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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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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 pressure-composition phase diagram explicitly describes the behavior of an ideal solution of two volatile liquids under varying pressures and compositions. A pressure-composition diagram has two main curves. The bubble point curve represents the plot of pressure versus liquid mole fraction. It indicates the pressure at which the first bubble of vapor forms from the liquid phase as the system pressure decreases.The dew point curve is the pressure versus vapor mole fraction. It indicates the...
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Phase Diagrams of Ternary Systems01:28

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Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
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The Seven Crystal Systems: Overview01:24

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Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...
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Crystallographic Point Groups01:29

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Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane...
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Novel Techniques for Observing Structural Dynamics of Photoresponsive Liquid Crystals
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Triply periodic smectic liquid crystals.

Christian D Santangelo1, Randall D Kamien

  • 1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
Summary
This summary is machine-generated.

Twist-grain-boundary phases in liquid crystals exhibit unique structures. Researchers analytically computed the energy of these phases, revealing new defects and privileged angles for specific configurations.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Liquid Crystal Physics

Background:

  • Twist-grain-boundary (TGB) phases in smectic liquid crystals are geometrically analogous to Abrikosov flux lattices in superconductors.
  • Nonlinear elasticity significantly influences the energetics of TGB phases at large twist angles.

Purpose of the Study:

  • To analytically construct the height function of a pi2 twist-grain-boundary phase in smectic-A liquid crystals.
  • To compute the energy of this structure utilizing elliptic functions.
  • To investigate the topological structure of grain boundaries at various angles.

Main Methods:

  • Analytical construction of the height function for a pi2 TGB phase using elliptic functions.
  • Energetic calculations based on the constructed height function.
  • Identification and analysis of topological defects along the pitch axis.

Main Results:

  • Successfully constructed the height function for the pi2 TGB phase (Schnerk's first surface).
  • Analytically computed the energy of the pi2 TGB phase.
  • Identified novel defects along the pitch axis.
  • Determined the existence of privileged angles for TGB structures.

Conclusions:

  • The pi2 and pi3 twist-grain-boundary structures are particularly simple.
  • The study provides insights into the topological requirements for grain boundaries at different twist angles.