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 CoMoO4 (Materials Project id mp-19435)

       262      101       99        0       21        0  
       101      207      101        0        0        0  
        99      101      202        0        7        0  
         0        0        0       29        0      -17  
        21        0        7        0       72        0  
         0        0        0      -17        0       63  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 141.44 GPaEV = 151.84 GPaGV = 57.467 GPaνV = 0.32109
ReussKR = 138.88 GPaER = 125.1 GPaGR = 46.337 GPaνR = 0.34988
HillKH = 140.16 GPaEH = 138.6 GPaGH = 51.902 GPaνH = 0.3352

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21.958 GPa 68.215 GPa 70.042 GPa 104.11 GPa 142.96 GPa 427.71 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.51 GPa 223.27 GPa 1.6871 TPa–1 2.9399 TPa–1 21.958 GPa 75.823 GPa-0.0716070.80058Value
Anisotropy 3.037 1.7426 3.453Anisotropy
Axis -0.2622
0.7143
-0.6488
-0.9061
0.0000
-0.4231
0.9395
-0.0000
0.3426
-0.3426
0.0000
0.9395
0.3827
-0.0003
0.9239
-0.9568
0.2676
0.1137
-0.8800
0.4324
-0.1964
0.8335
0.4838
0.2669
Axis
0.0001
1.0000
0.0002
-0.2666
-0.6512
-0.7105
-0.4296
-0.5483
0.7175
-0.2061
0.7203
-0.6624
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