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Properties of Transition Metals

Properties of Transition Metals

Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.

Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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.

Bonding in Metals

Bonding in Metals

Metallic bonds are formed between two metal atoms. A simplified model to describe metallic bonding has been developed by Paul Drüde called the “Electron Sea Model”.

Phase Transitions

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...

Cooperative Allosteric Transitions

Cooperative Allosteric Transitions

Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...

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Related Experiment Video

Updated: Jan 23, 2026

Preparation of Liquid-exfoliated Transition Metal Dichalcogenide Nanosheets with Controlled Size and Thickness: A State of the Art Protocol

Preparation of Liquid-exfoliated Transition Metal Dichalcogenide Nanosheets with Controlled Size and Thickness: A State of the Art Protocol

Published on: December 20, 2016

Engineering Zero-Dimensional Quantum Confinement in Transition-Metal Dichalcogenide Heterostructures.

Christopher C Price¹, Nathan C Frey¹, Deep Jariwala^1,2

¹Department of Materials Science and Engineering , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States.

|June 27, 2019

Summary

Researchers engineered nanoscale transition-metal dichalcogenide (TMD) heterostructures to create localized quantum states. This breakthrough enables robust confinement of massive Dirac fermions in 2D materials for future quantum technologies.

Keywords:

Dirac fermions heterostructure multiscale modeling quantum dot transition-metal dichalcogenides two-dimensional materials

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Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

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Last Updated: Jan 23, 2026

Preparation of Liquid-exfoliated Transition Metal Dichalcogenide Nanosheets with Controlled Size and Thickness: A State of the Art Protocol

Preparation of Liquid-exfoliated Transition Metal Dichalcogenide Nanosheets with Controlled Size and Thickness: A State of the Art Protocol

Published on: December 20, 2016

Preparation of Large-area Vertical 2D Crystal Hetero-structures Through the Sulfurization of Transition Metal Films for Device Fabrication

Preparation of Large-area Vertical 2D Crystal Hetero-structures Through the Sulfurization of Transition Metal Films for Device Fabrication

Published on: November 28, 2017

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Published on: June 3, 2015

Area of Science:

Materials Science
Condensed Matter Physics
Quantum Information Science

Background:

Confining Dirac fermions in 2D materials like graphene is crucial for quantum applications but remains challenging.
Existing quantum dot technologies face limitations in solid-state device integration due to surface chemistry and positioning issues.

Purpose of the Study:

To design and optimize nanoscale transition-metal dichalcogenide (TMD) heterostructures for hosting massive Dirac fermion bound states.
To develop a multiscale approach for translating electronic structure from first-principles to continuum models for arbitrary 2D quantum dot geometries.

Main Methods:

Integrated multiscale modeling approach combining first-principles calculations and continuum models.
Simulation of nanoscale monolayer TMD heterostructures, focusing on MoS2 quantum dots in a WS2 matrix.
Optimization of quantum dot geometries and sizes for maximal isolation of bound states.

Main Results:

Demonstrated discrete bound states in triangular MoS2/WS2 quantum dots with side lengths up to 20 nm.
Identified key figures of merit for engineering maximally isolated bound states at room temperature.
Predicted optimal MoS2/WS2 (6.5 nm) and MoSe2/WSe2 (4.5 nm) triangular dots for Dirac fermion confinement.

Conclusions:

Nanoscale TMD heterostructures offer a viable platform for creating localized quantum states and confining massive Dirac fermions.
The developed design principles are applicable across the family of semiconducting TMDs, paving the way for novel quantum devices.
Optimized TMD heterostructures show promise for robust room-temperature quantum information processing and optoelectronics.