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-619461)

       136       13       68        0       19        0  
        13      133        4        0       27        0  
        68        4      162        0       20        0  
         0        0        0       56        0       -5  
        19       27       20        0       60        0  
         0        0        0       -5        0       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 66.778 GPaEV = 132.88 GPaGV = 56.867 GPaνV = 0.16835
ReussKR = 55.185 GPaER = 118.95 GPaGR = 52.137 GPaνR = 0.14075
HillKH = 60.981 GPaEH = 125.98 GPaGH = 54.502 GPaνH = 0.1557

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48.028 GPa 49.28 GPa 59.72 GPa 78.791 GPa 138.51 GPa 225.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 101.74 GPa 177.14 GPa 1.4518 TPa–1 8.3945 TPa–1 39.913 GPa 75.52 GPa-0.218230.49607Value
Anisotropy 1.741 5.7822 1.892Anisotropy
Axis 0.9769
-0.0000
-0.2137
0.6366
-0.0000
0.7712
-0.6772
-0.0000
-0.7358
0.7358
0.0000
-0.6772
0.6981
-0.0002
0.7160
0.4089
0.7071
-0.5769
-0.5952
0.0000
0.8036
-0.2109
0.0000
-0.9775
Axis
0.7160
-0.0004
-0.6981
-0.4089
0.7071
0.5769
-0.0001
-1.0000
0.0000
0.9775
0.0000
-0.2109
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