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 BaNb4O6 (Materials Project id mp-505517)

       419       90       98        0        0        0  
        90      419       98        0        0        0  
        98       98      282        0        0        0  
         0        0        0       89        0        0  
         0        0        0        0       89        0  
         0        0        0        0        0      106  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 188 GPaEV = 281.17 GPaGV = 112.4 GPaνV = 0.25074
ReussKR = 182.57 GPaER = 266.97 GPaGR = 106.25 GPaνR = 0.25629
HillKH = 185.28 GPaEH = 274.07 GPaGH = 109.33 GPaνH = 0.25347

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
89 GPa 89 GPa 106 GPa 216.36 GPa 329 GPa 574.64 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 229.61 GPa 376.81 GPa 1.4799 TPa–1 2.5175 TPa–1 89 GPa 164.5 GPa0.13660.37972Value
Anisotropy 1.641 1.7011 1.848 2.7797Anisotropy
Axis -0.4213
0.4213
-0.8031
0.0000
1.0000
0.0000
0.4993
0.8664
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.8710
-0.0002
0.4912
0.8071
-0.0000
0.5905
Axis
0.1734
0.9849
-0.0000
-0.7071
0.7071
0.0000
0.0001
1.0000
0.0001
0.5905
0.0000
-0.8071
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