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 CaAlSiH (Materials Project id mp-568177)

       151       46       23      -13        0        0  
        46      151       23       13        0        0  
        23       23       53        0        0        0  
       -13       13        0       38        0        0  
         0        0        0        0       38      -13  
         0        0        0        0      -13       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 59.889 GPaEV = 104.74 GPaGV = 43.333 GPaνV = 0.20852
ReussKR = 44.469 GPaER = 85.881 GPaGR = 36.448 GPaνR = 0.17812
HillKH = 52.179 GPaEH = 95.369 GPaGH = 39.891 GPaνH = 0.19538

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30.492 GPa 33.287 GPa 45.994 GPa 60.508 GPa 109.71 GPa 204.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.629 GPa 145.27 GPa 3.1973 TPa–1 16.093 TPa–1 27.981 GPa 60.23 GPa0.0404710.52262Value
Anisotropy 3.05 5.0333 2.153 12.9134Anisotropy
Axis 0.0000
0.0000
1.0000
-0.8306
0.4845
-0.2746
0.9915
0.1304
-0.0000
0.0000
0.0000
1.0000
0.0001
0.8526
0.5225
-0.7497
0.4280
0.5047
-0.0000
0.5029
-0.8643
-1.0000
0.0000
0.0000
Axis
-0.0003
0.5225
-0.8526
-0.4944
-0.8692
0.0026
0.0000
0.8643
0.5029
0.0000
-0.6998
0.7143
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