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(PRh)2 (Materials Project id mp-8583)

       167       67       57        0        0        0  
        67      167       57        0        0        0  
        57       57      116        0        0        0  
         0        0        0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       87  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 90.222 GPaEV = 120.86 GPaGV = 47.333 GPaνV = 0.27673
ReussKR = 86.748 GPaER = 104.46 GPaGR = 40.199 GPaνR = 0.2993
HillKH = 88.485 GPaEH = 112.72 GPaGH = 43.766 GPaνH = 0.28769

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 30 GPa 75.105 GPa 87 GPa 100 GPa 274.89 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 82.665 GPa 175.97 GPa 2.8577 TPa–1 5.8123 TPa–1 30 GPa 87 GPa0.0113150.52557Value
Anisotropy 2.129 2.0339 2.9 46.4485Anisotropy
Axis 0.5447
-0.0000
0.8386
0.7071
0.7071
0.0000
0.8660
0.5000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
-0.0003
-0.0000
0.7071
0.7071
-0.0000
-0.6285
0.6284
0.4583
Axis
0.1736
0.9848
-0.0000
0.0003
1.0000
0.0000
-0.7071
0.7071
0.0000
-0.3240
0.3241
-0.8888
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