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The cluster expansion method was used to do a ground state analysis, and to calculate the phase diagram. The predicted\ndiagram has four ordered ground-states in the range 0 \\leq X \\leq 1/2, but one of these, at X=5/12, is predicted to disproportionate at T \\approx 20K, well below the experimentally investigated range T \\approx 420K. Thus, at T \\succeq 420K, the first-principles based calculation predicts three"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.4300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2011-07-21T15:47:40Z","cross_cats_sorted":[],"title_canon_sha256":"3efea76a39a393105cd522bad547484c91a201cf75fd5bc229944d0c92791a70","abstract_canon_sha256":"2e172e8ae6942d36635d7a93c861d8121914a101432eb354376bf2049bed29ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:54.329427Z","signature_b64":"oV96E3QwJDpeW2v7GPNPjWDEURyAUIPi3p4ZfPNncGXZO7+dRMxgo4gLjrbRNs4nU7u2x+YcAKt+XzW2hrTcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69a0582f1980d252c897d4ed6311db80edce66d334c49a9243f2298381ad7dee","last_reissued_at":"2026-05-18T00:56:54.328906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:54.328906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First Principles Phase Diagram Calculations for the Octahedral-Interstitial System ZrO$_{X}$, $0 \\leq X \\leq 1/2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Axel van de Walle, Benjamin P. 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