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 Fe (Materials Project id mp-136)

       538      170      153        0        0        0  
       170      538      153        0        0        0  
       153      153      622        0        0        0  
         0        0        0      168        0        0  
         0        0        0        0      168        0  
         0        0        0        0        0      184  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 294.44 GPaEV = 459.85 GPaGV = 185.47 GPaνV = 0.23971
ReussKR = 293.7 GPaER = 455.4 GPaGR = 183.4 GPaνR = 0.24157
HillKH = 294.07 GPaEH = 457.63 GPaGH = 184.43 GPaνH = 0.24064

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
168 GPa 168 GPa 184 GPa 368 GPa 444.39 GPa 885.61 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 433.72 GPa 555.87 GPa 1.0215 TPa–1 1.1917 TPa–1 168 GPa 211.62 GPa0.180910.30643Value
Anisotropy 1.282 1.1667 1.26 1.6938Anisotropy
Axis 0.2608
0.7580
0.5978
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.5644
0.4260
0.7071
0.1058
0.9944
-0.0000
0.6611
0.0001
-0.7503
Axis
-0.7660
-0.6428
0.0000
0.5646
0.4258
-0.7071
-0.0000
0.0000
1.0000
-0.7503
-0.0001
-0.6611
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