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 CuS (Materials Project id mp-555599)

       136       35       93        0        0        0  
        35      131       16        0        0        0  
        93       16      129        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       24        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76 GPaEV = 73.381 GPaGV = 27.4 GPaνV = 0.33908
ReussKR = 71.833 GPaER = 55.157 GPaGR = 20.101 GPaνR = 0.37202
HillKH = 73.917 GPaEH = 64.358 GPaGH = 23.75 GPaνH = 0.35489

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 15 GPa 24 GPa 37.552 GPa 120.46 GPa 237.98 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.79 GPa 121.03 GPa 1.8513 TPa–1 6.4529 TPa–1 14 GPa 46.634 GPa-0.0650350.70056Value
Anisotropy 2.828 3.4857 3.331Anisotropy
Axis 0.0000
0.6485
0.7612
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.0000
0.2688
0.7071
0.6540
-0.0002
0.0001
1.0000
0.0000
0.0000
1.0000
Axis
-0.0000
1.0000
-0.0000
-0.2688
0.7071
-0.6540
0.0000
-1.0000
0.0001
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