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Related Concept Videos

Structures of Solids02:22

Structures of Solids

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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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X-ray Crystallography02:18

X-ray Crystallography

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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
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Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
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Crystal Growth: Principles of Crystallization01:25

Crystal Growth: Principles of Crystallization

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Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
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Recrystallization: Solid–Solution Equilibria01:10

Recrystallization: Solid–Solution Equilibria

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Recrystallization is a purification technique used to separate impurities from solid compounds. In this technique, no chemical reactions occur. Instead, it exploits physical properties only, specifically, the solubility differences between the desired compound and impurities, either at a single temperature or at different temperatures, and under other selected conditions. The solid-solution equilibrium (solubility equilibrium) of each component in the solution represents a binary phase...
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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.
Types of Unit Cells
Imagine taking a large number of identical...
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Metallic Solids02:37

Metallic Solids

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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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A Deterministic Method to Construct a Common Supercell Between Two Similar Crystalline Surfaces.

Weon-Gyu Lee1,2, Jung-Hoon Lee1

  • 1Computational Science Research Center, Korean Institute of Science and Technology (KIST), Seoul, 02792, South Korea.

Small Methods
|August 28, 2024
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Summary
This summary is machine-generated.

A new deterministic algorithm efficiently constructs common supercells for crystalline surfaces, enabling rapid design of 2D heterostructures and discovery of novel moiré patterns with potential stability.

Keywords:
common supercellcomplex planeeigenvector–eigenvalue relationheterostructuremoiré pattern

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Crystallography

Background:

  • Constructing common supercells for similar crystalline surfaces is crucial for designing 2D heterostructures.
  • Conventional methods often involve computationally expensive brute-force approaches, limiting efficiency.

Purpose of the Study:

  • To develop a deterministic algorithm for efficiently constructing common supercells between two similar crystalline surfaces.
  • To accelerate the design and discovery of novel 2D heterostructures and their associated moiré patterns.

Main Methods:

  • Representing 2D lattices as complex vectors in the complex plane.
  • Defining the relationship between surfaces as an eigenvector-eigenvalue problem.
  • Directly determining the transformation matrix from lattice parameters and rotation angles with O(log Nmax) time complexity.

Main Results:

  • A deterministic algorithm was developed and implemented in Python, significantly outperforming brute-force methods.
  • The algorithm successfully generated experimental 2D heterostructures and their moiré patterns.
  • New, potentially stable moiré patterns were discovered and predicted using density functional theory (DFT) calculations.

Conclusions:

  • The proposed algorithm offers a computationally efficient tool for constructing common supercells.
  • This method facilitates the design of new 2D heterostructures with unique properties.
  • The approach is expected to be widely applicable in materials design and discovery.