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 LaPd5 (Materials Project id mp-30753)

       167       95       80        0        0        0  
        95      167       80        0        0        0  
        80       80      192        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       43        0  
         0        0        0        0        0       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 115.11 GPaEV = 113.45 GPaGV = 42.467 GPaνV = 0.33574
ReussKR = 115.04 GPaER = 111.14 GPaGR = 41.5 GPaνR = 0.33899
HillKH = 115.08 GPaEH = 112.29 GPaGH = 41.983 GPaνH = 0.33736

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36 GPa 43 GPa 43 GPa 72 GPa 108.57 GPa 345.43 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 105.22 GPa 143.15 GPa 2.7197 TPa–1 2.9863 TPa–1 36 GPa 48.178 GPa0.224440.46135Value
Anisotropy 1.36 1.0980 1.338 2.0556Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0008
-0.0000
0.1241
0.6961
0.7071
0.9482
0.3176
-0.0000
-0.6862
0.7274
0.0000
Axis
0.0008
1.0000
-0.0000
0.1241
0.6961
-0.7071
0.0001
-0.0002
-1.0000
-0.7274
-0.6862
0.0000
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