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 BaZnSi (Materials Project id mp-31147)

        93       20       25        0        0        0  
        20       93       25        0        0        0  
        25       25       72        0        0        0  
         0        0        0       29        0        0  
         0        0        0        0       29        0  
         0        0        0        0        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 44.222 GPaEV = 76.433 GPaGV = 31.533 GPaνV = 0.21194
ReussKR = 43.86 GPaER = 75.029 GPaGR = 30.879 GPaνR = 0.21489
HillKH = 44.041 GPaEH = 75.732 GPaGH = 31.206 GPaνH = 0.21341

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29 GPa 29 GPa 37 GPa 51.631 GPa 73 GPa 133.37 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.938 GPa 83.439 GPa 6.8254 TPa–1 9.149 TPa–1 27.973 GPa 37 GPa0.127560.30293Value
Anisotropy 1.369 1.3404 1.323 2.3748Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
1.0000
-0.0002
-0.0000
0.7071
0.7071
0.0000
0.7071
0.7071
0.0000
Axis
-0.7071
-0.0002
-0.7071
0.0002
1.0000
-0.0000
-0.7071
0.7071
-0.0000
-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