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 MgZrN2 (Materials Project id mp-1029536)

       204      133       90        0        0        0  
       133      194       94        0        0        0  
        90       94      325        0        0        0  
         0        0        0      118        0        0  
         0        0        0        0      112        0  
         0        0        0        0        0       34  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 150.78 GPaEV = 203.64 GPaGV = 79.867 GPaνV = 0.2749
ReussKR = 148.1 GPaER = 152.42 GPaGR = 57.367 GPaνR = 0.32847
HillKH = 149.44 GPaEH = 178.53 GPaGH = 68.617 GPaνH = 0.30089

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34 GPa 65.764 GPa 112 GPa 118 GPa 198.57 GPa 458.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 102.92 GPa 277.66 GPa 1.6233 TPa–1 2.7095 TPa–1 32.921 GPa 118 GPa-0.132090.70925Value
Anisotropy 2.698 1.6691 3.584Anisotropy
Axis 0.0000
1.0000
0.0000
-0.0000
0.2914
0.9566
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
-0.0000
-0.0000
1.0000
-0.0000
0.6720
-0.7406
0.7748
0.0005
0.6322
Axis
-0.7071
-0.7071
0.0000
0.0000
1.0000
0.0000
0.0000
-0.7406
-0.6720
-0.0006
1.0000
-0.0000
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