{
  "node": {
    "id": "term:warburg-impedance",
    "type": "Term",
    "label": "Warburg impedance",
    "properties": {
      "id": "warburg-impedance",
      "name": "Warburg impedance",
      "section": "topic-transport",
      "definition": "The impedance of diffusion, which appears as a 45° line at the low-frequency end of a Nyquist plot. Its slope and onset frequency give a route to the diffusion coefficient.",
      "related": [
        "randles-circuit",
        "nyquist-plot",
        "diffusion-coefficient",
        "electrochemical-impedance-spectroscopy"
      ],
      "url": "https://lemonergy.com/learn/glossary/warburg-impedance/",
      "mentions": [
        "impedance",
        "diffusion"
      ]
    }
  },
  "edges": [
    {
      "id": "edge:2169",
      "source": "term:warburg-impedance",
      "target": "topic:topic-transport",
      "type": "belongsTo",
      "properties": {
        "sourceFile": "terms.json"
      }
    },
    {
      "id": "edge:2170",
      "source": "term:warburg-impedance",
      "target": "term:randles-circuit",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:2171",
      "source": "term:warburg-impedance",
      "target": "term:nyquist-plot",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:2172",
      "source": "term:warburg-impedance",
      "target": "term:diffusion-coefficient",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:2173",
      "source": "term:warburg-impedance",
      "target": "term:electrochemical-impedance-spectroscopy",
      "type": "relatedTo",
      "properties": {
        "sourceFile": "terms.json",
        "meaning": "Related context; not a causal claim"
      }
    },
    {
      "id": "edge:mentions/warburg-impedance/impedance",
      "source": "term:warburg-impedance",
      "target": "term:impedance",
      "type": "mentions",
      "properties": {
        "sourceFile": "terms.json",
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        "field": "definition",
        "meaning": "Text mention; not a causal claim"
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    {
      "id": "edge:mentions/warburg-impedance/diffusion",
      "source": "term:warburg-impedance",
      "target": "term:diffusion",
      "type": "mentions",
      "properties": {
        "sourceFile": "terms.json",
        "method": "build_glossary.mention_index + mentions",
        "field": "definition",
        "meaning": "Text mention; not a causal claim"
      }
    }
  ],
  "neighbors": [
    {
      "id": "topic:topic-transport",
      "type": "Topic",
      "label": "Transport and modelling",
      "properties": {
        "id": "topic-transport",
        "name": "Transport and modelling",
        "lede": "How ions move, and the equations and models that describe a cell.",
        "context": "Specify phase, direction and boundaries.",
        "example": "The same concentration difference across 10 μm gives ten times the gradient across 100 μm; at equal D, first-law flux magnitude is ten times greater.",
        "lesson_url": "https://lemonergy.com/learn/transport/ficks-first-law/",
        "lesson_label": "Open diffusion"
      }
    },
    {
      "id": "term:randles-circuit",
      "type": "Term",
      "label": "Randles circuit",
      "properties": {
        "id": "randles-circuit",
        "name": "Randles circuit",
        "section": "topic-transport",
        "definition": "The classic equivalent circuit for one electrode interface: electrolyte resistance in series with a double-layer capacitance that shunts the charge-transfer resistance and a Warburg diffusion element. It is the template for reading an impedance spectrum.",
        "related": [
          "electrochemical-impedance-spectroscopy",
          "warburg-impedance",
          "double-layer",
          "charge-transfer"
        ],
        "url": "https://lemonergy.com/learn/glossary/randles-circuit/",
        "mentions": [
          "impedance",
          "electrode",
          "electrolyte",
          "diffusion"
        ]
      }
    },
    {
      "id": "term:nyquist-plot",
      "type": "Term",
      "label": "Nyquist plot",
      "properties": {
        "id": "nyquist-plot",
        "name": "Nyquist plot",
        "section": "topic-transport",
        "definition": "The usual display of an impedance spectrum: negative imaginary part against real part, one point per frequency. Reading left to right, the ohmic intercept, one or two semicircles for interfaces and a diffusion tail each tell a different story about the cell.",
        "related": [
          "electrochemical-impedance-spectroscopy",
          "impedance",
          "warburg-impedance",
          "randles-circuit"
        ],
        "url": "https://lemonergy.com/learn/glossary/nyquist-plot/",
        "mentions": [
          "diffusion"
        ]
      }
    },
    {
      "id": "term:diffusion-coefficient",
      "type": "Term",
      "label": "Diffusion coefficient",
      "properties": {
        "id": "diffusion-coefficient",
        "name": "Diffusion coefficient",
        "abbr": "D",
        "aka": [
          "diffusivity"
        ],
        "section": "topic-transport",
        "definition": "The proportionality constant D in Fick’s first law, in m²/s. It sets how fast a species spreads for a given concentration gradient.",
        "unit": "m²/s",
        "related": [
          "ficks-first-law",
          "solid-state-diffusion",
          "gitt",
          "diffusion"
        ],
        "lesson": "transport/ficks-first-law/#law",
        "url": "https://lemonergy.com/learn/glossary/diffusion-coefficient/",
        "mentions": [
          "concentration-gradient"
        ]
      }
    },
    {
      "id": "term:electrochemical-impedance-spectroscopy",
      "type": "Term",
      "label": "Electrochemical impedance spectroscopy",
      "properties": {
        "id": "electrochemical-impedance-spectroscopy",
        "name": "Electrochemical impedance spectroscopy",
        "abbr": "EIS",
        "section": "topic-testing",
        "definition": "Measuring a cell’s impedance across a range of frequencies, from kilohertz to millihertz, with a small alternating signal. The spectrum separates ohmic, interface and diffusion processes by their time scale and is read on a Nyquist plot.",
        "related": [
          "nyquist-plot",
          "impedance",
          "randles-circuit",
          "charge-transfer",
          "warburg-impedance"
        ],
        "url": "https://lemonergy.com/learn/glossary/electrochemical-impedance-spectroscopy/",
        "mentions": [
          "diffusion"
        ]
      }
    },
    {
      "id": "term:impedance",
      "type": "Term",
      "label": "Impedance",
      "properties": {
        "id": "impedance",
        "name": "Impedance",
        "abbr": "Z",
        "section": "topic-units",
        "definition": "The frequency-dependent generalisation of resistance, with a magnitude and a phase. A cell’s impedance separates ohmic, charge-transfer and diffusion contributions that a single DC resistance lumps together.",
        "unit": "Ω",
        "related": [
          "internal-resistance",
          "electrochemical-impedance-spectroscopy",
          "nyquist-plot"
        ],
        "url": "https://lemonergy.com/learn/glossary/impedance/",
        "mentions": [
          "diffusion"
        ]
      }
    },
    {
      "id": "term:diffusion",
      "type": "Term",
      "label": "Diffusion",
      "properties": {
        "id": "diffusion",
        "name": "Diffusion",
        "section": "topic-transport",
        "definition": "The net movement of a species from where it is concentrated to where it is scarce, driven by random thermal motion. In a cell lithium diffuses through the electrolyte in the pores and, far more slowly, through the solid particles themselves.",
        "related": [
          "ficks-first-law",
          "diffusion-coefficient",
          "solid-state-diffusion",
          "concentration-gradient",
          "migration"
        ],
        "lesson": "transport/ficks-first-law/#in-a-cell",
        "url": "https://lemonergy.com/learn/glossary/diffusion/",
        "mentions": [
          "electrolyte"
        ]
      }
    }
  ]
}