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 YMgAl (Materials Project id mp-13090)

       105       28       37        0        0        0  
        28      105       37        0        0        0  
        37       37      102        0        0        0  
         0        0        0       59        0        0  
         0        0        0        0       59        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 57.333 GPaEV = 107.76 GPaGV = 45.4 GPaνV = 0.18675
ReussKR = 57.291 GPaER = 102.48 GPaGR = 42.632 GPaνR = 0.20188
HillKH = 57.312 GPaEH = 105.13 GPaGH = 44.016 GPaνH = 0.19427

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 59 GPa 59 GPa 62.927 GPa 77 GPa 172.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 81.414 GPa 119.7 GPa 5.4488 TPa–1 6.003 TPa–1 32.981 GPa 59 GPa0.00883270.32103Value
Anisotropy 1.47 1.1017 1.789 36.3453Anisotropy
Axis 0.0000
0.0000
1.0000
0.5214
0.5214
0.6755
0.0000
0.0000
1.0000
0.3810
0.9246
-0.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7069
-0.0003
0.7073
0.5917
-0.0004
-0.8062
Axis
0.7071
-0.0005
-0.7071
-0.1736
0.9848
-0.0000
0.7073
-0.0005
-0.7069
0.0007
1.0000
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