Projects

Current Projects

The Equations of Materials 2nd edition
I have completed an updated version of my 1st year undergraduate text book with 7 new chapters . It is due to be published later in 2026 or early in 2027.
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The front cover of the 1st edition of The Equations of Materials, featuring a wheel representation of the irrational number pi.
Complexity in Multicomponent High-Entropy Materials
I am currently writing a research paper on this topic, due to be published later in 2026 or early in 2027
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Schematic 10-component 2-D high entropy alloy. There are 20 trillion different local atomic nanostructures in an fcc high-entropy alloy with 5 components, and 10 million trillion with 10 components.
The Equations of Materials
I am developing a lecture series based on my book, covering some fundamental equations in materials science and biographies of the scientists who discovered them.

                   

                    Bravais Lattices: Crystals

                    Bernal Packing: Liquids and Glasses

                    The Hume-Rothery Rules: Alloys

                    Bragg’s Law: Diffraction

                    The Abbe Criterion: Microscopy        

                    Pauli’s Exclusion Principle: Spectroscopy

                    The Gibbs Phase Rule: Phases

                    The Boltzmann Equation: Thermodynamics

                    The Arrhenius Equation: Reactions

                    Ellingham Diagrams: Extraction

                    The Gibbs-Thomson Equation: Surfaces

                    Fick’s Laws: Diffusion

                    The Scheil Equation: Solidification

                    The Avrami Equation: Phase Transformations

                    Hooke’s Law: Elasticity

                    The Burgers Vector: Plasticity

                    Griffith’s Equation: Fracture

                    The Fermi Level: Electrical Properties

                    The Curie Point: Magnetic Properties

                    Snell’s Law: Optical Properties

Thermodynamics of Amorphous Alloys
I am currently writing a research paper on this topic, due to be published later in 2026 or early in 2027
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The Bernal holes or interstices in amorphous alloys. Thermodynamic properties of amorphous alloys can be explained based on the number and structure of their interstices.
Robert Cahn
I am writing a short biography of Robert Cahn for the Royal Society's Biographical Memoirs of Fellows, due to be published in 2027.
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Professor Robert Wolfgang Cahn. (Nature)
Heterogeneous Nucleation of Solidification
I am currently writing a review paper on this topic, due to be published in 2027.
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TEM pictures showing: (a) adsorbed Al3P layer on Al nucleating solidification of Si; (b) adsorbed TiAl3 layer on TiB2 nucleating solidification of Al. (Cantor Proc Roy Soc 2002)

Recent Projects

The Fundamentals of Multicomponent High-Entropy Materials.
In 2024 Oxford University Press published my book summarising our understanding of multicomponent and high-entropy materials after nearly two decades of intensive investigation by thousands of scientists worldwide.
bookcover
The front cover of Fundamentals of Multicomponent High-Entropy Materials, featuring a schematic equiaxed grain structure.
UK International Centre of Excellence in Strategic Resource Management (UK ICE-SRM)
In 2024/5 I helped set up a UN and DEFRA supported research centre to develop a sustainable economy based on circular materials using repair, recycling and re-use.
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Sustainable use of materials requires a circular economy based on repair, recycling and re-use.
The Equations of Materials
I have delivered the 1st part of a lecture series based on my book, covering some fundamental equations in materials science and biographies of the scientists who discovered them.

 

                   

                    Bravais Lattices: Crystals

                    Bragg’s Law: Diffraction

                    The Boltzmann Equation: Thermodynamics

                    The Arrhenius Equation: Reactions

                    Hooke’s Law: Elasticity

                    Griffith’s Equation: Fracture

                    The Fermi Level: Electrical Properties

20-component high-entropy alloy
I have recently published a paper in collaboration with Changming Fang modelling the chemistry and electronic and atomic structure of a 20-component alloy AlBCdGaGeHfInLaMoPbSbScSi
SnTaTiVWZn. (Fang & Cantor HEAM 2026)
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Snapshots of amorphous 20-component alloy atomic structure at (a) 3000K, (b) 1000K and (c) 0K
Thermodynamics of Multicomponent Materials
I have recently published a paper in the Journal of Materials Science on the fundamental thermodynamics of multicomponent high-entropy materials, which was awarded the Cahn Prize for best paper in 2025.
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Ideal entropy of mixing and ideal free energy of mixing at 1000K for an equiatomic fcc or bcc solid solution versus the number of components.
Liaoning Academy of Materials (LAM) Fellowship Lecture
At the award of my LAM Fellowship in 2025, my lecture on multicomponent high-entropy Cantor alloys was live-streamed in China and was watched by more than 10,000 Chinese scientists.
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Ashby map of strength versus toughness for different materials.
Nanostructure in Multicomponent Materials
I have recently published a paper in High Entropy Alloys & Materials on the enormous number of different local nanostructures (many trillions) in multicomponent single-phase high-entropy solid-solution materials, and the effect this has on their stability and their mechanical, electrical and other properties.
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Schematic 10-component 2-D high entropy alloy. There are 20 trillion different local atomic nanostructures in an fcc high-entropy alloy with 5 components, and 10 million trillion with 10 components.
Faraday Discussion
I recently recently received a Spiers Medal from the Royal Society of Chemistry and gave an associated Spiers Lecture assessing the overall development of the field of multicomponent high-entropy materials. This was the keynote lecture leading off a 3-day Faraday Discussion on High-Entropy Alloy Nanostructures. The proceedings are published in the Faraday Discussions journal of the Royal Society of Chemistry.
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Faraday Discussions journal of the Royal Society of Chemistry
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