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(MnP)2 (Materials Project id mp-19857)

       143       63       59        0        0        0  
        63      143       59        0        0        0  
        59       59      117        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       47        0  
         0        0        0        0        0       78  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 85 GPaEV = 123.73 GPaGV = 49.2 GPaνV = 0.2574
ReussKR = 84.02 GPaER = 115.42 GPaGR = 45.401 GPaνR = 0.27105
HillKH = 84.51 GPaEH = 119.59 GPaGH = 47.301 GPaνH = 0.26415

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
47 GPa 47 GPa 66.937 GPa 78 GPa 80 GPa 256.06 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 83.204 GPa 151.1 GPa 3.3839 TPa–1 5.1342 TPa–1 35.006 GPa 78 GPa-0.031420.52012Value
Anisotropy 1.816 1.5172 2.228Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
1.0000
-0.0002
-0.0000
-0.7071
0.7071
-0.0000
-0.7071
0.7071
-0.0000
Axis
0.7071
-0.0005
-0.7071
0.0002
1.0000
-0.0000
-0.7071
-0.7071
0.0000
-0.0000
0.0000
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