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(P2Pd)2 (Materials Project id mp-28895)

       125       67       67        0        0        0  
        67      138       60        0        0        0  
        67       60      138        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       39        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 87.667 GPaEV = 91.732 GPaGV = 34.6 GPaνV = 0.3256
ReussKR = 87.622 GPaER = 89.416 GPaGR = 33.617 GPaνR = 0.32992
HillKH = 87.644 GPaEH = 90.576 GPaGH = 34.108 GPaνH = 0.32776

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 39 GPa 39 GPa 59.961 GPa 78 GPa 263.04 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.648 GPa 101.91 GPa 3.6774 TPa–1 4.0578 TPa–1 26 GPa 39 GPa0.184860.46237Value
Anisotropy 1.384 1.1034 1.5 2.5012Anisotropy
Axis 0.0000
0.7071
0.7071
0.5580
-0.0000
0.8298
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0003
-0.0000
1.0000
-0.0000
0.0000
1.0000
0.6979
0.5064
-0.5064
0.6229
0.5532
0.5532
Axis
0.0000
1.0000
0.0000
-1.0000
0.0000
-0.0000
-0.7162
0.4935
-0.4935
0.0000
0.7071
-0.7071
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