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 Ni (Materials Project id mp-23)

       276      159      159        0        0        0  
       159      276      159        0        0        0  
       159      159      276        0        0        0  
         0        0        0      132        0        0  
         0        0        0        0      132        0  
         0        0        0        0        0      132  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 198 GPaEV = 262.47 GPaGV = 102.6 GPaνV = 0.27907
ReussKR = 198 GPaER = 229.59 GPaGR = 87.85 GPaνR = 0.30674
HillKH = 198 GPaEH = 246.21 GPaGH = 95.225 GPaνH = 0.29276

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
117 GPa 117 GPa 132 GPa 132 GPa 132 GPa 594 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 159.77 GPa 324 GPa 1.6835 TPa–1 1.6835 TPa–1 58.5 GPa 132 GPa-0.0236440.58971Value
Anisotropy 2.028 1.0000 2.256Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0003
-0.7071
Axis
0.7071
-0.0005
-0.7071
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
0.0002
1.0000
-0.0003
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