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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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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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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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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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Two-dimensional Janus-like particles on a triangular lattice.

A Patrykiejew1, W Rżysko1

  • 1Department of Theoretical Chemistry, Faculty of Chemistry, MCS University, 20031 Lublin, Poland. andrzej.patrykiejew@poczta.umcs.lublin.pl.

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|July 4, 2020
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Summary
This summary is machine-generated.

This study explores Janus-like particle behavior on a triangular lattice. Different interaction models reveal distinct self-assembly into structures like stripped, zigzag, and kagome lattices, influencing phase transitions.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Materials Science

Background:

  • Understanding particle self-assembly is crucial for designing novel materials.
  • Janus-like particles, with distinct faces, exhibit complex interaction behaviors.
  • Lattice models provide simplified yet powerful frameworks for studying phase transitions.

Purpose of the Study:

  • To investigate the phase behavior of two-dimensional Janus-like particles on a triangular lattice.
  • To compare the effects of orientation-dependent versus orientation-independent interactions on self-assembly.
  • To map the phase diagrams and identify distinct ordered structures.

Main Methods:

  • Monte Carlo simulations in a grand canonical ensemble.
  • Modeling Janus-like particles with six possible orientations.
  • Analyzing two interaction models: orientation-dependent and orientation-independent attractive forces.

Main Results:

  • The orientation-dependent model yields diverse stripped structures (zigzag, lamellar) based on density and temperature, with varying phase transition orders.
  • The orientation-independent model shows a first-order transition to a kagome lattice (density 6/7) followed by a glass-like phase.
  • Both models exhibit qualitatively different phase behaviors and phase diagrams.

Conclusions:

  • The interaction model significantly dictates the self-assembly and phase behavior of Janus-like particles.
  • Complex structures like zigzag and kagome lattices emerge from simple particle interactions.
  • The study provides insights into controlling self-assembly through interaction design.