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 La2O3 (Materials Project id mp-1968)

       199      119       79      -32        0        0  
       119      199       79       32        0        0  
        79       79      132        0        0        0  
       -32       32        0       56        0        0  
         0        0        0        0       56      -32  
         0        0        0        0      -32       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 120.44 GPaEV = 125.4 GPaGV = 47.267 GPaνV = 0.32648
ReussKR = 110.88 GPaER = 75.977 GPaGR = 27.413 GPaνR = 0.3858
HillKH = 115.66 GPaEH = 101.14 GPaGH = 37.34 GPaνH = 0.35427

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15.015 GPa 21.181 GPa 79.635 GPa 80.985 GPa 114.82 GPa 370.37 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.189 GPa 199.49 GPa 1.797 TPa–1 5.4248 TPa–1 15.015 GPa 80.985 GPa-0.15960.96986Value
Anisotropy 4.415 3.0189 5.394Anisotropy
Axis 0.7572
0.4372
0.4853
-0.7409
0.4278
-0.5178
-0.3829
0.9238
-0.0000
0.0000
0.0000
1.0000
-0.0000
0.7882
0.6154
-0.5329
0.3077
0.7882
0.4975
0.2872
-0.8186
-0.5000
0.8660
0.0000
Axis
-1.0000
-0.0000
-0.0000
-0.5000
-0.8660
0.0000
-0.5000
0.8660
-0.0000
-0.7369
-0.4255
-0.5253
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