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 Ca3N2 (Materials Project id mp-844)

       113       45       45        0        0        0  
        45      113       45        0        0        0  
        45       45      113        0        0        0  
         0        0        0       33        0        0  
         0        0        0        0       33        0  
         0        0        0        0        0       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 67.667 GPaEV = 86.043 GPaGV = 33.4 GPaνV = 0.28807
ReussKR = 67.667 GPaER = 86.027 GPaGR = 33.393 GPaνR = 0.28811
HillKH = 67.667 GPaEH = 86.035 GPaGH = 33.396 GPaνH = 0.28809

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33 GPa 33 GPa 33 GPa 68 GPa 68 GPa 203 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 85.157 GPa 87.367 GPa 4.9261 TPa–1 4.9261 TPa–1 33 GPa 34 GPa0.279370.29847Value
Anisotropy 1.026 1.0000 1.03 1.0684Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.3536
0.8536
-0.3827
0.7934
0.0000
0.6088
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0000
-0.7071
Axis
0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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