Combinatorial Explosion: The Challenge of Infinite Possibilities#
Consider the task of discovering a new material by testing every possible combination of elements in the periodic table. With 118 elements, the number of possible combinations is astronomical - greater than the number of atoms in the observable universe. This represents the fundamental challenge we face in materials discovery: combinatorial explosion.
The Scale of the Problem#
To put this in perspective:
Binary compounds (2 elements): ~7,000 possibilities
Ternary compounds (3 elements): ~250,000 possibilities
Quaternary compounds (4 elements): ~7 million possibilities
And that’s merely counting element combinations - each can form multiple compounds with different:
Stoichiometric ratios (NaCl vs Na₂Cl vs NaCl₂)
Crystal structures (diamond vs graphite for carbon)
Oxidation states (Fe²⁺ vs Fe³⁺)
The total number of possible materials is effectively infinite, making experimental trial-and-error impractical.
Why This Matters#
This combinatorial explosion means:
We can’t test everything: Even with high-throughput methods, we can only explore a small fraction
We need smart filters: Chemical rules to eliminate impossible combinations
We need efficient algorithms: Computational methods to navigate this vast space
We might miss discoveries: The next revolutionary material could be hidden in unexplored regions
What You’ll Learn#
In this section, we’ll explore:
How to calculate and visualise the scale of chemical space
Why some element combinations are more promising than others
How SMACT helps us navigate this complexity efficiently
Strategies for systematic exploration of materials space
The Power of Informatics#
The encouraging news is that while the space is vast, it isn’t random. Chemical principles, data from known materials, and machine learning can guide us to the most promising regions. This is where materials informatics becomes valuable - transforming an overwhelming search into a manageable problem.
Let’s begin!