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 Co(AsO3)2 (Materials Project id mp-19292)

       334      144       61        0       -6        0  
       144      334       61        0        6        0  
        61       61      183        0        0        0  
         0        0        0       49        0        6  
        -6        6        0        0       49        0  
         0        0        0        6        0       95  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 153.67 GPaEV = 199.26 GPaGV = 77.6 GPaνV = 0.28388
ReussKR = 133.39 GPaER = 173.68 GPaGR = 67.685 GPaνR = 0.28299
HillKH = 143.53 GPaEH = 186.47 GPaGH = 72.643 GPaνH = 0.28347

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48.23 GPa 48.491 GPa 95.77 GPa 159.63 GPa 190.51 GPa 501.37 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 131.81 GPa 266.04 GPa 1.5244 TPa–1 4.4482 TPa–1 48.23 GPa 95.77 GPa0.0942160.45059Value
Anisotropy 2.018 2.9180 1.986 4.7825Anisotropy
Axis 0.3247
0.5625
-0.7604
0.9984
0.0000
-0.0562
0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
-0.1273
-0.0000
0.9919
-0.0000
1.0000
0.0000
0.2226
0.3856
0.8954
0.3737
0.6473
0.6644
Axis
0.0000
1.0000
0.0000
-0.9919
-0.0000
-0.1272
-0.8660
0.5000
-0.0000
0.3322
0.5754
-0.7474
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