Dataset DOI: https://doi.org/10.5061/dryad.vmcvdnd6s

---

1. Dataset Overview

This dataset accompanies the publication:

Behrendt, D.; Banerjee, S.; Zhang, J.; Rappe, A. M.
Discovery of wurtzite solid solutions with enhanced piezoelectric response using machine learning, Phys. Rev. Materials (2024).

The dataset contains all computational data, machine learning features, and analysis used to identify doped wurtzite materials with enhanced piezoelectric response.

The study explores over 3000 candidate ternary solid solutions derived from nine base wurtzite materials:
AlN, BeO, CdS, CdSe, GaN, ZnO, ZnS, ZnSe, and AgI.

Using a multilevel screening workflow combining density functional theory (DFT) and machine learning:

• ~500 candidates were screened using a proxy model
• 30 promising materials were identified
• 11 materials were predicted to have significantly improved piezoelectric response

---

2. File Inventory and Structure

Main archive:

PiezoML-dryad.zip

---

2.1 Basemats/

Optimized base wurtzite materials used as starting structures.

Contents:

• Relaxed structures (DFT outputs)
• Piezoelectric tensor calculations (including e₃₃)
• Full input/output files for each calculation

---

2.2 Firstrun/

Initial dataset (~53 materials) used for proxy selection and model training.

---

2.2.1 AlN/

Dataset for dopant screening in AlN.

Subdirectories:

• AlN/: pure AlN calculations
• dopingtest*/: individual dopant configurations

Files:

• .csv: summary of calculated properties
• proxies.csv: computed proxy features used in screening
• dope.py: dopant structure generation
• features.py, configfeatures.py: feature extraction scripts
• .sh: workflow scripts

---

2.2.2 generice33/

General workflow for computing the piezoelectric coefficient e₃₃.

Method:

• Structures are strained along the c-axis from −1% to +1%
• Atomic positions are relaxed at each strain
• Polarization is computed using the Berry phase method
• e₃₃ is obtained from the slope of polarization vs. strain

Key scripts:

• generate.py: applies strain and runs calculations
• gete33.py: extracts e₃₃ and uncertainty

---

2.3 Secondrun/

Active learning workflow used for large-scale screening of doped wurtzite materials.

This directory contains the primary machine learning and high-throughput computational workflow used to screen more than 3000 candidate ternary solid solutions derived from nine wurtzite base materials.

Directories and workflow components:

• candidates/: untested candidate materials generated for scra eening
• dataset/: database of tested materials and calculated properties stored in .csv format
• newcalcs/: DFT calculations for newly selected candidate materials
• generic/: template calculation files and scripts for base materials, modified automatically for new doped systems
• piezotest/: materials selected for explicit e₃₃ piezoelectric response calculations
• tools/: workflow automation and machine learning scripts used throughout the active learning procedure
• high-throughput tools/: scripts and utilities used for automated calculation setup, batch job submission, file organization, workflow management, and automated data collection during large-scale screening calculations
• formation energies/: calculations and analysis used to evaluate thermodynamic stability and formation energies of candidate solid solutions
• formationenergies-fixcell/: fixed-cell formation energy calculations used to compare energetic stability while constraining lattice parameters for consistency across candidate materials

Filess:

• .csv files are used for intermediate datasets, machine learning training data, candidate tracking, and calculated material properties
• ./tools/runall.sh: executes one full iteration of the active learning and screening workflow

Machine learning methods used:

• Linear regression
• LASSO
• Ridge regression
• Recursive feature elimination (RFE)
• Random forest

Workflow overview:

1. Generate candidate materials
2. Compute primitive atomic descriptors and material features
3. Train machine learning models to predict lattice c/a ratio
4. Select promising low c/a candidates
5. Run DFT calculations for selected materiathe ls
6. Update dataset and repeat iterative screening

Python scripts in tools/:

• cleancandidates.py: removes previously studied materials from the candidate database

• finishprediction.py: organizes and transfers files required to complete a screening iteration

• generatecandidate.py: generates possible doped atomic configurations according to user-defined constraints

• generatefeature.py: converts material compositions and atomic descriptor databases into machine learning feature vectors

  Usage:
  python3 generatefeature.py (matlist.csv) (outputfeaturelist.csv)

• featureselection.py: identifies important features correlated with target material response using multiple machine learning methods

• pearson.py: generates Pearson correlation matrices for material descriptors

• materialselection.py: predicts c/a ratios for candidate materials using trained machine learning models and selects new materials for DFT calculations

• runnewmats.py: performs vc-relax calculations for newly selected materials using template inputs from the generic/directory

• collectratios.py: collects calculated c/a ratios from completed calculations and appends them to the growing dataset

---

2.4 plots/

Data used to generate figures in the publication:

• crossvalidateplot/ → model validation (Figure 3)
• primaryfeatsel/ → feature importance (Figure 4)
• e33scatter/ → final results (Figure 5)
• proxies/ → proxy selection (Figure 2)

---

3. Data Generation Methods

All first-principles calculations were performed using Quantum ESPRESSO.

Key computational details:

• 2 × 2 × 1 wurtzite supercells (16 atoms total)
• Two cation sites substituted with dopants
• Polarization compthe uted via Berry phase method
• Piezoelectric coefficient e₃₃ obtained via finite differences

---

4. Data Processing and Machine Learning

• Primitive features derived from atomic properties:
  • Atomic mass
  • Electronegativity
  • Atomic radius
  • Preferred valence
  • Periodic table row and column
  • Elemental melting temperature
• Feature statistics:
  • Mean
  • Standard deviation
  • Minimum
  • Maximum
  • Range
• Approximately 50 primitive descriptors were generated for each material

Key insight:

• The lattice c/a ratio was identified as the most effective proxy for predicting enhanced piezoelectric response.

---

5. Variables and DataFilesats

• .csv files contain tabular material data
• Each row corresponds to a material composition or DFT calculation

Typical columns include:

• Composition and dopant identity
• Lattice parameters (including c/a ratio)
• Piezoelectric response (e₃₃, units: C/m²)
• Formation energies
• Machine learning feature descriptors
• Predicted screening metrics

---

6. Reuse Instructions

To reproduce the workflow:

1. Install:
   • Quantum ESPRESSO
   • Python 3.x
   • scikit-learn and standard scientific Python libraries
2. Run:
   • generice33/ for piezoelectric calculations
   • Secondrun/tools/ for machine learning workflows
   • formation energy workflows as described in the formation energies/ directoriethe s
3. Follow iterative screening workflow:
   • Generate candidates
   • Compute material descriptors
   • Train machine learning models
   • Select promising candidates
   • Run DFT calculations
   • Update datasets and repeat screening

---

7. Notes and Caveats

• Some candidate materials may become structurally unstable and deviate from the wurtzite phase during relaxation
• Failed calculations are assigned high c/a values to exclude them from future candidate selection
• Batch scripts and submission files are HPC-dependent and may require modification for different computing environments
• Not all low c/a materials exhibit enhanced piezoelectric response
• Some workflows assume directory structures consistent with the included automation scripts

---

8. Access Information

No additional external repositories are associated with this dataset.

---

9. Software Versions

• Quantum ESPRESSO
• Python 3.x
• scikit-learn for machine learning workflows

---

10. Contact Information

For questions regarding the dataset or workflow implementation, please contact the corresponding author of the associated publication.