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 CoAs2 (Materials Project id mp-2715)

       249       54       72        0       40        0  
        54      316       60        0       10        0  
        72       60      264        0      -16        0  
         0        0        0      107        0       28  
        40       10      -16        0       72        0  
         0        0        0       28        0       82  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 133.44 GPaEV = 230.47 GPaGV = 95.067 GPaνV = 0.21215
ReussKR = 130.25 GPaER = 205.21 GPaGR = 82.917 GPaνR = 0.23743
HillKH = 131.85 GPaEH = 217.94 GPaGH = 88.992 GPaνH = 0.22451

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
58.081 GPa 63.837 GPa 125.16 GPa 197.01 GPa 241.52 GPa 404.39 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 139.36 GPa 296.3 GPa 1.876 TPa–1 3.5629 TPa–1 51.364 GPa 125.16 GPa0.00102830.54908Value
Anisotropy 2.126 1.8992 2.437533.9443Anisotropy
Axis -0.8531
0.2481
0.4590
-0.1309
0.9711
-0.1995
-0.5264
0.0000
-0.8503
-0.8503
0.0000
0.5263
-0.2987
0.0001
0.9543
0.5442
0.0001
0.8389
-0.0275
0.6034
-0.7970
0.4668
0.1245
0.8756
Axis
-0.9543
-0.0000
-0.2987
-0.0002
1.0000
-0.0000
-0.6556
-0.6127
-0.4413
-0.8817
-0.0121
0.4717
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