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 Ba(AgGe)2 (Materials Project id mp-13910)

        91       16       39        0        0        0  
        16       91       39        0        0        0  
        39       39       91        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51.222 GPaEV = 77.665 GPaGV = 31.133 GPaνV = 0.24729
ReussKR = 50.338 GPaER = 73.103 GPaGR = 29.056 GPaνR = 0.25796
HillKH = 50.78 GPaEH = 75.391 GPaGH = 30.095 GPaνH = 0.25256

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 37 GPa 37 GPa 43.269 GPa 75 GPa 154.73 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 55.067 GPa 90.15 GPa 4.3316 TPa–1 7.767 TPa–1 21.838 GPa 37 GPa-0.00961470.4318Value
Anisotropy 1.637 1.7931 1.694Anisotropy
Axis 0.7071
0.7071
0.0000
0.7678
0.0000
0.6407
0.0000
0.0000
1.0000
0.9239
0.3827
0.0000
-0.5002
0.4998
-0.7071
0.0000
0.0000
1.0000
1.0000
0.0007
0.0000
0.4268
0.4268
0.7973
Axis
0.4999
-0.5001
-0.7071
-0.9397
-0.3420
0.0000
-0.0007
1.0000
-0.0000
-0.7071
0.7071
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