References#

Literature citations used throughout ad_hoc_diffractometer. Geometries, algorithms, and conventions are traced to their primary sources.

Diffractometer geometries#

Busing & Levy (1967) : W.R. Busing and H.A. Levy. Angle calculations for 3- and 4-circle X-ray and neutron diffractometers. Acta Crystallographica 22, 457–464 (1967). DOI: 10.1107/S0365110X67000970

Foundational reference for the four-circle geometry, B matrix, U matrix, and UB matrix. Defines the orientation refinement least-squares procedure. Used by: fourcv(), fourch(), kappa4cv(), kappa4ch().

Bloch (1985) : J.M. Bloch. Angle and distance calculations for X-ray diffraction with the Z-axis geometry. Journal of Applied Crystallography 18, 33–36 (1985). DOI: 10.1107/S0021889885009858

Defines the Z-axis diffractometer geometry. Used by: zaxis().

Vlieg et al. (1987) : E. Vlieg, A.E.M.J. Fischer, J.F. van der Veen, B.N. Dev, and G. Materlik. Surface X-ray diffraction: a study of relaxation in the Cu(110) system. Journal of Applied Crystallography 20, 330–337 (1987). DOI: 10.1107/S0021889887087266

Defines the five-circle geometry. Used by: fivec().

Lohmeier & Vlieg (1993) : M. Lohmeier and E. Vlieg. Angle calculations for a six-circle surface X-ray diffractometer. Journal of Applied Crystallography 26, 706–716 (1993). DOI: 10.1107/S0021889893006198

Defines the six-circle surface diffractometer geometry. Used by: sixc().

Evans-Lutterodt & Tang (1995) : K.W. Evans-Lutterodt and M.-T. Tang. Angle calculations for a ‘2+2’ surface X-ray diffractometer. Journal of Applied Crystallography 28, 318–326 (1995). DOI: 10.1107/S0021889895001063

Defines the S2D2 (2+2) diffractometer geometry. Used by: s2d2().

You (1999) : H. You. Angle calculations for a ‘4S+2D’ six-circle diffractometer. Journal of Applied Crystallography 32, 614–623 (1999). DOI: 10.1107/S0021889899001223

Defines the psic (4S+2D) six-circle geometry; axis sign conventions (mixed handedness); ψ angle definitions (eqs. 10–11). Used by: psic(), kappa6c().

ITC Vol. C §2.2.6 (2006) : International Tables for Crystallography, Volume C, Section 2.2.6. Single-crystal X-ray techniques. DOI: 10.1107/97809553602060000577

Confirms the kappa 50° tilt convention and normal-beam equatorial geometry. Used by: kappa4cv(), kappa4ch(), kappa6c().

Walko (2016) : D.A. Walko. X-ray diffractometers. Reference Module in Materials Science and Materials Engineering, Elsevier (2016).

Comprehensive survey of diffractometer geometry designations (S/D system); kappa convention; zaxis, s2d2 geometries. Used throughout the geometry factory descriptions.

Physical constants#

CODATA 2022 / 2019 SI : NIST CODATA 2022 recommended values. BIPM SI Brochure, 9th edition (2019).

  • \(hc = 12.398\,419\,843\,320\,026\,\text{keV·Å}\) — exact (h and c are defined constants since the 2019 SI redefinition).

  • \(h^2/(2m_n) = 81.804\,210\,235\,2\,\text{meV·Å}^2\) — from CODATA 2022 neutron mass \(m_n\).

See HC_KEV_ANGSTROM and NEUTRON_MEV_ANGSTROM2.

Numerical methods#

Nelder & Mead (1965) : J.A. Nelder and R. Mead. A simplex method for function minimization. The Computer Journal 7(4), 308–313 (1965). DOI: 10.1093/comjnl/7.4.308

Derivative-free simplex optimisation algorithm used by refine_lattice_simplex().

APS alignment session#

Walko (2020) : D.A. Walko, private communication (December 2020). Crystal alignment session at APS beamline 7-ID-C using a sapphire sample. Documented in Align a Four-Circle Diffractometer (fourcv).