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 TbRh5 (Materials Project id mp-11562)

       278      140      125        0        0        0  
       140      278      125        0        0        0  
       125      125      360        0        0        0  
         0        0        0       64        0        0  
         0        0        0        0       64        0  
         0        0        0        0        0       69  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 188.44 GPaEV = 197.4 GPaGV = 74.467 GPaνV = 0.32541
ReussKR = 186.88 GPaER = 190.75 GPaGR = 71.717 GPaνR = 0.32988
HillKH = 187.66 GPaEH = 194.08 GPaGH = 73.092 GPaνH = 0.32764

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
64 GPa 64 GPa 69 GPa 138 GPa 209.86 GPa 568.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 176.15 GPa 285.24 GPa 1.409 TPa–1 1.971 TPa–1 64 GPa 93.149 GPa0.204250.41705Value
Anisotropy 1.619 1.3988 1.455 2.0418Anisotropy
Axis -0.6083
0.5444
-0.5776
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
-0.4023
0.5815
-0.7071
0.4505
0.8928
-0.0000
0.3080
0.5349
-0.7868
Axis
1.0000
0.0000
-0.0000
0.4024
-0.5815
-0.7071
0.0000
-0.0000
-1.0000
0.3927
0.6818
0.6172
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