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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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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 and...

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A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...

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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 requirements are not imposed on the...

Law of Rational Indices

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The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.To illustrate, consider a crystal with...

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The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...

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Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source

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On the allowed values for the triclinic unit-cell angles.

James Foadi¹, Gwyndaf Evans

¹MPL, Imperial College, London SW7 2AZ, England. j.foadi@imperial.ac.uk

Acta Crystallographica. Section A, Foundations of Crystallography

|December 22, 2010

Summary

This summary is machine-generated.

The triclinic crystal system has three angles that are not independent. This paper calculates and presents the allowed ranges for these angles, which are not typically specified in crystallography resources.

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Area of Science:

Crystallography
Solid-state chemistry
Materials science

Background:

The triclinic system is the least symmetric crystal system.
Unit cell angles in crystallography are typically presented without explicit constraints.

Purpose of the Study:

To investigate the interdependence of the three unit cell angles in the triclinic system.
To determine and present the mathematically allowed range of values for these angles.

Main Methods:

Mathematical derivation of angle constraints.
Analysis of unit cell geometry.

Main Results:

The three unit cell angles (alpha, beta, gamma) in the triclinic system are not independent.
A specific, limited range of values is mathematically permissible for these angles.

Conclusions:

Crystallographic databases and literature should include the derived constraints for triclinic unit cell angles.
Understanding these constraints is crucial for accurate crystal structure analysis and modeling.