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 Na8Ti5O14 (Materials Project id mp-28017)

       154       39       37       -2       -6       -8  
        39      142       37       -8        5        4  
        37       37      149        9        1       -3  
        -2       -8        9       37        0        5  
        -6        5        1        0       38      -11  
        -8        4       -3        5      -11       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 74.556 GPaEV = 112.25 GPaGV = 44.933 GPaνV = 0.24907
ReussKR = 74.359 GPaER = 101.24 GPaGR = 39.76 GPaνR = 0.27309
HillKH = 74.457 GPaEH = 106.79 GPaGH = 42.347 GPaνH = 0.26095

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24.314 GPa 35.651 GPa 50.422 GPa 108.98 GPa 115.65 GPa 223.99 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 66.395 GPa 141.43 GPa 4.0249 TPa–1 4.9219 TPa–1 24.029 GPa 59.349 GPa-0.0278480.58509Value
Anisotropy 2.13 1.2229 2.47Anisotropy
Axis -0.5201
0.7117
0.4723
-0.9912
0.1055
0.0798
-0.8472
0.5150
0.1306
0.5303
0.8350
0.1466
0.1598
0.6972
0.6988
-0.6564
0.2712
0.7040
0.7034
0.6781
-0.2131
0.5428
-0.1543
0.8256
Axis
-0.9692
0.2453
-0.0231
-0.7456
-0.0908
-0.6602
-0.4285
0.1654
-0.8882
-0.5575
0.6690
0.4916
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