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 Ba2CuF6 (Materials Project id mp-554352)

       102       33       44        0        0        0  
        33      102       44        0        0        0  
        44       44       75        0        0        0  
         0        0        0       25        0        0  
         0        0        0        0       25        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 57.889 GPaEV = 64.49 GPaGV = 24.533 GPaνV = 0.31433
ReussKR = 57.367 GPaER = 61.58 GPaGR = 23.307 GPaνR = 0.32109
HillKH = 57.628 GPaEH = 63.038 GPaGH = 23.92 GPaνH = 0.31769

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 25 GPa 25 GPa 35.92 GPa 69 GPa 174.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.319 GPa 75.559 GPa 4.9576 TPa–1 7.5164 TPa–1 18.464 GPa 34.5 GPa0.094330.53133Value
Anisotropy 1.631 1.5161 1.869 5.6326Anisotropy
Axis 0.0000
0.0000
1.0000
0.9842
0.0000
0.1773
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5000
0.5000
0.7071
0.7071
0.7071
-0.0001
1.0000
-0.0003
-0.0000
1.0000
-0.0000
0.0000
Axis
0.5000
-0.5000
0.7071
-0.7071
0.7071
0.0000
0.0003
1.0000
0.0000
0.0000
0.0002
-1.0000
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