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State Space Representation01:27

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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The temperature-composition phase diagram of two solids, A and B, which are immiscible in the solid phase but form miscible liquids, shows that when the temperature is low, these two exist as separate, pure solids (A and B). As the temperature increases, they transition into a single-phase liquid solution where A and B coexist. Moving from point a1 to a2 in the phase diagram, the composition changes such that solid B begins to separate from the solution, enriching the remaining liquid with A.
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Spatial Separation of Molecular Conformers and Clusters
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Direct Space Structure Solution Applications.

Maryjane Tremayne1

  • 1School of Chemistry, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK.

Journal of Research of the National Institute of Standards and Technology
|July 2, 2016
PubMed
Summary
This summary is machine-generated.

Crystal structures of four compounds were solved using X-ray powder diffraction and Monte Carlo methods. Complex hydrogen bonding and C-H⋯π interactions dictate the resulting molecular architectures and frameworks.

Keywords:
Monte Carlochlorothalonilcocrystalscrystal engineeringdirect-space methodshydrogen bondingnicotinic acidpolymorphismpowder diffractionpreferred orientationstructure solutionsulfonamide

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Area of Science:

  • Crystallography and Materials Science
  • Solid-state chemistry
  • Powder Diffraction Analysis

Background:

  • Determining crystal structures from powder diffraction data presents challenges, especially with complex molecules and preferred orientation effects.
  • Understanding molecular interactions, such as hydrogen bonding and C-H⋯π interactions, is crucial for predicting and controlling solid-state structures.
  • Direct space methods offer an alternative to traditional reciprocal space approaches for structure solution from diffraction data.

Purpose of the Study:

  • To solve and refine the crystal structures of 2,4,6-triisopropylbenzenesulfonamide, a cocrystal of 1,2,3-trihydroxybenzene-hexamethylenetetramine, 5-bromonicotinic acid, and chlorothalonil form II.
  • To investigate the role of hydrogen bonding and other non-covalent interactions in the formation of diverse molecular architectures.
  • To assess the applicability of direct space methods, specifically Monte Carlo, for structure solution from challenging X-ray powder diffraction data.

Main Methods:

  • X-ray powder diffraction (XRPD) data collection.
  • Structure solution using a direct space approach with the Monte Carlo method.
  • Structure refinement using the Rietveld method, with special attention to minimizing preferred orientation effects.

Main Results:

  • Crystal structures were successfully determined for all four target compounds.
  • Detailed analysis revealed diverse hydrogen-bonding motifs (e.g., N-H⋯O, O-H⋯N) and C-H⋯π interactions leading to 2D sheets, 3D frameworks, and ribbons.
  • Structure solution for chlorothalonil form II was achieved by minimizing preferred orientation effects, yielding both disordered and ordered structural models.

Conclusions:

  • The Monte Carlo direct space method is effective for solving crystal structures from XRPD data, even in the presence of preferred orientation.
  • Non-covalent interactions play a significant role in dictating the packing and dimensionality of the determined crystal structures.
  • The study demonstrates a robust approach for tackling challenging structure determination problems in solid-state chemistry.