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High-Precision Structural Measurements


Atomic arrangements underpin the properties of all solids and, as such, are fundamentally important for materials development.  The power of computational materials science depends on effective models, which in turn accurate data on the atomic order.  This input is critical to the successful design and accelerated commercial deployment of new and improved materials and targeted functionalities, which is the primary goal of the Material Genome initiative.  Practical materials tend to be complex, and detailed structural determination is often challenging, particularly with three-dimensional fidelity and precision across the sub-nanometer to macroscopic length scales, which are needed to correlate structure and function.  Some of the existing limitations are associated with instrumental and data-processing deficiencies, whereas others are caused by the inability to integrate data from different experimental sources, and to combine theoretical and experimental information in the structure determination process.  This project seeks to address these issues.


On the instrumental and data processing side, we focus on improving the precision of structural information derived using transmission electron microscopy (TEM).  Aberration-corrected scanning TEM enables direct imaging of atomic columns but the precision of column positions extracted from the images remains limited by sample drift.  Likewise, while recent advances in electron tomography have enabled the qualitative determination of structures at the atomic scale, the technique currently lacks the required quantitative precision.  The research under this project is aimed at drastically improving the precision of both techniques by developing and applying compressive sampling and related computational algorithms and software for the removal of sample drift and other artifacts, thus revealing the true intrinsic material signature with picometer precision, as needed for effective computational studies.

On the data analysis side, this project targets problems related to data fusion, which is necessary to elucidate comprehensive structural models of complex materials.   Combining inputs from different experimental measurements as well as theoretical calculations requires a computational framework for simultaneous fitting of multiple datasets.  A basic example of data fusion in structure determination involves the joint fitting of neutron and X-ray powder diffraction data.  Currently, the use of this technique is hindered by the inability to appropriately treat systematic errors associated with each dataset.   We are developing a Bayesian-statistics approach that accounts for the presence of unknown systematic errors in structural refinements, thus providing significantly more accurate structural models compared to standard fits.  Data fusion becomes particularly critical for determination of local and nanoscale atomic arrangements which control the properties and resulting functionality of many advanced materials.  As a part of this project, we are developing a computational framework and relevant computer software for simultaneous fitting of various diffraction and spectroscopic data to determine local and nanoscale atomic arrangements in bulk materials and nanoparticles with high fidelity.  

Major Accomplishments

Our recent developments of the RMCProfile software ( turned it into a powerful modeling framework for comprehensive determination of the local and nanoscale atomic arrangements in crystalline materials using a combined input from multiple experimental techniques and theory.  The new methodology has been already applied to solve several long-standing problems in electroceramics.   In the most recent example, detailed understanding of local atomic displacements in a class of ceramic dielectric based on barium titanate helped to uncover the origins of their highly complex dielectric response which renders these materials promising for applications in power electronics.  These results were achieved using a Reverse Monte Carlo algorithm implemented in RMCProfile to simultaneously fit 17 experimental datasets, which included different representations of X-ray and neutron total scattering data, extended X-ray absorption fine structure (EXAFS) and patterns of diffuse scattering in electron diffraction.  

In principle, an RMC approach can provide a model that consistently describes structural behavior on the local, nanometer, and macroscopic scales.   However, for such a description to be correct, the size of an atomic configuration has to be significantly larger than the effective length of relevant local/nanoscale interatomic correlations in the system.  The currently distributed version of RMCProfile can sample interatomic distances only up to about 3 nm, which is insufficient for probing the truly nanoscale atomic order; larger configuration sizes are computationally prohibitive.  Recently, we addressed this problem by performing a sophisticated optimization of the RMCProfile software which yielded more than an order-of -magnitude gain in computing speed, extending the distance range accessible by these analyses to 10 nm.  Fitting a real-space pair-distribution function (PDF) to long distances requires accounting for a limited resolution of the diffraction data, which causes progressive diminishing and broadening of PDF peaks with increasing distance.  We developed a procedure that corrects a calculated PDF for instrument resolution during RMC fits, thereby enabling the usage of the entire interatomic-distance range sampled by experimental data.

We have also developed a method addressing the effects of systematic errors in Rietveld refinements using powder diffraction data. Relevant errors were categorized into multiplicative, additive, and peak-shape types. Corrections for these errors were incorporated into structural refinements using a Bayesian statistics approach, with the corrections themselves treated as nuisance parameters and marginalized out of the analysis. Structural parameters refined using the proposed method represent probability-weighted averages over all possible error corrections. The developed formalism has been adapted to least-squares minimization algorithms and implemented as an extension to the Rietveld software package GSAS-II.  The technique was first tested using neutron and X-ray diffraction data simulated for PbSO4 and then applied to the equivalent experimental datasets for the same compound. The results obtained using the simulated data confirmed that the proposed method yields significantly more accurate estimates of structural parameters and their uncertainties than standard refinements. The benefits were particularly significant for joint refinements using neutron and X-ray diffraction data; accounting for systematic errors enabled more adequate weighting of the individual datasets.  We further demonstrated the power of this approach by performing refinements of a complex AgNbO3 structure using the data that were collected with four different instruments (2 neutron and 2 X-ray diffractometers), each having its own systematic errors.  After correcting for these errors, the structural parameters obtained using the distinct datasets became statistically similar.


A. Gagin and I. Levin, "Applications of Bayesian Corrections for Systematic Errors in Rietveld Refinements," Journal of Applied Crystallography, 49, 814 (2016)

I. Levin, V. Krayzman, J. C. Woicik, F. Bridges, G. E. Sterbinsky, T-M. Usher, J. L. Jones, and D. Torrejon, "Local Structure in BaTiO3-BiScO3 Dipole Glasses," Physical Review B., 93, 104106 (2016)

V. Krayzman, I. Levin, J. C. Woicik, F. Bridges, "Correlated rattling-ion origins of dielectric properties in reentrant dipole glasses BaTiO3-BiScO3," Applied Physics Letters., 107, 192903 (2015)

A. Gagin and I. Levin, "Accounting for unknown systematic errors in Rietveld refinements: a Bayesian statistics approach," Journal of Applied Crystallography, 48, 1201 (2015)


Created October 24, 2017, Updated April 2, 2019