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 NaZnF3 (Materials Project id mp-3795)

       124       60       76        0        0        0  
        60      115       57        0        0        0  
        76       57      134        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 84.333 GPaEV = 85.694 GPaGV = 32.2 GPaνV = 0.33065
ReussKR = 83.215 GPaER = 84.267 GPaGR = 31.65 GPaνR = 0.33123
HillKH = 83.774 GPaEH = 84.98 GPaGH = 31.925 GPaνH = 0.33093

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 33 GPa 37 GPa 51.601 GPa 67.17 GPa 254.23 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 72.458 GPa 98.557 GPa 3.2139 TPa–1 5.2476 TPa–1 26.334 GPa 37 GPa0.235270.49906Value
Anisotropy 1.36 1.6328 1.405 2.1212Anisotropy
Axis 1.0000
0.0000
0.0000
0.6497
-0.0000
0.7602
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.7071
-0.0002
0.7071
-0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
Axis
0.7071
-0.0006
-0.7071
-1.0000
0.0000
-0.0000
0.0000
-1.0000
0.0000
1.0000
0.0000
-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