International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. D. ch. 1.10, p. 256

Table 1.10.4.3 

T. Janssena*

a Institute for Theoretical Physics, University of Nijmegen, 6524 ED Nijmegen, The Netherlands
Correspondence e-mail: ted@sci.kun.nl

Table 1.10.4.3 | top | pdf |
Elastic constants for icosahedral quasicrystals

Type Free parameters Relations
Phonon–phonon 2 [ c_{1111}=c_{2222}=c_{3333}=x]
    [c_{1122}=c_{1133}=c_{2233}=y]
    [c_{1212}=c_{1313}=c_{2323}=x-y]
Phason–phason 2 [c_{1414}=c_{1616}=c_{2424}=c_{2525}=c_{3535}=c_{3636}=x]
    [c_{1416}=c_{1424}=-c_{1425}=c_{1426}=-c_{1436}=y]
    [c_{1524}=c_{1536}=-c_{1624}=c_{1634}=c_{1635}=-y]
    [c_{1636}=c_{2425}=c_{2435}=c_{2534}=-c_{2535}=-y]
    [c_{2536}=c_{2635}=c_{3536}=y, c_{1515}=c_{2626}=c_{3434}=x+2y]
    [c_{1415}=c_{1535}=-c_{1626}=-c_{2434}=-c_{2526}=-c_{3436}=y\tau]
    [c_{1434}=-c_{11516}=-c_{1525}=-c_{2426}=-c_{2636}=c_{3435}=y/\tau]
Phonon–phason 1 [-c_{1114}=c_{1134}=c_{1225}=c_{2225}=c_{2336}=c_{3326}=c_{3336}]
    [\quad=-c_{1115}/\tau =c_{1125}/\tau =-c_{1135}\tau=c_{1215}\tau =c_{1226}\tau]
    [\quad=-c_{1334}\tau =-c_{2226}\tau =c_{2236}\tau =c_{2326}\tau =c_{2334}\tau ]
    [\quad=-c_{3334}\tau =-c_{1116}\tau^2 =-c_{1126}\tau^2 =-c_{1216}\tau^2 ]
    [\quad=-c_{1335}\tau^2 =-c_{2224}\tau^2 =-c_{2234}\tau^2 =c_{3335}\tau^2 ]
    [\quad=-c_{1136}\tau =c_{1224}\tau =-c_{1316}\tau =-c_{2335}\tau ]
    [\quad=-c_{1124}/\tau^3 =-c_{1336}/\tau^3 =c_{2235}/\tau^3 =c_{2325}/\tau^3 ]