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 SmGe2 (Materials Project id mp-12750)

       103       48       44        0        0        0  
        48      103       44        0        0        0  
        44       44      115        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       51  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65.889 GPaEV = 71.111 GPaGV = 26.933 GPaνV = 0.32012
ReussKR = 65.82 GPaER = 51.298 GPaGR = 18.72 GPaνR = 0.37011
HillKH = 65.854 GPaEH = 61.388 GPaGH = 22.827 GPaνH = 0.34464

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 51 GPa 55 GPa 68.223 GPa 197.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 36.694 GPa 109.13 GPa 4.6691 TPa–1 5.262 TPa–1 11 GPa 51 GPa0.0585620.73714Value
Anisotropy 2.974 1.1270 4.636 12.5874Anisotropy
Axis 0.7198
-0.0000
0.6942
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0007
-0.0000
0.6456
0.6456
0.4079
0.5217
0.5217
-0.6750
Axis
-0.7880
0.6157
-0.0000
-0.0007
1.0000
-0.0000
-0.7071
0.7071
-0.0000
0.4773
0.4773
0.7378
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