International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 4.3, pp. 259-429
https://doi.org/10.1107/97809553602060000593

Chapter 4.3. Electron diffraction

C. Colliex,a J. M. Cowley,b S. L. Dudarev,c M. Fink,d J. Gjønnes,e R. Hilderbrandt,f A. Howie,g D. F. Lynch,h L. M. Peng,i G. Ren,j A. W. Ross,d V. H. Smith Jr,k J. C. H. Spence,l J. W. Steeds,m J. Wang,k M. J. Whelanc and B. B. Zvyaginn

aLaboratoire Aimé Cotton, CNRS, Campus d'Orsay, Bâtiment 505, F-91405 Orsay CEDEX, France,bDepartment of Physics and Astronomy, Arizona State University, Tempe, AZ 85287-1504, USA,cDepartment of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, England,dDepartment of Physics, The University of Texas at Austin, Austin, TX 78712, USA,eDepartment of Physics, University of Oslo, PO Box 1048, Blindern, N-0316 Oslo, Norway,fChemistry Division, Room 1055, The National Science Foundation, 4201 Wilson Blvd, Arlington, VA 22230, USA,gCavendish Laboratory, Madingley Road, Cambridge CB3 0HE, England,hCSIRO Division of Materials Science & Technology, Private Bag 33, Rosebank MDC, Clayton, Victoria 3169, Australia,iDepartment of Electronics, Peking University, Beijing 100817, People's Republic of China,jBeijing Laboratory of Electron Microscopy, Chinese Academy of Sciences, PO Box 2724, Beijing 100080, People's Republic of China,kDepartment of Chemistry, Queen's University, Kingston, Ontario, Canada K7L 3N6,lDepartment of Physics, Arizona State University, Tempe, AZ 85287, USA,mH. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, England, and nInstitute of Ore Mineralogy, Akad. Nauk Russia, Staromonetny 35, 109017 Moscow, Russia

The first section of this chapter concerns scattering factors for the diffraction of electrons by crystalline solids. An explanation of the theory of scattering by a perfect crystal is followed by a discussion of the kinematical, two-beam and phase-grating approximations. Relativistic and absorption effects are considered. Extensive tables of atomic scattering amplitudes for electrons for neutral and ionized atoms are presented. The second section of the chapter briefly discusses the parameterization of electron atomic scattering factors. Tables of useful parameters as a function of accelerating voltage and elastic atomic scattering factors for neutral atoms are given. Complex scattering factors for the diffraction of electrons by gases are discussed in the third section of the chapter. This section includes tables of scattering factors of interest for gas-phase electron diffraction from atoms and molecules in the keV energy region. In addition to the tables and a description of their uses, a discussion of the theoretical uncertainties related to the material in the tables is also provided. The tables give scattering factors for elastic and inelastic scattering from free atoms. The theory of molecular scattering based on these atomic quantities is also discussed. Electron energy-loss spectroscopy on solids is discussed in the fourth section of the chapter. Topics covered include: the use of electron beams; single and multiple scattering; the classification of the different excitations in a spectrum; instrumentation; and the excitation spectra of valence and core electrons. The fifth section of the chapter describes oriented texture patterns. Lamellar and fibre texture patterns are discussed and applications to metals and organic materials are mentioned. The computation of dynamic wave amplitudes in then described in the sixth section of the chapter. This section deals first with the multislice method. The numerical procedure is outlined and factors that influence the choice of thickness of the slice are discussed. Two checks that can be performed during a multislice calculation are noted. The Bloch-wave method is then described. The use of Bloch waves to describe electron diffraction and electron imaging in thin crystals is outlined together with the concept of the dispersion surface. These emerge as natural solutions of the Schrödinger equation with a periodic optical potential to generate the elastic scattering and also the loss of intensity from the coherent wave field due to thermal diffuse and inelastic scattering. The Bloch-wave approach is a useful complement to the multislice method and provides a clear picture of wave propagation in perfect and imperfect crystals. In the seventh section of the chapter, the measurement of structure factors and the determination of crystal thickness by electron diffraction are described. The use of convergent-beam electron diffraction to obtain integrated intensities is discussed and the relationship between intensity features and the dispersion surface is explained. The last section of the chapter concerns crystal-structure determination by high-resolution microscopy. This technique allows the arrangement of atomic columns in thin crystals to be observed directly. The resolution of the best instruments is now slightly below 0.1 nm. The images usually show a projection through a slice of crystal about 20 nm thick, however tomographic (three-dimensional) reconstruction is now possible at nanometre resolution. The images show the host of microphases, grain boundaries, twins, line and planar defects which broad-beam methods, such as X-ray diffraction, provide the average scattering from. These defects often control the properties of crystals, engineering materials and electronic devices. Individual nanostructures, such as carbon nanotubes and catalyst particles, may be imaged at atomic resolution. Fine twinning, polytypes, intergrowth of oxide phases etc. can be identified, and increasingly the detailed atomic structure of defects (such as oxide, superconductor and semiconductor interfaces) is being determined. Substitutional dopant atoms have recently been imaged for the first time. In biology the method is limited by radiation damage; however by summing many images of identical randomly oriented macromolecules, tomographic density maps can be reconstructed at subnanometre resolution from hydrated proteins which cannot be crystallized (e.g. membrane proteins). This section reviews the theoretical principles of high-resolution electron microscopy, including few-beam and structure image formation, effects of electron-optical lens aberrations, partial coherence, resolution-limiting factors, image-simulation methods, dynamical effects, and a summary of super-resolution schemes.

4.3.1. Scattering factors for the diffraction of electrons by crystalline solids

| top | pdf |
J. M. Cowleyb

4.3.1.1. Elastic scattering from a perfect crystal

| top | pdf |

The most important interaction of electrons with crystalline matter is the interaction with the electrostatic potential field. The scattering into sharp, Bragg reflections is considered in terms of the interaction of an incident plane wave with a time-independent, averaged, periodic potential field which may be written [\varphi({\bf r}) ={1\over \Omega}\sum_{\bf h}V({\bf h})\exp\{-2\pi i {\bf h}\cdot{\bf r}\}, \eqno (4.3.1.1)]where [\Omega] is the unit-cell volume and the Fourier coefficients, [V({\bf h})], may be referred to as the structure amplitudes corresponding to the reciprocal-lattice vectors h. In conformity with the crystallographic sign convention used throughout this volume [see also Volume B (IT B, 2001[link])], we choose a free-electron approximation for the incident electron beam of the form [\exp(-i{\bf k}\cdot {\bf r})] and the interaction is represented by inserting the potential (4.3.1.1)[link] in the Schrödinger wave equation [\nabla^2\psi(r)+2k\sigma\{E+\varphi(r)\}\psi(r)=0, \eqno (4.3.1.2)]where eE is the kinetic energy of the incident beam, [k\,(=2\pi/\lambda)] is the magnitude of the wavevector for the incident electrons, and σ is an `interaction constant' defined by [\sigma=2\pi me\lambda/h^2, \eqno (4.3.1.3)]where h is Planck's constant. Relativistic values of m and λ are assumed (see Subsection 4.3.1.4[link]).

The solution of equation (4.3.1.2)[link], subject to the boundary conditions imposed by the need to fit the waves in the crystal with the incoming and outgoing waves in vacuum at the crystal surfaces, then allows the directions and amplitudes of the diffracted beams to be obtained in terms of the crystal periodicities and the Fourier coefficients, [V({\bf h})], of [\varphi({\bf r})] by the eigenvalue or Bloch-wave method (Bethe, 1928[link]).

Alternatively, the scattered amplitudes may be obtained from the integral form of (4.3.1.2)[link], [\eqalignno{ \psi({\bf r})&=\exp\{-i{\bf k}_0\cdot{\bf r}\} \cr&\quad +K\int\displaystyle {\exp\{-ik|{\bf r}-{\bf r}'|\}\over |{\bf r}-{\bf r}'|}\varphi({\bf r}')\psi({\bf r}')\,{\rm d}\tau_{\bf r'}, &(4.3.1.4)}]where [\exp\{-i{\bf k}_0\cdot{\bf r}\}] represents the incident beam, K = σ/λ, and the integral is taken over the space of the variable, [{\bf r}']. An iterative solution of (4.3.1.4)[link] leads to the Born series, [\psi=\psi_0+\psi_1+\psi_2+\ldots,]where [\psi_0= \exp\{-i{\bf k}_0\cdot{\bf r}\}]and [\psi_n({\bf r})=K \int{\exp\{-ik|{\bf r}-{\bf r}'|\}\over|{\bf r}-{\bf r}'|}\varphi({\bf r}')\psi_{n-1}({\bf r}')\,{\rm d}\tau_{\bf r'}, \eqno (4.3.1.5)]for [n\ge1]. Terms of the series for [n=1,2,\ldots] may be considered to represent the contributions from single, double and multiple scattering of the incident electron beam. This method has been applied to the diffraction from crystals by Fujiwara (1959[link]).

A further formulation of the scattering problem in integral form is that due to Cowley & Moodie (1957[link]) who considered the progressive modification of an incident plane wave as it passed through successive thin slices of a crystal. The effect of the nth slice on the incident electron wave is that of a phase-grating so that the wavefunction is modified by multiplication by a transmission function, [q_n(xy)=\exp\{-i\sigma\varphi_n(xy)\}, \eqno (4.3.1.6)]where [\varphi_n(xy)] is the projection of the potential distribution within the slice in the direction of the incident beam, taken to be the z axis; [\varphi_n(x,y)=\textstyle\int\limits^{z_n+\Delta z}_{z_n}\,\varphi(x,y,z)\,{\rm d} z. \eqno (4.3.1.7)]Propagation of the wave between the centres of slices is represented by convolution with a propagation function, p(xy), so that the wave entering the (n + 1)th slice may be written [\psi_{n+1}(xy)=[\psi_n(xy)\cdot q_n(xy)]*p_n(xy). \eqno (4.3.1.8)]In the small-angle approximation, the function [p_n(xy)] is given by the usual Fresnel diffraction theory as [p(xy)=(i/\lambda\Delta z)\exp\{-ik(x^2+y^2)/2\Delta z\}. \eqno (4.3.1.9)]

In the limit that the slice thickness, [\Delta z], tends to zero, the iteration of (4.3.1.8)[link] gives an exact account of the diffraction by the crystal.

On the basis of the above-mentioned and other related formulations of the diffraction problem, several computing methods have been devised for calculation of the amplitudes and intensities of the many diffracted beams of appreciable intensity that may emerge simultaneously from a crystal (see Section 4.3.6[link]). In this way, a degree of accuracy may be achieved in the calculation of the intensities of spots in diffraction patterns or of the contrast in electron-microscope images of crystals (Section 4.3.8[link]).

4.3.1.2. Atomic scattering factors

| top | pdf |

All such calculations require a knowledge of the potential distribution, [\varphi({\bf r})], or its Fourier coefficients, [V({\bf h})]. It is usually convenient to express the potential distribution in terms of the sum of contributions of individual atoms centred at the positions [{\bf r}={\bf r}_i]. Thus: [\varphi({\bf r})=\textstyle\sum\limits_i \varphi_i({\bf r}-{\bf r}_i) \eqno (4.3.1.10)]or, in terms of the Fourier transforms, [V_i], of the [\varphi_i({\bf r})] [V({\bf h})=\textstyle\sum\limits_i V_i({\bf h})\exp\{+2\pi i{\bf h}\cdot{\bf r}_i\}. \eqno (4.3.1.11)]

As a first approximation, the functions [\varphi_i({\bf r})] may be identified with the potential distributions for individual, isolated atoms or ions, with the usual spreading due to thermal motion. The interatomic binding and the interactions of ions that are thereby neglected may have important effects on diffraction intensities in some cases.

In this approximation, the Fourier transforms for individual atoms may be written [V_i(s)=f^B_i(s)/K, \eqno (4.3.1.12)]where [s=4\pi\lambda^{-1}\sin\theta=|{\bf k}-{\bf k}_0|] and the [f^B] are the Born electron scattering amplitudes, as conventionally defined, in units of Å. Here [\theta] is half the scattering angle and, again, K = σ/λ. Some values of [f^B(s)] listed in the accompanying Tables 4.3.1.1[link] and 4.3.1.2[link] are obtained from the atomic potentials [\varphi_0({\bf r})] for isolated, spherically symmetrical atoms or ions by the relation [f^{B}(s)=4\pi K \int\limits^\infty_0 r^2\varphi(r){\sin sr\over sr}{\rm d} r.\eqno (4.3.1.13)]

Table 4.3.1.1| top | pdf |
Atomic scattering amplitudes (Å) for electrons for neutral atoms

Self-consistent field calculations: HF: non-relativistic Hartree–Fock; RHF, *RHF: relativistic Hartree–Fock.

ElementHHeLiBeBCNOFNeNa
Z1234567891011
MethodHFRHFRHFRHFRHFRHFRHFRHFRHFRHFRHF
(sin [\theta])/λ (Å−1)           
0.00 0.529 0.418 3.286 3.052 2.794 2.509 2.211 1.983 1.801 1.652 4.778
0.01   0.418 3.265 3.042 2.788 2.505 2.209 1.982 1.800 1.651 4.749
0.02   0.417 3.200 3.011 2.768 2.492 2.201 1.976 1.796 1.648 4.663
0.03   0.415 3.097 2.961 2.736 2.471 2.187 1.966 1.789 1.642 4.527
0.04 0.51 0.413 2.961 2.892 2.693 2.442 2.168 1.953 1.779 1.635 4.348
0.05 0.51 0.410 2.800 2.807 2.638 2.406 2.144 1.937 1.767 1.626 4.138
                       
0.06 0.50 0.407 2.622 2.710 2.574 2.363 2.116 1.917 1.752 1.615 3.908
0.07 0.49 0.404 2.435 2.601 2.502 2.313 2.083 1.893 1.735 1.602 3.667
0.08 0.48 0.399 2.245 2.484 2.423 2.259 2.047 1.867 1.716 1.587 3.425
0.09 0.47 0.395 2.058 2.362 2.339 2.200 2.007 1.839 1.694 1.570 3.190
0.10 0.45 0.390 1.879 2.237 2.250 2.138 1.963 1.808 1.671 1.552 2.967
                       
0.11 0.44 0.384 1.710 2.111 2.159 2.072 1.918 1.774 1.646 1.533 2.759
0.12 0.425 0.378 1.554 1.987 2.067 2.005 1.870 1.739 1.619 1.512 2.569
0.13 0.411 0.372 1.411 1.865 1.974 1.936 1.821 1.702 1.591 1.490 2.395
0.14 0.396 0.366 1.282 1.748 1.882 1.866 1.770 1.664 1.562 1.467 2.239
0.15 0.382 0.359 1.166 1.635 1.791 1.796 1.718 1.625 1.532 1.443 2.099
                       
0.16 0.366 0.352 1.063 1.528 1.702 1.727 1.666 1.585 1.501 1.418 1.974
0.17 0.353 0.345 0.971 1.427 1.616 1.658 1.614 1.545 1.469 1.393 1.863
0.18 0.338 0.338 0.889 1.332 1.533 1.591 1.561 1.504 1.436 1.367 1.763
0.19 0.324 0.330 0.817 1.243 1.453 1.524 1.510 1.463 1.404 1.340 1.674
0.20 0.311 0.323 0.753 1.161 1.377 1.460 1.458 1.422 1.371 1.313 1.594
                       
0.22 0.285 0.308 0.646 1.013 1.235 1.337 1.358 1.341 1.304 1.259 1.458
0.24 0.261 0.293 0.562 0.887 1.107 1.222 1.262 1.261 1.238 1.204 1.344
0.25 0.249 0.286 0.526 0.832 1.048 1.168 1.216 1.222 1.206 1.176 1.295
0.26 0.238 0.278 0.494 0.781 0.993 1.117 1.171 1.184 1.173 1.149 1.249
0.28 0.218 0.264 0.440 0.690 0.892 1.020 1.085 1.110 1.110 1.095 1.167
0.30 0.199 0.250 0.396 0.614 0.803 0.932 1.006 1.040 1.049 1.043 1.095
                       
0.32 0.182 0.236 0.359 0.549 0.725 0.853 0.932 0.974 0.991 0.991 1.031
0.34 0.167 0.224 0.328 0.494 0.657 0.781 0.863 0.911 0.935 0.942 0.973
0.35 0.160 0.217 0.314 0.469 0.625 0.748 0.831 0.881 0.908 0.918 0.946
0.36 0.153 0.211 0.301 0.446 0.596 0.717 0.800 0.853 0.882 0.894 0.921
0.38 0.141 0.200 0.279 0.406 0.543 0.658 0.742 0.798 0.831 0.849 0.872
0.40 0.130 0.189 0.259 0.371 0.497 0.606 0.689 0.747 0.784 0.805 0.827
                       
0.42 0.120 0.178 0.241 0.341 0.455 0.559 0.641 0.700 0.739 0.764 0.785
0.44 0.111 0.169 0.226 0.314 0.419 0.517 0.596 0.656 0.697 0.725 0.746
0.45 0.107 0.164 0.219 0.302 0.402 0.497 0.575 0.635 0.677 0.706 0.727
0.46 0.103 0.159 0.212 0.291 0.387 0.479 0.555 0.615 0.658 0.687 0.709
0.48 0.096 0.151 0.200 0.271 0.358 0.444 0.518 0.577 0.621 0.652 0.675
0.50 0.089 0.143 0.188 0.253 0.333 0.413 0.484 0.542 0.586 0.619 0.642
                       
0.55 0.075 0.125 0.164 0.215 0.280 0.348 0.411 0.466 0.510 0.544 0.569
0.60 0.064 0.110 0.145 0.186 0.239 0.297 0.353 0.403 0.445 0.479 0.505
0.65 0.055 0.097 0.128 0.164 0.207 0.256 0.305 0.350 0.390 0.424 0.450
0.70 0.048 0.086 0.115 0.145 0.182 0.223 0.266 0.307 0.344 0.376 0.403
0.80 0.037 0.068 0.093 0.117 0.144 0.175 0.208 0.241 0.272 0.300 0.325
0.90 0.029 0.055 0.077 0.096 0.118 0.141 0.167 0.193 0.219 0.244 0.266
1.00 0.024 0.046 0.064 0.081 0.098 0.117 0.137 0.159 0.180 0.201 0.221
                       
1.10 0.020 0.038 0.054 0.069 0.083 0.099 0.115 0.133 0.150 0.168 0.185
1.20 0.017 0.032 0.046 0.059 0.072 0.085 0.098 0.113 0.128 0.143 0.158
1.30 0.014 0.028 0.040 0.051 0.062 0.073 0.085 0.097 0.110 0.123 0.135
1.40 0.012 0.024 0.035 0.045 0.055 0.064 0.074 0.085 0.095 0.106 0.117
1.50 0.011 0.021 0.031 0.040 0.048 0.057 0.065 0.074 0.084 0.093 0.103
                       
1.60   0.019 0.028 0.035 0.043 0.051 0.058 0.066 0.074 0.083 0.092
1.70   0.016 0.024 0.031 0.038 0.045 0.052 0.059 0.066 0.074 0.081
1.80   0.015 0.022 0.028 0.035 0.041 0.047 0.053 0.060 0.066 0.073
1.90   0.013 0.019 0.026 0.031 0.037 0.043 0.048 0.054 0.060 0.065
2.00   0.012 0.017 0.023 0.028 0.034 0.039 0.044 0.049 0.054 0.059

ElementMgAlSiPSClArKCaScTi
Z1213141516171819202122
MethodRHFRHFRHFRHFRHFRHFRHFRHFRHFRHFRHF
(sin [\theta])/λ (Å−1)           
0.00 5.207 5.889 5.828 5.488 5.161 4.857 4.580 8.984 9.913 9.307 8.776
0.01 5.187 5.867 5.810 5.476 5.152 4.851 4.576 8.921 9.860 9.264 8.740
0.02 5.124 5.800 5.759 5.439 5.124 4.830 4.559 8.731 9.699 9.134 8.631
0.03 5.022 5.692 5.675 5.378 5.079 4.795 4.531 8.434 9.442 8.926 8.455
0.04 4.884 5.547 5.561 5.296 5.016 4.746 4.493 8.054 9.104 8.649 8.220
0.05 4.717 5.371 5.421 5.192 4.938 4.685 4.444 7.619 8.703 8.318 7.937
                       
0.06 4.527 5.170 5.258 5.071 4.845 4.613 4.386 7.157 8.258 7.946 7.618
0.07 4.320 4.949 5.077 4.935 4.740 4.529 4.320 6.691 7.789 7.548 7.274
0.08 4.102 4.717 4.882 4.785 4.623 4.436 4.245 6.239 7.312 7.139 6.917
0.09 3.879 4.478 4.677 4.625 4.496 4.335 4.163 5.815 6.841 6.729 6.556
0.10 3.656 4.237 4.467 4.457 4.362 4.227 4.074 5.426 6.388 6.328 6.199
                       
0.11 3.437 3.999 4.255 4.285 4.222 4.113 3.980 5.073 5.959 5.944 5.853
0.12 3.226 3.767 4.043 4.109 4.078 3.994 3.881 4.756 5.560 5.580 5.522
0.13 3.025 3.544 3.835 3.933 3.931 3.871 3.779 4.474 5.192 5.239 5.209
0.14 2.835 3.330 3.632 3.758 3.783 3.746 3.674 4.222 4.855 4.924 4.916
0.15 2.657 3.128 3.437 3.586 3.635 3.620 3.566 3.997 4.550 4.633 4.643
                       
0.16 2.492 2.938 3.249 3.417 3.487 3.493 3.458 3.795 4.273 4.366 4.390
0.17 2.340 2.760 3.070 3.253 3.342 3.367 3.348 3.612 4.023 4.122 4.157
0.18 2.199 2.595 2.900 3.094 3.200 3.242 3.239 3.446 3.797 3.899 3.943
0.19 2.071 2.441 2.740 2.942 3.061 3.118 3.130 3.295 3.593 3.695 3.745
0.20 1.953 2.299 2.589 2.796 2.927 2.997 3.022 3.154 3.408 3.509 3.564
                       
0.22 1.748 2.046 2.315 2.525 2.671 2.763 2.811 2.902 3.086 3.183 3.242
0.24 1.577 1.832 2.076 2.281 2.436 2.543 2.609 2.680 2.815 2.906 2.967
0.25 1.502 1.737 1.969 2.169 2.326 2.438 2.512 2.578 2.695 2.783 2.844
0.26 1.434 1.650 1.869 2.064 2.221 2.337 2.417 2.481 2.584 2.669 2.730
0.28 1.313 1.495 1.689 1.872 2.026 2.148 2.238 2.299 2.383 2.462 2.523
0.30 1.211 1.363 1.534 1.702 1.851 1.974 2.070 2.134 2.206 2.281 2.341
                       
0.32 1.123 1.251 1.400 1.553 1.694 1.816 1.915 1.982 2.048 2.119 2.178
0.34 1.047 1.154 1.284 1.422 1.554 1.672 1.772 1.842 1.905 1.974 2.032
0.35 1.013 1.111 1.231 1.362 1.490 1.606 1.705 1.776 1.838 1.906 1.964
0.36 0.980 1.070 1.182 1.306 1.429 1.542 1.641 1.714 1.775 1.842 1.899
0.38 0.921 0.997 1.094 1.205 1.318 1.425 1.522 1.595 1.657 1.722 1.778
0.40 0.868 0.932 1.017 1.115 1.218 1.319 1.412 1.487 1.548 1.612 1.668
                       
0.42 0.821 0.875 0.949 1.036 1.130 1.224 1.313 1.387 1.449 1.511 1.566
0.44 0.777 0.825 0.888 0.965 1.051 1.138 1.223 1.295 1.357 1.418 1.472
0.45 0.757 0.801 0.861 0.933 1.014 1.098 1.181 1.252 1.314 1.374 1.428
0.46 0.738 0.779 0.834 0.903 0.980 1.061 1.141 1.211 1.272 1.332 1.385
0.48 0.701 0.737 0.786 0.847 0.917 0.991 1.066 1.134 1.194 1.252 1.305
0.50 0.667 0.700 0.743 0.797 0.860 0.928 0.998 1.064 1.123 1.179 1.230
                       
0.55 0.592 0.618 0.651 0.692 0.741 0.796 0.854 0.912 0.966 1.018 1.067
0.60 0.528 0.551 0.578 0.610 0.648 0.692 0.740 0.790 0.838 0.885 0.930
0.65 0.473 0.494 0.517 0.543 0.573 0.609 0.648 0.690 0.733 0.775 0.816
0.70 0.425 0.445 0.465 0.487 0.513 0.541 0.574 0.609 0.647 0.684 0.721
0.80 0.347 0.366 0.383 0.401 0.419 0.440 0.462 0.488 0.515 0.544 0.573
0.90 0.286 0.304 0.320 0.335 0.350 0.366 0.383 0.402 0.422 0.444 0.467
                       
1.00 0.239 0.255 0.270 0.284 0.298 0.311 0.324 0.339 0.354 0.371 0.389
1.10 0.202 0.217 0.231 0.243 0.255 0.267 0.278 0.290 0.303 0.316 0.330
1.20 0.172 0.185 0.198 0.210 0.221 0.232 0.242 0.252 0.262 0.273 0.285
1.30 0.148 0.160 0.172 0.183 0.193 0.202 0.212 0.220 0.230 0.239 0.249
1.40 0.129 0.139 0.150 0.160 0.169 0.178 0.187 0.194 0.202 0.211 0.219
1.50 0.113 0.123 0.132 0.141 0.150 0.158 0.166 0.174 0.181 0.188 0.195
                       
1.60 0.100 0.109 0.117 0.125 0.133 0.141 0.148 0.156 0.162 0.169 0.175
1.70 0.089 0.096 0.104 0.111 0.119 0.126 0.132 0.138 0.144 0.151 0.157
1.80 0.080 0.087 0.093 0.100 0.107 0.113 0.119 0.127 0.132 0.137 0.143
1.90 0.072 0.078 0.084 0.090 0.096 0.102 0.108 0.112 0.118 0.124 0.129
2.00 0.065 0.070 0.076 0.082 0.087 0.093 0.098 0.101 0.107 0.112 0.117

ElementVCrMnFeCoNiCuZnGaGeAs
Z2324252627282930313233
MethodRHFRHFRHFRHFRHFRHFRHFRHFRHFRHFRHF
(sin [\theta])/λ (Å−1)           
0.00 8.305 6.969 7.506 7.165 6.854 6.569 5.600 6.065 7.108 7.378 7.320
0.01 8.274 6.945 7.484 7.145 6.836 6.552 5.587 6.051 7.088 7.359 7.306
0.02 8.180 6.875 7.412 7.081 6.779 6.501 5.547 6.009 7.027 7.303 7.260
0.03 8.029 6.762 7.296 6.978 6.687 6.418 5.482 5.941 6.927 7.211 7.184
0.04 7.826 6.610 7.140 6.839 6.562 6.306 5.395 5.849 6.792 7.088 7.081
0.05 7.581 6.427 6.949 6.669 6.410 6.169 5.287 5.735 6.629 6.935 6.953
                       
0.06 7.303 6.221 6.732 6.474 6.234 6.010 5.165 5.603 6.441 6.759 6.803
0.07 7.002 5.997 6.493 6.260 6.040 5.834 5.029 5.457 6.236 6.562 6.634
0.08 6.686 5.764 6.241 6.032 5.834 5.646 4.886 5.299 6.017 6.351 6.449
0.09 6.365 5.527 5.981 5.796 5.619 5.449 4.737 5.133 5.792 6.129 6.253
0.10 6.045 5.291 5.719 5.558 5.401 5.249 4.585 4.962 5.564 5.902 6.048
                       
0.11 5.732 5.061 5.459 5.320 5.182 5.048 4.434 4.790 5.337 5.672 5.838
0.12 5.430 4.838 5.206 5.087 4.967 4.848 4.285 4.618 5.113 5.442 5.625
0.13 5.142 4.625 4.962 4.861 4.758 4.654 4.139 4.449 4.896 5.217 5.411
0.14 4.871 4.423 4.728 4.644 4.555 4.465 3.998 4.283 4.686 4.996 5.200
0.15 4.616 4.231 4.506 4.436 4.361 4.283 3.862 4.123 4.486 4.783 4.992
                       
0.16 4.378 4.051 4.297 4.240 4.177 4.110 3.731 3.969 4.295 4.578 4.789
0.17 4.158 3.882 4.100 4.054 4.002 3.944 3.607 3.822 4.114 4.382 4.593
0.18 3.953 3.723 3.916 3.880 3.836 3.788 3.488 3.681 3.942 4.195 4.404
0.19 3.763 3.574 3.743 3.716 3.681 3.640 3.375 3.547 3.781 4.017 4.222
0.20 3.588 3.434 3.583 3.562 3.534 3.500 3.267 3.421 3.629 3.849 4.048
                       
0.22 3.276 3.179 3.292 3.284 3.267 3.245 3.067 3.186 3.352 3.541 3.724
0.24 3.006 2.953 3.039 3.039 3.032 3.018 2.885 2.977 3.108 3.268 3.433
0.25 2.885 2.849 2.924 2.928 2.924 2.914 2.800 2.880 2.997 3.143 3.299
0.26 2.772 2.750 2.817 2.824 2.823 2.816 2.719 2.789 2.892 3.026 3.172
0.28 2.568 2.568 2.620 2.632 2.637 2.636 2.568 2.620 2.701 2.813 2.940
0.30 2.386 2.403 2.445 2.461 1.471 2.474 2.428 2.468 2.531 2.623 2.733
                       
0.32 2.225 2.252 2.288 2.308 2.321 2.328 2.299 2.329 2.379 2.455 2.548
0.34 2.079 2.114 2.146 2.168 2.184 2.195 2.180 2.203 2.242 2.304 2.384
0.35 2.011 2.049 2.080 2.104 2.121 2.133 2.123 2.144 2.179 2.235 2.308
0.36 1.947 1.987 2.017 2.042 2.060 2.073 2.069 2.087 2.119 2.169 2.237
0.38 1.826 1.870 1.899 1.925 1.946 1.962 1.965 1.980 2.006 2.048 2.105
0.40 1.716 1.761 1.790 1.818 1.841 1.858 1.868 1.882 1.903 1.938 1.986
                       
0.42 1.614 1.660 1.690 1.719 1.743 1.763 1.777 1.790 1.808 1.837 1.878
0.44 1.520 1.567 1.597 1.628 1.653 1.674 1.691 1.704 1.720 1.745 1.780
0.45 1.476 1.523 1.553 1.584 1.610 1.631 1.651 1.663 1.679 1.702 1.734
0.46 1.433 1.480 1.511 1.542 1.569 1.591 1.611 1.624 1.639 1.661 1.691
0.48 1.352 1.399 1.431 1.462 1.490 1.513 1.535 1.549 1.563 1.583 1.608
0.50 1.277 1.323 1.356 1.388 1.416 1.440 1.464 1.478 1.492 1.510 1.533
                       
0.55 1.111 1.155 1.189 1.222 1.251 1.277 1.303 1.319 1.334 1.349 1.367
0.60 0.973 1.014 1.047 1.080 1.110 1.136 1.163 1.181 1.197 1.212 1.228
0.65 0.856 0.894 0.927 0.959 0.988 1.015 1.041 1.061 1.078 1.093 1.108
0.70 0.757 0.792 0.824 0.854 0.883 0.909 0.935 0.955 0.973 0.989 1.004
0.80 0.602 0.631 0.659 0.686 0.712 0.737 0.761 0.781 0.800 0.817 0.832
0.90 0.490 0.514 0.538 0.561 0.583 0.605 0.626 0.646 0.665 0.681 0.697
1.00 0.408 0.427 0.446 0.466 0.485 0.504 0.523 0.541 0.558 0.574 0.589
                       
1.10 0.345 0.361 0.377 0.393 0.409 0.425 0.442 0.457 0.473 0.488 0.502
1.20 0.297 0.310 0.323 0.336 0.350 0.364 0.378 0.391 0.405 0.418 0.431
1.30 0.259 0.269 0.280 0.291 0.303 0.315 0.327 0.339 0.350 0.362 0.374
1.40 0.228 0.237 0.246 0.255 0.265 0.275 0.285 0.296 0.306 0.317 0.327
1.50 0.203 0.210 0.218 0.226 0.235 0.243 0.252 0.261 0.270 0.279 0.288
                       
1.60 0.182 0.188 0.195 0.202 0.209 0.217 0.224 0.232 0.240 0.248 0.256
1.70 0.163 0.169 0.175 0.181 0.188 0.194 0.201 0.208 0.215 0.222 0.229
1.80 0.148 0.154 0.159 0.165 0.170 1.176 0.182 0.188 0.194 0.200 0.206
1.90 0.134 0.139 0.144 0.149 0.154 0.160 0.165 0.170 0.175 0.181 0.187
2.00 0.122 0.127 0.132 0.136 0.141 0.146 0.150 0.155 0.160 0.165 0.170

ElementSeBrKrRbSrYZrNbMoTcRu
Z3435363738394041424344
MethodRHFRHFRHFRHFRHF*RHF*RHF*RHF*RHF*RHF*RHF
(sin [\theta])/λ (Å−1)           
0.00 7.205 7.060 6.897 11.778 13.109 12.674 12.166 10.679 10.260 10.856 9.558
0.01 7.192 7.049 6.889 11.699 13.035       10.230    
0.02 7.154 7.016 6.861 11.460 12.816       10.138    
0.03 7.090 6.962 6.814 11.088 12.468       9.989    
0.04 7.004 6.888 6.750 10.613 12.013 11.79 11.41 10.13 9.790 10.35 9.18
0.05 6.895 6.795 6.670 10.073 11.476 11.34 11.04 9.86 9.548 10.10 8.99
                       
0.06 6.767 6.684 6.574 9.504 10.888 10.84 10.62 9.54 9.272 9.80 8.77
0.07 6.621 6.558 6.464 8.934 10.273 10.31 10.15 9.20 8.972 9.48 8.53
0.08 6.460 6.418 6.341 8.385 9.655 9.77 9.68 8.85 8.655 9.14 8.27
0.09 6.288 6.266 6.207 7.872 9.052 9.23 9.20 8.49 8.330 8.78 8.00
0.10 6.105 6.104 6.064 7.402 8.478 8.70 8.72 8.12 8.004 8.42 7.73
                       
0.11 5.916 5.935 5.913 6.976 7.940 8.20 8.26 7.77 7.680 8.07 7.46
0.12 5.722 5.760 5.755 6.593 7.443 7.722 7.818 7.421 7.364 7.720 7.190
0.13 5.525 5.580 5.593 6.248 6.988 7.278 7.400 7.090 7.058 7.383 6.928
0.14 5.328 5.399 5.428 5.938 6.575 6.865 7.007 6.772 6.763 7.057 6.672
0.15 5.132 5.217 5.260 5.658 6.200 6.485 6.640 6.472 6.481 6.746 6.426
                       
0.16 4.938 5.036 5.092 5.403 5.862 6.136 6.299 6.187 6.213 6.451 6.188
0.17 4.749 4.857 4.925 5.170 5.555 5.816 5.983 5.918 5.957 6.171 5.960
0.18 4.564 4.680 4.759 4.954 5.278 5.523 5.689 5.665 5.715 5.907 5.741
0.19 4.384 4.507 4.595 4.754 5.025 5.254 5.419 5.427 5.486 5.658 5.533
0.20 4.211 4.339 4.434 4.566 4.794 5.008 5.168 5.203 5.269 5.423 5.332
                       
0.22 3.884 4.017 4.123 4.224 4.387 4.570 4.721 4.792 4.868 4.994 4.959
0.24 3.585 3.718 3.829 3.916 4.039 4.195 4.333 4.426 4.507 4.614 4.618
0.25 3.446 3.578 3.690 3.773 3.882 4.027 4.158 4.258 4.341 4.439 4.459
0.26 3.314 3.443 3.556 3.636 3.735 3.869 3.995 4.099 4.182 4.273 4.306
0.28 3.069 3.192 3.303 3.382 3.465 3.583 3.697 3.804 3.888 3.969 4.021
0.30 2.849 2.963 3.071 3.149 3.224 3.329 3.433 3.539 3.622 3.695 3.759
                       
0.32 2.651 2.757 2.858 2.936 3.007 3.101 3.196 3.298 3.379 3.448 3.518
0.34 2.475 2.570 2.665 2.742 2.810 2.895 2.982 3.080 3.158 3.223 3.296
0.35 2.393 2.484 2.575 2.651 2.718 2.799 2.883 2.978 3.054 3.118 3.192
0.36 2.316 2.402 2.490 2.564 2.630 2.708 2.789 2.880 2.955 3.018 3.092
0.38 2.173 2.250 2.330 2.402 2.466 2.538 2.613 2.698 2.770 2.830 2.904
0.40 2.045 2.113 2.186 2.254 2.315 2.383 2.452 2.531 2.600 2.658 2.730
                       
0.42 1.929 1.989 2.055 2.119 2.178 2.241 2.305 2.379 2.444 2.500 2.570
0.44 1.824 1.877 1.936 1.995 2.052 2.111 2.171 2.239 2.300 2.355 2.421
0.45 1.776 1.825 1.881 1.938 1.993 2.049 2.108 2.173 2.233 2.287 2.351
0.46 1.729 1.775 1.828 1.883 1.936 1.991 2.047 2.110 2.168 2.221 2.284
0.48 1.642 1.683 1.730 1.780 1.830 1.881 1.934 1.991 2.046 2.098 2.157
0.50 1.562 1.598 1.640 1.686 1.733 1.780 1.829 1.883 1.934 1.984 2.040
                       
0.55 1.389 1.416 1.447 1.483 1.522 1.562 1.603 1.646 1.690 1.734 1.782
0.60 1.245 1.266 1.290 1.319 1.350 1.383 1.417 1.452 1.490 1.528 1.569
0.65 1.124 1.141 1.160 1.182 1.208 1.235 1.263 1.292 1.324 1.357 1.391
0.70 1.019 1.034 1.050 1.068 1.089 1.111 1.135 1.159 1.185 1.214 1.243
0.80 0.847 0.860 0.873 0.887 0.902 0.918 0.935 0.952 0.971 0.992 1.013
0.90 0.711 0.725 0.737 0.749 0.762 0.774 0.787 0.800 0.814 0.830 0.845
1.00 0.603 0.616 0.628 0.640 0.651 0.662 0.673 0.684 0.695 0.707 0.719
                       
1.10 0.515 0.528 0.540 0.551 0.562 0.572 0.582 0.591 0.601 0.611 0.621
1.20 0.444 0.456 0.467 0.478 0.488 0.498 0.507 0.516 0.525 0.534 0.542
1.30 0.385 0.396 0.407 0.417 0.427 0.436 0.445 0.454 0.462 0.470 0.478
1.40 0.337 0.347 0.357 0.365 0.375 0.384 0.393 0.401 0.408 0.416 0.423
1.50 0.297 0.306 0.315 0.325 0.333 0.341 0.349 0.356 0.364 0.371 0.378
                       
1.60 0.264 0.272 0.280 0.290 0.297 0.303 0.311 0.318 0.325 0.332 0.338
1.70 0.236 0.243 0.250 0.257 0.264 0.272 0.278 0.285 0.291 0.298 0.304
1.80 0.212 0.219 0.225 0.233 0.239 0.244 0.251 0.257 0.263 0.269 0.275
1.90 0.192 0.198 0.204 0.208 0.214 0.221 0.227 0.233 0.238 0.244 0.249
2.00 0.175 0.180 0.185 0.188 0.194 0.201 0.206 0.211 0.216 0.222 0.227

Element RhPdAgCdInSnSbTeIXeCs
Z4546474849505152535455
Method*RHF*RHFRHFRHFRHFRHFRHF*RHFRHFRHFRHF
(sin [\theta])/λ (Å−1)           
0.00 9.242 7.583 8.671 9.232 10.434 10.859 10.974 11.003 10.905 10.794 16.508
0.01     8.654 9.213 10.406 10.833 10.950   10.887 10.777 16.391
0.02     8.599 9.153 10.320 10.750 10.876   10.828 10.725 16.050
0.03     8.510 9.057 10.181 10.615 10.755   10.731 10.638 15.521
0.04 8.90 7.43 8.391 8.926 9.995 10.433 10.591 10.65 10.599 10.520 14.855
0.05 8.73 7.35 8.244 8.764 9.768 10.209 10.387 10.47 10.434 10.371 14.106
                       
0.06 8.53 7.26 8.075 8.577 9.509 9.950 10.150 10.25 10.238 10.194 13.326
0.07 8.31 7.16 7.888 8.369 9.224 9.664 9.884 10.01 10.017 9.993 12.556
0.08 8.01 7.03 7.689 8.144 8.923 9.357 9.596 9.74 9.773 9.771 11.823
0.09 7.83 6.91 7.480 7.909 8.612 9.037 9.291 9.46 9.511 9.530 11.145
0.10 7.58 6.77 7.267 7.666 8.297 8.709 8.976 9.16 9.235 9.274 10.525
                       
0.11 7.33 6.62 7.052 7.421 7.983 8.380 8.654 8.85 8.948 9.007 9.965
0.12 7.079 6.474 6.837 7.176 7.674 8.053 8.331 8.538 8.654 8.732 9.458
0.13 6.836 6.319 6.625 6.933 7.374 7.732 8.010 8.224 8.357 8.451 9.000
0.14 6.598 6.162 6.418 6.695 7.084 7.419 7.694 7.914 8.059 8.167 8.583
0.15 6.366 6.003 6.215 6.464 6.805 7.118 7.386 7.608 7.764 7.884 8.201
                       
0.16 6.143 5.843 6.018 6.240 6.539 6.829 7.088 7.309 7.472 7.603 7.848
0.17 5.929 5.684 5.827 6.024 6.286 6.552 6.800 7.018 7.186 7.325 7.519
0.18 5.722 5.526 5.643 5.817 6.045 6.289 6.524 6.738 6.908 7.053 7.212
0.19 5.524 5.369 5.464 5.618 5.817 6.039 6.261 6.467 6.639 6.787 6.922
0.20 5.334 5.214 5.293 5.427 5.601 5.803 6.010 6.209 6.379 6.529 6.649
                       
0.22 4.976 4.913 4.967 5.070 5.203 5.368 5.547 5.727 5.889 6.039 6.143
0.24 4.648 4.626 4.665 4.745 4.846 4.979 5.131 3.291 5.442 5.586 5.684
0.25 4.493 4.487 4.522 4.592 4.682 4.801 4.940 5.090 5.234 5.374 5.471
0.26 4.345 4.352 4.384 4.447 4.525 4.633 4.760 4.899 5.036 5.172 5.268
0.28 4.066 4.093 4.122 4.173 4.236 4.323 4.428 4.548 4.670 4.795 4.890
0.30 3.809 3.850 3.878 3.922 3.973 4.044 4.131 4.234 4.341 4.454 4.547
                       
0.32 3.572 3.622 3.651 3.690 3.734 3.792 3.865 3.952 4.046 4.147 4.235
0.34 3.353 3.408 3.440 3.476 3.515 3.564 3.625 3.700 3.780 3.870 3.953
0.35 3.249 3.306 3.339 3.375 3.412 3.458 3.514 3.583 3.658 3.742 3.822
0.36 3.150 3.208 3.242 3.278 3.313 3.356 3.408 3.472 3.541 3.620 3.697
0.38 2.962 3.022 3.058 3.093 3.127 3.165 3.210 3.265 3.325 3.394 3.465
0.40 2.788 2.848 2.886 2.922 2.955 2.990 3.030 3.078 3.130 3.191 3.255
                       
0.42 2.626 2.686 2.726 2.762 2.795 2.828 2.864 2.907 2.953 3.006 3.064
0.44 2.477 2.535 2.576 2.613 2.646 2.678 2.712 2.750 2.791 2.838 2.890
0.45 2.406 2.464 2.505 2.542 2.576 2.608 2.640 2.677 2.715 2.759 2.809
0.46 2.338 2.395 2.436 2.474 2.507 2.539 2.571 2.606 2.642 2.684 2.731
0.48 2.210 2.264 2.306 2.344 2.378 2.409 2.440 2.473 2.506 2.543 2.586
0.50 2.090 2.143 2.185 2.223 2.257 2.288 2.318 2.350 2.380 2.414 2.453
                       
0.55 1.828 1.875 1.915 1.953 1.987 2.019 2.048 2.077 2.104 2.132 2.163
0.60 1.609 1.650 1.688 1.724 1.758 1.790 1.819 1.847 1.871 1.897 1.923
0.65 1.426 1.462 1.497 1.531 1.563 1.594 1.622 1.649 1.673 1.697 1.721
0.70 1.273 1.304 1.335 1.366 1.397 1.426 1.453 1.479 1.503 1.526 1.548
0.80 1.035 1.058 1.082 1.107 1.132 1.157 1.181 1.205 1.227 1.248 1.269
0.90 0.861 0.879 0.897 0.916 0.936 0.956 0.976 0.997 1.016 1.036 1.055
1.00 0.731 0.745 0.758 0.773 0.789 0.805 0.821 0.838 0.855 0.871 0.888
                       
1.10 0.631 0.641 0.652 0.664 0.676 0.688 0.701 0.715 0.729 0.743 0.758
1.20 0.551 0.559 0.568 0.578 0.587 0.597 0.608 0.619 0.630 0.642 0.654
1.30 0.485 0.493 0.500 0.508 0.516 0.525 0.533 0.542 0.551 0.561 0.570
1.40 0.431 0.437 0.444 0.451 0.458 0.465 0.472 0.480 0.487 0.495 0.502
1.50 0.384 0.391 0.397 0.403 0.409 0.416 0.422 0.428 0.435 0.442 0.450
                       
1.60 0.345 0.351 0.357 0.362 0.368 0.374 0.379 0.385 0.391 0.397 0.405
1.70 0.310 0.316 0.321 0.327 0.332 0.337 0.343 0.348 0.353 0.358 0.363
1.80 0.281 0.286 0.291 0.297 0.302 0.307 0.311 0.316 0.321 0.325 0.332
1.90 0.255 0.260 0.265 0.270 0.274 0.279 0.284 0.288 0.293 0.297 0.299
2.00 0.232 0.237 0.241 0.246 0.250 0.255 0.259 0.264 0.268 0.272 0.272

ElementBaLaCePrNdPmSmEuGdTbDy
Z5657585960616263646566
MethodRHF*RHF*RHF*RMF*RHF*RHF*RHFRHF*RHF*RHF*RHF
(sin [\theta])/λ (Å−1)           
0.00 18.267 17.805 17.378 16.987 16.606 16.243 15.897 15.563 15.266 14.974 14.641
0.01 18.157             15.486      
0.02 17.828             15.260      
0.03 17.309             14.898      
0.04 16.636 16.45 16.10 15.62 15.30 14.99 14.70 14.425 14.30 13.90 13.64
0.05 15.854 15.79 15.46 14.94 14.67 14.39 14.12 13.867 13.81 13.37 13.14
                       
0.06 15.008 15.05 14.77 14.22 13.97 13.72 13.48 13.253 13.27 12.81 12.60
0.07 14.138 14.28 14.03 13.47 13.25 13.03 12.81 12.611 12.70 12.22 12.03
0.08 13.278 13.51 13.29 12.72 12.52 12.33 12.14 11.963 12.11 11.62 11.44
0.09 12.431 12.74 12.56 11.99 11.82 11.65 11.49 11.329 11.52 11.02 10.87
0.10 11.675 12.01 11.85 11.29 11.15 11.00 10.86 10.722 10.95 10.45 10.32
                       
0.11 10.958 11.32 11.19 10.65 10.52 10.40 10.27 10.150 10.39 9.91 9.79
0.12 10.302 10.671 10.561 10.052 9.944 9.833 9.722 9.618 9.871 9.407 9.303
0.13 9.707 10.072 9.981 9.506 9.412 9.316 9.218 9.128 9.382 8.942 8.848
0.14 9.168 9.522 9.448 9.008 8.928 8.843 8.758 8.678 8.926 8.512 8.429
0.15 8.682 9.017 8.958 8.556 8.486 8.413 8.336 8.267 8.505 8.121 8.045
                       
0.16 8.241 8.555 8.507 8.144 8.084 8.020 7.953 7.891 8.114 7.761 7.693
0.17 7.840 8.131 8.094 7.768 7.717 7.661 7.602 7.548 7.754 7.430 7.370
0.18 7.474 7.742 7.714 7.424 7.380 7.332 7.280 7.232 7.422 7.128 7.073
0.19 7.139 7.384 7.365 7.107 7.071 7.029 6.983 6.942 7.114 6.849 6.800
0.20 6.829 7.053 7.041 6.815 6.785 6.749 6.710 6.673 6.828 6.591 6.547
                       
0.22 6.275 6.462 6.462 6.291 6.272 6.247 6.218 6.191 6.316 6.127 6.092
0.24 5.791 5.948 5.957 5.831 5.822 5.806 5.787 5.768 5.868 5.720 5.693
0.25 5.570 5.714 5.728 5.620 5.615 5.605 5.589 5.574 5.664 5.534 5.510
0.26 5.361 5.495 5.312 5.421 5.421 5.413 5.402 5.390 5.472 5.358 5.337
0.28 4.975 5.092 5.115 5.053 5.059 5.059 5.055 5.030 5.117 5.030 5.016
0.30 4.628 4.730 4.759 4.719 4.731 4.737 4.739 4.740 4.796 4.731 4.723
                       
0.32 4.313 4.405 4.438 4.414 4.432 4.443 4.450 4.456 4.504 4.457 4.454
0.34 4.028 4.111 4.146 4.136 4.157 4.173 4.185 4.195 4.238 4.205 4.206
0.35 3.893 3.974 4.010 4.006 4.029 4.047 4.060 4.072 4.113 4.086 4.089
0.36 3.769 3.844 3.881 3.882 3.906 3.925 3.940 3.954 3.993 3.971 3.976
0.38 3.533 3.602 3.640 3.648 3.675 3.697 3.715 3.731 3.767 3.755 3.763
0.40 3.318 3.381 3.420 3.434 3.462 3.486 3.306 3.525 3.559 3.554 3.565
                       
0.42 3.123 3.180 3.219 3.238 3.267 3.292 3.314 3.335 3.367 3.368 3.380
0.44 2.944 2.997 3.035 3.057 3.087 3.114 3.137 3.159 3.189 3.194 3.209
0.43 2.861 2.911 2.949 2.973 3.003 3.029 3.053 3.075 3.105 3.113 3.128
0.46 2.781 2.829 2.866 2.891 2.922 2.948 2.973 2.995 3.025 3.034 3.050
0.48 2.631 2.676 2.712 2.739 2.769 2.796 2.821 2.844 2.872 2.884 2.901
0.50 2.494 2.535 2.570 2.598 2.628 2.655 2.680 2.703 2.730 2.745 2.763
                       
0.55 2.197 2.230 2.262 2.291 2.320 2.346 2.371 2.394 2.419 2.457 2.456
0.60 1.951 1.979 2.008 2.037 2.064 2.089 2.113 2.156 2.138 2.178 2.197
0.65 1.745 1.770 1.796 1.824 1.849 1.872 1.895 1.917 1.937 1.958 1.977
0.70 1.570 1.592 1.617 1.643 1.666 1.688 1.709 1.730 1.749 1.770 1.788
0.80 1.288 1.308 1.329 1.351 1.372 1.391 1.411 1.429 1.446 1.465 1.482
0.90 1.073 1.090 1.109 1.128 1.146 1.164 1.181 1.198 1.213 1.231 1.246
1.00 0.904 0.920 0.936 0.953 0.969 0.985 1.000 1.016 1.030 1.045 1.060
                       
1.10 0.772 0.785 0.799 0.814 0.828 0.842 0.856 0.870 0.883 0.897 0.910
1.20 0.666 0.678 0.690 0.702 0.715 0.727 0.739 0.752 0.763 0.776 0.787
1.30 0.580 0.391 0.602 0.612 0.623 0.634 0.644 0.655 0.666 0.676 0.687
1.40 0.511 0.521 0.530 0.539 0.548 0.557 0.566 0.575 0.383 0.595 0.604
1.50 0.436 0.463 0.470 0.478 0.486 0.494 0.502 0.511 0.519 0.527 0.535
                       
1.60 0.411 0.415 0.421 0.428 0.435 0.442 0.449 0.457 0.463 0.470 0.478
1.70 0.367 0.374 0.380 0.386 0.392 0.398 0.404 0.409 0.416 0.423 0.429
1.80 0.337 0.340 0.345 0.350 0.355 0.360 0.366 0.372 0.377 0.382 0.388
1.90 0.304 0.310 0.314 0.319 0.324 0.328 0.333 0.337 0.343 0.348 0.353
2.00 0.277 0.284 0.288 0.292 0.296 0.301 0.305 0.307 0.313 0.318 0.322

ElementHoErTmYbLuHfTaWReOsIr
Z6768697071727374757677
Method*RHF*RHF*RHF*RHF*RHF*RHF*RHF*RHF*RHF*RHF*RHF
(sin [\theta])/λ (Å−1)           
0.00 14.355 14.080 13.814 13.557 13.486 13.177 12.856 12.543 12.263 11.987 11.718
0.01                      
0.02                      
0.03                      
0.04 13.57 13.16 12.92 12.70 12.74 12.55 12.31 12.06 11.83 11.59 11.37
0.05 13.14 12.70 12.48 12.28 12.38 12.23 12.01 11.80 11.60 11.39 11.18
                       
0.06 12.66 12.19 12.00 11.81 11.95 11.85 11.69 11.51 11.34 11.15 10.96
0.07 12.15 11.66 11.48 11.31 11.50 11.45 11.33 11.18 11.04 10.88 10.72
0.08 11.61 11.11 10.96 10.80 11.03 11.02 10.95 10.83 10.73 10.59 10.45
0.09 11.08 10.58 10.44 10.29 10.55 10.59 10.55 10.47 10.40 10.29 10.17
0.10 10.55 10.06 9.93 9.80 10.08 10.16 10.15 10.10 10.05 9.98 9.88
                       
0.11 10.05 9.56 9.45 9.33 9.62 9.73 9.75 9.74 9.71 9.65 9.58
0.12 9.562 9.095 8.994 8.892 9.180 9.308 9.363 9.369 9.366 9.334 9.281
0.13 9.108 8.662 8.571 8.480 8.762 8.907 8.982 9.011 9.028 9.016 8.982
0.14 8.681 8.262 8.180 8.098 8.370 8.525 8.616 8.663 8.697 8.702 8.686
0.15 8.284 7.895 7.821 7.746 8.001 8.163 8.266 8.327 8.376 8.396 8.395
                       
0.16 7.917 7.557 7.490 7.421 7.660 7.822 7.933 8.006 8.067 8.099 8.111
0.17 7.577 7.247 7.185 7.123 7.343 7.502 7.617 7.699 7.769 7.813 7.836
0.18 7.262 6.962 6.905 6.849 7.047 7.202 7.321 7.408 7.485 7.537 7.570
0.19 6.971 6.698 6.646 6.595 6.774 6.922 7.040 7.132 7.213 7.272 7.313
0.20 6.700 6.454 6.407 6.360 6.520 6.660 6.776 6.870 6.954 7.019 7.067
                       
0.22 6.213 6.017 5.978 5.938 6.063 6.185 6.295 6.388 6.475 6.547 6.604
0.24 5.788 5.632 5.601 5.568 5.664 5.768 5.867 5.957 6.043 6.117 6.180
0.25 5.595 5.457 5.428 5.398 5.483 5.578 5.672 5.759 5.843 5.917 5.982
0.26 5.412 5.290 5.265 5.238 5.312 5.399 5.487 5.571 5.653 5.727 5.792
0.28 5.075 4.981 4.961 4.940 4.996 5.069 5.147 5.224 5.301 5.372 5.437
0.30 4.771 4.699 4.685 4.669 4.712 4.772 4.840 4.910 4.981 5.049 5.113
                       
0.32 4.494 4.440 4.430 4.419 4.453 4.503 4.563 4.626 4.691 4.755 4.816
0.34 4.240 4.200 4.195 4.188 4.215 4.258 4.310 4.366 4.425 4.485 4.543
0.35 4.121 4.087 4.084 4.078 4.103 4.143 4.191 4.245 4.301 4.359 4.415
0.36 4.007 3.978 3.976 3.973 3.996 4.033 4.078 4.129 4.182 4.237 4.293
0.38 3.790 3.771 3.773 3.773 3.793 3.825 3.865 3.910 3.959 4.010 4.061
0.40 3.591 3.579 3.583 3.586 3.604 3.632 3.668 3.709 3.753 3.800 3.848
                       
0.42 3.405 3.399 3.406 3.411 3.429 3.454 3.486 3.523 3.563 3.606 3.651
0.44 3.233 3.232 3.241 3.248 3.265 3.288 3.317 3.350 3.387 3.427 3.468
0.45 3.151 3.153 3.162 3.170 3.187 3.209 3.237 3.269 3.304 3.342 3.382
0.46 3.073 3.076 3.086 3.095 3.111 3.133 3.159 3.190 3.224 3.260 3.299
0.48 2.924 2.930 2.942 2.952 2.968 2.988 3.013 3.041 3.072 3.105 3.141
0.50 2.785 2.793 2.806 2.818 2.834 2.853 2.876 2.902 2.930 2.961 2.994
                       
0.55 2.477 2.490 2.505 2.518 2.534 2.551 2.571 2.592 2.616 2.641 2.669
0.60 2.216 2.232 2.248 2.263 2.278 2.294 2.311 2.330 2.349 2.371 2.394
0.65 1.995 2.012 2.028 2.043 2.058 2.073 2.089 2.105 2.122 2.140 2.160
0.70 1.085 1.823 1.839 1.854 1.868 1.882 1.896 1.911 1.926 1.942 1.959
0.80 1.497 1.515 1.530 1.545 1.558 1.571 1.583 1.596 1.608 1.621 1.634
0.90 1.260 1.276 1.291 1.305 1.317 1.329 1.341 1.352 1.363 1.374 1.385
1.00 1.073 1.088 1.101 1.114 1.126 1.138 1.148 1.159 1.169 1.179 1.189
                       
1.10 0.922 0.935 0.948 0.960 0.971 0.982 0.993 1.003 1.012 1.022 1.031
1.20 0.799 0.811 0.822 0.833 0.844 0.854 0.864 0.874 0.883 0.892 0.901
1.30 0.698 0.708 0.719 0.729 0.739 0.748 0.758 0.767 0.776 0.784 0.793
1.40 0.614 0.623 0.632 0.642 0.651 0.660 0.668 0.677 0.685 0.694 0.702
1.50 0.544 0.552 0.560 0.569 0.577 0.585 0.593 0.601 0.609 0.617 0.624
                       
1.60 0.485 0.492 0.500 0.507 0.515 0.522 0.530 0.537 0.544 0.551 0.558
1.70 0.436 0.442 0.449 0.455 0.462 0.469 0.475 0.482 0.489 0.495 0.502
1.80 0.394 0.399 0.405 0.411 0.417 0.423 0.429 0.435 0.441 0.447 0.453
1.90 0.358 0.363 0.368 0.373 0.379 0.384 0.389 0.395 0.400 0.406 0.411
2.00 0.327 0.331 0.336 0.341 0.345 0.350 0.355 0.360 0.365 0.370 0.374

ElementPtAuHgTlPbBiPoAtRnFrRa
Z7879808182838485868788
Method*RHFRHFRHF*RHFRHFRHF*RHF*RHFRHF*RHF*RHF
(sin [\theta])/λ (Å−1)           
0.00 10.813 10.573 10.964 12.109 12.597 13.096 13.368 13.473 13.492 18.715 20.561
0.01   10.559 10.948   12.573 13.070     13.470    
0.02   10.511 10.897   12.494 12.989     13.403    
0.03   10.434 10.813   12.366 12.857     13.292    
0.04 10.55 10.328 10.698 11.71 12.193 12.678 12.95 13.09 13.139 17.14 18.94
0.05 10.40 10.195 10.555 11.51 11.979 12.456 12.74 12.89 12.949 16.41 18.15
                       
0.06 10.23 10.040 10.387 11.27 11.730 12.197 12.49 12.65 12.724 15.64 17.31
0.07 10.03 9.865 10.197 11.00 11.454 11.908 12.21 12.38 12.469 14.87 16.42
0.08 9.82 9.673 9.989 10.72 11.155 11.595 11.90 12.08 12.187 14.13 15.54
0.09 9.60 9.467 9.766 10.42 10.840 11.264 11.57 11.76 11.884 13.42 14.69
0.10 9.37 9.251 9.533 10.12 10.516 10.921 11.22 11.43 11.565 12.77 13.88
                       
0.11 9.13 9.028 9.291 9.81 10.186 10.571 10.87 11.08 11.232 12.16 13.12
0.12 8.882 8.799 9.045 9.500 9.855 10.219 10.509 10.729 10.892 11.605 12.419
0.13 8.636 8.568 8.796 9.195 9.527 9.869 10.153 10.375 10.546 11.093 11.776
0.14 8.389 8.337 8.547 8.896 9.203 9.523 9.798 10.021 10.199 10.620 11.187
0.15 8.145 8.106 8.299 8.603 8.888 9.186 9.449 9.671 9.854 10.180 10.648
                       
0.16 7.904 7.877 8.055 8.320 8.581 8.857 9.109 9.328 9.512 9.770 10.155
0.17 7.667 7.652 7.815 8.046 8.285 8.539 8.779 8.991 9.177 9.386 9.702
0.18 7.436 7.431 7.579 7.781 7.999 8.233 8.459 8.666 8.849 9.023 9.285
0.19 7.210 7.214 7.350 7.526 7.724 7.939 8.151 8.350 8.531 8.681 8.899
0.20 6.991 7.003 7.128 7.282 7.461 7.658 7.856 8.046 8.223 8.356 8.540
                       
0.22 6.572 6.598 6.702 6.822 6.969 7.132 7.303 3.474 7.639 7.754 7.891
0.24 6.181 6.216 6.305 6.399 6.520 6.654 6.800 6.952 7.102 7.208 7.318
0.25 5.995 6.035 6.116 6.201 6.310 6.432 6.567 6.709 6.852 6.954 7.055
0.26 5.817 5.859 5.934 6.011 6.110 6.221 6.345 6.477 6.612 6.712 6.807
0.28 5.478 5.525 5.591 5.654 5.736 5.828 5.933 6.047 6.166 6.261 6.347
0.30 5.164 5.214 5.272 5.327 5.395 5.472 5.560 5.658 5.762 5.852 5.931
                       
0.32 4.873 4.924 4.976 5.025 5.083 5.148 5.222 5.305 5.397 5.480 5.555
0.34 4.603 4.654 4.702 4.746 4.797 4.852 4.915 4.987 5.065 5.141 5.212
0.35 4.475 4.526 4.572 4.614 4.662 4.714 4.772 4.838 4.912 4.984 5.053
0.36 4.352 4.403 4.447 4.488 4.533 4.581 4.636 4.697 4.765 4.834 4.900
0.38 4.120 4.169 4.211 4.249 4.290 4.333 4.380 4.433 4.492 4.555 4.616
0.40 3.905 3.952 3.991 4.028 4.066 4.104 4.146 4.192 4.244 4.300 4.356
                       
0.42 3.704 3.750 3.787 3.823 3.858 3.893 3.931 3.972 4.017 4.067 4.118
0.44 3.518 3.562 3.597 3.632 3.665 3.698 3.732 3.769 3.808 3.854 3.901
0.45 3.430 3.472 3.507 3.541 3.573 3.606 3.639 3.673 3.711 3.754 3.798
0.46 3.345 3.386 3.420 3.454 3.485 3.517 3.548 3.582 3.617 3.658 3.700
0.48 3.184 3.223 3.256 3.288 3.318 3.348 3.378 3.408 3.441 3.477 3.516
0.50 3.034 3.070 3.102 3.133 3.162 3.191 3.219 3.248 3.277 3.311 3.346
                       
0.55 2.701 2.732 2.760 2.789 2.816 2.842 2.868 2.893 2.918 2.945 2.974
0.60 2.420 2.446 2.471 2.497 2.522 2.546 2.570 2.593 2.616 2.639 2.663
0.65 2.181 2.203 2.225 2.248 2.271 2.293 2.315 2.337 2.358 2.378 2.399
0.70 1.976 1.995 2.015 2.035 2.055 2.076 2.096 2.116 2.135 2.154 2.173
0.80 1.647 1.661 1.676 1.692 1.708 1.725 1.742 1.758 1.775 1.791 1.808
0.90 1.396 1.407 1.419 1.431 1.444 1.457 1.471 1.485 1.499 1.513 1.527
1.00 1.198 1.208 1.218 1.228 1.239 1.249 1.260 1.272 1.283 1.295 1.307
                       
1.10 1.040 1.048 1.057 1.066 1.075 1.084 1.093 1.102 1.112 1.122 1.132
1.20 0.909 0.918 0.926 0.934 0.942 0.949 0.957 0.965 0.974 0.982 0.990
1.30 0.801 0.809 0.816 0.824 0.831 0.838 0.846 0.853 0.860 0.867 0.874
1.40 0.709 0.717 0.724 0.731 0.738 0.745 0.752 0.758 0.765 0.771 0.778
1.50 0.632 0.639 0.646 0.653 0.659 0.666 0.672 0.678 0.684 0.690 0.696
                       
1.60 0.565 0.572 0.579 0.585 0.591 0.598 0.603 0.609 0.615 0.621 0.626
1.70 0.508 0.514 0.521 0.527 0.533 0.538 0.544 0.550 0.555 0.561 0.566
1.80 0.459 0.465 0.471 0.476 0.482 0.488 0.493 0.498 0.503 0.508 0.513
1.90 0.416 0.422 0.427 0.432 0.438 0.443 0.448 0.453 0.458 0.463 0.468
2.00 0.379 0.384 0.389 0.394 0.399 0.404 0.409 0.413 0.418 0.423 0.427

ElementAcThPaUNpPuAmCmBkCf
Z89909192939495969798
Method*RHF*RHF*RHFRHF*RHF*RHF*RHF*RHF*RHF*RHF
(sin [\theta])/λ (Å−1)          
0.00 20.484 20.115 19.568 19.119 18.759 18.191 17.840 17.710 17.406 16.841
0.01       19.047            
0.02       18.825            
0.03       18.470            
0.04 19.10 18.92 18.37 17.999 17.70 17.10 16.80 16.80 16.53 16.28
0.05 18.41 18.33 17.77 17.436 17.16 16.55 16.28 16.33 16.08 15.85
                     
0.06 17.64 17.66 17.11 16.805 16.55 15.95 15.70 15.80 15.58 15.37
0.07 16.84 16.93 16.39 16.131 15.91 15.31 15.09 15.24 15.04 14.84
0.08 16.01 16.19 15.66 15.436 15.25 14.65 14.47 14.66 14.48 14.30
0.09 15.19 15.43 14.92 14.738 14.58 14.00 13.84 14.06 13.91 13.75
0.10 14.40 14.68 14.20 14.052 13.92 13.37 13.24 13.47 13.33 13.20
                     
0.11 13.64 13.95 13.51 13.389 13.28 12.76 12.65 12.90 12.78 12.66
0.12 12.923 13.255 12.850 12.756 12.665 12.191 12.095 12.344 12.241 12.135
0.13 12.253 12.594 12.228 12.157 12.085 11.653 11.572 11.817 11.729 11.637
0.14 11.632 11.972 11.646 11.595 11.540 11.149 11.083 11.319 11.243 11.164
0.15 11.058 11.388 11.102 11.069 11.029 10.679 10.626 10.848 10.784 10.716
                     
0.16 10.528 10.845 10.597 10.579 10.551 10.243 10.200 10.407 10.353 10.294
0.17 10.038 10.339 10.128 10.122 10.104 9.836 9.803 9.993 9.948 9.898
0.18 9.586 9.868 9.691 9.696 9.688 9.457 9.433 9.605 9.568 9.527
0.19 9.168 9.430 9.285 9.299 9.300 9.102 9.086 9.241 9.212 9.178
0.20 8.780 9.022 8.906 8.928 8.936 8.770 8.760 8.900 8.878 8.850
                     
0.22 8.083 8.287 8.221 8.254 8.275 8.163 8.164 8.277 8.266 8.249
0.24 7.474 7.645 7.617 7.659 7.689 7.619 7.631 7.721 7.720 7.713
0.25 7.196 7.353 7.341 7.387 7.420 7.368 7.384 7.465 7.468 7.466
0.26 6.935 7.079 7.081 7.129 7.165 7.129 7.148 7.222 7.229 7.231
0.28 6.455 6.578 6.600 6.652 6.694 6.683 6.708 6.770 6.784 6.793
0.30 6.025 6.129 6.167 6.221 6.266 6.274 6.304 6.358 6.378 6.393
                     
0.32 5.637 5.727 5.775 5.830 5.878 5.899 5.933 5.981 6.006 6.026
0.34 5.285 5.364 5.418 5.473 5.523 5.553 5.591 5.635 5.664 5.687
0.35 5.122 5.196 5.252 5.307 5.357 5.391 5.429 5.472 5.502 5.528
0.36 4.966 5.036 5.093 5.148 5.197 5.235 5.274 5.316 5.347 5.374
0.38 4.675 4.738 4.796 4.850 4.899 4.940 4.981 5.021 5.055 5.084
0.40 4.410 4.466 4.524 4.576 4.625 4.669 4.710 4.749 4.784 4.815
                     
0.42 4.168 4.218 4.275 4.325 4.372 4.417 4.459 4.497 4.532 4.565
0.44 3.946 3.992 4.046 4.094 4.140 4.185 4.226 4.263 4.299 4.333
0.45 3.842 3.885 3.938 3.985 4.030 4.076 4.116 4.152 4.189 4.222
0.46 3.742 3.784 3.835 3.881 3.925 3.970 4.010 4.046 4.082 4.116
0.48 3.554 3.592 3.641 3.685 3.727 3.771 3.810 3.844 3.880 3.914
0.50 3.381 3.416 3.462 3.503 3.543 3.586 3.624 3.657 3.693 3.726
                     
0.55 3.003 3.032 3.071 3.106 3.141 3.179 3.213 3.244 3.277 3.309
0.60 2.687 2.712 2.744 2.775 2.805 2.839 2.869 2.897 2.927 2.957
0.65 2.421 2.442 2.470 2.495 2.522 2.551 2.578 2.603 2.630 2.657
0.70 2.193 2.212 2.235 2.257 2.280 2.306 2.330 2.352 2.376 2.400
0.80 1.824 1.840 1.857 1.875 1.893 1.912 1.930 1.949 1.968 1.987
0.90 1.541 1.554 1.568 1.582 1.597 1.611 1.626 1.641 1.657 1.673
1.00 1.318 1.330 1.342 1.353 1.365 1.377 1.389 1.402 1.415 1.427
                     
1.10 1.142 1.152 1.161 1.171 1.181 1.191 1.201 1.212 1.222 1.233
1.20 0.999 1.007 1.016 1.024 1.033 1.041 1.049 1.058 1.067 1.076
1.30 0.882 0.889 0.896 0.904 0.911 0.918 0.926 0.933 0.941 0.948
1.40 0.784 0.791 0.797 0.803 0.810 0.816 0.823 0.830 0.836 0.843
1.50 0.702 0.708 0.714 0.720 0.725 0.731 0.737 0.743 0.748 0.754
                     
1.60 0.632 0.637 0.643 0.649 0.653 0.659 0.664 0.669 0.674 0.679
1.70 0.571 0.576 0.581 0.585 0.591 0.596 0.601 0.606 0.611 0.165
1.80 0.518 0.523 0.528 0.534 0.537 0.542 0.547 0.551 0.555 0.560
1.90 0.472 0.477 0.481 0.485 0.490 0.495 0.499 0.503 0.507 0.511
2.00 0.432 0.436 0.440 0.443 0.449 0.453 0.457 0.461 0.465 0.469

Table 4.3.1.2| top | pdf |
Atomic scattering amplitudes (Å) for electrons for ionized atoms

A discussion of the values quoted here for s = 0 is given in Subsection 4.3.1.6[link]. Self-consistent field calculations: HF: non-relativistic Hartree–Fock; DS: modified Dirac–Slater; RHF, *RHF: relativistic Hartree–Fock.

ElementH1−Li1+Be2+O1−F1−Na1+Mg2+Al3+Si4+Cl1−K1+
Z13489111213141719
MethodHFRHFRHFHFHFRHFRHFHFHFRHFRHF
(sin [\theta])/λ (Å−1)           
0.00   0.157 0.082     1.130 0.831     6.770 3.436
0.01   239.497 478.762     240.469 479.511     −232.585 242.773
0.02   59.992 119.752     60.963 120.500     −53.125 63.260
0.03   26.750 53.268     27.719 54.015     −19.957 30.004
0.04 −12.00 15.115 29.999 −11.74 −12.21 16.081 30.745 45.52 60.34 −8.423 18.349
0.05 −6.78 9.730 19.229 −6.41 −6.85 10.692 19.972 29.36 38.80 −3.162 12.939
                       
0.06 −4.03 6.804 13.378 −3.55 −3.97 7.762 14.119 20.58 27.10 −0.381 9.983
0.07 −2.45 5.040 9.850 −1.86 −2.25 5.993 10.589 15.29 20.05 1.219 8.184
0.08 −1.48 3.894 7.560 −0.79 −1.16 4.841 8.296 11.85 15.46 2.187 6.999
0.09 −0.87 3.109 5.990 −0.09 −0.43 4.049 6.722 9.49 12.32 2.783 6.169
0.10 −0.47 2.546 4.867 0.39 0.08 3.480 5.595 7.81 10.08 3.147 5.559
                       
0.11 −0.20 2.130 4.036 0.72 0.43 3.056 4.760 6.56 8.41 3.361 5.092
0.12 −0.023 1.813 3.404 0.949 0.688 2.731 4.123 5.610 7.147 3.472 4.720
0.13 0.095 1.567 2.912 1.107 0.870 2.475 3.626 4.868 6.162 3.513 4.416
0.14 0.173 1.370 2.522 1.215 1.000 2.269 3.230 4.280 5.379 3.504 4.160
0.15 0.224 1.212 2.207 1.285 1.092 2.100 2.909 3.804 4.747 3.461 3.939
                       
0.16 0.257 1.082 1.949 1.329 1.157 1.960 2.645 3.413 4.230 3.393 3.745
0.17 0.276 0.974 1.735 1.352 1.200 1.841 2.425 3.089 3.800 3.308 3.571
0.18 0.286 0.883 1.556 1.359 1.226 1.738 2.239 2.817 3.440 3.211 3.414
0.19 0.288 0.806 1.404 1.355 1.239 1.650 2.081 2.585 3.135 3.108 3.269
0.20 0.287 0.740 1.274 1.343 1.242 1.571 1.944 2.387 2.873 3.000 3.135
                       
0.22 0.276 0.634 1.066 1.300 1.228 1.440 1.720 2.066 2.451 2.779 2.893
0.24 0.259 0.552 0.907 1.243 1.194 1.332 1.546 1.819 2.129 2.563 2.676
0.25 0.250 0.518 0.841 1.212 1.173 1.284 1.472 1.716 1.995 2.458 2.575
0.26 0.240 0.487 0.783 1.179 1.150 1.240 1.406 1.624 1.876 2.357 2.479
0.28 0.221 0.435 0.685 1.112 1.099 1.161 1.290 1.466 1.674 2.165 2.300
0.30 0.203 0.393 0.605 1.046 1.046 1.092 1.193 1.336 1.509 1.988 2.135
                       
0.32 0.186 0.357 0.539 0.981 0.992 1.029 1.110 1.228 1.372 1.827 1.983
0.34 0.170 0.327 0.485 0.918 0.939 0.972 1.038 1.136 1.257 1.680 1.843
0.35 0.163 0.314 0.461 0.889 0.912 0.946 1.005 1.094 1.206 1.613 1.778
0.36 0.156 0.301 0.439 0.860 0.887 0.920 0.974 1.056 1.159 1.548 1.715
0.38 0.143 0.279 0.400 0.804 0.837 0.872 0.917 0.987 1.075 1.429 1.596
0.40 0.132 0.259 0.366 0.753 0.789 0.827 0.866 0.925 1.001 1.322 1.488
                       
0.42 0.122 0.242 0.337 0.704 0.744 0.785 0.820 0.871 0.937 1.226 1.388
0.44 0.112 0.227 0.312 0.660 0.702 0.746 0.777 0.822 0.880 1.139 1.296
0.45 0.108 0.220 0.300 0.639 0.682 0.727 0.757 0.799 0.853 1.099 1.253
0.46 0.104 0.213 0.290 0.618 0.662 0.709 0.738 0.778 0.829 1.061 1.212
0.48 0.096 0.200 0.270 0.580 0.625 0.675 0.701 0.737 0.783 0.991 1.135
0.50 0.090 0.189 0.252 0.544 0.590 0.642 0.668 0.701 0.741 0.928 1.064
                       
0.55 0.075 0.165 0.216 0.467 0.512 0.569 0.593 0.620 0.652 0.796 0.912
0.60 0.064 0.145 0.188 0.403 0.446 0.506 0.529 0.553 0.580 0.691 0.789
0.65 0.055 0.129 0.165 0.351 0.391 0.451 0.474 0.496 0.519 0.608 0.690
0.70 0.048 0.115 0.146 0.307 0.345 0.403 0.426 0.447 0.468 0.541 0.609
0.80 0.037 0.093 0.118 0.241 0.272 0.325 0.347 0.367 0.385 0.439 0.488
0.90 0.029 0.077 0.097 0.193 0.219 0.266 0.286 0.305 0.321 0.366 0.402
1.00 0.024 0.064 0.081 0.159 0.180 0.221 0.239 0.256 0.271 0.311 0.338
                       
1.10 0.020 0.054 0.069 0.133 0.150 0.185 0.201 0.217 0.231 0.267 0.290
1.20 0.017 0.046 0.059 0.113 0.128 0.157 0.172 0.186 0.198 0.232 0.252
1.30 0.014 0.040 0.052 0.097 0.110 0.135 0.148 0.160 0.172 0.202 0.221
1.40 0.012 0.035 0.045 0.085 0.095 0.118 0.129 0.140 0.150 0.178 0.195
1.50 0.011 0.031 0.040 0.075 0.084 0.103 0.113 0.123 0.132 0.158 0.173
                       
1.60   0.027 0.035     0.091 0.100     0.141 0.155
1.70   0.024 0.032     0.081 0.089     0.126 0.139
1.80   0.022 0.028     0.073 0.080     0.113 0.125
1.90   0.020 0.026     0.066 0.072     0.102 0.114
2.00   0.018 0.023     0.060 0.065     0.093 0.103

ElementCa2+Sc3+Ti2+Ti3+Ti4+V2+V3+V5+Cr2+Cr3+Mn2+
Z2021222222232323242425
MethodRHFHFHFHFHFRHFHFHFHFHFRHF
(sin [\theta])/λ (Å−1)           
0.00 2.711         2.904         2.846
0.01 481.390         481.582         481.525
0.02 122.375         122.566         122.510
0.03 55.883         56.074         56.018
0.04 32.602 47.08 32.80 47.15 61.67 32.791 47.18 76.36 32.79 47.19 32.738
0.05 21.817 30.91 22.01 30.98 40.13 22.005 31.02 49.43 22.00 31.03 21.953
                       
0.06 15.948 22.13 16.14 22.19 28.42 16.134 22.23 34.80 16.13 22.24 16.085
0.07 12.399 16.82 12.59 16.89 21.35 12.583 16.92 25.98 12.58 16.93 12.537
0.08 10.085 13.37 10.27 13.44 16.77 10.267 13.47 20.24 10.26 13.48 10.225
0.09 8.489 11.00 8.67 11.07 13.62 8.668 11.10 16.31 8.67 11.11 8.630
0.10 7.336 9.30 7.52 9.36 11.36 7.514 9.39 13.49 7.51 9.41 7.479
                       
0.11 6.473 8.03 6.65 8.09 9.68 6.648 8.13 11.41 6.65 8.14 6.618
0.12 5.807 7.057 5.977 7.120 8.400 5.980 7.155 9.815 5.983 7.172 5.954
0.13 5.279 6.295 5.444 6.359 7.400 5.449 6.394 8.574 5.455 6.410 5.428
0.14 4.850 5.684 5.011 5.747 6.603 5.018 5.782 7.584 5.026 5.800 5.002
0.15 4.495 5.185 4.653 5.247 5.954 4.661 5.284 6.784 4.671 5.302 4.650
                       
0.16 4.196 4.770 4.349 4.832 5.418 4.360 4.868 6.126 4.372 4.888 4.353
0.17 3.939 4.421 4.089 4.481 4.971 4.102 4.518 5.577 4.116 4.539 4.100
0.18 3.716 4.121 3.863 4.182 4.591 3.877 4.220 5.113 3.894 4.242 3.880
0.19 3.519 3.863 3.663 3.923 4.266 3.679 3.961 4.719 3.698 3.984 3.686
0.20 3.343 3.637 3.485 3.697 3.984 3.503 3.735 4.378 3.523 3.759 3.514
                       
0.22 3.041 3.259 3.178 3.318 3.520 3.200 3.358 3.824 3.224 3.384 3.220
0.24 2.787 2.953 2.920 3.012 3.155 2.946 3.053 3.391 2.973 3.081 2.975
0.25 2.674 2.821 2.806 2.879 2.998 2.833 2.921 3.209 2.862 2.950 2.865
0.26 2.568 2.699 2.699 2.757 2.857 2.727 2.799 3.045 2.758 2.830 2.764
0.28 2.376 2.482 2.504 2.540 2.610 2.536 2.584 2.761 2.569 2.616 2.579
0.30 2.204 2.294 2.331 2.352 2.399 2.365 2.396 2.524 2.401 2.430 2.415
                       
0.32 2.049 2.128 2.174 2.185 2.217 2.211 2.231 2.322 2.249 2.266 2.266
0.34 1.907 1.980 2.032 2.037 2.057 2.071 2.073 2.147 2.111 2.120 2.131
0.35 1.842 1.911 1.966 1.968 1.984 2.005 2.015 2.068 2.046 2.053 2.068
0.36 1.778 1.846 1.903 1.903 1.915 1.943 1.950 1.994 1.984 1.988 2.007
0.38 1.660 1.725 1.783 1.781 1.788 1.825 1.829 1.858 1.867 1.868 1.893
0.40 1.551 1.614 1.673 1.670 1.673 1.716 1.718 1.736 1.759 1.758 1.787
                       
0.42 1.451 1.512 1.572 1.568 1.569 1.615 1.616 1.627 1.659 1.657 1.688
0.44 1.359 1.419 1.478 1.474 1.473 1.522 1.522 1.528 1.566 1.563 1.597
0.45 1.316 1.375 1.433 1.429 1.428 1.477 1.477 1.481 1.522 1.519 1.553
0.46 1.274 1.333 1.391 1.387 1.385 1.435 1.434 1.437 1.480 1.476 1.511
0.48 1.196 1.253 1.310 1.306 1.304 1.354 1.354 1.354 1.399 1.395 1.432
0.50 1.124 1.180 1.235 1.232 1.229 1.279 1.279 1.277 1.324 1.320 1.357
                       
0.55 0.967 1.019 1.070 1.068 1.066 1.113 1.113 1.110 1.156 1.154 1.190
0.60 0.838 0.886 0.933 0.931 0.930 0.973 0.974 0.971 1.015 1.013 1.049
0.65 0.733 0.776 0.818 0.817 0.816 0.856 0.857 0.855 0.895 0.894 0.928
0.70 0.647 0.685 0.722 0.722 0.721 0.757 0.758 0.756 0.793 0.792 0.824
0.80 0.515 0.544 0.574 0.574 0.574 0.602 0.603 0.603 0.632 0.632 0.659
0.90 0.422 0.444 0.467 0.467 0.467 0.490 0.491 0.491 0.515 0.515 0.538
1.00 0.354 0.371 0.389 0.389 0.389 0.408 0.408 0.408 0.427 0.427 0.446
                       
1.10 0.302 0.316 0.331 0.331 0.330 0.345 0.346 0.345 0.361 0.361 0.377
1.20 0.262 0.273 0.285 0.285 0.285 0.297 0.297 0.297 0.310 0.310 0.323
1.30 0.230 0.239 0.249 0.249 0.249 0.259 0.259 0.259 0.270 0.270 0.280
1.40 0.203 0.211 0.220 0.220 0.219 0.228 0.228 0.228 0.237 0.237 0.246
1.50 0.180 0.188 0.195 0.195 0.195 0.203 0.203 0.202 0.211 0.211 0.218
                       
1.60 0.161         0.181         0.195
1.70 0.145         0.163         0.175
1.80 0.131         0.148         0.159
1.90 0.119         0.134         0.144
2.00 0.108         0.123         0.132

ElementMn3+Mn4+Fe<