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 NdGa2 (Materials Project id mp-2524)

       156       38       33        0        0        0  
        38      156       33        0        0        0  
        33       33      106        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 69.556 GPaEV = 130.83 GPaGV = 55.133 GPaνV = 0.1865
ReussKR = 67.102 GPaER = 128.04 GPaGR = 54.165 GPaνR = 0.18197
HillKH = 68.329 GPaEH = 129.44 GPaGH = 54.649 GPaνH = 0.18427

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 56 GPa 59 GPa 85.86 GPa 118 GPa 214.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 94.773 GPa 140.45 GPa 3.9704 TPa–1 6.9618 TPa–1 47.034 GPa 59 GPa0.116540.25209Value
Anisotropy 1.482 1.7534 1.254 2.1631Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0001
0.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.1047
0.9945
-0.0000
-0.1367
0.6441
0.7527
0.7436
0.6686
-0.0000
Axis
0.7071
-0.0005
-0.7071
-0.9945
0.1047
0.0000
0.1563
-0.7363
0.6584
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