Practical Guide · D3

Check a Piezoelectric Tensor Ledger

Separate invented clamped-ion and internal piezoelectric terms before applying an invented compliance conversion.

Evidence class: synthetic-only. This deterministic ledger uses invented piezoelectric entries in a declared local Voigt convention. It verifies the arithmetic e=eclamped+einternale=e^{\mathrm{clamped}}+e^{\mathrm{internal}} and then applies an explicitly invented compliance factor to show why a converted dd coefficient requires a separately declared elastic input. No number is a material property.

Do not use this ledger as the first action for a material. First open the crystal with labelled axes in VESTA or another structure viewer; save positive and negative strain or field inputs, their clamped-ion and internally relaxed outputs, the polarization-branch record, and the separately qualified elastic compliance. Tabulate every response component with units, tensor convention, sign, and source file before doing the arithmetic below.

Optional toy after the real tensor series exists

This page contains no real response series. Plot the real clamped and relaxed components before converting between ee and dd; the electronic-property resource landscape lists calculation routes.

Optional replay of the invented ledger

python3 examples/practical-guides/piezoelectric_tensor_ledger.py \
  --svg public/media/practical-guides/piezoelectric-response/check-piezoelectric-tensor-ledger/piezoelectric-tensor-ledger.svg

What this guide verifies

Execution verifies invented componentwise arithmetic, a locally named Voigt convention, invented compliance conversion, and original SVG rendering. It does not calculate a piezoelectric tensor, elastic compliance, polarization branch, response convergence, material response, or device coefficient.

If this script fails, repair only the local fixture or its declared convention. In a real response series, a branch jump, inconsistent relaxed geometry, broken positive/negative symmetry, axis mismatch, or unqualified compliance is a parent-evidence failure; do not conceal it with tensor conversion or component averaging.

Official sources

Ways to work: Python

Companion checked with: Python 3.12.

Reproducibility note

The companion material was checked with Python 3.12. It tests only the bounded software or analysis behaviour described here; it does not establish numerical convergence, model validity, or a material property.