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 Hf2CS (Materials Project id mp-13137)

       318       90      112        0        0        0  
        90      318      112        0        0        0  
       112      112      332        0        0        0  
         0        0        0      145        0        0  
         0        0        0        0      145        0  
         0        0        0        0        0      114  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 177.33 GPaEV = 302.47 GPaGV = 124.4 GPaνV = 0.21572
ReussKR = 176.87 GPaER = 297.62 GPaGR = 122.02 GPaνR = 0.21956
HillKH = 177.1 GPaEH = 300.05 GPaGH = 123.21 GPaνH = 0.21763

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
114 GPa 145 GPa 145 GPa 207.11 GPa 228 GPa 532.89 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 270.49 GPa 326.24 GPa 1.6671 TPa–1 1.9933 TPa–1 106.12 GPa 145 GPa0.124980.28975Value
Anisotropy 1.206 1.1957 1.366 2.3183Anisotropy
Axis 1.0000
0.0000
0.0000
0.6839
0.1797
0.7072
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0600
0.5233
0.8501
Axis
0.7071
-0.0005
-0.7071
0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
-0.9935
0.1139
-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