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 ZrFe2 (Materials Project id mp-1718)

       226      108      108        0        0        0  
       108      226      108        0        0        0  
       108      108      226        0        0        0  
         0        0        0       83        0        0  
         0        0        0        0       83        0  
         0        0        0        0        0       83  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 147.33 GPaEV = 188.84 GPaGV = 73.4 GPaνV = 0.28638
ReussKR = 147.33 GPaER = 184.38 GPaGR = 71.385 GPaνR = 0.29143
HillKH = 147.33 GPaEH = 186.61 GPaGH = 72.392 GPaνH = 0.2889

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
83 GPa 83 GPa 83 GPa 118 GPa 118 GPa 442 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 156.16 GPa 209.63 GPa 2.2624 TPa–1 2.2624 TPa–1 59 GPa 83 GPa0.163260.39986Value
Anisotropy 1.342 1.0000 1.407 2.4492Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-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