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Related Concept Videos

Crystal Growth: Principles of Crystallization01:25

Crystal Growth: Principles of Crystallization

Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent – the...
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Recrystallization: Solid–Solution Equilibria01:10

Recrystallization: Solid–Solution Equilibria

Recrystallization is a purification technique used to separate impurities from solid compounds. In this technique, no chemical reactions occur. Instead, it exploits physical properties only, specifically, the solubility differences between the desired compound and impurities, either at a single temperature or at different temperatures, and under other selected conditions. The solid-solution equilibrium (solubility equilibrium) of each component in the solution represents a binary phase...
Imperfections in Crystal Structure: Point, Line and Plane Defects01:25

Imperfections in Crystal Structure: Point, Line and Plane Defects

A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...

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Related Experiment Video

Updated: May 7, 2026

Optimization of Crystal Growth for Neutron Macromolecular Crystallography
12:29

Optimization of Crystal Growth for Neutron Macromolecular Crystallography

Published on: March 13, 2021

Crystal growth inside an octant.

Jason Olejarz1, P L Krapivsky

  • 1Center for Polymer Studies, and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
PubMed
Summary
This summary is machine-generated.

Crystal growth in an infinite octant follows a deterministic shape over time. Researchers developed a hyperbolic partial differential equation, validated by simulations, to predict this crystal growth pattern.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Mathematical Physics

Background:

  • Crystal growth is a fundamental process in materials science.
  • Understanding the interface dynamics of growing crystals is crucial for predicting material properties.
  • Previous studies have explored crystal growth in simpler geometries.

Purpose of the Study:

  • To investigate crystal growth within an infinite octant on a cubic lattice.
  • To determine the long-time deterministic behavior of the crystal interface.
  • To develop and validate a mathematical model for predicting the evolution of the crystal's limiting shape.

Main Methods:

  • Simulations of crystal growth via deposition of elementary cubes into inner corners.
  • Rescaling the interface by characteristic size to observe long-time behavior.
  • Derivation of a hyperbolic partial differential equation based on 2D corner growth results.
  • Interpretation of the PDE as a Hamilton-Jacobi equation for analytical solutions.

Main Results:

  • The crystal interface becomes progressively more deterministic in the long-time limit.
  • A hyperbolic partial differential equation accurately predicts the limiting shape of the crystal.
  • Simulations show excellent agreement with the analytical predictions derived from the model.
  • Analysis of subleading corrections to crystal volume, variance growth, and corner evolution.
  • Generalization of the model to arbitrary spatial dimensions.

Conclusions:

  • The study successfully models and predicts the deterministic long-time behavior of crystal growth in an octant.
  • The developed Hamilton-Jacobi equation provides an effective analytical tool for understanding crystal interface evolution.
  • The findings offer a generalized framework applicable to crystal growth in various dimensions.