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 Sb2Ru (Materials Project id mp-20928)

       223       82       70        0        0        0  
        82      273       31        0        0        0  
        70       31      193        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       87        0  
         0        0        0        0        0      110  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 117.22 GPaEV = 198.96 GPaGV = 81.733 GPaνV = 0.21712
ReussKR = 113.95 GPaER = 179.13 GPaGR = 72.348 GPaνR = 0.23799
HillKH = 115.59 GPaEH = 189.11 GPaGH = 77.04 GPaνH = 0.22732

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
43 GPa 87 GPa 110 GPa 128.75 GPa 199.01 GPa 361.24 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 120.47 GPa 262.37 GPa 2.3233 TPa–1 3.9342 TPa–1 43 GPa 110 GPa-0.0148730.48766Value
Anisotropy 2.178 1.6934 2.558Anisotropy
Axis -0.0000
0.6585
0.7526
0.5425
0.8400
-0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0003
-0.0000
1.0000
1.0000
-0.0000
0.0000
0.7089
0.5264
-0.4694
-0.6545
0.5696
0.4971
Axis
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0000
-0.7053
0.5250
-0.4763
-0.0163
-0.6680
0.7440
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