{"id":"https://openalex.org/W7223411040","doi":"https://doi.org/10.1149/osf.io/g8svr_v1","title":"Efficient formulation and simulation of solid-phase diffusion in silicon-like volume-expanding materials","display_name":"Efficient formulation and simulation of solid-phase diffusion in silicon-like volume-expanding materials","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7223411040","doi":"https://doi.org/10.1149/osf.io/g8svr_v1"},"language":"en","primary_location":{"id":"doi:10.1149/osf.io/g8svr_v1","doi":"https://doi.org/10.1149/osf.io/g8svr_v1","is_oa":true,"landing_page_url":"https://doi.org/10.1149/osf.io/g8svr_v1","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.1149/osf.io/g8svr_v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046553570","display_name":"Venkat R. Subramanian","orcid":"https://orcid.org/0000-0002-2092-9744","observed_orcids":["https://orcid.org/0000-0002-2092-9744"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Venkat R. Subramanian","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2092-9744","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040504211","display_name":"Puneet Jindal","orcid":"https://orcid.org/0000-0002-8302-9313","observed_orcids":["https://orcid.org/0000-0002-8302-9313"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Puneet Jindal","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8302-9313","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030058023","display_name":"Taylor Reed Garrick","orcid":"https://orcid.org/0000-0003-2251-8129","observed_orcids":["https://orcid.org/0000-0003-2251-8129"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Taylor R. Garrick","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2251-8129","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10018","display_name":"Advancements in Battery Materials","score":0.8720999956130981,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10018","display_name":"Advancements in Battery Materials","score":0.8720999956130981,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10663","display_name":"Battery Modeling and Management","score":0.056299999356269836,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12875","display_name":"Thermal Expansion and Ionic Conductivity","score":0.02070000022649765,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/solid-phase-diffusion","display_name":"solid-phase diffusion","score":0.9800000190734863},{"id":"https://openalex.org/keywords/silicon-anodes","display_name":"silicon anodes","score":0.7139999866485596},{"id":"https://openalex.org/keywords/lithium-ion-batteries","display_name":"lithium-ion batteries","score":0.8960000276565552},{"id":"https://openalex.org/keywords/diffusion-modeling","display_name":"diffusion modeling","score":0.7129999995231628}],"concepts":[{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5888000130653381},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.45750001072883606},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3172000050544739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3163999915122986},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25360000133514404},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2533999979496002},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.24950000643730164},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.24220000207424164},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.24199999868869781}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1149/osf.io/g8svr_v1","doi":"https://doi.org/10.1149/osf.io/g8svr_v1","is_oa":true,"landing_page_url":"https://doi.org/10.1149/osf.io/g8svr_v1","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:share.osf.io:52b2f7d9-f63a-4f3c-bac6-69c10445e7b5","doi":null,"is_oa":true,"landing_page_url":"https://osf.io/g8svr","pdf_url":null,"source":{"id":"https://openalex.org/S4306402531","display_name":"ECSarXiv (OSF Preprints)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2799848540","host_organization_name":"Center for Open Science","host_organization_lineage":["https://openalex.org/I2799848540"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23606566","doi":"https://doi.org/10.5281/zenodo.23606566","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23606566","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.23606567","doi":"https://doi.org/10.5281/zenodo.23606567","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23606567","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1149/osf.io/g8svr_v1","doi":"https://doi.org/10.1149/osf.io/g8svr_v1","is_oa":true,"landing_page_url":"https://doi.org/10.1149/osf.io/g8svr_v1","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3126739909","https://openalex.org/W2913127307","https://openalex.org/W7097749435","https://openalex.org/W2360430455","https://openalex.org/W2042291983","https://openalex.org/W2921165497","https://openalex.org/W4238483615","https://openalex.org/W2230159491","https://openalex.org/W3107856185","https://openalex.org/W2053030627"],"abstract_inverted_index":{"Silicon-like":[0],"electrode":[1,294],"materials":[2],"expand":[3],"several-fold":[4],"on":[5],"lithiation,":[6],"so":[7],"solid-phase":[8],"diffusion":[9,103,136],"must":[10],"be":[11,55],"solved":[12],"in":[13,104,148,219,277,280,327],"a":[14,59,67,70,74,81,92,105,149,193,232,292,297,344,348,371,383],"sphere":[15,107],"whose":[16],"radius,":[17],"volume":[18,298],"and":[19,51,73,181,211,230,255,273,279,339,367],"host-site":[20],"concentration":[21,133,221],"change":[22,372],"with":[23,46,153,203,284,316],"the":[24,63,86,88,98,113,131,141,145,154,159,171,174,176,182,187,204,209,220,226,235,238,241,245,249,252,258,270,285,310,313,328,332,360,364,368,375],"state":[25,188],"of":[26,85,91,101,134,144,173,184,189,214,228,237,257,323,373],"lithiation.":[27],"The":[28,386],"reduced-order":[29],"solutions":[30],"developed":[31],"for":[32,49,80,112,199,231,266,269,274,336,343],"fixed":[33,106],"particles":[34],"(polynomial":[35],"profiles,":[36],"eigenfunction":[37],"Galerkin":[38,43],"collocation":[39],"and,":[40],"most":[41],"recently,":[42],"weak":[44,314,377],"forms":[45,378],"symmetric":[47],"polynomials":[48],"constant":[50,267,337],"concentration-dependent":[52,233,275],"diffusivity)":[53],"cannot":[54],"applied":[56],"to":[57,97,288,291,307,318,325,341,354,390],"such":[58],"particle":[60,94],"directly,":[61],"because":[62],"governing":[64],"equation":[65],"contains":[66],"lattice":[68],"velocity,":[69],"dilution":[71],"term":[72],"moving":[75],"boundary.":[76],"We":[77,263],"show":[78],"that,":[79],"homogeneous":[82],"isotropic":[83],"expansion":[84],"particle,":[87,175],"lithium":[89],"balance":[90],"swelling":[93,246],"reduces":[95],"exactly":[96],"standard":[99,250],"problem":[100,247],"spherical":[102],"when":[108],"it":[109],"is":[110,139,162,170,179,186],"written":[111],"scaled":[114],"moles":[115,124,387],"X":[116,185],"=":[117,168,207],"R_a\u00b3":[118],"C_a":[119],"/":[120],"(R_a0\u00b3":[121],"C^H_a0)":[122],"(the":[123],"per":[125],"unit":[126],"initial":[127,311],"volume,":[128,312],"that":[129,151,300],"is,":[130],"referential":[132],"finite-deformation":[135],"theory,":[137],"which":[138,216],"also":[140],"local":[142],"occupancy":[143,330],"host":[146],"sites)":[147],"coordinate":[150],"moves":[152],"lattice.":[155],"In":[156],"this":[157,197],"variable":[158],"time":[160],"derivative":[161],"multiplied":[163],"by":[164,392],"\u03c4Z\u00b2,":[165],"where":[166,347],"Z":[167],"R_a/R_a0":[169],"stretch":[172,195],"surface":[177,329],"flux":[178],"Z\u00b2\u03c4Q/3":[180],"average":[183,227],"lithiation":[190],"exactly.":[191],"For":[192,296],"prescribed":[194],"history":[196],"holds":[198],"any":[200],"diffusivity":[201,234,239,338,345],"law;":[202],"closure":[205],"Z\u00b3":[206],"f(X_avg)":[208],"radius":[210],"its":[212],"rate":[213],"change,":[215],"appear":[217],"explicitly":[218],"equation,":[222],"are":[223,379,388],"eliminated":[224],"through":[225],"X,":[229],"argument":[236],"carries":[240],"time-dependent":[242],"stretch.":[243],"Because":[244],"takes":[248],"form,":[251,282],"weak-form":[253],"equations":[254],"tables":[256],"symmetric-polynomial":[259],"formulation":[260],"apply":[261],"directly.":[262],"give":[264],"them":[265,290],"diffusivity,":[268,276],"moment":[271],"form":[272,315],"non-dimensional":[278],"dimensional":[281],"together":[283],"relations":[286],"needed":[287],"couple":[289],"pseudo-two-dimensional":[293],"model.":[295],"law":[299],"reaches":[301,321],"3.75":[302],"at":[303],"full":[304],"capacity,":[305],"charged":[306],"2.47":[308],"times":[309],"three":[317],"six":[319],"unknowns":[320],"errors":[322],"10\u207b\u2074":[324,340],"10\u207b\u2078":[326],"after":[331,370],"first":[333,365],"100":[334],"s":[335],"10\u207b\u2077":[342],"D_ref\u00b7e^(6X),":[346],"cell-centered":[349],"finite-difference":[350],"scheme":[351],"needs":[352],"32":[353],"more":[355],"than":[356,382],"128":[357],"cells.":[358],"Over":[359],"whole":[361],"history,":[362],"including":[363],"seconds":[366],"instants":[369],"current,":[374],"low-order":[376],"less":[380],"accurate":[381],"fine":[384],"mesh.":[385],"conserved":[389],"round-off":[391],"all":[393],"schemes.":[394]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-24T00:00:00"}