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 LiAuC2 (Materials Project id mp-29868)

        38       19        9        0        0        0  
        19       38        9        0        0        0  
         9        9      555        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0        5        0  
         0        0        0        0        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 78.333 GPaEV = 110.33 GPaGV = 43.6 GPaνV = 0.26525
ReussKR = 27.828 GPaER = 22.056 GPaGR = 8.062 GPaνR = 0.3679
HillKH = 53.08 GPaEH = 66.677 GPaGH = 25.831 GPaνH = 0.29064

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 10 GPa 19 GPa 56.675 GPa 555.33 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 16.447 GPa 552.16 GPa 1.2392 TPa–1 17.348 TPa–1 5 GPa 27.624 GPa0.0947940.77059Value
Anisotropy 33.57 14.0000 5.525 8.1291Anisotropy
Axis 0.7762
-0.0000
-0.6304
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.5000
0.5000
-0.7071
-0.2071
0.2071
-0.9561
0.2931
0.2931
0.9100
Axis
-0.7660
0.6428
-0.0000
-0.5000
-0.5000
-0.7071
-0.7071
-0.7071
-0.0000
0.6435
0.6435
-0.4145
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