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Related Concept Videos

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

12.6K
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...
12.6K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

26.8K
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:
26.8K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.5K
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.
1.5K
Chemical Equations03:10

Chemical Equations

82.2K
Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right)...
82.2K
The Nernst Equation02:59

The Nernst Equation

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Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
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Thermochemical Equations02:55

Thermochemical Equations

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For a chemical reaction (the system) carried out at constant pressure – with the only work done caused by expansion or contraction – the enthalpy of reaction (also called the heat of reaction, ΔHrxn) is equal to the heat exchanged with the surroundings (qp).
36.1K

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Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
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Lattice Wigner equation.

S Solórzano1, M Mendoza1, S Succi2

  • 1ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland.

Physical Review. E
|February 17, 2018
PubMed
Summary
This summary is machine-generated.

A new numerical scheme solves the Wigner equation using momentum space discretization. This method accurately recovers Wigner function moments and is validated for quantum systems, enabling transport property studies.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Numerical analysis

Background:

  • The Wigner equation describes quantum systems.
  • Solving the Wigner equation is computationally challenging.
  • Accurate numerical methods are needed for quantum transport studies.

Purpose of the Study:

  • To develop a novel numerical scheme for solving the Wigner equation.
  • To ensure accurate recovery of Wigner function moments.
  • To enable the study of quantum transport in open systems.

Main Methods:

  • Lattice discretization of momentum space for the Wigner equation.
  • Inclusion of a collision operator for numerical stability.
  • Validation using quantum harmonic and anharmonic potentials.

Main Results:

  • Exact recovery of Wigner function moments up to a desired order.
  • Accurate numerical solutions for quantum potentials.
  • Successful application to 1D and 2D open quantum systems.

Conclusions:

  • The lattice Wigner scheme is accurate and numerically stable.
  • The method is effective for studying quantum transport properties.
  • The scheme is computationally viable for 3D open quantum systems.