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 Al5Rh2 (Materials Project id mp-1791)

       224       87       74        0        0        0  
        87      224       74        0        0        0  
        74       74      265        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       69  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 131.44 GPaEV = 192.98 GPaGV = 76.867 GPaνV = 0.25531
ReussKR = 131.12 GPaER = 191.13 GPaGR = 76.024 GPaνR = 0.25706
HillKH = 131.28 GPaEH = 192.06 GPaGH = 76.446 GPaνH = 0.25618

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
69 GPa 78 GPa 78 GPa 137 GPa 180.85 GPa 395.15 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 181.69 GPa 229.78 GPa 2.2809 TPa–1 2.6727 TPa–1 68.5 GPa 84.032 GPa0.188140.32624Value
Anisotropy 1.265 1.1718 1.227 1.7340Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
0.5000
0.5000
-0.7071
1.0000
0.0002
-0.0000
1.0000
-0.0001
-0.0000
Axis
-0.7071
-0.7071
0.0000
-0.5000
-0.5000
-0.7071
-0.0000
0.0000
-1.0000
0.0001
1.0000
0.0000
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