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 Dy2AlGe2 (Materials Project id mp-21382)

       120       65       65        0        0        0  
        65      111       52        0        0        0  
        65       52      111        0        0        0  
         0        0        0       39        0        0  
         0        0        0        0       77        0  
         0        0        0        0        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 78.444 GPaEV = 122.21 GPaGV = 49.267 GPaνV = 0.24034
ReussKR = 77.692 GPaER = 100.45 GPaGR = 39.1 GPaνR = 0.28452
HillKH = 78.068 GPaEH = 111.51 GPaGH = 44.183 GPaνH = 0.26193

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 47.095 GPa 59 GPa 77 GPa 77 GPa 235.9 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.16 GPa 145.75 GPa 2.9703 TPa–1 4.9505 TPa–1 24.846 GPa 77 GPa-0.129350.60892Value
Anisotropy 2.138 1.6667 3.099Anisotropy
Axis 1.0000
0.0000
0.0000
-0.6658
0.5276
0.5276
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.0000
1.0000
0.7059
-0.0000
-0.7083
-0.7543
0.6565
-0.0000
Axis
-0.7071
0.0002
-0.7071
1.0000
0.0000
-0.0000
-0.7083
0.0003
-0.7059
0.0000
0.0000
1.0000
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