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 V3Cd (Materials Project id mp-983607)

       227       87       87        0        0        0  
        87      227       87        0        0        0  
        87       87      227        0        0        0  
         0        0        0       16        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       16  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 133.67 GPaEV = 103.13 GPaGV = 37.6 GPaνV = 0.37141
ReussKR = 133.67 GPaER = 65.634 GPaGR = 23.14 GPaνR = 0.41816
HillKH = 133.67 GPaEH = 84.696 GPaGH = 30.37 GPaνH = 0.39439

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 16 GPa 16 GPa 140 GPa 140 GPa 401 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.158 GPa 178.79 GPa 2.4938 TPa–1 2.4938 TPa–1 16 GPa 70 GPa0.0878180.77087Value
Anisotropy 3.873 1.0000 4.375 8.7780Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
1.0000
0.0000
0.2500
0.9330
0.2588
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
0.0001
0.7071
-0.0001
-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