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 Si2Ru (Materials Project id mp-569815)

       338      103      121        0        0        0  
       103      283      127        0        0        0  
       121      127      348        0        0        0  
         0        0        0      122        0        0  
         0        0        0        0      102        0  
         0        0        0        0        0      114  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 185.67 GPaEV = 273.06 GPaGV = 108.8 GPaνV = 0.25488
ReussKR = 183.6 GPaER = 269.97 GPaGR = 107.56 GPaνR = 0.25493
HillKH = 184.63 GPaEH = 271.52 GPaGH = 108.18 GPaνH = 0.2549

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
102 GPa 114 GPa 122 GPa 183.53 GPa 225.35 GPa 560.11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 224.95 GPa 297.44 GPa 1.4426 TPa–1 2.2465 TPa–1 93.054 GPa 122 GPa0.164040.3582Value
Anisotropy 1.322 1.5572 1.311 2.1836Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.5900
0.8074
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.7071
0.7071
0.0004
0.0003
1.0000
0.5797
0.7380
0.3453
-0.0000
-0.0000
1.0000
Axis
-0.0000
0.7071
-0.7071
-0.0000
1.0000
-0.0003
-0.6328
0.6747
-0.3798
-0.0000
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