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 GaCl2 (Materials Project id mp-568848)

         4        0        1        0        0        0  
         0        9        0        0        0        0  
         1        0        6        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 2.3333 GPaEV = 4.6667 GPaGV = 2 GPaνV = 0.16667
ReussKR = 2.1789 GPaER = 3.703 GPaGR = 1.5217 GPaνR = 0.21676
HillKH = 2.2561 GPaEH = 4.192 GPaGH = 1.7608 GPaνH = 0.19033

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 2 GPa 3.5858 GPa 6.4142 GPa 9 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.8083 GPa 9 GPa 111.11 TPa–1 217.39 TPa–1 1 GPa 3.5085 GPa9.1195e-140.48937Value
Anisotropy 3.205 1.9565 3.5085366238062241.4756Anisotropy
Axis 0.7568
0.5168
0.4003
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.7071
-0.7071
-1.0000
0.0000
-0.0027
0.6426
0.0000
0.7662
Axis
1.0000
0.0000
-0.0000
-0.0000
0.7071
0.7071
-0.0000
-1.0000
0.0000
0.7662
0.0000
-0.6426
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