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 YSiAu (Materials Project id mp-9025)

       196       81       74        0        0        0  
        81      196       74        0        0        0  
        74       74       83        0        0        0  
         0        0        0       51        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       58  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 103.67 GPaEV = 125.65 GPaGV = 48.4 GPaνV = 0.298
ReussKR = 81.898 GPaER = 102.84 GPaGR = 39.836 GPaνR = 0.29072
HillKH = 92.782 GPaEH = 114.25 GPaGH = 44.118 GPaνH = 0.29478

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37.308 GPa 51 GPa 51 GPa 58 GPa 115 GPa 322.69 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 43.462 GPa 142.03 GPa 0.74757 TPa–1 10.715 TPa–1 23.204 GPa 58 GPa0.028580.79236Value
Anisotropy 3.268 14.3333 2.5 27.7238Anisotropy
Axis 0.0000
0.0000
1.0000
-0.6423
0.6423
0.4181
-0.0172
0.9999
-0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
0.0007
0.0000
0.7004
0.0002
-0.7138
0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
-0.0007
1.0000
0.0000
-0.7138
-0.0002
-0.7004
0.0001
-0.0001
-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