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  • 1
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 596-604 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The valence charge and difference densities of GaAs have been calculated without previous refinements of a charge density model using six different data sets of X-ray structure amplitudes published until now. Since the data sets have been measured by means of different experimental methods and due to the different data treatment, the individual structure factors differ on the absolute scale. Furthermore, different temperature factors have been published. In order to bring the data to a common level, we used the same two harmonic temperature factors and the same algorithm for correcting the different sets of experimental data for anomalous dispersion. Because of the non-centrosymmetry of the zinc blende structure, these procedures are not strictly model-independent. A simple bond charge model was used to obtain phases of the structure amplitudes and to perform the above-mentioned corrections. In general, the details of `experimental' charge densities depend sensitively on the balanced ratio among the structure factor moduli used. A smooth density map is only obtained if all F have the same high level of accuracy [δ(F)/F 〈 1%] and if `outliers' are omitted. Only four of the six data sets describe the covalent bond and the partial charge transfer between neighboring atoms, in qualitative agreement with our expectation based on the results of pseudo-potential calculations. However, some quantitative discrepancies remain, particularly in the height of the charge density maximum between nearest neighbours and in some details outside the bonding region.
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  • 2
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 780-780 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 20 (1987), S. 8-10 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The sensitivity of measurements of the lattice-parameter difference in monocrystalline heterostructures can be enhanced by use of an extremely asymmetrical diffraction geometry. If the angle of incidence is somewhat higher than the critical angle for total external reflection, the Bragg peak is shifted from the position calculated by kinematic theory. The amount of shift depends on the angle of incidence as well as on the mass density of the material used. For heteroepitaxic structures both the layer and the substrate peaks are shifted but by different amounts. Therefore it becomes possible to characterize layers of totally lattice-matched structures also.
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  • 4
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 21 (1988), S. 386-392 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The compositional depth profile in semiconductor heterostructures can be determined from X-ray diffraction patterns. Different grading profiles were studied through theoretical simulations with regard to their features in the rocking curve. It was found that the thickness and the grading of a particular layer cannot be determined independently of each other. A linear grading gives rise to an increased peak width of the layer diffraction peak whereas an exponential grading can be detected from the damping of high-order interference fringes. The exponential model can be applied to determine the abruptness of the heterointerfaces. The proposed evaluation method of experimental rocking curves includes the case of overlapping peaks of the layer and the substrate diffraction. The simulation results are discussed for a GaAs/Ga1−xAlxAs/GaAs[001] double heterostructure. When the experimental resolution is taken into account, the sensitivity of the interface width determination was 100–200 Å.
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  • 5
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 23 (1990), S. 228-233 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Synchrotron radiation has been used to measure the rocking curves from a (GaIn)(AsP) single layer grown on an InP (100)-oriented substrate. For angles of incidence ΦB = (ΘB − φ) ≤ 0.7° measured at the Bragg angle ΘB (φ is the angle between the diffracting lattice plane and the surface), the rocking curve (RC) is very strongly influenced by total external reflection (TER). This causes a decrease in the full width at half-maximum (FWHM) and an asymmetrical shape for the RC for small ΦB. Both of these effects are due to the Bragg-angle shift from the actual incident angle Φ which is not considered in the conventional dynamical theory. In this paper the essential influence of TER on any thin-layer rocking curve is investigated using a numerical solution of the extended dynamical theory. The pattern can be interpreted up to ΦB ≥ ΘC (ΘC is the angle of TER) by semiempirical incorporation of the results of the extended theory with the coupling formalism of Barrels, Hornstra & Lobeek [Acta Cryst. (1986). A42, 539–545].
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  • 6
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 21 (1988), S. 240-244 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Synchrotron radiation was used to measure the rocking curves from (Ga,In)(As,P) single layers grown on an InP (100) oriented substrate. The incident angle was varied (changing correspondingly the X-ray incident-beam wavelength) in order to measure at extremely asymmetrical Bragg diffraction down to a glancing angle of 0.35°. The measured rocking curves could be interpreted by the semi-kinematic model of Petrashen [Fiz. Tverd. Tela (1974). 16, 2168–2175] with corrections for X-ray refraction and for the width of the rocking curve from the extended dynamical theory.
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  • 7
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 32 (1999), S. 1033-1038 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A new electron diffractometer with a diffraction-pattern scanning system in front of a fixed counter has been developed. Significant improvement was achieved in the measured diffraction intensities by using fast electronics and additional control of the stability of the electron beam. The measurement of and accounting for the gear-frequency characteristic of the registration system was performed, and the signal accumulation mode for intensity measurements together with advanced statistical data processing were employed. Good agreement between the experimental and Hartree–Fock structure factors for LiF, NaF and MgO was achieved (to avoid strong extinction effects, rather thin polycrystalline films were used as samples).
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 1034-1037 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In order to understand the induced electron-density response of covalently bonded materials to an externally applied electric field, the change of structure-factor phases of several weak reflections of GaAs has been measured by three-beam interferences. Using a modulation technique, phase variations of the order of 1° for a field strength of 1 kV mm−1 were determined. Although the statistics of these first experiments are rather poor, the experiment verifies qualitatively the predictions of a semi-empirical bond-charge model. The measured phase variation is the smallest value determined up to now.
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  • 9
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 54 (1998), S. 231-239 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The current best sets of X-ray structure amplitudes for GaAs, gallium arsenide, are completed by highly precise data recorded at 0.50 〈 sin θ/λ 〈 1.35 Å−1. For the strong reflections the required accuracy of ΔF/F ≤ 1% was realized by the use of Pendellösung measurements at λ = 0.30 Å, recording the integral intensities as a function of the effective thickness from ∼500 µm thick GaAs wafers. Additionally, several weak reflections were determined from their integral intensities within the kinematic limit at wavelengths λ = 0.3, 0.56 and 0.71 Å. From these data individual Debye–Waller factors for gallium and arsenic were determined using the model of independent spherical atoms [BGa = 0.666 (4) and BAs = 0.566 (4) Å2]. The extended set of experimental structure factors now available is compared with those obtained by ab initio solid-state Hartree–Fock (HF) and density functional (DF) calculations. Therefore, the theoretical data were adapted to room temperature using the experimentally evaluated Debye–Waller factors and the model mentioned above. The valence and difference charge densities obtained from experimental and theoretical data show the expected charge accumulation between nearest neighbours slightly shifted towards the arsenic site. The disagreement remaining between the experimental and theoretical data, on the one hand, and between those of both ab initio methods, on the other hand, are of the same order of magnitude.
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  • 10
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 52 (1996), S. 586-595 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The electronic charge density of cubic boron nitride is calculated within the ab initio Hartree–Fock approximation using the program CRYSTAL. Based on Debye hypothesis, the thermal motion of atoms is considered by disturbing the atomic orbitals by mean-square displacements given from experiment. The calculated difference charge density obtained by subtraction of the total density and that of an independent atomic model (IAM) is characterized by a charge-density accumulation between next neighbours slightly shifted towards the nitrogen. The calculated X-ray structure amplitudes are compared with two different data sets [Josten (1985). Thesis. University of Bonn, Germany; Eichhorn, Kirfel, Grochowski & Serda (1991). Acta Cryst. B47, 843–848]. In both cases, very good agreement is found beyond the 420 reflection. The first six structure amplitudes are generally lower or larger compared with Josten's and Eichhorn et al.'s data, respectively. Whereas our charge density can be interpreted by a balanced ratio between covalent overlap and electronic charge transfer between neighbouring valence shells, the density plots calculated from experimental data express either the charge transfer (Josten, 1985) or the covalency (Eichorn et al., 1991).
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