{ "node": { "id": "term:square-root-of-time", "type": "Term", "label": "Square-root-of-time law", "properties": { "id": "square-root-of-time", "name": "Square-root-of-time law", "section": "topic-aging", "definition": "The observation that SEI-driven capacity loss in storage grows roughly with the square root of time, because the growing film slows its own growth. A cell that lost 4 % in its first year will lose about 1.7 % more in the second.", "formula": "Q_loss ∝ √t", "related": [ "sei", "calendar-aging", "aging-model" ], "example": { "title": "Compare equal time intervals", "text": "If an illustrative diffusion-limited loss is 1% after 100 h and follows only a square-root law, it is 2% after 400 h. Reaching twice the modeled loss takes four times the elapsed time." }, "url": "https://lemonergy.com/learn/glossary/square-root-of-time/", "mentions": [] } }, "edges": [ { "id": "edge:23", "source": "term:square-root-of-time", "target": "workflow:film-growth", "type": "usedIn", "properties": { "sourceFile": "wiki-blocks.json" } }, { "id": "edge:1600", "source": "term:square-root-of-time", "target": "topic:topic-aging", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:1601", "source": "term:square-root-of-time", "target": "term:sei", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1602", "source": "term:square-root-of-time", "target": "term:calendar-aging", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1603", "source": "term:square-root-of-time", "target": "term:aging-model", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1604", "source": "term:square-root-of-time", "target": "visual:film", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:1605", "source": "term:square-root-of-time", "target": "reference:edge-degradation", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "workflow:film-growth", "type": "Workflow", "label": "Explore film growth", "properties": { "id": "film-growth", "title": "Explore film growth", "kind": "core", "summary": "Lemonergy Core evaluates this relation.", "steps": [ "Open the lesson and inspect the equation.", "Change one input while holding the others fixed." ], "example": "At a factor of one, 10 nm at 1 h becomes 20 nm at 4 h and 30 nm at 9 h.", "observe": "Compare the result with the equation and units.", "limits": "This does not identify SEI chemistry or fit state of health.", "url": "https://lemonergy.com/learn/fundamentals/battery-aging/#sei", "label": "Open the worked lesson", "evidence": [ "src/battery_core/aging.py" ] } }, { "id": "topic:topic-aging", "type": "Topic", "label": "Aging and degradation", "properties": { "id": "topic-aging", "name": "Aging and degradation", "lede": "Why a cell loses capacity and gains resistance, and the mechanisms behind it.", "context": "Separate mechanisms, observations and fitted models.", "example": "Capacity loss and resistance rise can have different causes; a film-growth curve cannot identify both.", "lesson_url": "https://lemonergy.com/learn/fundamentals/battery-aging/", "lesson_label": "Open aging" } }, { "id": "term:sei", "type": "Term", "label": "Solid–electrolyte interphase", "properties": { "id": "sei", "name": "Solid–electrolyte interphase", "abbr": "SEI", "section": "topic-aging", "definition": "A film of electrolyte reaction products on the negative-electrode particles — graphite, and also silicon or lithium metal. It protects the electrode from further reaction but grows slowly for the whole life of the cell, consuming cyclable lithium.", "related": [ "passivation", "formation", "calendar-aging", "loss-of-lithium-inventory", "cei" ], "lesson": "fundamentals/battery-aging/#sei", "url": "https://lemonergy.com/learn/glossary/sei/", "mentions": [ "electrode", "graphite", "electrolyte" ] } }, { "id": "term:calendar-aging", "type": "Term", "label": "Calendar aging", "properties": { "id": "calendar-aging", "name": "Calendar aging", "section": "topic-aging", "definition": "Degradation that happens with time even when a cell is not cycled — in storage, for example. It is driven mainly by side reactions such as SEI growth and accelerates with temperature.", "related": [ "cycle-aging", "sei", "arrhenius", "square-root-of-time", "calendar-life" ], "lesson": "fundamentals/battery-aging/#whole-cell", "url": "https://lemonergy.com/learn/glossary/calendar-aging/", "mentions": [] } }, { "id": "term:aging-model", "type": "Term", "label": "Aging model", "properties": { "id": "aging-model", "name": "Aging model", "aka": [ "degradation model", "lifetime model" ], "section": "topic-transport", "definition": "A model that predicts capacity fade and resistance growth as functions of time, temperature, SOC and throughput. Empirical models fit power laws and Arrhenius terms to test data; physics-based models simulate the SEI, plating and cracking mechanisms themselves.", "related": [ "square-root-of-time", "arrhenius", "calendar-aging", "cycle-aging", "remaining-useful-life", "digital-twin" ], "url": "https://lemonergy.com/learn/glossary/aging-model/", "mentions": [ "sei", "state-of-charge", "capacity-fade", "impedance-rise" ] } }, { "id": "visual:film", "type": "Visual", "label": "Diffusion-limited film growth", "properties": { "title": "Diffusion-limited film growth", "summary": "Four times the elapsed time gives twice the film thickness in this model.", "readout": "At four reference time units, thickness is 2× the reference thickness.", "formula": "δ / δ_ref = √[(t / t_ref) A]", "note": "Normalized analytical relation, not a capacity-loss or SOH prediction.", "software": { "status": "implemented", "label": "Implemented in battery-core", "body": "parabolic_film_thickness uses reference thickness × √(relative time × acceleration). Converting film thickness to capacity loss requires a calibrated relationship.", "href": "../fundamentals/battery-aging/" }, "html": "
Relative film growth
Relative film growthTime / reference time versus Thickness / reference thickness. Selected acceleration; Reference conditions. Interpretation follows the graphs.002448612816Time / reference timeThickness / referencethickness
Selected accelerationReference conditions (dashed)
" } }, { "id": "reference:edge-degradation", "type": "Reference", "label": "Lithium ion battery degradation: what you need to know", "properties": { "title": "Lithium ion battery degradation: what you need to know", "publisher": "Physical Chemistry Chemical Physics", "url": "https://doi.org/10.1039/D1CP00359C", "type": "Review article", "scope": "Degradation mechanisms, modes, operational effects and their interactions.", "year": 2021, "accessed": "2026-10-27" } } ] }