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Related Experiment Video

Updated: Jun 14, 2026

Magnetometric Characterization of Intermediates in the Solid-State Electrochemistry of Redox-Active Metal-Organic Frameworks

Magnetometric Characterization of Intermediates in the Solid-State Electrochemistry of Redox-Active Metal-Organic Frameworks

Published on: June 9, 2023

Modulation functions of incommensurately modulated Cr2P2O7 studied by the maximum entropy method (MEM).

Liang Li¹, Andreas Schönleber, Sander van Smaalen

¹Laboratory of Crystallography, University of Bayreuth, 95440 Bayreuth, Germany.

Acta Crystallographica. Section B, Structural Science

|March 23, 2010

Summary

The maximum entropy method revealed electron density in modulated chromium pyrophosphate. This analysis clarified disordered regions, improving structural understanding of this complex material.

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A Technical Guide for Performing Spectroscopic Measurements on Metal-Organic Frameworks

A Technical Guide for Performing Spectroscopic Measurements on Metal-Organic Frameworks

Published on: April 28, 2023

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Last Updated: Jun 14, 2026

Magnetometric Characterization of Intermediates in the Solid-State Electrochemistry of Redox-Active Metal-Organic Frameworks

Magnetometric Characterization of Intermediates in the Solid-State Electrochemistry of Redox-Active Metal-Organic Frameworks

Published on: June 9, 2023

A Technical Guide for Performing Spectroscopic Measurements on Metal-Organic Frameworks

A Technical Guide for Performing Spectroscopic Measurements on Metal-Organic Frameworks

Published on: April 28, 2023

Area of Science:

Crystallography
Materials Science
Solid State Chemistry

Background:

Incommensurately modulated structures present challenges in crystallographic analysis.
Chromium pyrophosphate (Cr(2)P(2)O(7)) exhibits both ordered and disordered regions.
Previous studies by Palatinus et al. (2006) provided initial crystallographic data.

Purpose of the Study:

To determine the electron density distribution in superspace for modulated chromium pyrophosphate.
To analyze the nature of disorder within the crystal structure.
To refine the structural model using X-ray diffraction data.

Main Methods:

Application of the Maximum Entropy Method (MEM) to X-ray diffraction data.
Analysis of electron density in superspace to identify modulation functions.
Development of a structural model based on MEM density interpretation.

Main Results:

The MEM successfully determined electron density, revealing displacive modulation functions in ordered regions.
Disordered regions were characterized by dual conformations and atomic positions with continuous occupational probabilities.
A new structure model based on MEM density matched the quality of existing models.

Conclusions:

The MEM is effective for analyzing electron density in complex modulated structures.
Understanding modulation functions is key to describing disorder in chromium pyrophosphate.
Limitations in MEM accuracy and anharmonic ADP modeling affect model refinement.