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 Zr2Ga3 (Materials Project id mp-30686)

       215       59       56        0        0        0  
        59      209       78        0        0        0  
        56       78      189        0        0        0  
         0        0        0       69        0        0  
         0        0        0        0       70        0  
         0        0        0        0        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 111 GPaEV = 167.75 GPaGV = 67.2 GPaνV = 0.24813
ReussKR = 110.75 GPaER = 165.67 GPaGR = 66.233 GPaνR = 0.25068
HillKH = 110.88 GPaEH = 166.71 GPaGH = 66.716 GPaνH = 0.2494

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 69 GPa 70 GPa 120.18 GPa 159.37 GPa 333.45 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 150.27 GPa 191.12 GPa 2.7009 TPa–1 3.2702 TPa–1 57 GPa 76.901 GPa0.171320.3591Value
Anisotropy 1.272 1.2108 1.349 2.0961Anisotropy
Axis 0.6527
0.7577
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0001
-0.0000
0.7071
0.5798
0.4048
0.0000
0.0000
1.0000
-0.0000
1.0000
-0.0000
Axis
0.0001
1.0000
0.0000
-0.7071
0.5798
0.4048
-1.0000
0.0000
0.0000
-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