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 Y4C5 (Materials Project id mp-9459)

       175       56       60        0        0        0  
        56      251       39        0        0        0  
        60       39      179        0        0        0  
         0        0        0       55        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 101.67 GPaEV = 140.65 GPaGV = 55.4 GPaνV = 0.26942
ReussKR = 100.1 GPaER = 124.66 GPaGR = 48.227 GPaνR = 0.29244
HillKH = 100.88 GPaEH = 132.72 GPaGH = 51.814 GPaνH = 0.28074

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 42 GPa 55 GPa 115.22 GPa 177.94 GPa 311.84 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 94.43 GPa 230.61 GPa 2.5926 TPa–1 3.8239 TPa–1 30 GPa 84.745 GPa0.0849490.59139Value
Anisotropy 2.442 1.4749 2.825 6.9617Anisotropy
Axis 0.7496
0.6619
-0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
0.0000
0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.6406
0.7679
0.0000
Axis
0.0002
1.0000
0.0000
-0.0000
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
-0.7679
-0.6406
-0.0000
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