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 As2Rh (Materials Project id mp-15954)

       259       67       78        0       35        0  
        67      317       78        0       20        0  
        78       78      251        0       -2        0  
         0        0        0       90        0       24  
        35       20       -2        0       72        0  
         0        0        0       24        0       72  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 141.44 GPaEV = 216.73 GPaGV = 87.067 GPaνV = 0.24462
ReussKR = 135.9 GPaER = 197.83 GPaGR = 78.666 GPaνR = 0.25739
HillKH = 138.67 GPaEH = 207.31 GPaGH = 82.866 GPaνH = 0.25085

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55.368 GPa 63.297 GPa 106.63 GPa 181.31 GPa 223.92 GPa 430.47 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 139.87 GPa 281.99 GPa 1.6763 TPa–1 3.61 TPa–1 55.368 GPa 111.84 GPa0.0476530.47364Value
Anisotropy 2.016 2.1536 2.02 9.9393Anisotropy
Axis 0.7060
0.5502
-0.4458
-0.0577
0.9947
-0.0852
0.6288
-0.0000
0.7776
-0.7776
-0.0000
0.6288
-0.8219
0.0000
0.5696
0.6888
0.7071
0.1599
-0.8584
-0.0000
0.5129
0.5162
0.0000
0.8565
Axis
-0.0000
-1.0000
-0.0000
-0.6888
0.7071
-0.1598
0.0000
-1.0000
-0.0000
-0.8565
-0.0000
0.5162
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