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 HoPd (Materials Project id mp-832)

       140       72       72        0        0        0  
        72      140       72        0        0        0  
        72       72      140        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 94.667 GPaEV = 86.763 GPaGV = 32.2 GPaνV = 0.34725
ReussKR = 94.667 GPaER = 86.603 GPaGR = 32.134 GPaνR = 0.34753
HillKH = 94.667 GPaEH = 86.683 GPaGH = 32.167 GPaνH = 0.34739

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 31 GPa 31 GPa 68 GPa 68 GPa 284 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 83.848 GPa 91.094 GPa 3.5211 TPa–1 3.5211 TPa–1 31 GPa 34 GPa0.318950.37982Value
Anisotropy 1.086 1.0000 1.097 1.1909Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7500
0.4330
0.5000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0004
-0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
-0.0000
-0.7071
-0.0002
-0.7071
0.0003
1.0000
-0.0003
-0.7071
0.0002
-0.7071
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