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 Cu (Materials Project id mp-30)

       180      127      127        0        0        0  
       127      180      127        0        0        0  
       127      127      180        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       78  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 144.67 GPaEV = 152.09 GPaGV = 57.4 GPaνV = 0.32479
ReussKR = 144.67 GPaER = 119.57 GPaGR = 43.885 GPaνR = 0.36225
HillKH = 144.67 GPaEH = 136.05 GPaGH = 50.643 GPaνH = 0.34326

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
53 GPa 53 GPa 78 GPa 78 GPa 78 GPa 434 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 74.925 GPa 198.35 GPa 2.3041 TPa–1 2.3041 TPa–1 26.5 GPa 78 GPa-0.0994090.77569Value
Anisotropy 2.647 1.0000 2.943Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.7934
0.0000
0.6088
0.3314
0.8001
0.5000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
0.0000
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