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 Na4Ti5O12 (Materials Project id mp-555678)

       250       97       60       -2        4        0  
        97      250       60        2       -4        0  
        60       60      247        0        0        0  
        -2        2        0       37        0       -4  
         4       -4        0        0       37       -2  
         0        0        0       -4       -2       76  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 131.22 GPaEV = 168.1 GPaGV = 65.333 GPaνV = 0.28649
ReussKR = 130.63 GPaER = 144.73 GPaGR = 55.014 GPaνR = 0.31535
HillKH = 130.93 GPaEH = 156.54 GPaGH = 60.174 GPaνH = 0.30073

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36.494 GPa 36.656 GPa 76.506 GPa 153.34 GPa 198.51 GPa 395.49 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 109.02 GPa 226.25 GPa 2.3819 TPa–1 2.8914 TPa–1 36.494 GPa 92.75 GPa0.0881320.58439Value
Anisotropy 2.075 1.2139 2.541 6.6308Anisotropy
Axis 0.4604
0.5698
0.6807
0.0000
0.0000
1.0000
0.9910
0.1338
0.0000
0.0000
0.0000
1.0000
-0.1110
0.0172
-0.9937
0.6916
-0.0002
0.7223
-0.5280
0.0811
-0.8454
-0.6703
0.1016
-0.7351
Axis
0.1537
0.9881
-0.0001
0.7223
-0.0004
-0.6916
-0.1519
-0.9884
0.0001
0.7267
-0.1105
-0.6780
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