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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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Coordination Number and Geometry02:57

Coordination Number and Geometry

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For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
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The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

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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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Valence Bond Theory02:42

Valence Bond Theory

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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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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.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability....
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Coordination Compounds and Nomenclature02:54

Coordination Compounds and Nomenclature

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In most main group element compounds, the valence electrons of the isolated atoms combine to form chemical bonds that satisfy the octet rule. For instance, the four valence electrons of carbon overlap with electrons from four hydrogen atoms to form CH4. The one valence electron leaves sodium and adds to the seven valence electrons of chlorine to form the ionic formula unit NaCl (Figure 1a). Transition metals do not normally bond in this fashion. They primarily form coordinate covalent bonds, a...
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Related Experiment Video

Updated: Mar 18, 2026

Structure and Coordination Determination of Peptide-metal Complexes Using 1D and 2D 1H NMR
14:44

Structure and Coordination Determination of Peptide-metal Complexes Using 1D and 2D 1H NMR

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Solid-angle based nearest-neighbor algorithm adapted for systems with low coordination number.

A Ulugöl1, F Smallenburg2, L Filion1

  • 1Soft Condensed Matter and Biophysics Group, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, Utrecht 3584 CC, Netherlands.

The Journal of Chemical Physics
|March 16, 2026
PubMed
Summary
This summary is machine-generated.

A new geometric modification improves the solid-angle-based nearest-neighbor (SANN) algorithm for analyzing local structures in materials. This enhancement accurately identifies neighbors in low-coordination systems without adding complexity.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Materials Science

Background:

  • Nearest-neighbor identification is crucial for understanding local structure in condensed matter.
  • The solid-angle-based nearest-neighbor (SANN) algorithm is a popular, efficient, parameter-free method.
  • Original SANN struggles with overcounting neighbors in low-coordination number systems.

Purpose of the Study:

  • To address the overcounting issue in the SANN algorithm for low-coordination systems.
  • To introduce a geometric modification that enhances SANN accuracy without new parameters.
  • To provide a robust and computationally efficient neighbor identification method.

Main Methods:

  • Proposed a geometric modification: the "inscribed circle modification" to the SANN algorithm.
  • Benchmarked the modified SANN against Voronoi and original SANN algorithms.
  • Tested the algorithms in crystalline, quasicrystalline, and heterogeneous systems in 2D and 3D.

Main Results:

  • The inscribed circle modification successfully resolves systematic overcounting in low-coordination lattices.
  • The modified SANN algorithm demonstrates robust neighbor identification across diverse system types.
  • Maintained computational efficiency and parameter-free nature of the original SANN algorithm.

Conclusions:

  • The inscribed circle modification offers a significant improvement to SANN for low-coordination systems.
  • This enhanced SANN provides accurate and efficient nearest-neighbor identification in various material structures.
  • The method is a valuable tool for local structure analysis in condensed matter research.