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 Ca2Zn (Materials Project id mp-1039208)

        12       16       16        0        0        0  
        16       36       25        0        0        0  
        16       25       36        0        0        0  
         0        0        0        9        0        0  
         0        0        0        0        7        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 22 GPaEV = 17.503 GPaGV = 6.4 GPaνV = 0.3674
ReussKR = 10.476 GPaER = 11.213 GPaGR = 4.2422 GPaνR = 0.32161
HillKH = 16.238 GPaEH = 14.391 GPaGH = 5.3211 GPaνH = 0.35229

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3.1496 GPa 7 GPa 7 GPa 9 GPa 11 GPa 69.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.6066 GPa 21.944 GPa -18.182 TPa–1 131.82 TPa–1 2.0183 GPa 9 GPa-0.18771.3211Value
Anisotropy 6.085 4.459Anisotropy
Axis 1.0000
0.0000
0.0000
0.4102
0.6449
0.6449
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0002
0.7071
0.0004
0.0003
1.0000
0.6739
-0.0001
0.7388
0.0000
0.7071
0.7071
Axis
0.7071
-0.0006
-0.7071
-0.0001
1.0000
-0.0003
0.7388
-0.0002
-0.6739
-1.0000
0.0000
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