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 ZrIr3 (Materials Project id mp-1438)

       404      197      197        0        0        0  
       197      404      197        0        0        0  
       197      197      404        0        0        0  
         0        0        0      198        0        0  
         0        0        0        0      198        0  
         0        0        0        0        0      198  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 266 GPaEV = 400.25 GPaGV = 160.2 GPaνV = 0.24922
ReussKR = 266 GPaER = 368.18 GPaGR = 145.03 GPaνR = 0.26931
HillKH = 266 GPaEH = 384.34 GPaGH = 152.62 GPaνH = 0.25918

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
198 GPa 198 GPa 198 GPa 207 GPa 207 GPa 798 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 274.85 GPa 475.92 GPa 1.2531 TPa–1 1.2531 TPa–1 103.5 GPa 198 GPa0.0159980.47982Value
Anisotropy 1.732 1.0000 1.913 29.9930Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
0.5773
0.2053
0.7663
0.6088
0.8660
0.0000
0.5000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
0.0001
1.0000
0.0001
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