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 Zr3Tl (Materials Project id mp-977585)

       175       94       94        0        0        0  
        94      175       94        0        0        0  
        94       94      175        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       78  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 121 GPaEV = 161.05 GPaGV = 63 GPaνV = 0.27817
ReussKR = 121 GPaER = 147.61 GPaGR = 56.919 GPaνR = 0.29668
HillKH = 121 GPaEH = 154.38 GPaGH = 59.959 GPaνH = 0.28736

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
78 GPa 78 GPa 78 GPa 81 GPa 81 GPa 363 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 109.3 GPa 192.61 GPa 2.7548 TPa–1 2.7548 TPa–1 40.5 GPa 78 GPa0.0370880.51722Value
Anisotropy 1.762 1.0000 1.926 13.9458Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9239
0.0000
0.3827
0.3794
0.9160
-0.1305
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
-0.0000
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