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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Ladder diagrams are useful for evaluating equilibria involving metal-ligand complexes. The vertical scale of the ladder diagram represents the concentration of unreacted or free ligand, pL. The horizontal lines on the scale depict the log of stepwise formation constants for metal-ligand complexes and indicate the dominant species in all the regions.
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Wood's structural properties derive from fibers aligned along the tree's length, contributing significantly to its mechanical strength. Wood exhibits up to twenty times greater tensile strength along these fibers compared to across them, and generally shows better performance under compression than tension. The length of fibers varies, with hardwoods having fibers around one twenty-fifth inch long and softwoods ranging from one-eighth to one-third inch.
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Data-Driven Bi-Directional Lattice Property Customization and Optimization.

Fuyuan Liu1,2, Huizhong Wu1,2, Xiaoteng Wu1,2

  • 1School of Advanced Technology, Xi'an Jiaotong-Liverpool University, Suzhou 215123, China.

Materials (Basel, Switzerland)
|November 27, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a data-driven generative method for lattice material design. It uses machine learning to accurately predict and optimize material properties, achieving significant performance improvements.

Keywords:
data-driven lattice explorationgenerative designlattice customizationmachine learningparametric lattice design

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Area of Science:

  • Materials Science
  • Computational Engineering
  • Machine Learning Applications

Background:

  • Customizing and optimizing lattice materials presents significant design challenges.
  • Existing methods often lack the flexibility and accuracy needed for specific performance requirements.

Purpose of the Study:

  • To propose a data-driven generative method for customizing and optimizing lattice materials.
  • To develop a machine learning framework for predicting elastic modulus and optimizing mechanical performance.

Main Methods:

  • Utilized subdivision modeling for parametric description of lattice structures.
  • Employed the homogenization method to analyze elastic moduli and generate a dataset.
  • Developed a two-tiered machine learning (ML) framework for forward design (elastic modulus prediction).

Main Results:

  • The two-tiered ML model achieved less than 10% error in elastic modulus prediction compared to finite element analysis.
  • Optimization strategies resulted in up to a 25% improvement in mechanical performance under relative density constraints.
  • Demonstrated practical value through case studies in customization and optimization.

Conclusions:

  • The proposed data-driven generative method offers a flexible and accurate approach to tailoring lattice material properties.
  • Combining generative design, ML, and genetic algorithms enhances material performance and navigates complex design spaces effectively.