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 V6C5 (Materials Project id mp-28731)

       454      117      133        0      -21        0  
       117      454      133        0       21        0  
       133      133      474        0        0        0  
         0        0        0      189        0       21  
       -21       21        0        0      189        0  
         0        0        0       21        0      169  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 238.67 GPaEV = 423.82 GPaGV = 176 GPaνV = 0.20404
ReussKR = 238.37 GPaER = 418.68 GPaGR = 173.4 GPaνR = 0.20727
HillKH = 238.52 GPaEH = 421.25 GPaGH = 174.7 GPaνH = 0.20565

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
155.74 GPa 183.26 GPa 202.26 GPa 328.26 GPa 342.74 GPa 716.74 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 381.58 GPa 473.61 GPa 1.2963 TPa–1 1.4494 TPa–1 155.47 GPa 202.26 GPa0.148220.29136Value
Anisotropy 1.241 1.1180 1.301 1.9657Anisotropy
Axis 0.9526
0.0000
0.3044
0.3912
0.6754
0.6251
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
0.4285
0.7315
0.5304
0.5338
0.0003
0.8456
0.5751
0.0001
0.8181
0.5622
0.0002
0.8270
Axis
-0.8568
0.5153
-0.0184
-0.0001
1.0000
-0.0003
0.8181
0.0004
-0.5751
-0.0001
1.0000
-0.0002
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