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 HoPO4 (Materials Project id mp-4104)

       344       95       95        0        0        0  
        95      249       35        0        0        0  
        95       35      249        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       73  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 143.56 GPaEV = 189.3 GPaGV = 73.933 GPaνV = 0.28022
ReussKR = 134.54 GPaER = 129.87 GPaGR = 48.49 GPaνR = 0.33912
HillKH = 139.05 GPaEH = 160.14 GPaGH = 61.212 GPaνH = 0.30805

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 73 GPa 73 GPa 176.34 GPa 214 GPa 451.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 62.311 GPa 280.44 GPa 1.1802 TPa–1 3.1263 TPa–1 18 GPa 95.718 GPa-0.122220.8357Value
Anisotropy 4.501 2.6489 5.318Anisotropy
Axis 0.0000
0.7071
-0.7071
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0002
0.0001
1.0000
0.7071
0.0001
-0.7071
-0.7628
0.4572
0.4572
-0.7018
0.5037
0.5038
Axis
-0.0000
1.0000
-0.0001
-0.7071
-0.0002
-0.7071
-0.6466
-0.5394
-0.5394
0.0000
-0.7071
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