# Algorithm for systematic peak extraction from atomic pair distribution functions

## Abstract

The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python programSrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C _{60}. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1354259

- Report Number(s):
- BNL-112775-2016-JA¿¿¿

Journal ID: ISSN 2053-2733; ACSAD7

- DOE Contract Number:
- SC00112704

- Resource Type:
- Journal Article

- Journal Name:
- Acta Crystallographica. Section A, Foundations and Advances (Online)

- Additional Journal Information:
- Journal Volume: 71; Journal Issue: 4; Journal ID: ISSN 2053-2733

- Publisher:
- International Union of Crystallography

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Granlund, L., Billinge, S. J. L., and Duxbury, P. M.
```*Algorithm for systematic peak extraction from atomic pair distribution functions*. United States: N. p., 2015.
Web. doi:10.1107/S2053273315005276.

```
Granlund, L., Billinge, S. J. L., & Duxbury, P. M.
```*Algorithm for systematic peak extraction from atomic pair distribution functions*. United States. doi:10.1107/S2053273315005276.

```
Granlund, L., Billinge, S. J. L., and Duxbury, P. M. Fri .
"Algorithm for systematic peak extraction from atomic pair distribution functions". United States. doi:10.1107/S2053273315005276.
```

```
@article{osti_1354259,
```

title = {Algorithm for systematic peak extraction from atomic pair distribution functions},

author = {Granlund, L. and Billinge, S. J. L. and Duxbury, P. M.},

abstractNote = {The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python programSrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.},

doi = {10.1107/S2053273315005276},

journal = {Acta Crystallographica. Section A, Foundations and Advances (Online)},

issn = {2053-2733},

number = 4,

volume = 71,

place = {United States},

year = {2015},

month = {5}

}