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 ErIr (Materials Project id mp-2713)

       208      114      114        0        0        0  
       114      208      114        0        0        0  
       114      114      208        0        0        0  
         0        0        0       60        0        0  
         0        0        0        0       60        0  
         0        0        0        0        0       60  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 145.33 GPaEV = 146.04 GPaGV = 54.8 GPaνV = 0.33252
ReussKR = 145.33 GPaER = 144.2 GPaGR = 54.023 GPaνR = 0.33463
HillKH = 145.33 GPaEH = 145.12 GPaGH = 54.411 GPaνH = 0.33357

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
60 GPa 60 GPa 60 GPa 94 GPa 94 GPa 436 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 127.28 GPa 158.23 GPa 2.2936 TPa–1 2.2936 TPa–1 47 GPa 60 GPa0.242990.4149Value
Anisotropy 1.243 1.0000 1.277 1.7074Anisotropy
Axis 0.0000
1.0000
0.0000
0.5774
0.5774
0.5773
0.7934
0.0000
0.6088
0.3536
0.8536
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0004
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0003
1.0000
-0.0003
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