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 BiRh (Materials Project id mp-22868)

       119       75       99        0        0        0  
        75      119       99        0        0        0  
        99       99      207        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 110.11 GPaEV = 85.188 GPaGV = 31.067 GPaνV = 0.37106
ReussKR = 96.962 GPaER = 77.773 GPaGR = 28.461 GPaνR = 0.36632
HillKH = 103.54 GPaEH = 81.483 GPaGH = 29.764 GPaνH = 0.36883

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 38 GPa 38 GPa 44 GPa 60.342 GPa 340.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.981 GPa 107.45 GPa-0.19459 TPa–1 5.2539 TPa–1 22 GPa 38 GPa0.229320.54919Value
Anisotropy 1.762 1.727 2.3949Anisotropy
Axis 0.3827
0.9239
0.0000
0.1130
0.3270
0.9382
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.9573
0.2890
0.0000
0.0000
0.0000
1.0000
0.7391
0.2585
-0.6220
0.4624
0.2374
0.8543
Axis
-0.2890
0.9573
-0.0000
-0.7660
0.6428
-0.0000
0.5871
0.2054
0.7830
-0.4567
0.8896
-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