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 YFe2 (Materials Project id mp-1570)

       128       73       73        0        0        0  
        73      128       73        0        0        0  
        73       73      128        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       43        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 91.333 GPaEV = 97.328 GPaGV = 36.8 GPaνV = 0.32239
ReussKR = 91.333 GPaER = 93.317 GPaGR = 35.089 GPaνR = 0.32971
HillKH = 91.333 GPaEH = 95.328 GPaGH = 35.945 GPaνH = 0.32604

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
43 GPa 43 GPa 43 GPa 55 GPa 55 GPa 274 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 74.975 GPa 111.5 GPa 3.6496 TPa–1 3.6496 TPa–1 27.5 GPa 43 GPa0.155760.48148Value
Anisotropy 1.487 1.0000 1.564 3.0911Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.7934
0.0000
0.6088
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