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 Hf2Pd (Materials Project id mp-11454)

       224       87      117        0        0        0  
        87      224      117        0        0        0  
       117      117      153        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 138.11 GPaEV = 157.38 GPaGV = 60.067 GPaνV = 0.31008
ReussKR = 135.6 GPaER = 134.3 GPaGR = 50.301 GPaνR = 0.33494
HillKH = 136.86 GPaEH = 145.94 GPaGH = 55.184 GPaνH = 0.32228

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48.645 GPa 61 GPa 73 GPa 73 GPa 137 GPa 415.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 64.968 GPa 182.74 GPa 1.7817 TPa–1 3.8109 TPa–1 28.688 GPa 73 GPa-0.0183650.77875Value
Anisotropy 2.813 2.1389 2.545Anisotropy
Axis 0.0000
0.0000
1.0000
0.8319
0.0000
0.5549
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5001
0.4999
-0.7071
0.0000
0.0000
1.0000
-1.0000
0.0000
0.0000
1.0000
0.0003
0.0000
Axis
0.4999
-0.5001
-0.7071
0.5000
0.8660
-0.0000
-0.0000
-1.0000
-0.0000
0.0000
0.0002
-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