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Malyi (1","submitted_at":"2025-12-13T18:24:43Z","abstract_excerpt":"Graphite, the standard commercial anode for Li-ion batteries, is thermodynamically incompatible with Na-ion batteries, leading researchers to search for alternative C-based structures (e.g., hard carbon, expanded graphite). In a simplified picture, the main idea of such search relies on identifying disordered C structures with a large interlayer spacing and distribution of local structural motifs (e.g., pores) with target electrochemical properties. 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Malyi (1","submitted_at":"2025-12-13T18:24:43Z","abstract_excerpt":"Graphite, the standard commercial anode for Li-ion batteries, is thermodynamically incompatible with Na-ion batteries, leading researchers to search for alternative C-based structures (e.g., hard carbon, expanded graphite). In a simplified picture, the main idea of such search relies on identifying disordered C structures with a large interlayer spacing and distribution of local structural motifs (e.g., pores) with target electrochemical properties. Such exploration is typically done via trial-and-error experimentation, which often does not allow precise understanding of the role of interlayer"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Na intercalation becomes thermodynamically possible in large concentrations above 4.21 Å even without a change in interlayer spacing. Conversely, Li intercalation has a narrow optimal window, with maximum capacity at approximately 3.75 Å.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The cluster-expansion model trained on a limited set of DFT configurations accurately predicts energies and voltages across the full range of interlayer spacings and concentrations relevant to real disordered carbons.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"DFT and cluster-expansion calculations identify 4.21 Å as the threshold above which Na intercalates readily in graphite-like carbon while Li capacity peaks narrowly near 3.75 Å with AA stacking preferred for both ions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Na intercalation in carbon becomes thermodynamically stable above 4.21 Å spacing while Li capacity maximizes narrowly at 3.75 Å","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"14519848e9627509a357957f12e7ae98be34fa588f7595f12bbe68ea20f0078c"},"source":{"id":"2512.12422","kind":"arxiv","version":1},"verdict":{"id":"6d4661e6-1ca9-4d8d-a141-1fa594d0f9a2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T22:27:22.913127Z","strongest_claim":"Na intercalation becomes thermodynamically possible in large concentrations above 4.21 Å even without a change in interlayer spacing. Conversely, Li intercalation has a narrow optimal window, with maximum capacity at approximately 3.75 Å.","one_line_summary":"DFT and cluster-expansion calculations identify 4.21 Å as the threshold above which Na intercalates readily in graphite-like carbon while Li capacity peaks narrowly near 3.75 Å with AA stacking preferred for both ions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The cluster-expansion model trained on a limited set of DFT configurations accurately predicts energies and voltages across the full range of interlayer spacings and concentrations relevant to real disordered carbons.","pith_extraction_headline":"Na intercalation in carbon becomes thermodynamically stable above 4.21 Å spacing while Li capacity maximizes narrowly at 3.75 Å"},"references":{"count":56,"sample":[{"doi":"","year":null,"title":"Introduction Materials design sets the limits of rechargeable batteries, with structure and thermodynamics determining battery operational voltage and electrode material performance [1]. While graphit","work_id":"7d8ea7eb-c061-4f33-b16e-dc52d3125591","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"for Na-ion batteries. The main idea behind their design lies in (i) increasing the interlayer distance in the graphite-like domains, (ii) introducing the higher energy sites (e.g., point defects and n","work_id":"32114203-2acd-4e1d-99fd-d860672a454f","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Results and Discussion While, from a theoretical perspective, AB graphite (space group: P6 3/mmc) is a thermodynamically stable form of carbon, in the context of C -based electrode materials one usual","work_id":"41e4dddd-bab2-4796-985f-20090703314b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Conclusions By combining DFT with cluster expansion across a range of interlayer spacings and AA/AB stackings, we transform the messy structural complexity of hard carbon and expanded graphite into a ","work_id":"b4008c42-6ccf-4307-81da-95c41a49038d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Methods All the density functional theory (DFT) calculations were done using the Vienna ab initio Simulation Package (VASP) version 6.2.1 [32–34], using the projector augmented wave (PAW) method [35].","work_id":"dd20a347-0f56-424f-bb15-eda159c0382a","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":56,"snapshot_sha256":"b146bef453f0b98fed195c83ed671f7b939740ae1363d3e2e0cbd3e76ec8d3a5","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"dddb7811c42d50b0344f47432fa2be26209f1df6f97f7b1807f4ad4036193ccf"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2512.12422","created_at":"2026-05-17T23:39:00.534251+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.12422v1","created_at":"2026-05-17T23:39:00.534251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.12422","created_at":"2026-05-17T23:39:00.534251+00:00"},{"alias_kind":"pith_short_12","alias_value":"AI57CB5VKQB5","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"AI57CB5VKQB54FIJ","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"AI57CB5V","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7","json":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7.json","graph_json":"https://pith.science/api/pith-number/AI57CB5VKQB54FIJNP5U5EGUW7/graph.json","events_json":"https://pith.science/api/pith-number/AI57CB5VKQB54FIJNP5U5EGUW7/events.json","paper":"https://pith.science/paper/AI57CB5V"},"agent_actions":{"view_html":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7","download_json":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7.json","view_paper":"https://pith.science/paper/AI57CB5V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.12422&json=true","fetch_graph":"https://pith.science/api/pith-number/AI57CB5VKQB54FIJNP5U5EGUW7/graph.json","fetch_events":"https://pith.science/api/pith-number/AI57CB5VKQB54FIJNP5U5EGUW7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7/action/storage_attestation","attest_author":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7/action/author_attestation","sign_citation":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7/action/citation_signature","submit_replication":"https://pith.science/pith/AI57CB5VKQB54FIJNP5U5EGUW7/action/replication_record"}},"created_at":"2026-05-17T23:39:00.534251+00:00","updated_at":"2026-05-17T23:39:00.534251+00:00"}