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 Mn3Ge (Materials Project id mp-865027)

       248      161      161        0        0        0  
       161      248      161        0        0        0  
       161      161      248        0        0        0  
         0        0        0      134        0        0  
         0        0        0        0      134        0  
         0        0        0        0        0      134  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 190 GPaEV = 250.43 GPaGV = 97.8 GPaνV = 0.28032
ReussKR = 190 GPaER = 194.46 GPaGR = 73.137 GPaνR = 0.32942
HillKH = 190 GPaEH = 222.97 GPaGH = 85.468 GPaνH = 0.30441

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
87 GPa 87 GPa 134 GPa 134 GPa 134 GPa 570 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 121.25 GPa 325.48 GPa 1.7544 TPa–1 1.7544 TPa–1 43.5 GPa 134 GPa-0.14540.74358Value
Anisotropy 2.684 1.0000 3.08Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
-0.3363
0.8119
0.4772
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
-1.0000
-0.0000
0.0000
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