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 NiF3 (Materials Project id mp-561428)

        82       -4       38      -29        0        0  
        -4       82       38       29        0        0  
        38       38      122        0        0        0  
       -29       29        0       63        0        0  
         0        0        0        0       63      -29  
         0        0        0        0      -29       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 47.778 GPaEV = 107.99 GPaGV = 48.067 GPaνV = 0.1233
ReussKR = 38.988 GPaER = 75.192 GPaGR = 31.9 GPaνR = 0.17857
HillKH = 43.383 GPaEH = 91.76 GPaGH = 39.983 GPaνH = 0.14748

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22.324 GPa 31.906 GPa 41.931 GPa 83.676 GPa 117.09 GPa 158.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.64 GPa 158.14 GPa 0.30175 TPa–1 12.674 TPa–1 22.324 GPa 83.676 GPa-0.332960.67207Value
Anisotropy 3.123 42.0000 3.748Anisotropy
Axis 0.8367
0.4831
0.2579
0.6339
0.3660
-0.6813
0.0000
0.0000
1.0000
-0.7934
0.6088
0.0000
1.0000
0.0000
-0.0000
0.5027
0.2902
0.8143
-0.7197
0.4155
-0.5562
0.3397
0.1961
0.9199
Axis
-0.0000
0.8142
0.5805
-0.5000
0.8660
0.0000
-0.5000
-0.8660
-0.0000
-0.5000
0.8660
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