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 ErRh2 (Materials Project id mp-1762)

       199      116      116        0        0        0  
       116      199      116        0        0        0  
       116      116      199        0        0        0  
         0        0        0       80        0        0  
         0        0        0        0       80        0  
         0        0        0        0        0       80  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 143.67 GPaEV = 168.54 GPaGV = 64.6 GPaνV = 0.30448
ReussKR = 143.67 GPaER = 154.17 GPaGR = 58.348 GPaνR = 0.32115
HillKH = 143.67 GPaEH = 161.4 GPaGH = 61.474 GPaνH = 0.31276

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
80 GPa 80 GPa 80 GPa 83 GPa 83 GPa 431 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 113.57 GPa 202.43 GPa 2.3202 TPa–1 2.3202 TPa–1 41.5 GPa 80 GPa0.0581690.54901Value
Anisotropy 1.782 1.0000 1.928 9.4381Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
-0.7071
0.0002
-0.7071
0.0001
1.0000
0.0001
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