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 AcN (Materials Project id mp-866056)

       107       78       66        0        0        0  
        78      107       66        0        0        0  
        66       66       80        0        0        0  
         0        0        0       28        0        0  
         0        0        0        0       28        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 79.333 GPaEV = 54.326 GPaGV = 19.6 GPaνV = 0.38587
ReussKR = 75.16 GPaER = 48.049 GPaGR = 17.241 GPaνR = 0.39345
HillKH = 77.247 GPaEH = 51.192 GPaGH = 18.42 GPaνH = 0.38955

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 25.41 GPa 28 GPa 28 GPa 29 GPa 239.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 32.908 GPa 59.564 GPa 2.2996 TPa–1 8.7057 TPa–1 13.072 GPa 28 GPa0.0374730.65307Value
Anisotropy 1.81 3.7857 2.142 17.4278Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.7628
0.6466
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.4999
0.5001
-0.7071
-0.0000
0.0000
1.0000
0.4986
0.4986
-0.7091
-0.5392
0.5392
0.6470
Axis
-0.5001
-0.4999
-0.7071
-0.5000
0.8660
-0.0000
0.5014
0.5014
0.7051
-0.7071
-0.7071
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