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 CuO (Materials Project id mp-1692)

       198       75      119        0        0        0  
        75      198      119        0        0        0  
       119      119      332        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0       13        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 150.44 GPaEV = 95.546 GPaGV = 34.267 GPaνV = 0.39415
ReussKR = 135.17 GPaER = 44.146 GPaGR = 15.27 GPaνR = 0.44557
HillKH = 142.81 GPaEH = 70.243 GPaGH = 24.768 GPaνH = 0.41802

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 13 GPa 13 GPa 123 GPa 131.64 GPa 473.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.056 GPa 228.26 GPa 0.56167 TPa–1 3.4182 TPa–1 7 GPa 66.982 GPa0.049760.83117Value
Anisotropy 8.76 6.0857 9.569 16.7037Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
0.0001
0.7071
-0.0000
-0.7071
-0.7071
0.7071
-0.0000
0.6377
-0.0000
-0.7703
Axis
0.0002
1.0000
-0.0000
-0.7071
0.0002
-0.7071
-0.0004
-0.0004
-1.0000
-0.7703
0.0001
-0.6377
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