ISSRNS 2012: Abstracts / Synchrotron Radiation in Natural Science Vol. 11, No 1 – 2 (2012) P 33
SINGULAR VALUE DECOMPOSITION ANALYSIS OF TIME-RESOLVED POWDER DIFFRACTION DATA
A.F. Mabied1∗, S. Nozawa2, M. Hoshino3,4, A. Tomita2, T. Sato2, and S. Adachi1,2,5
1Department of Materials Structure Science, School of High Energy Accelerator Science (KEK), The Graduate University for Advanced Studies (Sokendai), Tsukuba, 305–0801, Japan
2Photon Factory, High Energy Accelerator Research Organization (KEK), Tsukuba, 305–0801, Japan
3Department of Chemistry and Materials Science, Tokyo Institute of Technology, Meguro-ku, Japan
4CREST, Japan Science and Technology Agency (JST), Japan
5PRESTO, Japan Science and Technology Agency (JST), Japan
Keywords: synchrotron radiation, SVD, time-resolved, powder diffraction, photodimerization
∗e-mail : mabied@post.kek.jp
Singular value decomposition (SVD) analysis has proved efficiency for treating time dependant crystallographic and spectroscopic data revealing important information [1, 2]. SVD method can factorize an experimental data matrix into several components matrices, which can be written math- ematically as follow; for an A m-by-n real matrix (m ≥ n) can be decomposed into three matrices (A = U SVT) U is an m-by-n orthogonal matrix, S is an n-by-n diagonal matrix with positive or zero elements and VT is the transpose of an orthogonal n-by-n matrix V . Physically, the columns of U ma- trix represents the measurements base spectrum and S elements give its singular values, which indicate the significant of U spectrum. V matrix separates the time dependant vectors of U elements [2].
In our work, we present the first exam- ple of the SVD analysis of the photodimeriza- tion time-resolved powder diffraction data of 1- chloroanthracene (1-chA) and 9-methylanthracene (9-MA), in order to add useful information about their photodimerization reaction dynamics. An- thracene derivatives have important applications in modern technology, such as fabrication of photo- switchable devices [3]. The powder data were set into m-by-n matrix its columns are the diffraction
Figure 1 : Global fitting results of 9-MA time dependant v spectra of SVD analysis.
intensity at the 2 theta angle points (details in ref. [4]).
The SVD results showed that, in case of 1-chA only one significant singular value was obtained (S1). The u1 spectrum vector accompanying to S1
referred to the original spectrum of 1-chA monomer phase, which mean that the reaction did not occur.
For 9-MA, three significant S components were ob- tained. Figure 1 illustrates the global fitting anal- ysis of V time dependant spectra. It was success- fully fitted to double exponential function, giving two time dependant components. Fast decay com- ponent assigned to dimerization process and slow decay component can be interpreted that a small amount of monomer still did not react, which in agreement with the reported in ref [5]. UV-Vis and IR spectroscopic measurements supported the re- sults.
Acknowledgments: The synchrotron X-ray experi- ment at KEK, Japan was approved by the Photon Factory Program Advisory Committee (PF-PAC No.
2004S2–001).
References
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