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 PdI2 (Materials Project id mp-27747)

         5        2        2        0       -1        0  
         2        7        3        0        0        0  
         2        3       24        0       -1        0  
         0        0        0        6        0       -0  
        -1        0       -1        0        1        0  
         0        0        0       -0        0        4  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 5.5556 GPaEV = 9.9359 GPaGV = 4.1333 GPaνV = 0.20192
ReussKR = 3.2767 GPaER = 4.8689 GPaGR = 1.9439 GPaνR = 0.25235
HillKH = 4.4161 GPaEH = 7.4151 GPaGH = 3.0386 GPaνH = 0.22015

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.70325 GPa 3.9958 GPa 4 GPa 6 GPa 7.4653 GPa 24.836 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1.5964 GPa 22.488 GPa -31.514 TPa–1 263.76 TPa–1 0.71867 GPa 6 GPa-0.515451.3305Value
Anisotropy 14.09 8.349Anisotropy
Axis 0.8164
0.0000
0.5775
-0.0365
-0.0000
0.9993
-0.4373
-0.0000
0.8993
0.8993
0.0000
0.4373
-0.9934
0.0000
0.1147
0.0000
0.0000
1.0000
0.4153
0.7546
0.5080
-0.3244
0.4561
0.8287
Axis
-0.1147
0.0000
-0.9934
0.0000
1.0000
-0.0000
-0.6171
0.6440
-0.4522
-0.8866
0.1588
-0.4345
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