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 ZrCr2 (Materials Project id mp-1919)

       273      131      139        0        0        0  
       131      273      139        0        0        0  
       139      139      252        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       71  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 179.56 GPaEV = 149.55 GPaGV = 54.933 GPaνV = 0.36119
ReussKR = 179.45 GPaER = 138.16 GPaGR = 50.363 GPaνR = 0.37168
HillKH = 179.5 GPaEH = 143.88 GPaGH = 52.648 GPaνH = 0.36641

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 37 GPa 71 GPa 117.24 GPa 142 GPa 538.76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 115.57 GPa 181.3 GPa 1.7889 TPa–1 1.9947 TPa–1 37 GPa 71 GPa0.212810.56663Value
Anisotropy 1.569 1.1150 1.919 2.6626Anisotropy
Axis 0.2398
0.6336
0.7356
0.7934
0.6088
0.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
-0.0836
0.9965
0.0000
0.5885
0.5103
-0.6271
0.6106
0.4253
0.6681
Axis
-0.7648
0.6443
0.0000
-0.9965
-0.0836
-0.0000
-0.6551
0.7555
-0.0000
-0.5482
-0.3818
0.7441
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