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 CaZrS3 (Materials Project id mp-7781)

       147       37       56        0        0        0  
        37      136       34        0        0        0  
        56       34       97        0        0        0  
         0        0        0       24        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 70.444 GPaEV = 96.769 GPaGV = 38.067 GPaνV = 0.27105
ReussKR = 68.076 GPaER = 89.808 GPaGR = 35.078 GPaνR = 0.28013
HillKH = 69.26 GPaEH = 93.295 GPaGH = 36.572 GPaνH = 0.2755

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 40 GPa 42 GPa 59.433 GPa 105.87 GPa 214.7 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 65.182 GPa 121.45 GPa 2.9558 TPa–1 6.9132 TPa–1 24 GPa 51.119 GPa0.142270.52825Value
Anisotropy 1.863 2.3388 2.13 3.7131Anisotropy
Axis -0.0000
0.5646
-0.8254
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0003
-0.0000
1.0000
0.6725
0.7071
-0.2186
-0.4796
0.7553
0.4466
1.0000
-0.0003
0.0000
Axis
0.0000
1.0000
0.0000
-0.6725
0.7071
0.2186
-0.8385
-0.2445
-0.4869
0.0000
-0.0004
-1.0000
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