.. _dtxrd: ************ dtxrd ************ x-ray diffraction calculator (dynamical theory of x-ray diffraction) :author: Stanislav Stoupin :email: SYNOPSIS ============ :: dtxrd [options] crystal h k l eta phi T d ["a" | "e"] [theta | Ex] DESCRIPTION ============ Calculates parameters of a given crystal reflection for a monochromatic incident wave using dynamical theory of x-ray diffraction for perfect crystals in the 2-beam approximation For a brief summary run:: dtxrd -h INPUT PARAMETERS ================= :crystal: available crystal models: C (diamond), Si (silicon), Ge (germanium), GaN (wurtzite), SiC-4H, SiC-6H, SiO2 (quartz), Al2O3 (sapphire) :h k l: Miller indicies of a chosen reflection :eta: asymmetry angle (:math:`\eta` [degrees]) :phi: azimuthal angle of incidence (:math:`\phi` [degrees]) :T: crystal temperature [K] :d: crystal thickness [mm] :flag: ===== ================================================================= flag description ===== ================================================================= a perform calculation at a given glancing angle of incidence theta e perform calculation at a given photon energy Ex ===== ================================================================= :theta: glancing angle of incidence, theta (:math:`\theta`) :Ex: photon energy, Ex (:math:`E_{\mathrm X}`) OPTIONS ============ :-v, --version: show program version :-h, --help: show summary of options. :-o FILENAME, --output FILENAME: write results to file (default to stdout) :-w FILENAME, --write FILENAME: write data to file (default: no action) :-p, --pi: :math:`\pi` polarization for the incident wave (default: :math:`\sigma` polarization) :-c CONST, --conv CONST: convolve the reflectivity curve with a virtual instrument resolution function with FWHM = CONST [urad], plot the result and and report the resulting width of the convoluted curve :-s CONST, --syield CONST: calculate shape of the secondary yield curve (e.g., photoelectrons) with escape depth CONST [Angstrom] :-z STRING, --zblock STRING: calculate reflectivity/transmissivity curves for a mosaic crystal (uncorrelated block model) with STRING = 't s', where t is the block thickness [um] and s is the standard deviation of misorientation [urad] (assuming Gaussian distribution) :-n CONST, --nsteps CONST: CONST - number of points in the angular/energy interval (default: 1000) OUTPUT PARAMETERS ====================== Basic parameters of the chosen h k l reflection: :d[A]: :math:`d` [Angstrom] interplanar distance (d-spacing) of the chosen h k l reflection :Eb[keV]: :math:`E_B = \frac{hc}{2d}` [keV] Bragg energy :thr[deg]: :math:`\theta_R` [degrees] incident glancing angle for the exact backscattering (a wave with photon energy :math:`E_R` incident at this angle is reflected exactly backwards) :Er[keV]: :math:`E_R` [keV] photon energy for the exact backscattering :bh: :math:`b_{H}` asymmetry factor in the chosen scattering geometry for symmetric reflection :math:`\eta = 0` and :math:`b_{H} = - 1` Susceptibilities and refraction corrections: :chi_{0}: :math:`\chi_0` susceptibility :chi_{h}: :math:`\chi_{H}` susceptibility :chi_{-h}: :math:`\chi_{\bar{H}}` susceptibility :wh(s): :math:`\omega_{H}^s` refraction correction for symmetric reflection :wh: :math:`\omega_{H} = \omega_{H}^s \frac{b_{H}-1}{2b_{H}}` refraction correction for the chosen reflectoin Central energy and angle: :Ec[keV]: :math:`E_c` [keV] central energy of the chosen reflection :thc[deg]: :math:`\theta_c` [deg] central glancing angle of incidence of the chosen reflection Energy intrinsic (Darwin) widths (thick non-absorbing crystal) at fixed glancing angle of incidence :math:`\theta_c`: :eps_s: :math:`\varepsilon^s` relative energy width of symmetric h k l reflection (same for entrance and exit) :eps: :math:`\varepsilon` relative entrance energy width of the chosen h k l reflection :eps_pr: :math:`\varepsilon'` relative exit energy width of the chosen h k l reflection :Delta_E_s[meV]: :math:`\Delta E^s` [meV] absolute energy width of symmetric h k l reflection (same for entrance and exit) :Delta_E[meV]: :math:`\Delta E` [meV] absolute entrance energy width of the chosen h k l reflection :DeltaE_pr[meV]: :math:`\Delta E'` [meV] absolute exit energy width of symmetric reflection Angular intrinsic (Darwin) widths (thick non-absorbing crystal) at fixed photon energy :math:`E_c`: :dth_s[urad]: :math:`\Delta \theta^s` [microradian] angular width of the symmetric h k l reflection (same for entrance and exit) :dth[urad]: :math:`\Delta \theta` [microradian] angular entrance width of the chosen h k l reflection :dth_pr[urad]: :math:`\Delta \theta'` [microradian] angular exit width of the chosen h k l reflection Additional characteristics of the chosen h k l reflection: :dE/dth[meV/urad]: :math:`\frac{dE}{d\theta}` [meV/microradian] tangent of the Bragg's Law :Dr[urad/meV]: :math:`D_r` [microradian/meV] intrinsic angular dispersion rate of the chosen h k l reflection :de[um]: :math:`d_e` [micrometer] extinction length of the chosen h k l reflection Reflectivity and Transmissivity: :Rc[%]: :math:`R_c` [%] reflectivity at center :Tc[%]: :math:`T_c` [%] transmissivity at center EXAMPLES =========== A rocking curve of the symmetric Si 111 reflection (Bragg case, 1-mm-thick crystal at 300 K) :: dtxrd Si 1 1 1 0 0 300 1 e 8 .. image:: ../../examples/snapshots/Si111_8keV.png :width: 70 % :alt: Si111 at 8keV A rocking curve of the symmetric diamond 220 reflection (Laue case, 0.1-mm-thick crystal plate at 300 K) :: dtxrd C 2 2 0 90 0 300 0.1 e 12 .. image:: ../../examples/snapshots/C220_Laue.png :width: 70 % :alt: C220 Laue at 12keV Reflectivity curve of the diamond 008 reflection in exact backscattering (0.5-mm-thick crystal plate at 300 K). Accurate sampling of the thickness oscillations is achieved using 10000 points. :: dtxrd -n 10000 C 0 0 8 0 0 300 0.5 a 90 .. image:: ../../examples/snapshots/C008_90deg.png :width: 70 % :alt: C008 in backscattering Rocking curve of the diamond 220 reflection (0.5-mm-thick crystal plate at 300 K at 20 keV). Reflectivity/transmissivity of a perfect crystal compared with those of the mosaic crystal with 10 um block size having misorientation of 20 microradian r.m.s. (uncorrelated block model) :: dtxrd -n 10000 -z '10 20' C 2 2 0 90 0 300 0.5 e 20 .. image:: ../../examples/snapshots/C220_mosaic.png :width: 70 % :alt: C220 mosaic Note: reflectivity for a mosaic crystal in backscattering has not been implemented yet SEE ALSO ============ * :ref:`throughput` * :ref:`rcpeak` :author: Stanislav Stoupin :email: :date: |today|