X-Ray Diffraction Contrast from Impurity Precipitates in CdS Single Crystals

1966 ◽  
Vol 10 ◽  
pp. 153-158 ◽  
Author(s):  
Jun-ichi Chikawa
Keyword(s):  
Strain Field ◽  
Crystal Surface ◽  
Bragg Angle ◽  
X Rays ◽  
Bragg Condition ◽  
X Ray Diffraction ◽  
Crystal Surfaces ◽  
X Ray ◽  
Impurity Doped ◽  
Free Plane

AbstractImpurity-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.

Measurement of Elastic Strains in Crystal Surfaces by X-Ray Diffraction Topography

1967 ◽  
Vol 11 ◽  
pp. 385-393
Author(s):  
Brian R. Lawn
Keyword(s):  
Strain Field ◽  
Crystal Surface ◽  
Silicon Surfaces ◽  
X Ray Diffraction ◽  
Crystal Surfaces ◽  
Strain Fields ◽  
Diamond Surfaces ◽  
X Ray ◽  
Detailed Nature ◽  
Elastic Strains

AbstractThe use of X-ray topographic techniques for studying elastic strains in crystals deformed at their surfaces is becoming widespread, especially in the field of silicon semiconductor devices. Although the broad features of the phenomenological processes involved in producing the strain patterns on the X-ray micrographs are understood, little attention has been devoted to evaluating the detailed nature or range of the strain fields in the crystal. In this paper, an clastic model is proposed for cases in which a region of crystal surface is uniformly deformed over a thin layer. With this model, the associated strain field in the surrounding crystal, which is readily computed from elasticity theory, may be characterized by a single parameter. The model is in accord with observed strain patterns on topographs of abraded diamond surfaces and silicon surfaces onto which a strip of metal film has been evaporated. From the spatial range of the diffraction contrast, an estimate of the parameter characterizing the strain field may be made.

scholarly journals Comments on A new theory for X-ray diffraction

2018 ◽  
Vol 74 (5) ◽  
pp. 447-456 ◽  
Author(s):  
Jack T. Fraser ◽  
Justin S. Wark
Keyword(s):  
Diffraction Pattern ◽  
Bragg Angle ◽  
X Rays ◽  
Bragg Scattering ◽  
Bragg Condition ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray ◽  
Individual Crystallite ◽  
Small Crystallite

In an article entitled A new theory for X-ray diffraction [Fewster (2014). Acta Cryst. A70, 257–282], hereafter referred to as NTXRD, it is claimed that when X-rays are scattered from a small crystallite, whatever its size and shape, the diffraction pattern will contain enhanced scattering at angles of exactly 2θB, whatever the orientation of the crystal. It is claimed that in this way scattering from a powder, with randomly oriented crystals, gives rise to Bragg scattering even if the Bragg condition is never satisfied by an individual crystallite. The claims of the theory put forward in NTXRD are examined and they are found to be in error. Whilst for a certain restricted set of shapes of crystals it is possible to obtain some diffraction close to (but not exactly at) the Bragg angle as the crystallite is oriented away from the Bragg condition, this is generally not the case. Furthermore, contrary to the claims made within NTXRD, the recognition of the origin of the type of effects described is not new, and has been known since the earliest days of X-ray diffraction.

IN SITU STUDIES OF EPITAXIAL GROWTH BY SYNCHROTRON X-RAY DIFFRACTION

2006 ◽  
Vol 13 (02n03) ◽  
pp. 155-166 ◽  
Author(s):  
WOLFGANG BRAUN ◽  
KLAUS H. PLOOG
Keyword(s):  
Ostwald Ripening ◽  
Crystal Surface ◽  
High Energy ◽  
Molecular Beam Epitaxy Growth ◽  
X Rays ◽  
Surface Kinetics ◽  
X Ray Diffraction ◽  
X Ray ◽  
Kinetics Of

X-rays are ideal to study the structure of crystals due to their weak interaction with matter and in most cases allow a quantitative analysis using kinematical theory. To study the incorporation of atoms during crystal growth and to analyze the kinetics on the crystal surface high primary beam intensities available at synchrotrons are required. Our studies of the molecular beam epitaxy growth of III–V semiconductors reveal that, despite their similarity in crystal structure, the surface kinetics of GaAs (001), InAs (001) and GaSb (001) differ strongly. GaAs shows an unexpectedly large coarsening exponent outside the predicted range of Ostwald ripening models during recovery. GaSb exhibits dramatically different surface morphology variations during growth and recovery. Overgrowth of GaAs by epitaxial MnAs demonstrates the ability of X-ray diffraction to follow an interface as it is buried during heteroepitaxy, which is not possible by reflection high-energy electron diffraction.

Measuring Techniques of Parallel Beam-Diffraction Micrography

1966 ◽  
Vol 10 ◽  
pp. 80-90
Author(s):  
H. Barth
Keyword(s):  
Resolving Power ◽  
X Rays ◽  
X Ray Diffraction ◽  
Crystal Surfaces ◽  
Parallel Beam ◽  
X Ray ◽  
Fixed Sample ◽  
Independent Field ◽  
Measuring Techniques ◽  
Beam Method

AbstractExamination 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.

Strain Measurement of Pure Titanium Covered With Soft Tissue Using X-Ray Diffraction

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Kazuhiro Fujisaki ◽  
Shigeru Tadano
Keyword(s):  
Pure Titanium ◽  
Physiological Saline ◽  
Skin Tissue ◽  
Bragg Angle ◽  
X Rays ◽  
X Ray Diffraction ◽  
Diffraction Profile ◽  
X Ray ◽  
Bending Loads ◽  
Lattice Planes

Measurement of the stress and strain applied to implants and bone tissue in the human body are important for fracture prediction and evaluations of implant adaptation. The strain of titanium (Ti) materials can be measuring by X-ray diffraction techniques. This study applied X-ray diffraction to the skin tissue-covered Ti. Characteristic X-rays of Mo Kα were used and the X-rays diffracted from the Ti were detected through the covering skin tissue. The X-ray absorption by skin tissue is large under the diffracted X-rays detected in low angles because the length of penetration depends on the angle of inclination, equal to the Bragg angle. The effects of skin tissue to detect the diffracted X-rays were investigated in the experiments. And the strain measurements were conducted under bending loads applied to the Ti specimen. The effect of skin tissue was absorption of X-rays as well as the X-rays scattered from the physiological saline contained in the tissue. The X-rays scattered by the physiological saline creates a specific background pattern near the peaks from the (002) and (011) lattice planes of Ti in the X-ray diffraction profile. Diffracted X-rays from the Ti were detected after being transmitted through 1 mm thick skin tissue by Mo Kα. Individual peaks such as (010), (002), (011), and (110) were clearly established by using a parallel beam arrangement. The strains of (110) lattice planes were measured with or without the tissue cover were very similar. The strain of the (110) lattice planes of Ti could be measured by Mo Kα when the Ti specimen was located under the skin tissue.

Observation of the strain field near the Si(111) 7 × 7 surface with a new X-ray diffraction technique

1998 ◽  
Vol 5 (3) ◽  
pp. 964-966 ◽  
Author(s):  
Takashi Emoto ◽  
Koichi Akimoto ◽  
Ayahiko Ichimiya
Keyword(s):  
Strain Field ◽  
Critical Angle ◽  
Total Reflection ◽  
Surface Structures ◽  
Native Oxide ◽  
Oxide Surface ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Glancing Angle

A new X-ray diffraction technique has been developed in order to measure the strain field near a solid surface under ultrahigh vacuum (UHV) conditions. The X-ray optics use an extremely asymmetric Bragg-case bulk reflection. The glancing angle of the X-rays can be set near the critical angle of total reflection by tuning the X-ray energy. Using this technique, rocking curves for Si surfaces with different surface structures, i.e. a native oxide surface, a slightly oxide surface and an Si(111) 7 × 7 surface, were measured. It was found that the widths of the rocking curves depend on the surface structures. This technique is efficient in distinguishing the strain field corresponding to each surface structure.

Pendellosung interference in the Bragg reflexion of X-rays from a crystal surface

1979 ◽  
Vol 368 (1734) ◽  
pp. 313-329 ◽  
Keyword(s):  
Crystal Surface ◽  
Dynamical Theory ◽  
Bragg Angle ◽  
X Rays ◽  
X Ray Diffraction ◽  
Fringe Visibility ◽  
Spatial Intensity Distribution ◽  
Spherical Waves ◽  
Parallel Polarization ◽  
Fringe Patterns

The dynamical theory of X-ray diffraction by perfect crystals applied to Bragg-case reflexion of a spatially narrow beam of coherent spherical waves at a crystal surface predicts that the spatial intensity distribution of the reflected beam contains oscillations due to Pendellosung interference, but with amplitudes very rapidly decaying in comparison with those occurring in the transmission (Laue) case. Computed intensity profiles for the Bragg case show that when unpolarized X-radiation is used superimposition of fringe patterns due to the perpendicular and parallel polarization modes will destroy fringe visibility unless the Bragg angle, 0 B , is quite small or 20 B is close to 90°; doubt is thus cast on Uragami’s (1969) claim to have observed fringes in an experiment with 20 B = 43°.

X-ray diffracted intensity for double-reflection channel-cut Ge monochromators at extremely asymmetric diffraction conditions

2011 ◽  
Vol 44 (2) ◽  
pp. 353-358 ◽  
Author(s):  
Claudio Ferrari ◽  
Fabrizio Germini ◽  
Dusan Korytár ◽  
Petr Mikulík ◽  
Luca Peverini
Keyword(s):  
Critical Angle ◽  
Crystal Surface ◽  
Total External Reflection ◽  
Double Diffraction ◽  
Bragg Condition ◽  
X Ray Diffraction ◽  
Diffraction Profile ◽  
X Ray ◽  
Integrated Intensity ◽  
Incidence Condition

The width and integrated intensity of the 220 X-ray double-diffraction profile and the shift of the Bragg condition due to refraction have been measured in a channel-cut Ge crystal in an angular range near the critical angle of total external reflection. The Bragg angle and incidence condition were varied by changing the X-ray energy. In agreement with the extended dynamical theory of X-ray diffraction, the integrated intensity of the double diffraction remained almost constant, even for the grazing-incidence condition very close to the critical angle for total external reflection. A broadening of the diffraction profile not predicted by the extended theory of X-ray diffraction was observed when the Bragg condition was at angles of incidence lower than 0.6°. Plane wave topographs revealed a contrast that could be explained by a slight residual crystal surface undulation of 0.3° due to etching to remove the cutting damage and the increasing effect of refraction at glancing angles close to the critical angle. These findings confirm that highly asymmetric channel-cut Ge crystals can also work as efficient monochromators or image magnifiers at glancing angles close to the critical angle, the main limitation being the crystal surface preparation.

SURFACE AND INTERFACE STRAINS REVEALED BY X-RAY DIFFRACTION

1999 ◽  
Vol 06 (06) ◽  
pp. 963-966 ◽  
Author(s):  
KOICHI AKIMOTO ◽  
TAKASHI EMOTO ◽  
YUYA ISHIKAWA ◽  
AYAHIKO ICHIMIYA
Keyword(s):  
Silicon Substrate ◽  
Strain Field ◽  
Theoretical Calculations ◽  
Incident Angle ◽  
Experimental Results ◽  
Lattice Expansion ◽  
X Rays ◽  
X Ray Diffraction ◽  
Strain Fields ◽  
X Ray

We measured strain fields near semiconductor surface by X-ray diffraction. The diffraction geometry was using the extremely asymmetric Bragg-case bulk reflection of a small incident angle to the surface and a large angle exiting from the surface. The incident angle of the X-rays was set near critical angle of total reflection by tuning X-ray energy of synchrotron radiation. The X-ray intensity of the silicon substrate 311 reflection was measured to study a Si(111) surface in the ultrahigh vacuum chamber. A clean Si (111)-(7 × 7) surface was found to give a sharper X-ray diffraction peak than that of the native oxide/Si(111) system. By comparison of experimental results and theoretical calculations, it was concluded that the thin silicon oxide film itself gives strong strain fields to the silicon substrates of lattice expansion toward the [311] direction. The strain fields at the Al- and Ag- induced [Formula: see text] surface reconstruction on the Si(111) substrate were also measured. By comparison of experimental results and theoretical calculations, Al-induced reconstruction was suggested to give a strain field to the silicon substrate of lattice expansion toward the [311] direction, whereas Ag-induced reconstruction was suggested to give a strain field to the silicon substrate of lattice compression toward the [311] direction.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

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