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 ZnP2 (Materials Project id mp-11025)

       112       48       43        0        0        0  
        48      112       43        0        0        0  
        43       43      121        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       43        0  
         0        0        0        0        0       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 68.111 GPaEV = 106.71 GPaGV = 43.067 GPaνV = 0.23888
ReussKR = 68.096 GPaER = 103.25 GPaGR = 41.389 GPaνR = 0.24729
HillKH = 68.103 GPaEH = 104.99 GPaGH = 42.228 GPaνH = 0.24307

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
43 GPa 43 GPa 59 GPa 64 GPa 76.639 GPa 204.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 85.651 GPa 123.45 GPa 4.7248 TPa–1 4.9802 TPa–1 32 GPa 59 GPa0.0462260.34628Value
Anisotropy 1.441 1.0541 1.844 7.4910Anisotropy
Axis 1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
1.0000
-0.0000
0.0000
0.7071
0.7071
-0.0000
0.8629
-0.0002
-0.5054
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.0000
-0.7071
0.7071
0.0001
0.0001
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