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 SiNi (Materials Project id mp-351)

       271       84      158        0        0        0  
        84      230      142        0        0        0  
       158      142      220        0        0        0  
         0        0        0      106        0        0  
         0        0        0        0      126        0  
         0        0        0        0        0      128  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 165.44 GPaEV = 238.09 GPaGV = 94.467 GPaνV = 0.26016
ReussKR = 162.68 GPaER = 182.27 GPaGR = 69.395 GPaνR = 0.31327
HillKH = 164.06 GPaEH = 210.72 GPaGH = 81.931 GPaνH = 0.28594

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57.416 GPa 106 GPa 126 GPa 128 GPa 165 GPa 498.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 85.454 GPa 292.36 GPa 1.1966 TPa–1 2.8374 TPa–1 33.654 GPa 128 GPa-0.329140.90754Value
Anisotropy 3.421 2.3712 3.803Anisotropy
Axis 0.0000
0.0000
1.0000
0.6637
0.4591
-0.5904
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0001
0.7071
-0.7071
1.0000
0.0000
-0.0000
0.7251
0.6886
0.0000
-0.7631
0.6462
-0.0000
Axis
0.0000
-0.7071
-0.7071
-0.0000
1.0000
-0.0000
-0.6886
0.7251
0.0000
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