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 TlNO3 (Materials Project id mp-5915)

        36       13       12        0        0        0  
        13       32       20        0        0        0  
        12       20       30        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 20.889 GPaEV = 20.175 GPaGV = 7.5333 GPaνV = 0.33903
ReussKR = 20.824 GPaER = 14.929 GPaGR = 5.4069 GPaνR = 0.38052
HillKH = 20.857 GPaEH = 17.591 GPaGH = 6.4701 GPaνH = 0.35943

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 4 GPa 10.971 GPa 13 GPa 24.297 GPa 62.732 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 9.8257 GPa 32.219 GPa 13.276 TPa–1 17.641 TPa–1 3 GPa 13 GPa0.0759890.73109Value
Anisotropy 3.279 1.3288 4.333 9.6210Anisotropy
Axis -0.6710
0.7415
0.0000
0.0000
0.7165
0.6976
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0007
0.0000
0.0004
0.0003
1.0000
-0.6409
0.5190
0.5656
-0.6855
0.5277
0.5016
Axis
0.0007
1.0000
-0.0001
-0.0000
1.0000
-0.0003
0.1332
-0.6505
0.7478
-0.7211
-0.5870
-0.3679
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