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 Li2VO2F (Materials Project id mp-763051)

       202       64       33       18        0        0  
        64      202       33      -18        0        0  
        33       33      194        0        0        0  
        18      -18        0       55        0        0  
         0        0        0        0       55       18  
         0        0        0        0       18       69  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95.333 GPaEV = 162.85 GPaGV = 67 GPaνV = 0.2153
ReussKR = 94.686 GPaER = 149.07 GPaGR = 60.225 GPaνR = 0.23761
HillKH = 95.01 GPaEH = 156.02 GPaGH = 63.612 GPaνH = 0.22631

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42.687 GPa 47.815 GPa 81.313 GPa 145.19 GPa 171.06 GPa 288.94 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 111.24 GPa 195.42 GPa 3.2574 TPa–1 4.0465 TPa–1 42.687 GPa 84.688 GPa-0.0195890.47107Value
Anisotropy 1.757 1.2422 1.984Anisotropy
Axis 0.6936
0.4005
-0.5988
0.8272
0.4775
0.2962
1.0000
0.0003
-0.0000
0.0000
0.0000
1.0000
0.4890
0.2823
0.8253
0.5102
0.2946
0.8080
-0.0000
0.5190
-0.8548
0.5000
0.8660
-0.0000
Axis
-0.5000
0.8660
-0.0000
0.6998
0.4040
-0.5891
-1.0000
0.0000
0.0000
-0.7391
0.4267
-0.5212
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