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Related Concept Videos

The Phase Rule01:20

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
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A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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A novel iterative solution to the phase problem.

Jianglin Feng1

  • 1Structure Solutions and Scientific Computing Inc., Crozet, Virginia 22932, USA. jf@sxmatrix.com

Acta Crystallographica. Section A, Foundations of Crystallography
|February 18, 2012
PubMed
Summary
This summary is machine-generated.

A novel Fourier cycling phasing method, based on global minimization, offers superior performance for crystal structure determination. This advanced technique bypasses the need for preliminary data or critical parameters, improving phase accuracy.

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Area of Science:

  • Crystallography
  • Materials Science
  • Computational Chemistry

Background:

  • Accurate phase determination is crucial for solving crystal structures.
  • Traditional Fourier cycling methods often require preliminary information or critical parameters, limiting their applicability and performance.
  • Existing methods can be sensitive to initial phase assignments, impacting the reliability of structure solution.

Purpose of the Study:

  • To introduce a new Fourier cycling phasing method utilizing global minimization.
  • To develop a method that is independent of preliminary crystallographic information.
  • To enhance the robustness and accuracy of phase determination in X-ray crystallography.

Main Methods:

  • The proposed method employs a mixed Fourier coefficient in reciprocal space: (2E(o)(2) - E(c)(2))E(c).
  • A peak-picking procedure is integrated to modify the Fourier map in direct space.
  • The method initiates phasing with randomly assigned or zero-valued initial phases, requiring no prior knowledge.

Main Results:

  • The new Fourier cycling method demonstrates significantly improved performance compared to conventional techniques.
  • It achieves reliable phase determination without reliance on preliminary data or critical parameters.
  • The method shows robustness, performing well even with arbitrary initial phase assignments.

Conclusions:

  • The proposed global minimization-based Fourier cycling method represents a significant advancement in crystallographic phase determination.
  • Its independence from preliminary information and critical parameters makes it a versatile and powerful tool.
  • This method offers a more reliable and efficient approach to solving crystal structures.