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 Fe3Ge (Materials Project id mp-21078)

       284      140       94        0        0        0  
       140      284       94        0        0        0  
        94       94      296        0        0        0  
         0        0        0       51        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       72  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 168.89 GPaEV = 185.74 GPaGV = 70.533 GPaνV = 0.3167
ReussKR = 168.49 GPaER = 173.85 GPaGR = 65.453 GPaνR = 0.32803
HillKH = 168.69 GPaEH = 179.82 GPaGH = 67.993 GPaνH = 0.32234

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 51 GPa 72 GPa 144 GPa 212.46 GPa 507.54 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 149.63 GPa 254.32 GPa 1.8733 TPa–1 2.1886 TPa–1 51 GPa 95.055 GPa0.200590.47346Value
Anisotropy 1.7 1.1683 1.864 2.3604Anisotropy
Axis 0.3362
0.6612
0.6707
0.0000
0.0000
1.0000
0.2549
0.9670
-0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
-0.4586
0.0551
-0.8869
0.3454
0.5792
0.7383
Axis
-0.7660
0.6428
-0.0000
-0.5291
-0.4692
-0.7071
-0.1192
-0.9929
-0.0000
0.3783
0.6341
-0.6744
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