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 BaNiO3 (Materials Project id mp-19138)

       152       58       30        0        0        0  
        58      152       30        0        0        0  
        30       30      231        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0       47  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 85.667 GPaEV = 101.13 GPaGV = 38.8 GPaνV = 0.30325
ReussKR = 84.62 GPaER = 26.166 GPaGR = 9.0325 GPaνR = 0.44846
HillKH = 85.143 GPaEH = 65.606 GPaGH = 23.916 GPaνH = 0.37158

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4 GPa 4 GPa 47 GPa 94 GPa 176.79 GPa 264.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 15.323 GPa 222.43 GPa 3.2113 TPa–1 4.3031 TPa–1 4 GPa 73.68 GPa0.0236330.91748Value
Anisotropy 14.52 1.3400 18.42 38.8222Anisotropy
Axis 0.6585
0.2708
0.7022
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0682
0.7038
-0.7071
-0.3169
0.4575
0.8308
0.3081
0.5723
-0.7599
Axis
1.0000
0.0000
-0.0000
-0.0681
-0.7038
-0.7071
-0.8220
-0.5695
0.0000
-0.3602
-0.6691
-0.6500
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