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 P2W (Materials Project id mp-11329)

       381       74      154        0      -11        0  
        74      309      104        0       18        0  
       154      104      370        0      -13        0  
         0        0        0       63        0       18  
       -11       18      -13        0      146        0  
         0        0        0       18        0      149  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 191.56 GPaEV = 298.09 GPaGV = 120.13 GPaνV = 0.24064
ReussKR = 186.45 GPaER = 266.11 GPaGR = 105.42 GPaνR = 0.26212
HillKH = 189 GPaEH = 282.2 GPaGH = 112.78 GPaνH = 0.25115

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
59.385 GPa 140.49 GPa 152.62 GPa 212.19 GPa 266.56 GPa 586.76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 179.86 GPa 393.25 GPa 1.3546 TPa–1 2.3972 TPa–1 59.385 GPa 155.16 GPa-0.0399340.55188Value
Anisotropy 2.186 1.7697 2.613Anisotropy
Axis -0.1398
0.7240
0.6755
0.7242
-0.0000
-0.6896
0.1045
-0.0000
0.9945
0.0000
1.0000
0.0000
-0.1969
-0.0000
0.9804
-0.9301
0.3422
0.1334
-0.5978
0.6536
-0.4641
-0.6850
0.5476
0.4804
Axis
0.0000
-1.0000
-0.0000
-0.1699
-0.7229
0.6697
-0.8016
-0.4848
0.3499
0.0028
-0.6575
0.7534
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