This article describes the R package DEoptim, which implements the differential evolution algorithm for global optimization of a real-valued function of a real-valued parameter vector. The implementation of differential evolution in DEoptim interfaces with C code for efficiency. The utility of the package is illustrated by case studies in fitting a Parratt model for X-ray reflectometry data and a Markov-switching generalized autoregressive conditional heteroskedasticity model for the returns of the Swiss Market Index.

The National Institute of Standards and Technology ͑NIST͒ certifies a variety of standard reference materials ͑SRM͒ to address specific aspects of instrument performance for divergent beam diffractometers. This paper describes SRM 640d, the fifth generation of this powder diffraction SRM, which is certified with respect to the lattice parameter. It consists of approximately 7.5 g silicon powder specially prepared to produce strain-free particles in a size range between 1 and 10 m to eliminate size-broadening effects. It is typically used for calibrating powder diffractometers for the line position and line shape. A NIST built diffractometer, incorporating many advanced design features, was used to certify the lattice parameter of the silicon powder measured at 22.5°C. Both type A, statistical, and type B, systematic, errors have been assigned to yield a certified value for the lattice parameter of a = 0.543 159Ϯ 0.000 020 nm.

Intentionally deposited thin films exposed to atmosphere often develop unintentionally deposited few monolayer films of surface contamination. This contamination arises from the diverse population of volatile organics and inorganics in the atmosphere. Such surface contamination can affect the uncertainties in determination of thickness, roughness and density of thin film structures by X-Ray Reflectometry (XRR). Here we study the effect of a 0.5 nm carbon surface contamination layer on thickness determination for a 20 nm titanium nitride thin film on silicon. Uncertainties calculated using Markov-Chain Monte Carlo Bayesian statistical methods from simulated data of clean and contaminated TiN thin films are compared at varying degrees of data quality to study (1) whether synchrotron sources cope better with contamination than laboratory sources and (2) whether cleaning off the surface of thin films prior to XRR measurement is necessary. We show that, surprisingly, contributions to uncertainty from surface contamination can dominate uncertainty estimates, leading to minimal advantages in using synchrotronover laboratory-intensity data. Further, even prior knowledge of the exact nature of the surface contamination does not significantly reduce the contamination's contribution to the uncertainty in the TiN layer thickness. We conclude, then, that effective and standardized cleaning protocols are necessary to achieve high levels of accuracy in XRR measurement.

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The fundamental parameters approach (FPA) as implemented in TOPAS is investigated for analyses of conventional X-ray powder diffraction (XRPD) data. The FPA involves the convolution of a series of models, each one constituting an individual contribution to the geometric portion of the instrument profile function (IPF). Parameters within each model are refined by least squares to yield a presumably accurate description of the experiment. If one wishes to interrogate the functionality of said models, a diffractometer wherein the uncertainties in optical character are minimized is required. To this end, a diffractometer was built at NIST which featured conventional divergent beam optics in conjunction with a well aligned, stiff, and accurate goniometer assembly. Initial results indicated that the detector arm was flexing; this problem has been addressed with the fabrication and installation of a new arm and counterweight assembly. Data collected from NIST Standard Reference Material (SRM) 660a, lanthanum hexaboride, are analyzed using the FPA method to yield conclusions on the validity of the models with respect to shape and position of the diffraction profiles.