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 CaGa2 (Materials Project id mp-992)

       123       23       27        0        0        0  
        23      123       27        0        0        0  
        27       27       38        0        0        0  
         0        0        0       28        0        0  
         0        0        0        0       28        0  
         0        0        0        0        0       50  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48.667 GPaEV = 84.696 GPaGV = 35 GPaνV = 0.20994
ReussKR = 35.877 GPaER = 65.423 GPaGR = 27.349 GPaνR = 0.19608
HillKH = 42.272 GPaEH = 75.07 GPaGH = 31.174 GPaνH = 0.20402

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25.864 GPa 28 GPa 28 GPa 50 GPa 100 GPa 158.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 28.014 GPa 103.68 GPa 2.6895 TPa–1 22.494 TPa–1 17.081 GPa 50 GPa0.0514630.68441Value
Anisotropy 3.701 8.3636 2.927 13.2992Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0002
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7889
0.6145
-0.0000
0.5182
0.4478
-0.7287
-0.8433
0.5374
0.0000
Axis
0.7071
-0.0005
-0.7071
-0.6145
0.7889
0.0000
-0.5514
-0.4764
-0.6849
0.0000
0.0000
-1.0000
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