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 CdSe (Materials Project id mp-2691)

        57       39       39        0        0        0  
        39       57       39        0        0        0  
        39       39       57        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 45 GPaEV = 44.822 GPaGV = 16.8 GPaνV = 0.33399
ReussKR = 45 GPaER = 37.915 GPaGR = 13.944 GPaνR = 0.35957
HillKH = 45 GPaEH = 41.401 GPaGH = 15.372 GPaνH = 0.34666

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 22 GPa 22 GPa 22 GPa 135 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 25.312 GPa 56.752 GPa 7.4074 TPa–1 7.4074 TPa–1 9 GPa 22 GPa-0.0157960.69502Value
Anisotropy 2.242 1.0000 2.444Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
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