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 GeAs (Materials Project id mp-9548)

        37       21       18        0       18        0  
        21      109        7        0        4        0  
        18        7       44        0       21        0  
         0        0        0       14        0       12  
        18        4       21        0       19        0  
         0        0        0       12        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 31.333 GPaEV = 51.896 GPaGV = 21.2 GPaνV = 0.22396
ReussKR = 9.2259 GPaER = 21.125 GPaGR = 9.4446 GPaνR = 0.11837
HillKH = 20.28 GPaEH = 36.719 GPaGH = 15.322 GPaνH = 0.19823

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4.5188 GPa 6.2996 GPa 20.587 GPa 32.7 GPa 65.639 GPa 118.25 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.428 GPa 92.447 GPa -1.25 TPa–1 110.58 TPa–1 5.625 GPa 40.528 GPa-0.149071.0568Value
Anisotropy 12.45 7.205Anisotropy
Axis 0.7267
-0.0000
-0.6870
0.0000
1.0000
0.0000
-0.6986
0.0000
-0.7155
-0.7156
-0.0000
0.6985
-0.2663
0.3960
0.8788
-0.4046
0.7071
-0.5799
-0.0896
-0.0000
-0.9960
0.6273
0.3744
0.6828
Axis
-0.7736
-0.6317
0.0503
-0.4047
-0.7071
-0.5799
-0.9960
0.0000
0.0896
0.5808
0.3592
-0.7305
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