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Lecture 6 - Multicomponent High-Entropy Cantor Alloys

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  • Speaker: Prof. Brian Cantor - Department of Materials

Human history is deeply intertwined with the discovery and development of new materials.

All materials are alloys.

There are countless materials.

Multicomponent alloys are essential to our future well-being and sustainability.

Human Development and New Materials

  • Stone Age: Flint tools
  • Agricultural Revolution: Clay bricks and pots
  • Bronze Age: Cu-Sn alloys
  • Iron age: Fe-C alloys
  • Industrial Revolution: Steels
  • Information Revolution: Silicon chips

Alloying Stratrgies

  • Conventional alloying strategy: One major component for main properties and small-scale alloying additions for secondary properties.
  • Multicomponent alloying strategy: A large number of components in equal or near-equal proportions.

Multicomponent Solution Thermodynamics

The structure of a material depends on the free energy of mixing the different components GG, which itself depends on the chemical interactions HH and the entropy SS:

G=∑(xiμi)+ΔGmixG = \sum (x_{i}\mu_{i}) + \Delta G_{\text{mix}}
ΔGmix=ΔHmix−TΔSmix\Delta G_{\text{mix}} = \Delta H_{\text{mix}} - T \Delta S_{\text{mix}}

Multicomponent Meterial Counting

Consider a system with CC components, where each component can vary in composition.

Let different materials be distinct if they differ by x%x\%, i.e., there are n=100xn = \frac{100}{x} composition values for each component.

The total number of distinct alloys or materials NN is given by the law of combinations with repetition:

N=(C+n−1n)=(C+n−1)!(C−1)!n!N = \binom{C + n - 1}{n} = \frac{(C + n - 1)!}{(C - 1)! n!}

Conservatively, let C=60C = 60 and x=0.1%x = 0.1\%, so that:

N=1059!59!⋅1000!≈10100N = \frac{1059!}{59! \cdot 1000!} \approx 10^{100}

For comparison, there are approximately 106610^{66} atoms in the galaxy, 108010^{80} atoms in the observable universe, and the size of the universe is roughly 1034nm10^{34} \text{nm}.

The number of known materials is approximately 101210^{12}, a tiny fraction of the total possible materials.

There are nearly 20 trillion local clusters in a 5-component material and 600 trillion in a 6-component material.

Key Issues of Nanoscale Multicomponent Sturcture

  • Disorder and entropy
  • Heat of mixing
  • Nanostructure
  • Short range order
  • Lattice strain
  • Vacancies and diffusion
  • Dislocations and slip
  • Twinning and fracture
  • Radiation damage
  • Recycling

Properties and Uses of Multicomponent High-Entropy Alloys

  • Cryogenic and high temperature strength
  • Corrosion and radiation damage resistance
  • Tunable functional properties
  • Recycling and re-use

Conclusions

Human history is deeply intertwined with the discovery and development of new materials.

All materials are alloys.

There are countless materials.

There are countless new materials waiting to be discovered.

Generic alloys are essential for efficient recycling and sustainability.