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Related Concept Videos

Crystal Growth: Principles of Crystallization01:25

Crystal Growth: Principles of Crystallization

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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...
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Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

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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...
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Structures of Solids02:22

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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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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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
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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Related Experiment Video

Updated: Jan 3, 2026

Theoretical Calculation and Experimental Verification for Dislocation Reduction in Germanium Epitaxial Layers with Semicylindrical Voids on Silicon
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The dualism between adatom- and vacancy-based single crystal growth models.

Marcel J Rost1, Leon Jacobse2,3, Marc T M Koper4

  • 1Huygens-Kamerlingh Onnes Laboratory, Leiden University, Niels Bohrweg 2, 2333 CA, Leiden, The Netherlands. rost@physics.leidenuniv.nl.

Nature Communications
|November 22, 2019
PubMed
Summary

This study reveals a dualism in crystal growth, showing that vacancy-based growth mirrors standard atom-based growth modes, including nano-scale mound formation. Experimental results confirm this theoretical prediction for vacancy and adatom mound growth.

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Area of Science:

  • Surface science and materials science, focusing on crystal growth dynamics.

Background:

  • Established growth morphologies in homoepitaxial crystal growth include step-flow, layer-by-layer, mound formation, and random growth.
  • Mound formation is crucial for nano-scale surface patterning, but similar phenomena occur in ion bombardment and etching.

Purpose of the Study:

  • To explore the dualism between adatom and vacancy growth modes in crystal surface evolution.
  • To theoretically and experimentally verify the existence of vacancy-based growth morphologies analogous to adatom-based ones.

Main Methods:

  • Theoretical derivation of equations for mound formation considering both adatom and vacancy growth.
  • Analytical solution for the growth shape evolution during simultaneous adatom and vacancy deposition.
  • Experimental verification using a system where both adatom and vacancy mound formation are active.

Main Results:

  • Demonstrated the existence of vacancy growth modes as the dual counterpart to standard adatom growth modes.
  • Derived theoretical equations for mound formation, showing inverse similarity for vacancy growth.
  • Achieved excellent agreement between the theoretically predicted mound shape and experimental observations.

Conclusions:

  • Confirms the theoretical prediction of dualism between adatom and vacancy growth mechanisms.
  • Highlights the applicability of particle/anti-particle formalisms to understand crystal growth.
  • Provides a unified framework for understanding nano-scale surface patterning through mound formation.