ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of LaGaO3 (Materials Project id mp-3336)

       289      138      113       10        0        0  
       138      289      113      -10        0        0  
       113      113      299        0        0        0  
        10      -10        0       78        0        0  
         0        0        0        0       78       10  
         0        0        0        0       10       75  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 178.33 GPaEV = 209.69 GPaGV = 80.4 GPaνV = 0.30403
ReussKR = 178.25 GPaER = 205.62 GPaGR = 78.615 GPaνR = 0.30774
HillKH = 178.29 GPaEH = 207.66 GPaGH = 79.508 GPaνH = 0.30588

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
66.388 GPa 75.356 GPa 86.612 GPa 153.64 GPa 190.85 GPa 535.15 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 179 GPa 239.19 GPa 1.8211 TPa–1 1.968 TPa–1 66.388 GPa 91.809 GPa0.189420.43505Value
Anisotropy 1.336 1.0806 1.383 2.2967Anisotropy
Axis 0.7355
0.4290
-0.5244
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.0000
0.7577
-0.6526
0.4923
0.2659
0.8288
0.5019
0.8649
0.0026
0.5050
0.8631
0.0011
Axis
-1.0000
0.0000
-0.0000
0.7198
0.4109
-0.5594
-0.3446
0.1972
0.9178
-0.7920
0.4639
-0.3969
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane