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 HfCoAs (Materials Project id mp-9801)

       282      118      131        0        0        0  
       118      295      138        0        0        0  
       131      138      284        0        0        0  
         0        0        0       94        0        0  
         0        0        0        0      111        0  
         0        0        0        0        0      101  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 181.67 GPaEV = 237.89 GPaGV = 92.8 GPaνV = 0.28175
ReussKR = 181.46 GPaER = 233.56 GPaGR = 90.846 GPaνR = 0.28548
HillKH = 181.57 GPaEH = 235.73 GPaGH = 91.823 GPaνH = 0.28361

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
94 GPa 101 GPa 111 GPa 145.42 GPa 170.32 GPa 545.26 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 194.97 GPa 258.73 GPa 1.7362 TPa–1 1.9949 TPa–1 75.401 GPa 111 GPa0.153480.399Value
Anisotropy 1.327 1.1490 1.472 2.5996Anisotropy
Axis 0.0000
0.0000
1.0000
-0.6621
0.4133
0.6251
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
0.7071
0.7071
0.0000
0.0000
1.0000
0.7020
-0.0002
0.7122
-0.6388
0.7693
-0.0000
Axis
0.0001
0.7071
-0.7071
-1.0000
0.0000
0.0000
0.7122
-0.0005
-0.7020
-0.0000
0.0000
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