Thermoelectrics

Thermoelectric Domain

The thermoelectric domain provides evaluation models for thermoelectric materials used in waste heat recovery and solid-state cooling. It covers bismuth telluride (Bi2Te3), lead telluride (PbTe), half-Heusler compounds, and skutterudites.

Physics Model

The thermoelectric figure of merit ZT is calculated from three coupled transport properties:

ZT = S^2 * sigma * T / kappa

Where S is the Seebeck coefficient, sigma is the electrical conductivity, T is the absolute temperature, and kappa is the total thermal conductivity (lattice + electronic).

• Seebeck coefficient is modeled using the Mott formula with carrier concentration estimated from doping level and host band structure parameters.
• Electrical conductivity is calculated from carrier concentration, mobility (limited by alloy scattering and phonon scattering), and effective mass.
• Thermal conductivity combines the electronic contribution (Wiedemann-Franz law) with the lattice contribution (Callaway model with alloy and boundary scattering).

Default Parameters

| Parameter | Type | Bounds | Unit | Description | |—————-|———|————|———|——————-| | bi_fraction | continuous | [0.35, 0.45] | — | Bi content | | sb_substitution | continuous | [0.0, 0.10] | — | Sb substitution on Bi site | | se_substitution | continuous | [0.0, 0.10] | — | Se substitution on Te site | | dopant_concentration | continuous | [1e-3, 0.05] | — | Carrier dopant level | | hot_press_temp | integer | [350, 550] | C | Consolidation temperature | | hot_press_pressure | continuous | [30, 80] | MPa | Consolidation pressure | | ball_mill_time | continuous | [1, 48] | hours | Mechanical alloying time |

Default Objectives

| Objective | Direction | Unit | |—————-|—————-|———| | zt | maximize | dimensionless | | power_factor | maximize | uW/(cm*K2) |

Key Trade-Offs

• ZT vs. mechanical robustness: Nanostructured materials with reduced lattice thermal conductivity achieve higher ZT but may be mechanically fragile.
• Seebeck vs. conductivity: Increasing carrier concentration raises electrical conductivity but reduces the Seebeck coefficient. The optimal carrier concentration is typically 10^19 to 10^20 per cm3.
• Operating temperature: Different materials excel at different temperatures. Bi2Te3 peaks near room temperature; PbTe peaks at 600-800 K.

Example: Bi2Te3-Based Optimization

name: bte-thermoelectric
domain: thermoelectric

parameters:
  - name: sb_substitution
    type: continuous
    bounds: [0.0, 0.08]
  - name: se_substitution
    type: continuous
    bounds: [0.0, 0.06]
  - name: dopant_concentration
    type: continuous
    bounds: [0.001, 0.03]
    log_scale: true
  - name: hot_press_temp
    type: integer
    bounds: [380, 500]
  - name: ball_mill_time
    type: continuous
    bounds: [2, 24]

objectives:
  - name: zt
    direction: maximize
  - name: power_factor
    direction: maximize
    unit: uW/(cm*K2)

optimizer:
  method: cma-es
  budget: 400
  batch_size: 20
  seed: 42

Typical Results

Optimized Bi2Te3-based compositions typically achieve:

• Peak ZT: 1.2—1.8 at 300 K with optimized Sb/Se substitution and nanostructuring
• Power factor: 30—45 uW/(cm*K2) at optimal carrier concentration
• Trade-off: Highest ZT compositions may have lower power factor due to reduced electrical conductivity from alloy scattering

Temperature-Dependent Optimization

The thermoelectric domain supports temperature-dependent evaluation. Specify the target operating temperature:

metadata:
  operating_temperature_k: 500

This shifts the evaluation to model transport properties at the specified temperature, which is critical for matching the material to the application.