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 ZrNiBi (Materials Project id mp-31452)

       176       69       69        0        0        0  
        69      176       69        0        0        0  
        69       69      176        0        0        0  
         0        0        0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 104.67 GPaEV = 105.02 GPaGV = 39.4 GPaνV = 0.33277
ReussKR = 104.67 GPaER = 97.843 GPaGR = 36.395 GPaνR = 0.3442
HillKH = 104.67 GPaEH = 101.45 GPaGH = 37.897 GPaνH = 0.33846

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 30 GPa 30 GPa 107 GPa 107 GPa 314 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 82.151 GPa 137.13 GPa 3.1847 TPa–1 3.1847 TPa–1 30 GPa 53.5 GPa0.187510.52172Value
Anisotropy 1.669 1.0000 1.783 2.7824Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3827
0.0000
0.9239
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
0.1736
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
-0.0000
-0.7071
0.0002
-0.7071
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