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 Ga (Materials Project id mp-569007)

        57       41       42       -0        0        0  
        41       57       42        0        0        0  
        42       42       64        0        0        0  
        -0        0        0        5        0        0  
         0        0        0        0        5       -0  
         0        0        0        0       -0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 47.556 GPaEV = 20.381 GPaGV = 7.1333 GPaνV = 0.42857
ReussKR = 47.31 GPaER = 19.006 GPaGR = 6.6314 GPaνR = 0.43304
HillKH = 47.433 GPaEH = 19.695 GPaGH = 6.8824 GPaνH = 0.4308

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 8 GPa 16 GPa 19.218 GPa 142.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 16.091 GPa 28 GPa 5.102 TPa–1 8.0175 TPa–1 5 GPa 9.1543 GPa0.280580.61508Value
Anisotropy 1.74 1.5714 1.831 2.1922Anisotropy
Axis 0.6787
0.2811
0.6785
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.1699
0.6864
-0.7071
0.5046
0.4483
-0.7378
0.3277
0.5738
-0.7506
Axis
-0.7660
0.6428
-0.0000
0.1700
-0.6864
-0.7071
-0.6642
0.7475
-0.0000
0.3722
0.6518
0.6608
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