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 Mg2Au (Materials Project id mp-11250)

        61       39       46        0        0        0  
        39      106       58        0        0        0  
        46       58      104        0        0        0  
         0        0        0       27        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       16  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 61.889 GPaEV = 62.658 GPaGV = 23.533 GPaνV = 0.33126
ReussKR = 54.837 GPaER = 56.825 GPaGR = 21.406 GPaνR = 0.32729
HillKH = 58.363 GPaEH = 59.742 GPaGH = 22.47 GPaνH = 0.32939

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 27 GPa 31.606 GPa 32 GPa 48.559 GPa 190.84 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 38.221 GPa 74.713 GPa 2.0042 TPa–1 12.49 TPa–1 16 GPa 32 GPa0.105130.54702Value
Anisotropy 1.955 6.2317 2 5.2033Anisotropy
Axis 0.9855
0.1695
0.0000
0.5862
0.0000
0.8102
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0009
0.0000
0.0000
0.0000
1.0000
0.6880
0.2160
-0.6928
0.3499
0.5609
0.7503
Axis
0.0009
1.0000
0.0000
-1.0000
0.0000
0.0000
-0.6672
-0.1874
-0.7210
-0.7390
0.6575
-0.1469
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