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 LaF3 (Materials Project id mp-8354)

       234      190      104        0        0        0  
       190      234      104        0        0        0  
       104      104      257        0        0        0  
         0        0        0       39        0        0  
         0        0        0        0       39        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 169 GPaEV = 115.85 GPaGV = 41.8 GPaνV = 0.38575
ReussKR = 167.31 GPaER = 91.596 GPaGR = 32.509 GPaνR = 0.40876
HillKH = 168.16 GPaEH = 103.82 GPaGH = 37.155 GPaνH = 0.3971

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 39 GPa 39 GPa 44 GPa 171.37 GPa 509.63 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 77.912 GPa 205.98 GPa 1.7519 TPa–1 2.4732 TPa–1 22 GPa 49.822 GPa0.0927780.77073Value
Anisotropy 2.644 1.4118 2.265 8.3073Anisotropy
Axis 1.0000
0.0001
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.9573
0.2890
0.0000
0.5291
0.4691
-0.7071
-0.2605
0.9655
-0.0000
0.9451
0.3269
-0.0000
Axis
-0.2890
0.9573
-0.0000
-0.5291
-0.4692
-0.7071
0.0000
-0.0000
-1.0000
-0.3269
0.9451
-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