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 HfNi3 (Materials Project id mp-7285)

       299      121      116       -7        0        0  
       121      299      116        7        0        0  
       116      116      323        0        0        0  
        -7        7        0       70        0        0  
         0        0        0        0       70       -7  
         0        0        0        0       -7       89  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 180.78 GPaEV = 217.45 GPaGV = 83.667 GPaνV = 0.29952
ReussKR = 180.64 GPaER = 212.32 GPaGR = 81.404 GPaνR = 0.30411
HillKH = 180.71 GPaEH = 214.89 GPaGH = 82.535 GPaνH = 0.30181

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
67.7 GPa 69.1 GPa 91.3 GPa 178.9 GPa 200.43 GPa 542.57 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 183.53 GPa 258.92 GPa 1.7288 TPa–1 1.9035 TPa–1 67.7 GPa 97.705 GPa0.187530.43789Value
Anisotropy 1.411 1.1011 1.443 2.3350Anisotropy
Axis 0.6737
0.3890
0.6283
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3690
0.9294
0.0000
-0.0000
0.3122
0.9500
0.0000
0.6578
0.7532
0.5356
0.3092
-0.7858
0.5490
0.3175
-0.7732
Axis
-1.0000
-0.0000
-0.0000
0.0000
0.7532
-0.6578
-0.5000
0.8660
0.0000
-0.6698
-0.3861
-0.6342
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