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 Ba(NiP)2 (Materials Project id mp-9473)

       154       16       58        0        0        0  
        16      154       58        0        0        0  
        58       58      102        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 74.889 GPaEV = 102.15 GPaGV = 40.133 GPaνV = 0.27266
ReussKR = 74.732 GPaER = 89.062 GPaGR = 34.218 GPaνR = 0.30138
HillKH = 74.811 GPaEH = 95.679 GPaGH = 37.176 GPaνH = 0.28684

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 42 GPa 42 GPa 47.208 GPa 138 GPa 224.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 62.424 GPa 123.66 GPa 4.1462 TPa–1 5.0886 TPa–1 23.712 GPa 69 GPa-0.140310.64841Value
Anisotropy 1.981 1.2273 2.91Anisotropy
Axis 0.0000
0.0000
1.0000
0.9100
0.0000
0.4147
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.4998
0.5003
0.7071
0.7071
0.7071
-0.0000
1.0000
0.0007
0.0000
1.0000
0.0000
-0.0000
Axis
0.5002
0.4997
-0.7071
-0.7071
0.7071
-0.0000
-0.0007
1.0000
-0.0000
-0.0000
0.0003
-1.0000
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