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 MoRh3 (Materials Project id mp-30787)

       437      173      178        0        0        0  
       173      437      178        0        0        0  
       178      178      489        0        0        0  
         0        0        0      113        0        0  
         0        0        0        0      113        0  
         0        0        0        0        0      132  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 269 GPaEV = 329.64 GPaGV = 127.2 GPaνV = 0.29576
ReussKR = 268.18 GPaER = 326.54 GPaGR = 125.88 GPaνR = 0.29706
HillKH = 268.59 GPaEH = 328.09 GPaGH = 126.54 GPaνH = 0.29641

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
113 GPa 113 GPa 132 GPa 264 GPa 290.6 GPa 808.4 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 309.38 GPa 385.12 GPa 1.0812 TPa–1 1.3238 TPa–1 113 GPa 141.91 GPa0.25040.37683Value
Anisotropy 1.245 1.2244 1.256 1.5049Anisotropy
Axis 0.0320
0.7699
-0.6374
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.4943
0.8693
0.0000
0.0000
0.0000
1.0000
-0.4023
0.5815
-0.7071
0.6596
0.2302
0.7155
0.6244
0.2311
-0.7461
Axis
1.0000
0.0001
-0.0000
0.4024
-0.5815
-0.7071
-0.3295
0.9441
0.0000
0.6997
0.2590
0.6658
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