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 YCuO2 (Materials Project id mp-2918)

       173       60       83        0        0        0  
        60      173       83        0        0        0  
        83       83      260        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       15        0  
         0        0        0        0        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 117.56 GPaEV = 114.34 GPaGV = 42.733 GPaνV = 0.33789
ReussKR = 111.17 GPaER = 75.514 GPaGR = 27.226 GPaνR = 0.38679
HillKH = 114.36 GPaEH = 95.23 GPaGH = 34.98 GPaνH = 0.36122

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 15 GPa 57 GPa 113 GPa 128.35 GPa 364.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.052 GPa 200.87 GPa 1.4316 TPa–1 3.7819 TPa–1 15 GPa 63.738 GPa0.0894870.77491Value
Anisotropy 3.786 2.6418 4.249 8.6595Anisotropy
Axis 0.7224
-0.0000
0.6915
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.5236
0.4753
-0.7071
0.5194
0.5194
0.6786
0.4616
0.4616
0.7575
Axis
0.1736
0.9848
-0.0000
-0.5235
-0.4753
-0.7071
-0.7071
0.7071
-0.0000
0.5356
0.5356
-0.6528
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