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 NdGa3 (Materials Project id mp-567454)

       119       38       38        0        0        0  
        38      119       38        0        0        0  
        38       38      119        0        0        0  
         0        0        0       32        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65 GPaEV = 89.883 GPaGV = 35.4 GPaνV = 0.26953
ReussKR = 65 GPaER = 88.876 GPaGR = 34.933 GPaνR = 0.27211
HillKH = 65 GPaEH = 89.38 GPaGH = 35.166 GPaνH = 0.27082

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 32 GPa 32 GPa 81 GPa 81 GPa 195 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 82.467 GPa 100.61 GPa 5.1282 TPa–1 5.1282 TPa–1 32 GPa 40.5 GPa0.207770.34937Value
Anisotropy 1.22 1.0000 1.266 1.6815Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.0000
0.7934
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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