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 ZrO2 (Materials Project id mp-2858)

       256      140       99        0       -1        0  
       140      357      152        0        3        0  
        99      152      301        0      -40        0  
         0        0        0      114        0        8  
        -1        3      -40        0       80        0  
         0        0        0        8        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 188.44 GPaEV = 227.69 GPaGV = 87.667 GPaνV = 0.29862
ReussKR = 177.56 GPaER = 211.51 GPaGR = 81.257 GPaνR = 0.30147
HillKH = 183 GPaEH = 219.6 GPaGH = 84.462 GPaνH = 0.3

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
68.459 GPa 68.591 GPa 115.41 GPa 157.3 GPa 192.17 GPa 576.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 146.73 GPa 280.29 GPa 0.83877 TPa–1 2.9826 TPa–1 61.918 GPa 115.41 GPa0.0695620.52362Value
Anisotropy 1.91 3.5559 1.864 7.5274Anisotropy
Axis 0.5465
0.0000
0.8374
0.0504
0.7893
0.6119
0.0000
1.0000
0.0000
0.8239
0.0000
0.5668
0.1156
0.5239
-0.8439
0.1735
0.0002
0.9848
-0.8243
0.4177
-0.3822
0.0000
1.0000
-0.0000
Axis
-0.8470
-0.3918
-0.3593
0.0005
1.0000
-0.0003
0.2318
-0.3669
-0.9009
-0.6774
-0.0000
-0.7356
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