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-1070)

        66       36       31        0        0        0  
        36       66       31        0        0        0  
        31       31       72        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0       13        0  
         0        0        0        0        0       15  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 44.444 GPaEV = 41.095 GPaGV = 15.267 GPaνV = 0.3459
ReussKR = 44.443 GPaER = 40.122 GPaGR = 14.865 GPaνR = 0.34954
HillKH = 44.444 GPaEH = 40.609 GPaGH = 15.066 GPaνH = 0.34771

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
13 GPa 13 GPa 15 GPa 30 GPa 40.664 GPa 133.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 36.876 GPa 53.157 GPa 7.3774 TPa–1 7.5618 TPa–1 13 GPa 18.673 GPa0.245320.43235Value
Anisotropy 1.441 1.0250 1.436 1.7624Anisotropy
Axis 0.7413
0.2159
0.6355
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
-0.4301
0.9028
0.0000
0.4958
0.4253
-0.7571
Axis
0.1735
0.9848
-0.0000
-0.5291
-0.4692
-0.7071
-0.0000
-0.0000
1.0000
-0.5747
-0.4930
-0.6533
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