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 HoCd3 (Materials Project id mp-11302)

        73       45       42        0        0        0  
        45       85       22        0        0        0  
        42       22      102        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       40        0  
         0        0        0        0        0       27  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 53.111 GPaEV = 72.887 GPaGV = 28.667 GPaνV = 0.27128
ReussKR = 52.947 GPaER = 65.017 GPaGR = 25.097 GPaνR = 0.29534
HillKH = 53.029 GPaEH = 68.988 GPaGH = 26.882 GPaνH = 0.28318

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 27 GPa 28.136 GPa 40 GPa 72.16 GPa 159.7 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 39.61 GPa 95.307 GPa 5.8104 TPa–1 7.0933 TPa–1 15.295 GPa 40 GPa-0.0679430.61722Value
Anisotropy 2.406 1.2208 2.615Anisotropy
Axis 1.0000
0.0000
0.0000
0.5361
-0.0000
-0.8442
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
-0.0002
0.0001
1.0000
0.0000
0.0000
1.0000
Axis
-0.7071
-0.7071
-0.0000
1.0000
0.0000
-0.0000
0.0000
-1.0000
0.0001
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