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 NaVO2 (Materials Project id mp-19391)

       197      125       50       -6        0        0  
       125      197       50        6        0        0  
        50       50      195        0        0        0  
        -6        6        0       55        0        0  
         0        0        0        0       55       -6  
         0        0        0        0       -6       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 115.44 GPaEV = 138.95 GPaGV = 53.467 GPaνV = 0.2994
ReussKR = 112.87 GPaER = 124.61 GPaGR = 47.345 GPaνR = 0.316
HillKH = 114.16 GPaEH = 131.82 GPaGH = 50.406 GPaνH = 0.30755

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34.264 GPa 51.49 GPa 56.736 GPa 75.51 GPa 163.46 GPa 353.54 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 104.91 GPa 179.47 GPa 2.5091 TPa–1 3.8415 TPa–1 34.264 GPa 65.281 GPa0.0836080.62944Value
Anisotropy 1.711 1.5310 1.905 7.5284Anisotropy
Axis -0.7984
0.4610
0.3873
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.0000
0.9606
0.2779
-0.7334
0.4235
0.5318
0.8497
0.4906
-0.1929
0.5000
0.8660
0.0000
Axis
-1.0000
0.0000
0.0000
-0.4607
0.2657
-0.8469
0.1671
0.0964
0.9812
-0.8543
0.4932
0.1637
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