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 Zr3Pd4 (Materials Project id mp-12712)

       181      130      117       -2       -6        0  
       130      181      117        2        6        0  
       117      117      215        0        0        0  
        -2        2        0       27        0        6  
        -6        6        0        0       27       -2  
         0        0        0        6       -2       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 145 GPaEV = 84.194 GPaGV = 30 GPaνV = 0.40323
ReussKR = 144.64 GPaER = 76.374 GPaGR = 27.045 GPaνR = 0.412
HillKH = 144.82 GPaEH = 80.296 GPaGH = 28.522 GPaνH = 0.40759

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
19.597 GPa 24.033 GPa 32.403 GPa 53.967 GPa 90.715 GPa 435.28 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 57.163 GPa 126.97 GPa 1.95 TPa–1 2.4818 TPa–1 19.609 GPa 39.604 GPa0.144520.66933Value
Anisotropy 2.221 1.2727 2.02 4.6315Anisotropy
Axis -0.5105
0.6914
0.5112
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1302
0.9915
-0.0000
0.7559
0.0778
-0.6501
-0.5769
-0.0588
0.8147
0.8060
0.5918
0.0030
0.8049
0.5934
0.0027
Axis
-0.1007
0.9949
0.0020
-0.8105
-0.0830
-0.5798
-0.2255
0.3118
-0.9230
-0.5485
0.7423
0.3848
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