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 Ca5Sb3 (Materials Project id mp-12467)

        90       24       17        0        0        0  
        24       90       17        0        0        0  
        17       17       50        0        0        0  
         0        0        0       21        0        0  
         0        0        0        0       21        0  
         0        0        0        0        0       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 38.444 GPaEV = 64.58 GPaGV = 26.467 GPaνV = 0.22003
ReussKR = 35.082 GPaER = 60.39 GPaGR = 24.891 GPaνR = 0.2131
HillKH = 36.763 GPaEH = 62.487 GPaGH = 25.679 GPaνH = 0.21671

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21 GPa 21 GPa 33 GPa 41.975 GPa 66 GPa 122.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 44.93 GPa 80.278 GPa 6.4428 TPa–1 15.619 TPa–1 21 GPa 33 GPa0.149120.28029Value
Anisotropy 1.787 2.4242 1.571 1.8796Anisotropy
Axis 0.0000
0.0000
1.0000
0.7934
0.6088
0.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1873
0.9823
0.0000
0.0000
0.0000
1.0000
-0.6605
0.6068
0.4422
Axis
-0.7660
-0.6428
0.0000
-0.9823
-0.1873
-0.0000
0.1736
0.9848
-0.0000
-0.3255
0.2992
-0.8969
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