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 InI3 (Materials Project id mp-567789)

         3        1        1        0       -0        0  
         1        2        1        0        0        0  
         1        1        4        0        1        0  
         0        0        0        1        0        0  
        -0        0        1        0        1        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 1.6667 GPaEV = 2.5 GPaGV = 1 GPaνV = 0.25
ReussKR = 1.5 GPaER = 2.1176 GPaGR = 0.83721 GPaνR = 0.26471
HillKH = 1.5833 GPaEH = 2.3092 GPaGH = 0.9186 GPaνH = 0.25692

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.61734 GPa 1 GPa 1 GPa 1.359 GPa 2.6735 GPa 5.3502 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1.3349 GPa 4.4297 GPa 83.333 TPa–1 333.33 TPa–1 0.52568 GPa 1.5 GPa6.1633e-080.59864Value
Anisotropy 3.318 4.0000 2.8539712979.2050Anisotropy
Axis 0.5307
-0.0000
-0.8476
0.3929
-0.0000
0.9196
-0.7071
0.0000
-0.7071
0.0000
1.0000
0.0000
0.4018
0.7071
-0.5819
-0.8817
0.0011
-0.4719
0.2898
0.0001
0.9571
-0.7889
0.3135
-0.5286
Axis
-0.4017
0.7071
0.5819
0.4719
-0.0007
-0.8817
0.9571
0.0004
-0.2898
0.5231
-0.1089
-0.8453
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