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 ZrSb (Materials Project id mp-10638)

       206       32       56        0        0        0  
        32      196       77        0        0        0  
        56       77      129        0        0        0  
         0        0        0       77        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95.667 GPaEV = 153.36 GPaGV = 62.2 GPaνV = 0.23282
ReussKR = 94.148 GPaER = 136.77 GPaGR = 54.367 GPaνR = 0.25788
HillKH = 94.907 GPaEH = 145.14 GPaGH = 58.284 GPaνH = 0.24512

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 71.133 GPa 73 GPa 77 GPa 171.31 GPa 288.55 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 89.356 GPa 188.24 GPa 2.7165 TPa–1 4.7692 TPa–1 36.448 GPa 84.456 GPa-0.0338070.60031Value
Anisotropy 2.107 1.7557 2.317Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.8221
0.5694
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.4128
0.5742
0.7071
0.7071
0.6587
0.2570
0.5234
0.4777
-0.7056
-0.0000
1.0000
0.0000
Axis
0.4129
0.5740
-0.7071
-0.7071
0.6587
0.2570
-0.5213
-0.4755
-0.7086
-0.0007
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