In recent years, a number of experimental X-ray diffraction techniques have been developed by which a topographical display of the microscopical defects in a crystal can be obtained. This brief review of the most useful of these techniques is intended to summarize the elements of the various methods and to compare their respective features and limitations. Contrary to microradiographic methods, in which image contrast is due entirely to variations in X-ray absorption from point to point in the specimen, X-ray diffraction topography is concerned with point-topoint variations in the directions or the intensities of X-rays that have been diffracted by crystals. From these variations the defect structure of the crystal may be examined. Methods that mainly measure local variations in the direction of the diffracted beam are useful for the detection of gross misorientations such as subgrains or grains (methods of Gui nier and Tennevin, Schulz, Weissmann). Intensity mapping methods are chiefly concerned with individual defects such as dislocations, stacking faults, etc. In both groups there are experimental arrangements with both Laue-case (transmission) and Bragg-case (back reflection) geometry.

A brief review of the different topographic methods is given in order to attempt a classification of the various types of contrast observed. Depending on whether the image is obtained by a reflection or transmission method, is simple or integrated, dynamic, direct, or intermediary, the contrast and image width vary greatly. A detailed analysis is given in the case of transmission section topographs.

Guided by the dispersion, surface of dynamical theory, we easily obtain evidence of the fact that in asymmetrical surface reflections (Bragg case) of X-rays at a perfect crystal, the angular widths of the incident and reflected beams are different from the same widths in the symmetrical Bragg case. The beam with the smaller glancing angle to the surface is angularly expanded, the other one, contracted (though in cross section, the former is contracted and the latter, expanded). Consequently, if the incident glancing angle is the smaller one (striping incidence, Vreftection), the angular width of the reflected beam is smaller than in the symmetric case (S-reflection), and that of the reflected section out of the primary beam is greater, and vice versa (striping emergence, if-reflection). At striping incidence, a contraction occurs, whereas at striping emergence, expansion of the angular reflection range occurs. These facts offer a number of possibilities for applying asymmetrical reflections to the well-known technique of the two crystal diffractometer—the author proposes the term “diffractometer” instead of the widely used “spectrometer”—in the (nv, −n)-position. These possibilities extend the efficiency of the double diffractometer with multiple effects, and some of them are given below: (1) Realization of rocking curves of extremely small angular width in the (nv, −nR)-position, and consequently increased sensibility of that width to lattice distortions, (2) Use of the extremely small angular width (or more strictly, the sharp θ-λ-coordination) of the beam emerging from a first crystal. This is in V-reflection for scanning the intrinsic diffraction pattern of the second crystal used in S- or V-reflection [(nv, −ns) or (nv, −nv) -position], (3) Increased steepness of the sides of the rocking curves using (nv, −nR) or (nv, −ns)-positions which allows double diffractometric topography (Bond-Andrus, Bonse-Kappler) of increased angular resolving power. (4) Repeated ^-reflections (eventually within a single crystal provided with a suitable groove) leading to further angular contraction of the resulting reflected beam and therefore further increased angular resolving power [(nv, −nv, nR, −nR)- and (nv, −nv, +nS)-positions]. Here the tails of the rocking curve are also suppressed by multiple reflection (Bonse-Hart).

A double diffractometric method which allows clean separation of the thermal diffuse contribution from X-ray reflection peaks is demonstrated.

The spherical wave theory of X-ray Pendellosung fringes in perfect crystals (N. Kato, Acta Cryst, 14: 526, 627, 1961) is extended to the case of crystals including a single stacking fault in an arbitrary way, Kelvin's stationary phase method is used extensively. The stationary phase condition gives us the trajectories of X-ray beams in the crystal. The phase and the amplitude along each trajectory are obtained by straightforward calculation. Based on this crystal wave field, the section patterns in X-ray diffraction topographs are obtained both for the direct and the Braggreflected waves. Characteristic fringe-patterns are expected. Through the image of a fault plane in a single section pattern, the geometrical configuration inside the crystal and the magnitude of the fault vector can be determined. Traverse patterns are also discussed. The fault image based on the plane wave theory (Whelan and Hirsch, Phil. Mag. 2: 1121, 1303, 1957) is also reformulated in the most general Laue case without the use of ad hoc assumptions on the shape of the dispersion surface.

Complete dynamical solutions for three coupled plane-wave components in crystal structures with inversion symmetry have been found. After reviewing briefly the dynamical solutions for wave fields with two coupled plane-wave components, the results for the three-beam case are discussed in qualitative terms. Attention is paid to singular points and lines on the ω-surface, and to the attenuation of the mode-intensity because of absorption. The most surprising result is that in the case one of the reflections is forbidden (Umweganregung) the absorption is reduced in comparison with the adjoining two-beam cases. Experimental data are in reasonable agreement with the theory. Quantitative data are presented for a few three-beam cases of simultaneous diffraction of Cu Kα. radiation in germanium.

Examination of the substructure of crystalline solids by diffractographic methods has recently developed into an independent field of work alongside atomicstructure analysis. Diffraction micrography with electrons is characterized by the small size of the distortion fields and the high resolving power in small crystal ranges (1000-3000Å thickness). X-ray diffraction micrography is characterized by great reciprocation between wave field and distortion field and by undisturbed preparation and undisturbed testing in the large crystal ranges (up to 15 cm2). There are two groups of examination methods for diffraction micrography with X-rays: (1) Examination with a finely limited, polychromatic or monochromatic X-ray source and moving sample, according to A. R. Lang et al. (2) Examination with a parallel-ray beam of polychromatic or monochromatic X-rays with fixed sample, in accordance with Berg-Barrett et al. For the examination of coarse defects in single-crystalline and poly crystalline matter, the parallel-beam method offers a wide scope for studies in the physics and applications of single-crystal line and polycrystalline solids. This paper therefore includes a summary of the methods using collimation systems and grating diaphragms. Measuring techniques and results are illustrated with the help of reflection and transmission pictures on various crystals. The various methods and refined measuring technique of the parallel-beam method enable the following to be defined: (1) Localization of crystallites from 20 μ diam. upward in a surface up to 15 cm2. (2) Determination of the faces of averted crystallites from 20 µ diam. upward in crystal surfaces. (3) Angle of avertence of crystallites or curvature angles of net faces from 1 to 3° in crystal surfaces up to 15 cm2. (4) Subangle grain boundaries, slip bands, and dislocation lines; also distortion fields (from 20 μ upward) resulting from mechanical, thermal, and radiation damage.

Dislocations, Inclusions, and Precipitates. Impurity precipitated after growth and foreign particles accidentally included during growth both produce intense local strain fields which give rise to diffraction contrast effects resembling those seen in electron microscope images of precipitates. The relationship between the dislocation configuration and these localized strain centers can show whether the latter arise from inclusions or precipitates. Precipitates will generally be found strung along the grown-in dislocations, decorating them. On the other hand, inclusions often generate dislocations by lattice closure errors; such dislocations then fan out from the inclusion in the general direction of advance of the growth interface.

Twin Boundaries and Fault Surfaces. The cases when the twins have parallel lattices, such as in Brazilian and Dauphiné twinning in quartz, are interesting. When the crystals on either side of the twin boundary are both Bragg reflecting, the twin boundary may exhibit ‘stacking fault’ type fringes. From an analysis of the variation of visibility of these fringes in different reflections, the fault vector at the twin boundary and its variation with boundary orientation may be found. In quartz, other types of fault surfaces producing fringe contrast may lie parallel to growth horizons or they may mark growth sector boundaries. In synthetic quartz, they can also mark cell boundaries under conditions of cellular growth.

Internal Magnetic Domain Structures. In plates of Fe + 3% Si roughly parallel to (110), a variety of previously undetected domain structures has been discovered and analyzed. Diffraction contrast is produced by 90° domain walls but not by 180° walls. The 90° walls produce strong diffraction contrast even though the magnetostriction of silicon-iron is only about 10−5. In plates parallel to (112), the main lamination pattern below the complex pattern of surface closures can be revealed and, in favorable cases, interpreted.

X-ray Moiré Patterns. The most direct method of observing X-ray moiré patterns—by topography of one crystal closely superimposed upon another—involves considerable theoretical complexities and produces a variety of curious diffraction patterns. However, it shows promise of providing a means for the comparison of lattice spacings to about one part in 107 and for mapping strain fields very sensitively.

That X-rays focused by reflection from concave surfaces exhibit anomalous image broadening was shown by Ehrenberg using a line source. Even flat nonfocusing surfaces of many different materials produced an anomalous striated reflection. According to Ehrenbevg, the common cause for the observed broadening in the focused image and the striated pattern in the nonfocused reflection is a periodic surface structure. In later years, Eliot, using a point source of X-rays reflected from a concave surface, observed a striated pattern at a position well beyond the focal plane. It is to be noted that Eliot's experiment combined elements of Ehrenberg's two experiments—a focusing surface and observations made far from any focal plane, real or virtual. Eliot observed his striations with fused silica surfaces but not with obsidian. Recently, Yoneda, using X-rays collimated by a Soller slit and incident on a plane surface, observed an anomalous line reflection not previously reported.

Various experiments performed by the present authors have attempted to duplicate some of the above situations as closely as possible, either directly with X-rays or in an analogous manner with visibic light. It will be shown that satisfactory explanations can be formulated from previously unsuspected diffraction phenomena, recently confirmed by experiment as well as by a simple experimental oversight. In spite of the dilemma presented, either horn eliminates all previous limitations due to surface conditions, so that the tolerable surface roughness is once again determined by the well-known Rayleigh criterion rather than by any periodic surface irregularities introduced through the polishing process or by nature.

Basic processing steps utilized in the fabrication of planar silicon devices include (a) substrate preparation, (b) epitaxial deposition, (c) thermal gvowth of silicon dioxide over the entire silicon wafer surface, (d) device pattern formation by photoetching techniques, and (e) diffusion of n-type or p-type elements through the holes to produce localized regions of desired conductivity, A detailed study of the various diffraction phenomena associated with such structures is presented. X-ray topographs of planar transistors show distinct contrast features such as excess diffraction intensity along the silicon oxide/silicon boundary and/or excess diffraction intensity inside the device area. The diffraction phenomena are discussed in terms of reversible elastic deformations, frozen-in lattice deformations, strain fields and imperfections generated by the various processing steps. A technique is presented to measure the sign of the elastic deformations. The phenomenon of stressjumping across semiconductors interfaces is described, and finally the implications of stress-strain relations on junction performance are stated.

The quality and interpretation of diffraction topographic images are strongly dependent on. the detailed laboratory techniques that are used in making them. In this paper practical instructions are given for the preparation of Berg-Barrett and Lang topographs. It is hoped that these suggestions will enable the novice in the field of X-ray topography to produce high quality images and to interpret them with a minimum of learning time. The topics treated include adjustment of the critical conditions for attaining highest resolution, choice of radiation and the specific hkl planes to be used, conditions limiting the size of the image, cause and avoidance of image distortion, choice of photographic emulsions, plate processing for best contrast and resolution, photomicrographs of the original image, and plate preservation.

Impurity-doped crystals CdS(GaGl3) have been studied by X-ray topography. Some large precipitates are formed close to the crystal surfaces by annealing at 300°C. In the symmetrical Laue case, the precipitates show circular images (30-60 μ in diameter) due to the radial strains around the precipitates which consist of two semicircles separated by a contrast-free plane parallel to the reflecting plane. The observations indicate that the strain field between the crystal surface and precipitate is not responsible for the contrast, and that the images are formed by X-rays which are deviated from the Bragg condition for the perfect region and satisfy the Bragg condition in the strain field on the inside of the precipitate. One of the semicircles is formed by the incident X-rays with larger glancing angles than the Bragg angle and the other with smaller ones. It is concluded that this contrast is due to the strain around a convex lens shaped precipitate.

Crystals of ruby (Al2O3:Cr) are being grown at the present time by several standard procedures, e.g., Verneuil, Czochralski, flux, and hydrothermal. Previous work has indicated wide variations in quality and type of defects. The present study is primarily concerned with ruby grown from PbO-PbF2 fluxes. All crystals were examined in transmission with Mo Kα1 radiation and a Rigaku Denki Lang camera. Samples were either sectioned from larger crystals or obtained as plates with natural growth faces. Results on flux-grown ruby have shown a severely banded substructure due to strain introduced by either the flux or chromium segregation. Crystals with a visible chromium gradient have shown fewer bands in those regions which were depleted of chromium. Annealing studies have been performed on ruby and all banded structure was dispersed into areas of fine particles with a much higher dislocation content. Other features of the substructure are described. These include the observation of Pendellosung fringes in wedgeshaped sections. Areas of nearly 0.5 cm2 were found to be dislocation free. The X-ray results confirm etching experiments but the former yield more information on internal details other than dislocations.

Recent data on sapphire (α-Al2O3) have confirmed several tentative conclusions. Flux grown crystals have some bands due to flux segregation. However, sapphire crystals show higher perfection when compared to ruby. These results have been confirmed by rocking curves obtained on a double crystal X-ray spectrometer used in the parallel position. Measurements on the (00.12) reflection from the natural growth faces were performed with Cu Kα1 radiation. Widths at half the maximum intensity were always found to be larger for ruby than for sapphire. Comparisons were made with respect to a perfect silicon crystal in the same geometry. Some preliminary experiments have been performed on Czochralski ruby prepared by the Linde Company and on hydrothermally grown ruby prepared at Airtron, Examples of defects observed in each case are given. They are highly unique to the growth method. The Lang method is shown to reveal more detail than other X-ray data. A brief discussion of ruby quality as a function of growth method is presented.

The geometry of Berg-Barrett skew reflections (the normal to the specimen surface and the incident and reflected beam vectors are not coplanar) is analyzed with particular reference to (111) silicon. Angular relationships required for obtaining the 78 most intense such reflections are presented on stereographic projections. Skew reflections are utilized to adapt the Berg-Barrett technique of extinction-contrast micrography to the examination of the (111) wafers generally used in integrated circuit technology. Skew reflections are shown to be more suitable for Berg-Barrett micrography than the zero-layer reflections described by Newkirk; in particular, their versatility in providing a means of varying the angle of incidence of the X-ray beam for a specific reflecting plane is demonstrated. A relatively simple experimental arrangement is described for recording skew reflection images. It permits a high resolution X-ray sensitive plate to be placed parallel to the specimen, and their separation to be increased to as much as 5 mm without excessive loss of resolution ; this avoids both image distortion and surface scattering. Furthermore, the specimen area recorded in a single micrograph is 1-3 cm2, which is large enough to eliminate the need for scanning. Exposure times are very short, in the order of 10 min. Micrographs of boron-diffused silicon are presented showing device components delineated by solute strain, strain fields induced in epitaxial silicon films by underlying buried-layer diffusions, and diffusion-induced Lomer-Cottrell dislocations. These micrographs demonstrate the resolution and contrast obtainable over large specimen areas. The capability of the Berg-Barrett technique is discussed in the examination of the near-surface regions directly involved in device fabrication and operation.

Magnesium has been shown to have a marked effect upon preprecipitation processes occurring in aluminum-13 wt.% zinc alloys containing 0.025, 0.098, 0.17, 0.19, 0.23, and 0.27 wt.% magnesium. X-ray small-angle scattering and resistance measurements have been used to monitor the rate of growth of Guinier-Preston zones in quenched foils and wires. The following results have been obtained: (a) small additions of magnesium noticeably decrease the rate of growth of G-P zones but the final zone size reached in the magnesium containing alloys is generally larger than in Al-Zn alloys quenched and aged under identical conditions; (b) the general pattern of preprecipitation found in Al-Zn alloys is not seriously changed by these small additions of magnesium; (c) the dependence of the rate of preprecipitation on quenching temperature is shown to be a function of magnesium content and aging temperature; (d) the dependence of the rate of preprecipitation on aging temperature is influenced by the range of aging temperature, magnesium content, and the quenching temperature.

A detailed analysis of the high angle diffuse scattering from small platelets is given. A large number of statistically centrosymmetric platelets is considered, and it is shown that, in this cage, the positive square root of the diffuse intensity from the platelets is proportional to the amplitude of the scattered radiation over particular regions in reciprocal space. The measured amplitude distribution is truncated from the true amplitude distribution by the limits of measurement and the influence of Bragg scattering. A truncation function is introduced to describe this truncated amplitude distribution in terms of the true amplitude distribution. This truncation introduces modulations on the measured electron density distribution. The measured electron density distribution is described in terms of the convolution of the true electron density distribution and the transform of the truncation function. The transform of the truncation function is knowi analytically, so the true electron density distribution can be found by a relaxation method. The true electron density distribution is given in terms of composition and strain parameters which are independently adjusted during the relaxation procedure to fit the measured values. Examples of the influence of the truncation function arc given and the technique is applied to G–P 1 zones in an aluminum - 1.67 at % copper alloy.

X-ray powder pattern line intensities were measured for the (Cr, Re)σ and (Re, Fe)σ phases by a step-scanning diffractometer, using CrKα radiation, scintillation counter, and a pulse height analyzer. The measured intensity ratios for all available pairs of adjacent lines were compared by means of a computer with the corresponding calculated intensity ratios based on approximately 1800 different ordering schemes for each alloy. The results showed ordering in both alloys, and indicated that the ordering was based on atomic size. These results are different from those obtained previously by Kasper and Waterstrat (no ordering), and by Ageyev et al. [In (Cr, Re)σ the Cr atoms are preferentially in large coordination number positions.]

A prolonged study has been roade of the unusual X-ray powder patterns generated by certain pyrolytically formed boron compounds, consisting of two to four moderately broad diffraction lines in the 1-4 Å range. These broad lines are unexpectedly made to disappear by a singie sharp blow with a hammer on the specimen in a Plattner diamond mortar, the disappearance being accompanied by the spontaneous generation of the standard diffraction lines expected for normally crystalline materials. The same diffraction pattern changes also may be brought about by regular grinding methods, fracture, or thermal annealing. Transmission electron diffraction yields results identical with those obtained by X-ray. Orientation studies demonstrate that the phenomenon is not orientation dependent. Controlled fracture has been applied in an attempt to develop a hypothesis. It appears from the constancy of the width and position of the diffraction lines among samples that the phenomenon being studied has a definite potential energy, well located somewhere between amorphous and crystalline states. Demonstration of this phenomenon of line broadening has been obtained with boron, boron carbide, and in part with silicon, carbide. These materials have been formed by various methods: pyrolytic decomposition of carborane, low pressure electrical discharge in diborane, chemical reaction between boron halide and hydrogen.

During the course of catalytic experiments on bulk copper single crystals, several crystals were intentionally oxidized to form thick (6000 Å) Cu2O films on the copper substrates. These oxidized crystals were investigated by means of a high temperature chamber installed on a General Electric XRD-5 X-ray diffractometer. It was discovered subsequently that the lattice spacings of the Cu2O decreased upon heating and increased upon cooling. Bulk single crystals and polycrystals of copper were oxidized at 3 Torr of air for several hours. All of the oxidized crystals were examined with copper and chromium radiation and both showed similar results. Typical of the results was an oxidized (110) copper disc which showed a net contraction upon heating of 1% for the (110) Cu2O planes. This slightly oriented Cu2O film was distinguished because -it contracted on heating to 440°C from room temperature, then expanded from 440°-540°C, and then expanded again when cooled from 540°C to room temperature. CuO also was detected in the diffraction pattern and the CuO and copper spacings were behaving normally with the temperature changes. A polycrystal of Cu2O was'examined and that, of course, also acted normally as its temperature was varied. Borie and co-workers have reported and explained very nicely similar anomalous behavior for thinner (500 Å) (110) oriented Cu2O films grown on (110) copper substrates. They showed that the epitaxial forces would cause an oxide film grown at high temperatures to contract parallel to the metal interface and expand normal to the interface as the copper cools and contracts. The oxide would expand normal to the surface in. order to keep its unit cell volume constant.

It is felt that epitaxial forces are not causing the anomalous behavior in the present work mainly because the 6000 Å of Cu2O is too thick for epitaxy to exert a meaningful force. The oxide film on the (110) copper was slightly (110) oriented but all of the Cu2O reflections behaved similarly. An additional reason to discount epitaxy is that this Cu2O film expanded upon heating from 440°-540°C. For these thick oxide films epitaxial forces do not seem to be the controlling factor; therefore, a point defect mechanism must be the cause. Changing oxidation and diffusion rates with temperature would produce various vacancy concentrations in the oxide layer and cause the spacings to vary.