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 Hf2Ge (Materials Project id mp-9939)

       259       70       70        0        0        0  
        70      246       81        0        0        0  
        70       81      246        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0      108        0  
         0        0        0        0        0      108  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 132.56 GPaEV = 228.35 GPaGV = 94.133 GPaνV = 0.21289
ReussKR = 132.55 GPaER = 225.05 GPaGR = 92.456 GPaνR = 0.21704
HillKH = 132.55 GPaEH = 226.7 GPaGH = 93.295 GPaνH = 0.21496

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
78 GPa 108 GPa 108 GPa 165 GPa 188.33 GPa 397.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 202.66 GPa 243.51 GPa 2.4969 TPa–1 2.5236 TPa–1 78 GPa 108 GPa0.109390.30298Value
Anisotropy 1.202 1.0107 1.385 2.7696Anisotropy
Axis 0.0000
0.7071
0.7071
0.7831
-0.0000
0.6219
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0004
-0.0002
1.0000
0.0000
0.0000
1.0000
0.6941
0.5090
-0.5091
0.4255
0.6399
-0.6399
Axis
-0.0000
1.0000
0.0002
-1.0000
0.0000
0.0000
-0.7199
0.4908
-0.4908
0.0000
0.7071
0.7071
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