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 HfPt (Materials Project id mp-1007691)

       285      154      170        0        0        0  
       154      296      110        0        0        0  
       170      110      207        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0      102        0  
         0        0        0        0        0       85  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 184 GPaEV = 175.42 GPaGV = 65.4 GPaνV = 0.34111
ReussKR = 173.09 GPaER = 128.05 GPaGR = 46.504 GPaνR = 0.37671
HillKH = 178.55 GPaEH = 151.98 GPaGH = 55.952 GPaνH = 0.35813

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 70.786 GPa 85 GPa 102 GPa 159.97 GPa 557.24 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 67.805 GPa 243.23 GPa 0.41426 TPa–1 3.5014 TPa–1 22 GPa 102 GPa-0.165960.9329Value
Anisotropy 3.587 8.4522 4.636Anisotropy
Axis -0.0000
0.6464
0.7630
0.7416
0.0000
0.6708
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0004
-0.0002
1.0000
-0.0000
0.0000
1.0000
0.7281
0.4537
-0.5138
0.7379
0.5123
-0.4394
Axis
-0.0000
1.0000
0.0002
-1.0000
0.0000
-0.0000
-0.6845
0.5200
-0.5108
-0.0301
0.6753
0.7369
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