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 Li3AlF6 (Materials Project id mp-15254)

        88       24       24        0      -12        0  
        24      107       32        0       -3        0  
        24       32       86        0       -6        0  
         0        0        0       33        0       -1  
       -12       -3       -6        0       22        0  
         0        0        0       -1        0       27  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 49 GPaEV = 74.331 GPaGV = 29.8 GPaνV = 0.24717
ReussKR = 45.753 GPaER = 69.813 GPaGR = 28.022 GPaνR = 0.24569
HillKH = 47.376 GPaEH = 72.072 GPaGH = 28.911 GPaνH = 0.24646

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
19.78 GPa 26.838 GPa 33.162 GPa 60.363 GPa 73.118 GPa 149.74 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.056 GPa 92.235 GPa 4.4258 TPa–1 12.171 TPa–1 19.809 GPa 37.864 GPa0.110430.50058Value
Anisotropy 2.047 2.7499 1.911 4.5330Anisotropy
Axis -0.7613
0.0000
-0.6483
0.0000
1.0000
0.0000
0.6533
0.0000
-0.7571
0.7571
-0.0000
0.6533
-0.9926
-0.0000
0.1212
-0.6765
0.7071
0.2060
0.8099
0.4635
0.3594
-0.6484
0.0000
0.7613
Axis
-0.1212
0.0000
-0.9926
-0.6764
-0.7071
0.2059
-0.2213
0.8089
-0.5447
-0.7613
0.0000
-0.6484
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