Numerical analysis as applied to x-ray scattering curves

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:6821218

Jeffries, T V

Various numerical methods involving polynomials were employed for both interpolation and linear least-square curve fitting of the atomic scattering factors of x-ray diffraction. This included use of Lagrangian and orthogonal Legendre polynomials, as well as cubic spline and Stineman interpolation. Interpolation is a method that uniquely matches known data points within small segments of an unknown curve to approximate points in between. Special emphasis was placed on establishing both the minimum grid spacing and polynomial degree that are needed to perform accurate interpolations. The grid spacing in a region of the x-argument near 1.0 A/sup -1/ that is commonly employed in standard tabulations of x-ray scattering factors was found to be too coarse for wholly accurate interpolation by polynomials of low degree. Least-squares curve fitting is a procedure that approximates the entire unknown curve with an analytical function that matches the known data points as closely as possible by minimizing the sum of their squared deviations from the fitted curve. Analytical representations of x-ray scattering curves are advantageous, since otherwise the complete scattering table must be sorted and the values of individual scattering factors derived by interpolation.

• Research Organization: Middle Tennessee State Univ., Murfreesboro (USA)
• OSTI ID: 6821218
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
COHERENT SCATTERING
DIFFRACTION
INTERPOLATION
LEAST SQUARE FIT
MATHEMATICS
MAXIMUM-LIKELIHOOD FIT
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
SCATTERING
X-RAY DIFFRACTION