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 Sb3Pb (Materials Project id mp-973199)

        79       75       36        0        0        0  
        75       79       36        0        0        0  
        36       36       54        0        0        0  
         0        0        0        3        0        0  
         0        0        0        0        3        0  
         0        0        0        0        0        2  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 56.222 GPaEV = 17.195 GPaGV = 5.9333 GPaνV = 0.44903
ReussKR = 48.508 GPaER = 8.5229 GPaGR = 2.8975 GPaνR = 0.47072
HillKH = 52.365 GPaEH = 12.884 GPaGH = 4.4154 GPaνH = 0.45899

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 3 GPa 3 GPa 4 GPa 32.642 GPa 175.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.3831 GPa 37.169 GPa 3.1447 TPa–1 14.326 TPa–1 2 GPa 5.9102 GPa0.0484850.92727Value
Anisotropy 5.034 4.5556 2.955 19.1250Anisotropy
Axis 0.1464
0.8898
0.4322
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.9573
0.2890
0.0000
0.7071
-0.0003
0.7071
0.9388
0.3446
0.0000
-0.4657
0.8849
-0.0000
Axis
-0.2890
0.9573
-0.0000
0.7071
-0.0005
-0.7071
-0.0000
0.0000
1.0000
-0.8849
-0.4657
-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