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 KAlF4 (Materials Project id mp-2910)

        92       33       17        0        0        0  
        33       92       17        0        0        0  
        17       17       96        0        0        0  
         0        0        0        3        0        0  
         0        0        0        0        3        0  
         0        0        0        0        0       71  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46 GPaEV = 73.117 GPaGV = 29.6 GPaνV = 0.23508
ReussKR = 45.871 GPaER = 19.351 GPaGR = 6.7676 GPaνR = 0.42969
HillKH = 45.936 GPaEH = 48.192 GPaGH = 18.184 GPaνH = 0.32515

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 3 GPa 59 GPa 71 GPa 82.424 GPa 138.58 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 11.3 GPa 129.47 GPa 6.9165 TPa–1 7.9671 TPa–1 3 GPa 46.202 GPa-0.0882090.91098Value
Anisotropy 11.46 1.1519 15.4Anisotropy
Axis 0.7091
-0.0000
0.7051
0.7071
0.7071
0.0000
-0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.4999
0.5001
-0.7071
-0.7071
0.7071
-0.0000
0.5258
0.5257
-0.6687
Axis
0.1735
0.9848
-0.0000
-0.5001
-0.4999
-0.7071
-0.7071
-0.7071
-0.0000
-0.4728
-0.4729
-0.7435
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