PiezoTensorNet: Crystallography informed multi-scale hierarchical machine learning model for rapid piezoelectric performance finetuning

Description:

a. Feature Engineering:

    The file data_of_145_features.csv consists of the datasets of the features. The datasets correspond to Fig. 1(a) of the paper.

b. HierCrystalNet  of PiezoTensorNet:

      The saved models after training HierCrystalNet are placed inside the zip folders, namely, (i) classification_saved_models.zip, (ii) PG1_cubic_saved_models.zip, (iii)        PG2_tetragonal42m_saved_models.zip, (iv) PG3_orthorhombic222_saved_models.zip, (v) PG4_hex6tetra4mm_saved_models.zip, and (vi) PG5_orthorhombicmm2_saved_models.zip.

c. ModularEnsembleNet of PiezoTensorNet :

     The prediction_results.zip folder consists the prediction results of the ModularEnsembleNet. 

d. Input data of piezoelectric tensors and stiffness tensors for the finite element analysis: 

(i)     piezoelectric_tensors_AlN_B0.3Er0.5Al0.2N_alloy.zip:  The coefficients of piezoelectric tensors (array shape: 3x6) for AlN  alloy and B0.3Er0.5Al0.2N alloy are respectively presented in  undoped_AlN_piezoelectric_tensor.csv and B0.3Er0.5Al0.2N_alloy_unrotated_piezoelectric_tensor.csv files. Both of these files contain the data for samples whose laboratory coordinate system is same with that of the orientation of crystal lattice (all of the three Euler angles theta, psi and phi  = 0 degree ), and so the compositional effect on the piezoelectric behavior can be assessed solely without considering the orientation effect.  Rotation or other transformation can cause the  vector value of  (theta, phi, phis) other than (0,0,0) which  indicates that the laboratory coordinate system of a sample being different than its  lattice orientation. The effect of two different magnitudes of rotation on the coefficients of piezoelectric tensors for B0.3Er0.5Al0.2N alloy are revealed through the files B0.3Er0.5Al0.2N_alloy_rotated_at_orientation_1_piezoelectric_tensor.csv and  B0.3Er0.5Al0.2N_alloy_rotated_at_orientation_2_piezoelectric_tensor.csv. Orientation 1 refers to theta = 0 degree, psi = 268.47 degree, 91.52 degree, 0 <= phi <= 360 degree whereas  theta = 180 degree, psi = 268.47 degree, 91.52 degree, 0 <= phi <= 360 for orientation 2.  The units of the coefficients are C/m^2. The description of the methodology on how to generate this data in this format is provided at https://piezoelectrictensorsdatabase.streamlit.app/ .

(ii) stiffness_tensors_AlN_B0.3Er0.5Al0.2N_alloy.csv: The stiffness tensors (array shape: 6x6) for the two materials AlN  alloy and B0.3Er0.5Al0.2N alloy at room temperature are presented through the four csv files.  The elements of stiffness tensors in the datasets are presented in GPa. The Cijkl tensors are provided first for isotropy and then for orthotropy assumptions. The description of these tensors for AlN and  B0.3Er0.5Al0.2N materials are provided in the web apps:  https://isotropic-elasticity.streamlit.app/ and  https://orthotropic-elasticity.streamlit.app/