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 BaBiO3 (Materials Project id mp-559051)

       184       55       73        0        3        0  
        55      168       87        0       -4        0  
        73       87      176        0        1        0  
         0        0        0       48        0        0  
         3       -4        1        0       45        0  
         0        0        0        0        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 106.44 GPaEV = 122.61 GPaGV = 46.867 GPaνV = 0.30803
ReussKR = 105.9 GPaER = 118.94 GPaGR = 45.301 GPaνR = 0.3128
HillKH = 106.17 GPaEH = 120.78 GPaGH = 46.084 GPaνH = 0.31041

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 44.576 GPa 48 GPa 83.019 GPa 125.47 GPa 319.93 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 99.807 GPa 151.78 GPa 2.5347 TPa–1 3.5367 TPa–1 37 GPa 59.953 GPa0.116080.43451Value
Anisotropy 1.521 1.3953 1.62 3.7430Anisotropy
Axis 0.6487
0.7599
0.0418
0.9945
0.0000
0.1045
-0.0199
-0.0000
0.9998
0.0000
1.0000
0.0000
1.0000
-0.0001
-0.0000
0.7136
0.6994
-0.0405
-0.0000
1.0000
0.0001
-0.0913
0.0000
0.9958
Axis
0.0001
1.0000
-0.0000
-0.6878
0.6886
-0.2296
-0.9869
-0.0000
-0.1615
-0.0000
1.0000
-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