Atomic Scattering Factors Calculated from the TFD Atomic Model

Thomas, L. H.; Umeda, Keiji

doi:10.1063/1.1743287

Cited by 190 publications

(59 citation statements)

References 17 publications

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“…In this section, we discuss the analysis of the GaAs results in terms of three sets of atomic scattering factors: (i) the relativistic Hartree-Fock (RHF) scattering factors of Doyle & Turner (1968), which have been used for the present work thus far; (ii) the Thomas-Fermi-Dirac (TFD) scattering factors of Thomas & Umeda (1957); (iii) the relativistic DiracSlater (RDS) scattering factors of Cromer & Waber (1965). In the case of the RHF and RDS scattering factors, nine parameter values determined by curvefitting procedures have been supplied for each atom (see Vand, Eiland & Pepinsky, 1957), i.e.…”

Section: Discussionmentioning

confidence: 99%

“…The Q values in the second column are obtained using the RHF scattering factors of Doyle & Turner (1968), those in the third column using the TFD scattering factors of Thomas & Umeda (1957), and those in the fourth column using the RDS scattering factors of Cromer & Waber (1965). …”

Section: Discussionmentioning

confidence: 99%

“…there are analytical approximations in terms of Gaussian functional forms. Thomas & Umeda (1957) supply values for the TFD scattering factors at 31 discrete values of S/2, from 0.00 to 1.50 in steps of 0.05 A-1, but not analytical approximations. It was thus necessary to carry out least-squares fits to this data, for neutral Ga and As atoms, to obtain values for the nine parameters in the conventional analytical approximation.…”

Section: Discussionmentioning

confidence: 99%

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Thermal vibrations and bonding in GaAs: an extended-face crystal study

Stevenson¹

1994

Acta Cryst Sect A

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Accurate X-ray integrated-intensity data collected from an extended-face crystal of GaAs are analysed to provide detailed information on the thermal vibrations of atomic species, including cubic anharmonicity, at room temperature. The values obtained for the thermal parameters are BGa = 0.622 (3) A 2, B s = 0.483(5)A 2 and ~GaAs'-" --0.6(1) X 10-18jX -3 (defined in the text). The inclusion of cubic anharmonic thermal vibrations is shown to be highly significant. In order to interpret the data collected for certain low-angle Bragg reflections for which m h + k + l = 4n + 2 (in particular, 200, 222 and 222), it is necessary to consider bonding effects. It is shown that there is a net transfer of electron charge from gallium to arsenic [Q --0.12 (3) e] and that the inclusion of bonding effects in the least-squares analysis is highly significant. The analysis includes allowance for the extremely severe extinction effects present for such a perfect sample (minimum extinction factor 0.286). The refined value of the mean radius of © 1994 International Union of Crystallography Printed in Great Britain -all rights reserved perfect-crystal domains is 4.6 (2)I~m. The final fit, for 153 independent Bragg reflections, is excellent, as indicated by the weighted R factor of 0.683% and the goodness-of-fit parameter of 1.083. The results of the least-squares analysis are compared for the cases of relativistic Hartree-Fock, Thomas-Fermi-Dirac and relativistic Dirac-Slater atomic scattering factors, the former being favoured.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Thermal vibrations and bonding in GaAs: an extended-face crystal study

Stevenson¹

1994

Acta Cryst Sect A

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“…The least-squares refinement was accomplished with a program written by P. K. (Thomas & Umeda, 1957) were modified for dispersion by adding --0-4 for Eu and --1.1 for W (Templeton, 1962). The imaginary dispersion term was neglected.…”

Section: Methodsmentioning

confidence: 99%

Crystal structure of europium tungstate

Templeton¹,

Zalkin²

1963

Acta Cryst

120

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The structure of europium tungstate, Eu2(WO4)8, has been determined by single-crystal X-ray diffraction data. The crystals are monoclinic, space group, C2/c, with a = 7.676 _+ 0.003, b = 11.463 +_ 0-003, c = 11.396 _+ 0.005/~, fl = 109.63 + 0-04 °, Z = 4, dz = 7.37 g.cm -3 .The atomic arrangement may be described as a scheelite superlattice with ordered vacancies in the cation positions, but atoms are displaced by considerable distances from the scheelite locations. Each W atom has four oxygen neighbors at average distances of 1.74 or 1.78 A. Some ~7 atoms have a fifth neighbor at 2.19 A. Each Eu atom has eight oxygen neighbors at an average distance of 2.43 A. IntroductionThe rare earth elements form a series of isomorphou,~ tungstates with the generic formula R~(WO4)8, where R stands for a rare earth element, and some of these compounds have interesting fluorescence properties (MacDonald, Vogel & Brookman, 1962). We have investigated single crystals of the europium compound by X-ray diffraction and have determined the structure. The atomic arrangement is closely related to that of CaWO4 (scheelite), and it may be described as a scheelite superlattice with ordered vacancies in the cation positions. Considerable distortions of the structure occur around these vacancies. These results may give an indication of the structure at defects in scheelite solid solutions.Single crystals of the isomorphous compound Ce2(WO4)8 were studied by Nelson & McKee (1946) who determined the unit cell and probable space group in agreement with our results. ExperimentalThe synthesis of europium tungstate from europium oxide and tungstic acid and the growth of single crystals at temperatures near the melting point (1130_+15 °C) has been described by MacDonald, Vogel & Brookman (1962 was measured with the General Electric XP~D-5 X-ray goniostat and MoK~ radiation. Unit cell dimensions are based on /~=0.70929 ~ for Mo Kaz. Intensities were measured with a scintillation counter equipped with a pulse height discriminator for the 839 independent reflections permitted by the space group in the sphere with sin 0//~ less than 0.596 (20 <50°); of these, 36 were assigned zero intensity. The data were corrected for absorption assuming that the crystal was a sphere ~dth/~r--2-3, according to the table given by Bond (1959) Unit cell and space groupThe dimensions of the monoclinic unit cell of Eu2(WO4)a are:a=7.676 ± 0.003, b= 11.463 +_ 0-003, c = 11-396 ± 0.005 J~, fl--109.63 ± 0-04 °. The lattice is pseudo-orthorhombic. A face-centered cell with double the volume of the one given above and which is called the 'second setting' (Fig. 1) It is possible that the deviation of fl from 90 ° is less than the experimental error, and this cell is convenient for the indexing of powder patterns. While the spot positions on the single crystal photographs fit an orthorhombic lattice, the monoclinic symmetry is clearly evident in the intensities. Twinning might be expected in this lattice with the result that the intensities would mimic orthorhombic symm...

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“…Though the agreement with experiment was surprisingly good, the improvement in computational technique and in the X-ray data themselves has stimulated a number of efforts to improve these results. To mention three notable examples, Thomas & Umeda (1957) have recently published a very extensive Thomas-Fermi-Dirac (1955) have made extensive Hartree-Fock selfconsistent field calculations, and McWeeny (1951) has considered the effects of chemical bonding on the atomic scattering factor.…”

Section: Introductionmentioning

confidence: 99%

Calculations of coherent scattering factors for helium-like ions from a radially correlated wave function

Hurst¹,

Miller²,

Matsen³

1958

Acta Cryst

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Coherent scattering factors are calculated for helium and helium-like ions from the HylleraasEckart radially correlated wave function. It is suggested that the method may be extended to other atoms with less labor than is required to make I-Iartree-Fock-type calculations. A sizeable disparity between corresponding correlated and uncorrelated results is noted for I-I-; this gradually becomes smaller with increasing atomic number. At the larger values of sin 0/2, the correlated results for I-I-agree quite well with corresponding factors for the hydrogen atom.

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Atomic Scattering Factors Calculated from the TFD Atomic Model

Abstract: Articles you may be interested inCalculation of Raman scattering parameters for methane and halomethanes from an atom dipole interaction model J. Chem. Phys. 66, 3455 (1977); 10.1063/1.434431Approximation of TFD molecular densities by the sum of separated atom TFD densities

Cited by 190 publications

References 17 publications

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Thermal vibrations and bonding in GaAs: an extended-face crystal study

Crystal structure of europium tungstate

Calculations of coherent scattering factors for helium-like ions from a radially correlated wave function

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