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 BaNaBi (Materials Project id mp-31235)

        39       12       15        0        0        0  
        12       39       15        0        0        0  
        15       15       48        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 23.333 GPaEV = 39.861 GPaGV = 16.4 GPaνV = 0.21528
ReussKR = 22.966 GPaER = 38.645 GPaGR = 15.844 GPaνR = 0.21954
HillKH = 23.149 GPaEH = 39.254 GPaGH = 16.122 GPaνH = 0.21739

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 20 GPa 20 GPa 27 GPa 28.234 GPa 70.766 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 32.754 GPa 44.715 GPa 10.511 TPa–1 16.517 TPa–1 13.5 GPa 20 GPa0.0982660.31889Value
Anisotropy 1.365 1.5714 1.481 3.2451Anisotropy
Axis 1.0000
0.0000
0.0000
0.4436
0.4436
0.7787
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
-0.0000
0.0000
1.0000
0.7162
0.0001
-0.6979
0.5538
0.0003
0.8326
Axis
-0.7071
0.7071
0.0000
-0.5000
0.8660
-0.0000
-0.6979
-0.0001
-0.7162
-0.0006
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