> ## Documentation Index
> Fetch the complete documentation index at: https://docs.ionworks.com/llms.txt
> Use this file to discover all available pages before exploring further.
# 用語と標準
> Battery modeling terms and PyBaMM sign conventions: anode/cathode, lithiation, capacity, current direction, stoichiometry, and SOC
Battery modeling terminology varies significantly across contexts. This page defines how terms are used throughout this guide, along with our chosen conventions where multiple standards exist.
## Terminology
| Term | Definition |
| ------------------------ | ------------------------------------------------------------------------------------------------------------------------------------------- |
| **Anode** | The electrode with the lower open-circuit potential, often graphite, silicon, or lithium. Commonly referred to as the "negative electrode". |
| **Cathode** | The electrode with the higher open-circuit potential, e.g., NMC or LFP. Commonly referred to as the "positive electrode". |
| **Negative electrode** | Used interchangeably with "anode". |
| **Positive electrode** | Used interchangeably with "cathode". |
| **Capacity** | Either the total available capacity of an electrode or cell (denoted $Q$), or the instantaneous capacity during operation (denoted $q$). |
| **Lithiation** | The amount of lithium intercalated relative to the minimum and maximum possible lithium content. Bounded between 0 and 1. |
| **Stoichiometry** | Used interchangeably with "lithiation". |
| **Nominal capacity** | The rated capacity of the cell. |
| **Theoretical capacity** | The total capacity extractable at open-circuit voltage (infinitely slow discharge) between voltage limits. |
| **Potential** | The electric potential of a single electrode relative to metallic lithium (0V). |
| **Voltage** | The difference between positive and negative electrode potentials. |
## Standards
### Direction of Current
Following the PyBaMM convention, **positive current corresponds to discharge** and **negative current corresponds to charge**.
The discharge capacity is given by:
$$
q_{\text{dchg}}(t) = Q_0 + \int I(t) \, dt
$$
where $Q_0$ is the starting capacity (equal to 0 if the cell is at 100% SOC and $Q_{\text{cell}}$ if the cell is at 0% SOC).
The charging capacity is defined as:
$$
q_{\text{chg}}(t) = -q_{\text{dchg}}(t)
$$
Lower case $q$ indicates a quantity that varies during operation, while capital $Q$ represents a scalar property of the electrodes or cell.
### Single Electrode
For a single electrode, we say that the electrode is **"charged"** when its lithiation/stoichiometry/capacity increases.
The instantaneous capacity of the electrode is defined by $q^{\text{elec}}(t)$. The mathematical definition depends on whether the electrode is the anode or cathode of a full cell (see below), but in general $q^{\text{elec}}$ equals $q_{\text{chg}}$ (or $q_{\text{dchg}}$) plus an offset.
We can express this in terms of electrode lithiation/stoichiometry:
$$
\theta(t) = \frac{q^{\text{elec}}(t)}{Q^{\text{tot}}}
$$
where $Q^{\text{tot}}$ is the total capacity of the electrode.
| Variable | Meaning |
| ----------------- | ------------------------------------------- |
| $q^{\text{elec}}$ | Instantaneous capacity of an electrode |
| $Q^{\text{tot}}$ | Total capacity of the electrode |
| $\theta(t)$ | Instantaneous stoichiometry of an electrode |
### Whole Cell
The negative and positive electrodes behave differently when combined in a full cell. During discharge:
* **Negative electrode**: Lithiation decreases → open-circuit potential increases
* **Positive electrode**: Lithiation increases → open-circuit potential decreases
The open-circuit voltage of the full cell is:
$$
U = U_p - U_n
$$
which is monotonically decreasing since $U_p$ is decreasing and $U_n$ is increasing.
#### Capacity Relationships
Defining min/max electrode capacities by $Q^{\min/\max}$, and electrode capacities at 0%/100% cell SOC by $Q^{0/100}$:
$$
\begin{aligned}
Q_n^{\min} &= Q_n^0 \\
Q_n^{\max} &= Q_n^{100} \\
Q_p^{\max} &= Q_p^0 \\
Q_p^{\min} &= Q_p^{100}
\end{aligned}
$$
The electrode instantaneous capacity is:
$$
q_n^{\text{elec}}(t) = Q_n^{100} - q_{\text{dchg}}
$$
for the negative electrode and:
$$
q_p^{\text{elec}}(t) = Q_p^{100} + q_{\text{dchg}}
$$
for the positive electrode.
For each electrode, $Q^{\max} = Q^{\min} + Q^{\text{cell}}$, where $Q^{\text{cell}}$ is the theoretical capacity of the cell.
#### Stoichiometry Relationships
In terms of stoichiometries:
$$
\theta_n^{\text{elec}}(t) = \theta_n^{100} - \frac{q_{\text{chg}}}{Q_n^{\text{tot}}}
$$
$$
\theta_p^{\text{elec}}(t) = \theta_p^{100} + \frac{q_{\text{chg}}}{Q_p^{\text{tot}}}
$$
The cell's state of charge is:
$$
z = \frac{q_{\text{chg}}}{Q_{\text{cell}}}
$$
| Variable | Meaning |
| ----------------- | ------------------------------------------ |
| $Q^{\text{cell}}$ | Usable capacity of the cell |
| $Q^{\min}$ | Capacity at the lower voltage cut-off |
| $Q^{\max}$ | Capacity at the upper voltage cut-off |
| $\theta^{\min}$ | Stoichiometry at the lower voltage cut-off |
| $\theta^{\max}$ | Stoichiometry at the upper voltage cut-off |
## Naming Standards
Always use "negative" and "positive" to refer to the electrodes, instead of "anode" and "cathode".
Use "lithiation" and "delithiation" to refer to individual electrodes. Reserve "charge" and "discharge" for the full cell.
During a whole-cell **discharge**, the negative electrode delithiates and the positive electrode lithiates. During a whole-cell **charge**, the negative electrode lithiates and the positive electrode delithiates.