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 Te2O5 (Materials Project id mp-12177)

        71        9        9        0       14        0  
         9      108       59        0        8        0  
         9       59      161        0       11        0  
         0        0        0       95        0       12  
        14        8       11        0       21        0  
         0        0        0       12        0       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 54.889 GPaEV = 108.48 GPaGV = 46.333 GPaνV = 0.17062
ReussKR = 37.743 GPaER = 73.576 GPaGR = 31.306 GPaνR = 0.1751
HillKH = 46.316 GPaEH = 91.028 GPaGH = 38.82 GPaνH = 0.17244

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16.786 GPa 25.916 GPa 68.183 GPa 74.424 GPa 97.084 GPa 201.61 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 35.427 GPa 195.41 GPa 0.13162 TPa–1 19.37 TPa–1 17.049 GPa 97.084 GPa-0.132710.71919Value
Anisotropy 5.516147.1686 5.695Anisotropy
Axis -0.8133
0.0000
0.5818
0.0889
0.6248
0.7757
0.4369
-0.0000
0.8995
-0.8995
0.0000
0.4369
0.9935
-0.0001
0.1140
-0.1711
0.0000
-0.9852
-0.2628
0.7454
0.6126
0.4944
0.4758
0.7274
Axis
0.1140
-0.0000
-0.9935
-0.0000
-1.0000
-0.0000
-0.6072
-0.6212
0.4954
-0.8609
0.1528
0.4852
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