Ceramics

Ceramic Domain

The ceramic domain provides evaluation models for structural and functional ceramic materials, including solid oxide fuel cell electrolytes, thermal barrier coatings, structural alumina/zirconia, and piezoelectric ceramics.

Physics Model

• Ionic conductivity is modeled using the Arrhenius equation with activation energies estimated from dopant type, concentration, and crystal structure. Oxygen vacancy concentration is derived from charge compensation requirements.
• Fracture toughness is calculated using a microstructure-dependent model accounting for transformation toughening (in zirconia), crack deflection, and grain size effects via the Hall-Petch-like relationship.
• Thermal conductivity is modeled using the Callaway model with phonon scattering from grain boundaries, point defects (dopants), and porosity.
• Density is estimated from sintering models (Coble sintering theory) accounting for temperature, time, and green body characteristics.

Default Parameters

| Parameter | Type | Bounds | Unit | Description | |—————-|———|————|———|——————-| | dopant_mol_pct | continuous | [0.0, 15.0] | mol% | Dopant concentration | | dopant_type | categorical | [Y2O3, CeO2, Gd2O3, Sc2O3, MgO] | — | Dopant oxide | | sintering_temp | integer | [1100, 1700] | C | Sintering temperature | | sintering_time | continuous | [0.5, 24.0] | hours | Hold time at temperature | | grain_size | continuous | [0.1, 50.0] | um | Target grain diameter | | porosity | continuous | [0.01, 0.30] | — | Volume fraction porosity |

Default Objectives

| Objective | Direction | Unit | |—————-|—————-|———| | ionic_conductivity | maximize | S/cm | | fracture_toughness | maximize | MPa*m^0.5 |

Key Trade-Offs

• Conductivity vs. mechanical strength: Higher dopant concentrations increase ionic conductivity by creating more oxygen vacancies but can destabilize the crystal structure, reducing toughness.
• Density vs. conductivity: Full densification improves mechanical properties but can trap dopants in unfavorable configurations. Some controlled porosity can improve gas-phase transport in SOFCs.
• Grain size effects: Larger grains improve ionic conductivity (less grain boundary resistance) but reduce fracture toughness (less crack deflection).

Example: SOFC Electrolyte

name: ysz-electrolyte
domain: ceramic

parameters:
  - name: dopant_mol_pct
    type: continuous
    bounds: [3.0, 12.0]
  - name: dopant_type
    type: categorical
    choices: [Y2O3, Sc2O3, Gd2O3]
  - name: sintering_temp
    type: integer
    bounds: [1300, 1600]
  - name: sintering_time
    type: continuous
    bounds: [2.0, 16.0]
  - name: grain_size
    type: continuous
    bounds: [0.5, 10.0]

objectives:
  - name: ionic_conductivity
    direction: maximize
    unit: S/cm
  - name: fracture_toughness
    direction: maximize
    unit: MPa*m^0.5

optimizer:
  method: cma-es
  budget: 300
  batch_size: 15
  seed: 42

Typical Results

YSZ electrolyte campaigns find:

• 8 mol% YSZ (classic composition): Conductivity ~0.1 S/cm at 1000 C, toughness ~2.5 MPa*m^0.5
• Sc-doped ZrO2: Higher conductivity (~0.15 S/cm) but lower toughness (~1.8 MPa*m^0.5)
• Co-doped systems: Intermediate performance with improved sinterability at lower temperatures

Thermal Barrier Coating Mode

For TBC applications, the evaluation model shifts to thermal resistance and thermal cycling durability:

objectives:
  - name: thermal_resistance
    direction: maximize
    unit: m2*K/W
  - name: cycling_lifetime
    direction: maximize
    unit: cycles

Parameters include coating thickness, bond coat composition, and spray deposition conditions.