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 Tm2O3 (Materials Project id mp-556253)

       220      131       89        0       19        0  
       131      282       86        0       11        0  
        89       86      312        0        6        0  
         0        0        0       38        0       -2  
        19       11        6        0       73        0  
         0        0        0       -2        0      103  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 158.44 GPaEV = 198.06 GPaGV = 76.667 GPaνV = 0.29167
ReussKR = 154.3 GPaER = 171.55 GPaGR = 65.243 GPaνR = 0.3147
HillKH = 156.37 GPaEH = 184.9 GPaGH = 70.955 GPaνH = 0.30293

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37.939 GPa 70.145 GPa 103.06 GPa 116.05 GPa 222.65 GPa 478.15 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 117.77 GPa 270.74 GPa 1.6656 TPa–1 3.1446 TPa–1 37.939 GPa 109.62 GPa0.000962690.63395Value
Anisotropy 2.299 1.8879 2.89658.5179Anisotropy
Axis 0.0232
0.7343
0.6784
-0.0192
-0.0000
0.9998
0.0000
1.0000
0.0000
-0.8999
0.0000
0.4361
0.0307
0.0000
0.9995
-0.3504
0.5997
-0.7195
0.6224
0.4904
-0.6100
-0.6150
0.5292
-0.5846
Axis
-0.0000
1.0000
-0.0000
-0.4620
0.5576
0.6897
-0.7623
0.5564
-0.3305
0.0789
-0.6964
-0.7133
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