraction gives us the possibility of verifying this expression by another, independent, method, since it is obvious that, in the scattering of matter waves, the internal structure of the atom must also in some way make itself felt. If the distribution of charges in the aluminium atom (Fig. 4), which served as the basis for curve 6 in Fig. 5, is correct, then it must also correctly reproduce the distribution of intensities in the diffraction of fast electrons.
In the experimental realization of this idea, there first arises the problem of quantitatively measuring the intensity of the bands of electron interference obtained on an aluminium foil. For this it is necessary to have sufficiently sharp interference rings that do not overlap one another. Fig. 6 presents a photograph of a thin gold foil at an electron velocity of 46 kV.
Fig. 6. Electron diffraction in a silver lattice. Electrons 36 kV, \(\lambda = 0.0645\) Å. Exposure time 0.1 sec.
Up to the index (620), the interference bands of this photograph possess sufficient sharpness. Indeed, from Fig. 6, or, still better, from the photometric curve presented in Fig. 7, it is seen that the individual rings here are sufficiently far from one another for the intensity of each of them to be determined with certainty. By comparison with an electrometrically graduated blackened scale, the intensities of eight reflected beams, plotted on the diagram in Fig. 5, were measured. As we see, here the predominance of the intensity of the beams, scat-
Fig. 7. Photometric curve of electron-diffraction images:
a) Al, weak intensity; b) Al, strong intensity; c) Ag.
scattered at small angles. In order to draw conclusions from the resulting curve concerning the distribution of charges in the scattering atom, it is necessary to take into account that, in contrast to X-rays, whose scattering is produced by charges, matter waves are scattered by the force field. Therefore, for X-rays the scattering intensity is determined directly by the distribution of charges in the atom, whereas for electrons an intermediate stage—the force field—enters into the calculation. Calculations carried out by Bethe1 give, for the atomic factor \(F^*\) in the case of fast electrons, the value
\[ F^*=\frac{Z-F}{\sin^2\vartheta}, \tag{5} \]
where \(Z\) is the atomic number of the scattering atom, and \(F\) is the atomic factor for X-rays. Thus, knowing the atomic number \(Z\) and the atomic factor for X-rays, one can calculate the atomic factor \(F^*\) for electrons and compare it with the experimental
data. This comparison is made in Fig. 5, where curves are given that were calculated by formula (5) for Al, Ag, and Au. We see that the measured points lie very well on these curves, i.e., that the distribution of intra-atomic charges found by means of X-ray scattering makes it possible also to predict the intensity of the diffraction of fast electrons. Thus, the theoretical determination of this distribution, based on quantum mechanics, has received good experimental confirmation in experiments on the scattering of both X-rays and cathode rays.
For the intensity of the scattered electrons we obtain, from formula (5),
\[ I = K \frac{(Z-F)^2}{\sin^4 \vartheta}. \tag{6} \]
This formula is analogous to the Rutherford formula discussed by Bethe1, corrected for the screening action of the electron shell:
\[ I = K \frac{Z^2}{(\sin^2 \vartheta + \alpha^2)^2}. \tag{7} \]
It is clear from this that the above-described experiments on electron diffraction make it possible to determine the difficult-to-measure screening constant \(\alpha\), as was first pointed out by F. Kirchner.2
3. DIFFRACTION OF FAST ELECTRONS BY INDIVIDUAL MOLECULES.
The Debye–Scherrer diagram of a thin metallic sheet shown in Fig. 6 was obtained with 36-kilovolt electrons at an exposure of only \(1/10\) second. Its relatively high intensity shows that the interaction between electrons and matter is of a much more intense character than in the case of X-rays. This fact suggests the possibility
obtain the diffraction of cathode rays on gas molecules and use the diagrams thus obtained in order to determine the arrangement of atoms in the molecule under study, similarly to what Debye and his collaborators did when studying the scattering of X-rays in gases.^1 In this connection, the advantage of electrons lies in the short exposure time, which makes it possible to complete long series of experiments more quickly.
Fig. 8. Diffraction of 45 kV electrons on molecules of carbon tetrachloride. Exposure time 0.1 sec.
Fig. 9. Diffraction of 45 kV electrons on molecules of germanium tetrachloride. Exposure time 0.1 sec.
The experiments carried out showed that in this way it is indeed possible to obtain the desired result. Fig. 8 shows the pattern obtained in the scattering of electrons by a thin jet of carbon tetrachloride vapor. In the photograph a series of concentric rings is clearly visible; their appearance, owing to the complete chaotic character of the mutual arrangement of the molecules, can be explained only by intramolecular interference.
In order to draw from this definite conclusions concerning the distribution of atoms in the molecule, it is necessary to turn to the theory developed by Debye, which in its essentials
^1 Cf., for example, P. Debye. Z. Elektrochemie, No. 9, 1930.
proceeds from the same conceptions as the derivation of formula (3). From this theory it follows that the elementary interference function determining the distribution of intensity in diffraction by a large number of randomly arranged “dumbbell” molecules (e.g., molecules of gaseous nitrogen), the distance between whose atoms is equal to \(a\), has the form
\[ J \sim 2F^{*2}\left(1+\frac{\sin x}{x}\right), \qquad x=\frac{4\pi a}{\lambda}\sin\vartheta . \tag{8} \]
In this equation \(F^*\) denotes the above-mentioned “atomic factor” for electrons. In the case of the molecule \(\mathrm{CCl}_4\), one must take both atomic distances \(\mathrm{C}-\mathrm{Cl}\) and \(\mathrm{Cl}-\mathrm{Cl}\), substitute them separately into equation (8), and sum the result. This gives
\[ J \sim F_{\mathrm{Cl}}^{*2}\,6\left(1+2\frac{\sin x}{x}\right) +8F_{\mathrm{Cl}}^*F_{\mathrm{C}}^*\,\frac{\sin x'}{x'} +F_{\mathrm{C}}^{*2}. \tag{9} \]
A graphical representation of the functions entering into equation (9), if expression (5) is substituted for \(F^*\), leads to an intensity-distribution curve that agrees well with the observations.
Especially remarkable is the fact that the scattering intensity at the four edges of the tetrahedron formed by the distances between chlorine atoms is considerably greater than the scattering intensity along the segment \(\mathrm{C}-\mathrm{Cl}\). For the best interpretation of the observations it is necessary to assign to the gaseous \(\mathrm{Cl}_4\mathrm{C}\) molecule the form of a tetrahedron, with the distance \(\mathrm{C}-\mathrm{Cl}\) equal to
\[ a=1.82\ \text{\AA}. \]
Following \(\mathrm{CCl}_4\), a series of heavier chlorinated tetravalent elements was investigated, as well as the chlorides of \(\mathrm{Si}\), \(\mathrm{Ti}\), \(\mathrm{Ge}\), and \(\mathrm{Sn}\). It turned out that an increase in the atomic number of the central atom affects the form of the diffraction pattern in two ways:
a) it increases the length of the edges of the tetrahedron, and
b) it increases the magnitude of the distance \(Z-\mathrm{Cl}\).
As an example, Fig. 9 shows the diagram of $\mathrm{CCl}_4$, which indeed differs sharply from the diagram of carbon tetrachloride.^1
As a further application of electron diffraction to questions of molecular structure, one may mention the comparison between benzene and cyclohexane. From X-ray studies of benzene and many of its derivatives it is known that the benzene ring in the crystal lattice, in its structure, is extremely similar to a regular plane hexagon; the distance between neighboring carbon atoms forming it is equal to 1.42 Å. On the other hand, for the analogous distance in hydrogenated benzene one must, on the basis of earlier X-ray experiments, expect a value of 1.55 Å, since the latter is the normal distance for any pair of aliphatically bonded carbon atoms.^2
Diffraction experiments on these gases, carried out under completely identical experimental conditions—voltage, distance between the plates, exposure time, etc.—give two analogous ring systems, with the ring diameter in benzene being somewhat larger than in cyclohexane. If the corresponding stereochemical models are taken as a basis, one can arrive at good agreement with the observed diagrams by assuming for benzene a plane hexagon with an interatomic distance of 1.4 Å, and for cyclohexane—a more complex ring with a distance of 1.5 Å.
Likewise, for cyclopentane—one of the aliphatic hydrocarbons for which stereochemistry gives a planar model—there is obtained a well measurable electron diagram, which can be satisfactorily explained if the cyclopentane molecule is regarded as a plane pentagonal ring with an interatomic distance of 1.5 Å.
^1 On the question of quantitative evaluation and comparison with Goldschmidt’s values of atomic radii, see R. Wierl, Leipzig Lectures on Electron Diffraction, 1930.
^2 A direct determination of the crystal structure of cyclohexane or of any of its derivatives has not yet been carried out.
Clear diagrams that lend themselves well to quantitative estimation are also obtained for 1,2-dichloroethylene. This molecule, as is known, exists in Cis and Trans modifications; the first boils at \(48^\circ\), the second—at \(60^\circ\). Making use of this, they can be separated from one another by simple distillation. It is to be expected that these two modifications will give diffraction patterns somewhat different from one another, since the distance between the “reflecting” chlorine atoms has different values in them. If the tetrahedral model is taken as a basis, then for the Cis form this distance will be \(3.41\) Å, and for the Trans form—about \(4.47\) Å.
The evaluation of the electron diagrams of both modifications leads to somewhat smaller numbers, whose ratio, however, agrees with the theoretical one.
These experiments show that the distances determined in crystal lattices by means of X-rays, characteristic of aliphatic and aromatic compounds, are preserved also in the free molecule, and they confirm the conclusions, drawn by stereochemistry from considerations of isomerism, concerning the form of these molecules.
However, the results obtained upon irradiating 1,2-dichloro-, dibromoethane and oxalyl chloride are at variance with the conclusions of classical stereochemistry.1 Indeed, if the single bond \(C — C\) possessed the complete free rotational capacity assumed by stereochemistry, then gaseous dichloroethane would represent a mixture of molecules in which the distance between the chlorine atoms would lie between \(3.6\) and \(4.6\) Å. From purely geometrical considerations it can be seen that, with complete freedom of rotation, i.e. with uniform rotation of one chlorine atom around the other, the distribution of distances between the above-mentioned limits cannot be uniform, and that the Cis and Trans forms must have a noticeable predominance (according to the sine law). With the aid of the formula given above it is easy to calculate that interference pat-
ture that should be obtained when such a mixture is irradiated and to which the actual diagram of this gas should correspond.
In experiment, however, diagrams are obtained that differ markedly from the theoretical ones.1 For example, the diagram of 1,2-dichloroethane has the appearance as though we had a mixture of the pure cis and pure trans modifications, taken in approximately equal proportions. It is extremely similar to the diagram obtained when photographing an equimolecular mixture of cis- and trans-dichloroethylene.
This result shows that complete freedom of rotation in 1,2-dichloroethane apparently does not exist. It is in agreement with the observations of Debye and his collaborators2 on the same gas, made by means of X-ray interference. The X-ray photographs of gaseous dichloroethane likewise argue against the assumption of complete freedom of rotation and testify to the predominance of quite definite configurations.
It must be noted that all experiments relating to this question have not yet been performed so cleanly that one could speak of its definitive resolution. They only show that the seemingly natural assumption of free rotatability of a simple C—C bond must still be subjected to detailed investigation before any final statements can be made.
4. Experiments with slow electrons: the refractive index and the properties of surface layers.
Fast electrons are in many respects extremely similar to X-rays; in particular, the positions of their interference maxima obey the simple Bragg law, in which the wavelength is expressed by de Broglie’s formula.
For slow electrons, however, the matter is more complicated. In this case, the interaction of the electrons with the force field of the lattice causes, in addition to diffraction, a noticeable refraction of the de Broglie waves, so that the positions of the maxima are no longer determined by the simple Bragg relation. Roughly speaking, here it is necessary—analogously to what is done in the optics of dispersive media—to introduce a refractive index that would express the presence of a strong interaction between the crystal lattice and the wave. A more exact analysis of the process of refraction of matter waves by a crystal lattice, given by Bethe1 and later by Morse,2 showed that, in order to characterize this interaction, a single refractive index is insufficient. To describe accurately the force field of the lattice inside the crystal, not one constant is required, but a whole series of constants.
Already the first experiments of Davisson and Germer with slow electrons revealed the necessity of introducing a refractive index. Physically this means that inside the crystal there is a certain average lattice potential, which in first approximation can thus be determined from the positions of the interference bands. In agreement with other experiments it turned out that, for nickel, this internal potential is approximately equal to 14 V. Subsequently, Rupp, in a series of papers, gave values of the lattice potential for crystals of certain metals and salts.
As in ordinary optics, the refractive index here too depends substantially on the wavelength, i.e., on the velocity of the electrons. This effect, first discovered by Farnsworth3 in copper, is entirely analogous to the dispersion of light and X-rays. Investigating it, Davisson and Germer4 discovered a phenomenon analogous to anomalous dispersion, for which a theoretical explanation has not yet been given.
The small depth of penetration of slow electrons into the crystalline lattice suggests making use of the scattering of these particles for studying the properties of surface layers. This seems all the more interesting because, with the aid of deeply penetrating X-rays, one can always observe only bulk effects.
Experiments of this kind with fast electrons were carried out by Kikuchi.¹ At first glance, his results indicate that the very upper plane of the lattice acts in electron diffraction as a two-dimensional lattice. However, owing to the great penetrating power of fast electrons, it is very probable that the cause of this effect lies in the mosaic structure of the crystal under investigation. In an analogous way, W. L. Bragg² gave the correct interpretation of Linnik’s experiments,³ who thought that he had obtained spectra of a two-dimensional lattice for X-rays.
With the aid of slow electrons, Davisson and Germer,⁴ and subsequently especially Rupp,⁵ studied in a number of directions the structure of the surface layer as a function of the adsorbed gas. In the reflection of slow electrons by metallic crystals, as in the scattering of X-rays, interference maxima of various orders are obtained, corresponding to different lattice planes. Alongside them, however, there also exist other maxima that cannot be interpreted as reflection from planes with integral indices. They admit of interpretation only as reflections from two-dimensional lattices, i.e., they are due to the very upper planes of the crystal, which thus becomes possible to investigate experimentally.
Rupp studied in this way those changes that are caused—
¹ Cf. Naturwiss. 17, 174, 1929.
² W. L. Bragg. Nature, 124, 125, 1929.
³ W. Linnik. Nature, 123, 604, 1929.
⁴ C. I. Davisson and L. H. Germer. Phys. Rev. 30, 705, 1928; L. H. Germer. Z. Physik. 54, 408, 1929.
⁵ E. Rupp. Ann. d. Phys. 5, 453, 1930.
are affected by the adsorption of gas on the surface of nickel. In Fig. 10a are shown the maxima obtained upon reflection of slow electrons from the octahedral surface of a nickel crystal. If refraction is taken into account, the results agree well with the conclusions of the theory. If, however, the nickel surface begins to adsorb hydrogen, then the appearance of the diffraction pattern, as shown in Fig. 10b, changes in a very characteristic way. First of all, the maxima obtained from the nickel lattice (with centered faces) become noticeably weaker and broaden, which is apparently explained by a disturbance of the regularity of the crystal lattice of the metal by the penetrating gas. Further, in the intervals between these maxima there appear new weak maxima, which grow as the duration of adsorption increases and therefore, evidently, must be attributed to hydrogen. If the metal is heated and the gas pumped off, these maxima again disappear, and the nickel maxima recover their former sharpness and intensity.
Fig. 10a. Reflection of electrons from the 111 surface of pure nickel, angle of incidence \(10^\circ\) (after Rupp).
Fig. 10b. Reflection of electrons from the same surface after prolonged exposure to hydrogen. The dotted curve is two days later (after Rupp).
Davyson and Germer, studying the arrangement of these new maxima, came to the conclusion that the arrangement of hydrogen atoms on the surface of nickel is regular, as shown in Fig. 11. In this figure one plane of the nickel lattice is represented, with the nickel atoms denoted by dots and the adsorbed hydrogen atoms by crosses. In an analogous manner
Rupp and Schmid¹ studied passivation phenomena on iron, and Rupp² investigated the thoriding of tungsten.
As is known, in X-ray investigations it has never been possible to localize hydrogen atoms in the lattice. This is explained by the fact that a hydrogen atom, on entering into a chemical compound, very often loses its valence electron, and therefore the spatial concentration of charge around the hydrogen nucleus becomes insufficient to produce an interference maximum. Electrons, however, whose diffraction, as already mentioned, is due chiefly to the force field of the nucleus, make it possible to determine the arrangement of hydrogen atoms and in this respect are considerably more convenient than X-rays.
Fig. 11. Arrangement of adsorbed gas atoms on the surface of nickel.
The past year has been extraordinarily rich in experimental studies in the field of electron diffraction, and great successes have been achieved along this path. However, a number of questions still remain unclear; many still await development. It is therefore possible to expect with confidence the appearance in the near future of new and interesting results on the diffraction of matter waves.
¹ E. Rupp and E. Schmid. Naturwiss. 18, 455, 1930.
² E. Rupp. Metallwirtschaft. 8, 448, 1929.