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 Ta3N5 (Materials Project id mp-27488)

       393      127      207        0        0        0  
       127      386      167        0        0        0  
       207      167      393        0        0        0  
         0        0        0      119        0        0  
         0        0        0        0       59        0  
         0        0        0        0        0      113  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 241.56 GPaEV = 270.39 GPaGV = 102.93 GPaνV = 0.31344
ReussKR = 239.62 GPaER = 250.65 GPaGR = 94.537 GPaνR = 0.32566
HillKH = 240.59 GPaEH = 260.56 GPaGH = 98.735 GPaνH = 0.3195

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
59 GPa 113 GPa 119 GPa 178.39 GPa 266.4 GPa 727.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 189.78 GPa 312.27 GPa 1.0861 TPa–1 1.6469 TPa–1 59 GPa 129.88 GPa0.105720.61064Value
Anisotropy 1.645 1.5164 2.201 5.7759Anisotropy
Axis 0.6869
-0.0000
0.7267
0.0000
0.9155
-0.4023
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.0000
-0.0000
-1.0000
0.7071
0.7071
-0.0000
-0.6092
0.6195
0.4951
0.7377
0.0001
-0.6752
Axis
-1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
-0.4427
-0.7837
0.4357
-0.6752
-0.0000
-0.7377
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