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 SrHfO3 (Materials Project id mp-13109)

       338      108      119        0        0        0  
       108      310       77        0        0        0  
       119       77      263        0        0        0  
         0        0        0       91        0        0  
         0        0        0        0       87        0  
         0        0        0        0        0       90  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 168.78 GPaEV = 237.99 GPaGV = 94.067 GPaνV = 0.26499
ReussKR = 165.26 GPaER = 234.74 GPaGR = 92.911 GPaνR = 0.26326
HillKH = 167.02 GPaEH = 236.37 GPaGH = 93.489 GPaνH = 0.26413

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
87 GPa 90 GPa 91 GPa 175.68 GPa 223.07 GPa 512.25 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 214.19 GPa 268.62 GPa 1.3841 TPa–1 2.5588 TPa–1 87 GPa 106.32 GPa0.141480.37796Value
Anisotropy 1.254 1.8487 1.222 2.6715Anisotropy
Axis 0.0000
0.3898
0.9209
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
-1.0000
0.7071
0.7071
0.0000
-0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
Axis
-1.0000
0.0000
-0.0000
-0.7071
0.7071
0.0000
0.0000
-1.0000
0.0000
0.0000
0.0000
-1.0000
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