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 GdSe (Materials Project id mp-510404)

       201       35       35        0        0        0  
        35      201       35        0        0        0  
        35       35      201        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 90.333 GPaEV = 116.22 GPaGV = 45.2 GPaνV = 0.28558
ReussKR = 90.333 GPaER = 77.903 GPaGR = 28.72 GPaνR = 0.35627
HillKH = 90.333 GPaEH = 97.572 GPaGH = 36.96 GPaνH = 0.31998

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 20 GPa 20 GPa 166 GPa 166 GPa 271 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 55.876 GPa 190.62 GPa 3.69 TPa–1 3.69 TPa–1 20 GPa 83 GPa0.0528040.69675Value
Anisotropy 3.411 1.0000 4.15 13.1950Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.9239
0.0000
0.3827
0.4830
0.6294
-0.6088
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
0.0000
-0.7071
0.0002
-0.7071
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