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 Si3Rh5 (Materials Project id mp-21012)

       250      142      182        0        0        0  
       142      236      181        0        0        0  
       182      181      357        0        0        0  
         0        0        0       94        0        0  
         0        0        0        0      114        0  
         0        0        0        0        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 205.89 GPaEV = 211.38 GPaGV = 79.533 GPaνV = 0.32889
ReussKR = 191.63 GPaER = 191.75 GPaGR = 71.912 GPaνR = 0.33323
HillKH = 198.76 GPaEH = 201.57 GPaGH = 75.723 GPaνH = 0.33098

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
77 GPa 94 GPa 99.648 GPa 114 GPa 115.23 GPa 628.12 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 128.5 GPa 256.49 GPa 0.30225 TPa–1 2.6299 TPa–1 50.394 GPa 114 GPa0.0623830.64437Value
Anisotropy 1.996 8.7009 2.262 10.3293Anisotropy
Axis 0.0000
1.0000
0.0000
0.5527
0.4041
-0.7288
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
-0.0000
0.0000
-1.0000
0.7119
-0.0003
0.7023
0.6135
0.0002
0.7897
Axis
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
0.0000
0.7023
-0.0005
-0.7119
-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