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 YCo (Materials Project id mp-865373)

       118       57       25        5        0        0  
        57      118       25       -5        0        0  
        25       25       69        0        0        0  
         5       -5        0       14        0        0  
         0        0        0        0       14        5  
         0        0        0        0        5       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 57.667 GPaEV = 65.072 GPaGV = 24.8 GPaνV = 0.31193
ReussKR = 50.822 GPaER = 52.293 GPaGR = 19.681 GPaνR = 0.32851
HillKH = 54.244 GPaEH = 58.699 GPaGH = 22.241 GPaνH = 0.31965

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12.566 GPa 12.959 GPa 31.434 GPa 58.29 GPa 62.041 GPa 185.71 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 35.656 GPa 90.04 GPa 4.0647 TPa–1 11.547 TPa–1 12.566 GPa 31.894 GPa0.0185820.60281Value
Anisotropy 2.525 2.8409 2.538 32.4408Anisotropy
Axis 0.6244
0.3628
-0.6918
0.0000
0.9921
-0.1254
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
-0.0000
0.2757
-0.9613
0.7071
0.6790
-0.1974
-0.4548
0.2608
0.8516
-0.6145
0.3499
0.7070
Axis
-1.0000
-0.0000
0.0000
-0.7071
0.6790
-0.1974
-0.4987
-0.8668
-0.0008
-0.6143
0.3500
-0.7072
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