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 WO3 (Materials Project id mp-18773)

       125      -11       29        0        0        0  
       -11      125       29        0        0        0  
        29       29      237        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       53        0  
         0        0        0        0        0      262  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 64.556 GPaEV = 201.63 GPaGV = 102.93 GPaνV = -0.020566
ReussKR = 53.678 GPaER = 146.2 GPaGR = 69.885 GPaνR = 0.046043
HillKH = 59.117 GPaEH = 174.3 GPaGH = 86.409 GPaνH = 0.0085916

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
53 GPa 53 GPa 101.58 GPa 136 GPa 249.42 GPa 262 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 119.71 GPa 222.25 GPa 2.2103 TPa–1 8.2097 TPa–1 53 GPa 262 GPa-0.661110.41501Value
Anisotropy 1.857 3.7143 4.943Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
-0.0000
1.0000
1.0000
0.0007
0.0000
-0.7071
0.7071
-0.0000
0.4678
0.4679
0.7498
Axis
1.0000
0.0002
0.0000
-0.0007
1.0000
-0.0000
-0.7071
-0.7071
0.0000
0.5303
0.5301
-0.6616
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