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 LaRhO3 (Materials Project id mp-5163)

       235      118      166        0        0        0  
       118      302      117        0        0        0  
       166      117      221        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       98        0  
         0        0        0        0        0       63  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 173.33 GPaEV = 170.96 GPaGV = 64 GPaνV = 0.33562
ReussKR = 172.84 GPaER = 143.61 GPaGR = 52.739 GPaνR = 0.36152
HillKH = 173.09 GPaEH = 157.41 GPaGH = 58.369 GPaνH = 0.34843

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
40 GPa 61.803 GPa 63 GPa 98 GPa 175.7 GPa 520.5 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 97.814 GPa 238 GPa 1.7368 TPa–1 2.267 TPa–1 30.927 GPa 98 GPa0.086880.68471Value
Anisotropy 2.433 1.3053 3.169 7.8812Anisotropy
Axis 0.0000
0.3596
0.9331
0.7183
-0.0000
-0.6957
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.0000
1.0000
0.6922
0.5298
-0.4901
1.0000
-0.0004
-0.0000
Axis
0.7071
-0.0006
-0.7071
-1.0000
0.0000
0.0000
-0.7200
0.4602
-0.5194
-0.0000
-0.0003
-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