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 BiO2 (Materials Project id mp-557993)

       129       45       30        0      -38        0  
        45      137       51        0       -1        0  
        30       51      136        0      -52        0  
         0        0        0       60        0       -3  
       -38       -1      -52        0       33        0  
         0        0        0       -3        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72.667 GPaEV = 103.95 GPaGV = 41.2 GPaνV = 0.26157
ReussKR = 5.5074 GPaER = 9.3232 GPaGR = 3.8277 GPaνR = 0.21786
HillKH = 39.087 GPaEH = 56.662 GPaGH = 22.514 GPaνH = 0.25839

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.93957 GPa 20.771 GPa 60.229 GPa 97.983 GPa 103.74 GPa 232.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1.689 GPa 174.4 GPa -84.101 TPa–1 319.06 TPa–1 1.0184 GPa 60.297 GPa-3.43474.8612Value
Anisotropy 103.3 59.21Anisotropy
Axis -0.6605
0.0000
-0.7508
-0.4369
-0.0000
0.8995
0.0000
1.0000
0.0000
0.6616
0.0000
0.7498
0.4671
0.7071
0.5309
-0.1735
0.3039
0.9368
-0.3442
0.0000
0.9389
-0.5654
0.0002
0.8248
Axis
-0.4670
0.7071
-0.5310
-0.3319
-0.9136
0.2349
-0.9389
0.0000
-0.3442
-0.8248
-0.0000
-0.5654
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