Related Experiment Video
Updated: Jun 5, 2026
08:23
Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
Ab initio reconstruction of difference densities by charge flipping
Lukáš Palatinus1, Frank Fleischer, Phillip Pattison
1Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague, Czech Republic. palat@fzu.cz
Acta Crystallographica. Section A, Foundations of Crystallography
|December 22, 2010
Summary
The band-flipping algorithm reconstructs scattering densities for superstructures and modulated structures. This method solves complex crystal structures without needing subcell reflection data, aiding in pseudosymmetry problems.
Area of Science:
- Crystallography
- Materials Science
- Computational Chemistry
Background:
- Accurate crystal structure determination is crucial for understanding material properties.
- Superstructures and modulated structures present unique challenges in diffraction analysis.
- Traditional methods often struggle with pseudosymmetry and complex structural variations.
Purpose of the Study:
- To demonstrate the utility of the band-flipping algorithm for ab initio structure determination.
- To apply the method to difference electron density reconstructions of superstructures.
- To showcase its versatility in solving various complex crystallographic problems.
Main Methods:
- Utilizing the band-flipping variant of the charge-flipping algorithm.
- Reconstructing difference electron densities from diffraction data.
- Applying the method to periodic crystals, quasicrystals, and modulated structures.
Main Results:
- Successful ab initio reconstruction of scattering densities, including positive and negative values.
- Application to difference electron density of superstructures without subcell reflection data.
- Demonstrated solutions for superstructures, quasicrystals, incommensurately modulated structures, and twinned crystals.
Conclusions:
- The band-flipping algorithm is a powerful tool for ab initio structure solution.
- It effectively addresses pseudosymmetry issues common in superstructure analysis.
- The method offers a versatile approach for complex crystallographic problems.
Related Concept Videos
01:21Energy Associated With a Charge Distribution
The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
01:24Electrochemical Systems
Electrochemical systems provide a fascinating insight into the dynamic interplay of charged species within various phases. One notable example is the interaction between a membrane permeable to K⁺ ions but not to Cl⁻ ions, separating an aqueous KCl solution from pure water. As K⁺ ions diffuse through the membrane, they generate net charges on each phase, leading to a potential difference between them.Similarly, when a piece of Zn is immersed in an aqueous ZnSO₄ solution, the Zn metal, composed...
01:17Continuous Charge Distributions
Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
The electric charge can also be subjected to an analogical...
01:30The Electrical Double Layer
In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...
01:29Potential Due to a Polarized Object
A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
01:30Electric Field of Two Equal and Opposite Charges
Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero.
A separation of the positive and negative charges can lead to a weak, remnant effect of the positive and negative charges. The expectation is that the more the distance between the positive and...
A separation of the positive and negative charges can lead to a weak, remnant effect of the positive and negative charges. The expectation is that the more the distance between the positive and...