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 NiP2 (Materials Project id mp-486)

        96       54       26        0        8        0  
        54      343       70        0        3        0  
        26       70      357        0      -22        0  
         0        0        0      128        0       13  
         8        3      -22        0       39        0  
         0        0        0       13        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 121.78 GPaEV = 202.64 GPaGV = 82.867 GPaνV = 0.22267
ReussKR = 81.224 GPaER = 128.61 GPaGR = 52.022 GPaνR = 0.2361
HillKH = 101.5 GPaEH = 165.64 GPaGH = 67.445 GPaνH = 0.22801

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30.271 GPa 35.844 GPa 85.61 GPa 129.73 GPa 283.47 GPa 430.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 74.695 GPa 345.21 GPa 1.0675 TPa–1 9.4272 TPa–1 30.271 GPa 138.09 GPa-0.082160.58664Value
Anisotropy 4.622 8.8312 4.562Anisotropy
Axis 0.8925
0.3015
-0.3354
-0.0910
0.0000
0.9959
0.0000
1.0000
0.0000
0.9980
-0.0000
-0.0637
-0.9913
0.0000
0.1318
0.0642
0.7071
-0.7042
0.0999
0.4294
-0.8976
-0.4098
0.8471
-0.3384
Axis
-0.0000
-1.0000
0.0001
0.0642
-0.7071
-0.7042
-0.7121
-0.5991
-0.3659
-0.9102
-0.4039
0.0912
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