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 YZn12 (Materials Project id mp-30886)

       126       48       48        0        0        0  
        48      163       34        0        0        0  
        48       34      163        0        0        0  
         0        0        0       44        0        0  
         0        0        0        0       55        0  
         0        0        0        0        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 79.111 GPaEV = 128.5 GPaGV = 52.267 GPaνV = 0.22928
ReussKR = 78.654 GPaER = 125.77 GPaGR = 50.98 GPaνR = 0.2335
HillKH = 78.882 GPaEH = 127.14 GPaGH = 51.624 GPaνH = 0.23138

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
44 GPa 55 GPa 55 GPa 84.895 GPa 129 GPa 238.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 102.61 GPa 143.48 GPa 3.8587 TPa–1 4.9965 TPa–1 42.931 GPa 64.5 GPa0.108590.33959Value
Anisotropy 1.398 1.2949 1.502 3.1273Anisotropy
Axis 1.0000
0.0000
0.0000
0.2891
-0.0000
0.9573
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.5000
0.5000
-0.0001
0.7071
0.7071
-0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
Axis
-0.7071
0.5000
0.5000
0.0001
0.7071
-0.7071
0.0000
-1.0000
0.0000
1.0000
0.0000
-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