Deep divefrom Episode 1Batteries25 August 202615 min

Machine-designed hard carbon structures for sodium-ion batte

A deep dive into one paper: what was known before, what the researchers did, what the numbers say and what they don't.

The paper: Atomistic Structure Generation and Neural-Network Screening of Hard Carbons (arXiv)

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Transcript

The script the two AI voices read from. The times are worked out from the script, not heard, so a line can start a few seconds early or late.

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Cold open

Host 1Welcome to the Hastrup Review of Science — where artificial intelligence reads real science, so you don't have to pretend you understood the paper. One paper today. A group of physicists asked a machine to design thirteen thousand carbon structures, then used a neural network to find the ones that store the most sodium.

Host 2Mclean, Emery, Walton, Taylor and Hepplestone at the University of Exeter combined machine-learned interatomic potentials with automated structure generation to build the first large-scale atomistic library of hard carbons and screen them for sodium-ion battery performance. The paper is called Atomistic Structure Generation and Neural-Network Screening of Hard Carbons to Identify High-Capacity Sodium Storage.

Why sodium

Host 1Let us start with why anyone cares about sodium batteries in the first place.

Host 2Lithium-ion batteries power nearly everything rechargeable today, from phones to electric vehicles. But lithium is geographically concentrated. Most of the world's economically extractable supply comes from Australia, Chile, and China, and demand is projected to strain those reserves within decades. Sodium is roughly a thousand times more abundant in the Earth's crust and is available virtually everywhere.

Host 1So sodium-ion batteries are the backup plan.

Host 2More than a backup. For stationary grid storage, where weight and volume matter less than cost and supply security, sodium-ion batteries are potentially a better fit than lithium-ion. The electrochemistry is similar. Both are rocking-chair batteries where ions shuttle between an anode and a cathode during charge and discharge. But sodium ions are larger than lithium ions, and that size difference creates specific materials challenges.

The graphite problem

Host 1What goes wrong when you try to put sodium into the same materials that work for lithium?

Host 2Graphite is the standard lithium-ion anode. It stores lithium by intercalating it between flat, regularly stacked graphene layers. Lithium fits neatly into the interlayer space and forms stable ordered compounds. Sodium does not. The sodium ion is about 0.3 angstroms larger in radius, and the thermodynamics of sodium intercalation into graphite are unfavourable. It barely goes in, and what little enters tends to come back out at erratic voltages.

Host 1So you need a different anode material entirely.

Host 2The leading candidate is hard carbon. Not graphite, not diamond, but a disordered form of carbon produced by heating organic precursors — biomass, polymers, pitch — to temperatures between about 1000 and 1500 degrees Celsius.

What hard carbons look like

Host 1What makes hard carbon different from graphite structurally?

Host 2Graphite is highly ordered. Flat graphene sheets stacked in a regular repeating pattern. Hard carbon is the opposite. Short, randomly oriented graphene-like fragments, typically three to five layers each, separated by nanoscale voids. The structure includes a mix of sp2-bonded carbon, the same bonding as in graphite, and a smaller fraction of sp3-bonded carbon, the same bonding as in diamond, along with defects, dangling bonds, and closed pores ranging from sub-nanometre to a few nanometres across.

Host 1And sodium stores in those pores.

Host 2In the pores and at defect sites, yes. The voltage profile of a hard carbon anode shows two characteristic regions. A sloping region at higher voltages, attributed to sodium adsorption at defects, edges, and between disordered graphene layers. And a low-voltage plateau near zero volts, attributed to sodium filling the closed nanopores. The balance between those two regions depends entirely on the microstructure.

The modelling problem

Host 1Which is where the computational challenge comes in.

Host 2If you want to predict how much sodium a given hard carbon structure can store, you need an atomistic model of that structure. But hard carbons are amorphous. There is no repeating unit cell, no long-range order. A realistic simulation needs thousands of atoms to capture the relevant pore sizes and domain orientations. Then you need to model sodium insertion into that structure, which means exploring an enormous configurational space of possible sodium positions.

Host 1And density functional theory is too expensive at that scale.

Host 2At the required scale, yes. A full quantum-mechanical DFT calculation on a four-thousand-atom carbon structure with hundreds of inserted sodium atoms would be computationally prohibitive. You could manage a handful of structures. You could not screen thousands.

Machine-learned potentials

Host 1So how did this group solve the scale problem?

Host 2Two tools. The first is universal machine-learned interatomic potentials, specifically the MACE architecture. These are neural-network models trained on large databases of DFT calculations across most of the periodic table. They learn the mapping from atomic positions to energies and forces, and then predict those quantities at a fraction of the computational cost of a full DFT calculation.

Host 1How much cheaper?

Host 2Orders of magnitude. A structure relaxation that takes days with DFT can take seconds with a machine-learned potential. The accuracy is lower than a carefully converged DFT calculation, but for the structural screening this paper performs, the trade-off is productive.

The RAFFLE framework

Host 1And the second tool?

Host 2A structure generation framework called RAFFLE — Random Approach for Fabricating Locally Low-Energy structures. The conventional method for generating amorphous structures in simulation is melt-quench: you heat the system above its melting point and cool it rapidly. That can work, but the resulting structures depend heavily on the quench rate and often fail to reproduce the specific pore distributions observed in real hard carbons.

Host 1RAFFLE does something different.

Host 2It builds structures incrementally, placing atoms or small fragments in energetically favourable positions while maintaining control over target properties such as density and porosity. The combination of RAFFLE for structure generation and MACE for energy evaluation allowed the group to generate 13,096 distinct hard carbon models, each containing up to 4,378 atoms.

Validation

Host 1Thirteen thousand structures. How do they know these look like real hard carbons?

Host 2They validated against experiment. The generated structures reproduce experimentally measured densities, porosities, and the ratio of sp2 to sp3 bonded carbon. This is not a library of hypothetical structures. It is a library of structures that match the kinds of hard carbons people actually synthesise.

Host 1What range of properties does the library cover?

Host 2Carbon densities spanning roughly 1.0 to 2.0 grams per cubic centimetre. Porosities from essentially zero to highly porous. A range of graphene domain sizes and orientations. The library captures the structural diversity that arises from different precursors, different pyrolysis temperatures, and different processing conditions.

Sodium intercalation

Host 1Then they put sodium in.

Host 2For representative structures, yes. They performed explicit sodium intercalation calculations, progressively inserting sodium atoms into each carbon host and relaxing the structure at each step using the machine-learned potential. This produces a voltage curve: the voltage at which each successive increment of sodium is stored.

Host 1And they reproduced the experimental voltage profile.

Host 2The characteristic sloping region at higher voltages followed by a low-voltage plateau. That qualitative agreement is significant because it means the generated structures are not just matching static structural properties. They are reproducing electrochemical behaviour.

Host 1What determines capacity?

Host 2The strongest correlations they found were with carbon density and porosity. Lower-density carbons with more pore volume store more sodium. This is consistent with the pore-filling mechanism: more void space means more room for sodium atoms, particularly in the plateau region of the voltage curve.

A word from our sponsor

Host 1A question about frozen water.

Host 2The Hastrup Review of Science is brought to you by ice cube trays. Precision-moulded receptacles for the controlled solidification of water.

Host 1We have spent most of this episode discussing the storage of ions in carefully engineered nanoscale cavities. An ice cube tray operates on the same principle, at a somewhat larger scale and a somewhat lower level of scientific ambition.

Host 2A good ice cube tray releases cleanly, does not crack in the freezer, and does not require a machine-learned interatomic potential to operate.

Host 1Ice cube trays. Because your drink deserves structure. Our referral link is in the show notes.

The surrogate model

Host 1Back to the science. With thirteen thousand structures, even machine-learned potentials become expensive if you want full sodium intercalation on all of them. So they built a shortcut.

Host 2They trained a lightweight neural network to predict sodium storage capacity directly from structural features of the empty carbon host, without performing any intercalation calculation at all.

Host 1What features does it use as input?

Host 2Two types. First, frozen descriptors from the MACE potential itself — the internal representations the potential uses to characterise atomic environments, repurposed as structural fingerprints. Second, geometric void features: quantitative measures of pore size distribution, pore connectivity, and total void volume within each structure.

Host 1So the neural network learns: given this arrangement of carbon atoms and this pore geometry, how much sodium will fit.

Host 2Precisely. Trained on a subset of structures where full intercalation was computed, it can then screen the entire library of thirteen thousand structures in seconds.

High-capacity candidates

Host 1What did it find?

Host 2Candidates with predicted capacities exceeding 800 milliamp hours per gram.

Host 1For context, how does that compare to current materials?

Host 2Graphite stores lithium at a theoretical maximum of 372 milliamp hours per gram. Current commercial hard carbons for sodium-ion batteries deliver roughly 300 milliamp hours per gram, with the best research-grade materials reaching 400 to 500. Eight hundred milliamp hours per gram would more than double the best current sodium-ion anode performance.

Host 1Were the surrogate predictions validated?

Host 2They went back and ran full intercalation calculations on the high-capacity candidates identified by the surrogate. The full calculations confirmed the high capacities. That round-trip validation — surrogate predicts, full calculation confirms — is the essential check for trusting any screening approach.

Design principles

Host 1What did they learn about what makes a good hard carbon for sodium storage?

Host 2The highest-capacity structures combine low carbon density with well-distributed nanopores that can accommodate sodium clusters. The surrogate model effectively encodes a set of atomistic design rules: which pore geometries, which defect configurations, and which domain arrangements maximise sodium uptake.

Host 1And those design rules connect back to synthesis.

Host 2That is the claim. The structural parameters in the model — density, porosity, sp2 to sp3 ratio — are quantities that can be tuned experimentally through precursor chemistry, pyrolysis temperature, heating rate, and post-treatment. The framework provides a bridge from atomistic structure to electrochemical performance, and in principle from performance targets back to synthesis conditions.

Caveats

Host 1What are the major caveats?

Host 2First, the machine-learned potential is an approximation. Universal potentials are impressive, but they can be less accurate than carefully fitted system-specific potentials, particularly for configurations far from their training data. Sodium at high concentrations packed inside carbon nanopores is an unusual chemical environment, and the accuracy of the potential in that regime deserves validation against targeted DFT calculations.

Host 1Second?

Host 2The surrogate predicts thermodynamic capacity — how much sodium the structure can accommodate at equilibrium. Real battery performance also depends on kinetics: how fast sodium ions move through the structure, what the rate capability is, how the material degrades over hundreds of charge-discharge cycles. None of that is captured here.

Host 1Third?

Host 2The voltage profiles are qualitatively correct, but quantitative agreement with experiment was not rigorously benchmarked. Accurately predicting the exact voltage at which sodium inserts is harder than predicting total capacity, and small voltage errors matter for real battery design because they affect energy density and safety margins.

Host 1Fourth?

Host 2This is a preprint on arXiv. It has not been peer-reviewed. The methodology is sound in principle, but the specific numerical claims, particularly the 800 milliamp hours per gram figures, need independent validation.

Host 1And I would add: 800 milliamp hours per gram is a computed number for a model structure at zero temperature. Real materials synthesised in a laboratory will inevitably perform below that ceiling.

Host 2Fair. Computed thermodynamic limits and practical delivered capacities can differ substantially. The value of the framework is in identifying which structural features matter and in ranking candidates relative to each other, not in predicting exact cell-level performance numbers.

What comes next

Host 1Where does this lead?

Host 2Two directions. First, experimental validation. The most promising structures from the screening need to be synthesised and tested in real electrochemical cells. The paper provides specific structural targets — density, porosity, pore geometry — that materials chemists can aim for.

Host 1And the second direction?

Host 2Extending the framework. The same workflow could be applied to hard carbons with heteroatom doping, where nitrogen, boron, or oxygen atoms are incorporated into the carbon lattice. Each dopant changes the local electronic structure and can create new adsorption sites. That is an additional dimension of chemical space that could be explored computationally with the same pipeline.

Host 1And beyond sodium-ion batteries?

Host 2The methodology is general. Any amorphous material where performance depends on nanoscale structure — porous carbons for supercapacitors, glasses for solid-state electrolytes, amorphous catalysts — could in principle be studied the same way. The combination of universal potentials, automated structure generation, and surrogate screening is a workflow template, not a one-off result.

Host 1Bottom line?

Host 2A well-designed computational pipeline that screens thousands of realistic hard carbon structures for sodium storage capacity at a scale that was previously inaccessible. The specific capacity numbers need experimental confirmation, but the framework itself — linking atomistic structure to electrochemical function and doing so for thirteen thousand candidates rather than a handful — is a methodological advance for amorphous materials design.

Sign-off

Host 1That is the deep dive. Atomistic Structure Generation and Neural-Network Screening of Hard Carbons to Identify High-Capacity Sodium Storage, from Mclean and colleagues at the University of Exeter. Link in the show notes.

Host 2This has been the Hastrup Review of Science. See you next week.