Normale und anomale Absorption von Röntgen-Strahlen in Germanium und Silicium/Normal and anomalous absorption of X-rays in Germanium and Silicon

1973 ◽  
Vol 28 (5) ◽  
pp. 588-600 ◽  
Author(s):  
G. Hildebrandt ◽  
J. D. Stephenson ◽  
H. Wagenfeld
Keyword(s):  
Cross Sections ◽  
Theoretical Data ◽  
Electric Quadrupole ◽  
Photoelectric Effect ◽  
Waller Factor ◽  
Dynamical Theory ◽  
X Rays ◽  
Linear Absorption ◽  
Debye Waller Factor ◽  
Silicon And Germanium

A brief discussion of G. Molière's generalized dynamical theory is given with respect to the interpretation of the experimental data|χ⊥ig/χi0 |obtained by means of the Borrmann effect. In order to compare theory and experiment photoelectric absorption cross sections for Silicon and Germanium have been calculated over the X-ray energy range from 5 to 25 keV. Linear absorption coefficients measured by us and other authors agree with theory within a few per cent. Taking the Debye-Waller factor into account, the same theoretical data have been used to calculate |χ⊥ig/χi0 | for Ge and Si. The agreement with extensive measurements of the Borrmann effect in Ge is very good in most cases. The experiments presented in this paper confirm the existence of the electric quadrupole transitions within the photoelectric effect.

In Situ Observation of the Oxygen Nucleation in Silicon with X-Ray Single Crystal Diffraction

2011 ◽  
Vol 178-179 ◽  
pp. 353-359 ◽  
Author(s):  
Johannes Will ◽  
Alexander Gröschel ◽  
Christoph Bergmann ◽  
Andreas Magerl
Keyword(s):  
Single Crystal ◽  
Waller Factor ◽  
Dynamical Theory ◽  
Mean Value ◽  
Single Crystal Diffraction ◽  
X Ray ◽  
Float Zone ◽  
Debye Waller Factor ◽  
The Mean

The measurement of Pendellösungs oscillations was used to observe the time dependent nucleation of oxygen in a Czochralski grown single crystal at 750°C. It is shown, that the theoretical approach of the statistical dynamical theory describes the data well. Within the framework of this theory it is possible to determine the static Debye-Waller-factor as a function of the annealing time by evaluating the mean value of the Bragg intensity and the period length. The temperature influence on the Pendellösungs distance was corrected for by measurement of a Float-zone sample at the same temperature.

Photon-Induced L-Shell X-Ray Production Cross Sections for Lanthanides at 59.54 keV

2017 ◽  
Vol 890 ◽  
pp. 223-226 ◽  
Author(s):  
Rıdvan Durak ◽  
Ferdi Akman ◽  
Abdulhalik Karabulut
Keyword(s):  
High Resolution ◽  
Cross Sections ◽  
Production Cross ◽  
Theoretical Data ◽  
Experimental Results ◽  
X Rays ◽  
X Ray ◽  
Reflection Geometry ◽  
Experimental Values ◽  
Annular Source

The Ll, Lα and Lβ X-ray production cross sections for Pr, Nd, Sm, Eu, Gd and Tb elements were determined using a reflection geometry. The excitation was performed with a 241Am radioactive annular source and the L X-rays emitted from targets were counted with a high-resolution Si (Li) detector. The experimental values were compared with other available experimental results and theoretical data. An agreement is observed between the measured and other experimental results or theoretical data.

Laue X-ray diffraction studies of the structural perfection of Al-doped thermomigration channels in silicon

2021 ◽  
Vol 54 (2) ◽  
pp. 588-596
Author(s):  
Andrey A. Lomov ◽  
Vasily I. Punegov ◽  
Boris M. Seredin
Keyword(s):  
Cross Sections ◽  
High Sensitivity ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
Structural Perfection ◽  
Laue Diffraction ◽  
X Ray ◽  
Structural Distortions ◽  
Further Development

Si(111) wafers patterned with an array of vertical 100 µm-wide Al-doped (1 × 1019 cm−3) p-channels extending through the whole wafer were studied by X-ray Laue diffraction techniques. The X-ray techniques included projection topography, and measurement of rocking curves and cross sections in the vicinity of the 02\overline 2 reciprocal space node in the double- and triple-crystal geometry, respectively. The channels are uniform along the depth of the wafer, and their structural perfection is comparable to that of the silicon matrix between the channels. Simulation of the rocking curves was performed using the methods of the dynamical theory of X-ray diffraction. The rocking-curve calculations both taking into account and neglecting the effect of the instrumental function were carried out using the Takagi–Taupin equations. The calculated angular dependences of intensities of both diffracted and transmitted X-rays correspond well to the experimentally obtained rocking curves and demonstrate their high sensitivity to the structural distortions in the channel. An unambiguous reconstruction of strain and structural distortions in the Si(Al) channel using the Laue diffraction data requires further development of the theoretical model.

die Streuung von Rontgen-Strahlen an Kristallen mit statistisch verteilten Defekten / On the Scattering of X-rays from Crystals Containing a Random Distribution of Defects

1973 ◽  
Vol 28 (6) ◽  
pp. 980-994
Author(s):  
Helmut Trinkaus
Keyword(s):  
Correlation Function ◽  
Random Distribution ◽  
Waller Factor ◽  
Scattering Data ◽  
X Rays ◽  
Single Defect ◽  
Debye Waller Factor ◽  
Variable Factor ◽  
Individual Contributions ◽  
The Individual

The static correlation function governing elastic scattering of X-rays or neutrons by a defective crystal is discussed for three degrees of imperfections, that is for slight, severe, and medium distortions of the scattering crystal. In the exponent of this correlation function the main term, which is linear in the defect concentration, is shown to be fairly independent of the particular type of statistics describing the random distribution of the defects. One condition for a successful analysis of defect structures using diffuse scattering data is that the scattering function can be split into the individual contributions of all single defects. For two regions, that is for the immediate vicinity of Bragg reflections (Huang scattering) and for the asymptotic regions of distortion scattering, this "single-defect approximation" is shown to be useful even for higher concentrations. In this case the correlations due to a single defect have to be corrected by a factor which takes into account the average correlation reduction by all other defects (static Debye-Waller factor in the Huang regions and a similar but variable factor in the asymptotic regions). The formulas given in this paper are applied to the sacttering by isotropic crystals containing point defects of spherical symmetry.

scholarly journals Symmetry of Terms in the Temperature Factor for Bragg Diffraction of X Rays or Neutrons

1985 ◽  
Vol 38 (3) ◽  
pp. 421
Author(s):  
SL Mair
Keyword(s):  
Point Group ◽  
Waller Factor ◽  
Bragg Diffraction ◽  
Group Symmetry ◽  
X Rays ◽  
Point Group Symmetry ◽  
Many Body ◽  
Crystal Potential ◽  
Debye Waller Factor ◽  
Particle Potential

Terms in the anharmonic Debye-Waller factor, taken as a perturbation about the harmonic case to second order in the van Hove ordering parameter, are classified according to the point-group symmetry of the vibrating atom. The classification is valid for a fully interacting (many-body) crystal potential. It is pointed out that certain terms, which are symmetry-allowed for such a general crystal potential, are excluded if an effective one-particle potential is employed.

Diffuse X-ray scattering by 2,3-dimethylnaphthalene

1999 ◽  
Vol 32 (2) ◽  
pp. 309-321 ◽  
Author(s):  
R. Schreier ◽  
J. Kalus
Keyword(s):  
Correlation Coefficients ◽  
Waller Factor ◽  
Mutual Orientation ◽  
X Rays ◽  
Static Disorder ◽  
Diffuse Intensity ◽  
X Ray Scattering ◽  
Debye Waller Factor ◽  
Isotropic Displacement Parameter ◽  
The Mean

The diffuse intensity distribution of X-rays scattered from a dipolar disordered single crystal of 2,3-dimethylnaphthalene (2,3-DMN) has been measured and was found to be nearly independent of temperature in some restricted regions of the reciprocal space. This behaviour was related to a static disorder of the crystal. Lattice parameters were determined between room temperature and 9 K and phase transitions at 227 K and 112 K were observed. The results of the data analysis at 298 K are: the equivalent isotropic displacement parameterUeqfor the thermal Debye–Waller factor is (0.18 Å)2; the displacement parameters describing the static disorder are U\raise.15em{_{xx}}\kern-.65em^C\le(0.05 Å)2, U\raise.15em{_{yy}}\kern-.65em^C=[0.22\,(2) Å]2and U_{zz}^C= [0.35\,(3) Å]2. The molecules show an orientational Gaussian distribution around thexaxis with a width of 5.0 (8)°. All these results refer to the molecular inertia system. Correlation coefficients characterizing the mean mutual orientation of neighbouring molecules were determined. The highest correlation coefficient was found along [010]: C=-0.231\pm 0.004.

X-ray diffraction in superabsorbing crystals: absorption intrinsic width

2019 ◽  
Vol 75 (5) ◽  
pp. 772-776
Author(s):  
A. N. C. Lima ◽  
M. A. R. Miranda ◽  
J. M. Sasaki
Keyword(s):  
Diffraction Theory ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
Linear Absorption ◽  
New Techniques ◽  
Diffraction Profile ◽  
X Ray ◽  
Kinematical Theory ◽  
Special Case

The several mathematical formulations of X-ray diffraction theory facilitate its understanding and use as a materials characterization technique, since one can opt for the simplest formulation that adequately describes the case being studied. As synchrotrons advance, new techniques are developed and there is a need for simple formulations to describe them. One of these techniques is soft resonant X-ray diffraction, in which the X-rays suffer large attenuation due to absorption. In this work, an expression is derived for the X-ray diffraction profiles of reflections where the linear absorption is far greater than primary extinction; in other words, the crystal is superabsorbing. The case is considered of a parallel plate crystal, for which the diffraction profile of the superabsorbing crystal is computed as a function of crystal size normal to the diffraction planes. For thin crystals or those with negligible absorption, the diffraction profile of a superabsorbing crystal coincides with the result of the kinematical theory. For thick crystals, the absorption intrinsic profile is obtained, described by a Lorentzian function and characterized by the absorption intrinsic width. This absorption intrinsic width is proportional to the linear absorption coefficient and its expression is similar to that for the Darwin width, while the absorption intrinsic profile is a special case of the Laue dynamical theory, and it is similar to the Ornstein–Zernike Lorentzian. The formulation of X-ray diffraction of superabsorbing crystals is simple and provides new perspectives for the soft resonant X-ray diffraction technique.

Thermal inelastic scattering of cold neutrons in polycrystalline solids

1955 ◽  
Vol 231 (1186) ◽  
pp. 293-307 ◽  
Keyword(s):  
Cross Sections ◽  
Correction Term ◽  
Transition Probability ◽  
Waller Factor ◽  
Lattice Points ◽  
Cold Neutrons ◽  
M 10 ◽  
Debye Waller Factor ◽  
Alternative Approach ◽  
Polycrystalline Solids

A general theory of the influence of thermal motion on the scattering of slow neutrons in polycrystals is discussed. Unlike Weinstock’s earlier treatment of the same problem, we express temperature displacements of the lattice points as a sum of emission and absorption operators. This alternative approach simplifies the calculation of the transition probability to a considerable extent and provides a simple proof of the Debye-Waller factor. The theory is also generalized to the case of multi-phonon processes. General expressions for both the incoherent and coherent cross-sections, corresponding to an ' l ' phonon process, are derived. The latter, hitherto not treated rigorously, is examined in detail. It is shown that it can be expressed as a sum of two terms, of which the main term, apart from a constant, is identical with the expression for the incoherent part and the other is a correction term. Both terms are put in 'Placzek’ form, and for cold neutrons explicit expressions are obtained for the cases: (i) M > 1 and T /0 > 1, and (ii) M ~ 10 and T/0 > 0.5. Numerical results for magnesium, aluminium, iron, lead and beryllium are discussed and compared with experiment. The agreement is found to be satisfactory.

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