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 Al3Fe2Si3 (Materials Project id mp-29066)

       313       80       77        0       18        0  
        80      230       94        0        6        0  
        77       94      257        0       13        0  
         0        0        0       73        0       -3  
        18        6       13        0      123        0  
         0        0        0       -3        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 144.67 GPaEV = 226.09 GPaGV = 91.2 GPaνV = 0.23953
ReussKR = 142.3 GPaER = 215.94 GPaGR = 86.579 GPaνR = 0.24708
HillKH = 143.48 GPaEH = 221.03 GPaGH = 88.89 GPaνH = 0.24326

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
71.394 GPa 78.606 GPa 120.4 GPa 148.44 GPa 215.4 GPa 438.75 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 184.89 GPa 304.73 GPa 1.7665 TPa–1 2.7269 TPa–1 71.394 GPa 121.73 GPa0.0759220.40402Value
Anisotropy 1.648 1.5437 1.705 5.3216Anisotropy
Axis 0.3073
0.9363
0.1703
-0.8595
0.0000
-0.5111
0.8643
-0.0000
0.5029
0.0000
1.0000
0.0000
0.4719
0.0000
0.8817
0.0301
0.0000
0.9995
-0.6665
-0.0001
0.7455
0.5553
0.4774
0.6809
Axis
0.0000
1.0000
-0.0000
-0.9995
0.0000
0.0301
-0.7455
0.0000
-0.6665
-0.3434
0.8774
-0.3351
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