TY - JOUR

T1 - Automated structure factor refinement from convergent-beam patterns

AU - Zuo, J. M.

AU - Spence, John

N1 - Funding Information:
This work was supported by NSF award DMR88-13879, thNeS F-ASU National Facility for HREM, and the supporto f the Universityo f Trondheimfo r J.C.H.S. during a sabbaticavl isit. We are most gratefult o R. Hoier and L. Bakken for many usefuld iscussions.

PY - 1991/6

Y1 - 1991/6

N2 - An algorithm is described which automatically adjusts values of the low-order structure factors, crystal thickness and absorption coefficients for the best fit to experimental convergent-beam electron diffraction (CBED) patterns recorded in the systematics orientation. A fitting index is defined, by analogy with R factors used in neutron diffraction. A comparison of several least-squares optimization routines is made, and the "Simplex" method found to be most useful. An analysis of errors, background and noise is presented. Source-code listings of most of the program have been published elsewhere. This treats three-dimensional dynamical diffraction by the Bloch-wave method from non-centrosymmetric crystals with absorption. The use of perturbation methods for the final 33-beam refinement is found to reduce the computation time from 6 h to 30 min. An example of the use of the program is given. For MgO, we find U(200) = 0.05847 ± 0.00051 and U(400) = 0.02484 ± 0.00028. This algorithm may be used to measure and study any of the parameters (such as atomic coordinates, bonding effects or Debye-Waller factors) on which crystal structure factors depend. Similar methods allow lattice parameters to be refined to an accuracy of {reversed tilde} 0.05%.

AB - An algorithm is described which automatically adjusts values of the low-order structure factors, crystal thickness and absorption coefficients for the best fit to experimental convergent-beam electron diffraction (CBED) patterns recorded in the systematics orientation. A fitting index is defined, by analogy with R factors used in neutron diffraction. A comparison of several least-squares optimization routines is made, and the "Simplex" method found to be most useful. An analysis of errors, background and noise is presented. Source-code listings of most of the program have been published elsewhere. This treats three-dimensional dynamical diffraction by the Bloch-wave method from non-centrosymmetric crystals with absorption. The use of perturbation methods for the final 33-beam refinement is found to reduce the computation time from 6 h to 30 min. An example of the use of the program is given. For MgO, we find U(200) = 0.05847 ± 0.00051 and U(400) = 0.02484 ± 0.00028. This algorithm may be used to measure and study any of the parameters (such as atomic coordinates, bonding effects or Debye-Waller factors) on which crystal structure factors depend. Similar methods allow lattice parameters to be refined to an accuracy of {reversed tilde} 0.05%.

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U2 - 10.1016/0304-3991(91)90071-D

DO - 10.1016/0304-3991(91)90071-D

M3 - Article

AN - SCOPUS:0026174242

SN - 0304-3991

VL - 35

SP - 185

EP - 196

JO - Ultramicroscopy

JF - Ultramicroscopy

IS - 3-4

ER -