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 GdGa (Materials Project id mp-20353)

        85       39       49        0        0        0  
        39      119       29        0        0        0  
        49       29      109        0        0        0  
         0        0        0       34        0        0  
         0        0        0        0       63        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 60.778 GPaEV = 95.704 GPaGV = 38.667 GPaνV = 0.23756
ReussKR = 60.454 GPaER = 86.204 GPaGR = 34.145 GPaνR = 0.26234
HillKH = 60.616 GPaEH = 90.999 GPaGH = 36.406 GPaνH = 0.24979

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 34 GPa 43.544 GPa 63 GPa 86.803 GPa 182.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 56.915 GPa 127.67 GPa 4.8379 TPa–1 6.663 TPa–1 22.918 GPa 63 GPa-0.0164150.54689Value
Anisotropy 2.243 1.3772 2.749Anisotropy
Axis 1.0000
0.0000
0.0000
0.6386
0.0000
0.7696
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0002
0.7071
-0.0000
0.0000
1.0000
0.7060
-0.0000
-0.7082
0.0000
0.0000
1.0000
Axis
0.7071
-0.0006
-0.7071
-1.0000
0.0000
-0.0000
-0.7082
0.0003
-0.7060
1.0000
0.0000
-0.0000
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