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 HfP (Materials Project id mp-9953)

       222      100      109        0        0        0  
       100      222      109        0        0        0  
       109      109      263        0        0        0  
         0        0        0      132        0        0  
         0        0        0        0      132        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 149.22 GPaEV = 226.74 GPaGV = 90.933 GPaνV = 0.24675
ReussKR = 147.87 GPaER = 202.96 GPaGR = 79.828 GPaνR = 0.27124
HillKH = 148.55 GPaEH = 214.96 GPaGH = 85.381 GPaνH = 0.25882

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
61 GPa 122 GPa 132 GPa 132 GPa 135.55 GPa 449.45 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 159.83 GPa 259.5 GPa 1.707 TPa–1 2.5277 TPa–1 61 GPa 132 GPa-0.0249780.48172Value
Anisotropy 1.624 1.4808 2.164Anisotropy
Axis 1.0000
0.0000
0.0000
0.6600
-0.0000
0.7513
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
0.5325
0.4635
-0.7082
0.3793
0.5590
-0.7373
Axis
0.0002
1.0000
0.0000
1.0000
0.0000
-0.0000
0.5342
0.4650
0.7060
-0.8275
0.5615
0.0000
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