New Experimental Methods for Perturbation Crystallography.

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Heunen, G.W.J.C.

Publication date

2000

Link to publication

Citation for published version (APA):

Heunen, G. W. J. C. (2000). New Experimental Methods for Perturbation Crystallography.

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Appendixx A

PiezoelectricPiezoelectric Moduli

T h ee piezoelectric tensor can be written in a matrix form as is discussed in §2.2. The matrix notation off all the crystal classes are listed in Table A - 1 .

TableTable A-l: Crystal classes and their piezoelectric moduli represented in matrix notationnotation d:j (from Nye )

® ®

FormForm of the (<£tf) matrix

K E YY TO NOTATION zeroo m o d u l u s

non-zeroo m o d u l u s 11 equal m o d u l i

>> moduli numerically e q u a l , b u t opposite in sign aa modulus equal to m i n u s 2 t i m e s t h e h e a v y d o t modulus

too which it is joined.

CentrosymmetricatCentrosymmetricat classes Alll m o d u l i v a n i s h

Non-centNon-cent rosy mtnetrtcal classes

2\\x2\\xt t ( s t a n d a r d d o r i e n t a t i o n ) ) ( s t a n d a r d d o r i e n t a t i o n ) )

G G

C C

/

v. .

( : : Classs 2 Classs m Classs 222 Classs 4

:: :x

V...

T R I C L I I Class s NN IC 1 1 MONOCLINIO O J J ) ) 7(io) ) m j _ x3 3 O R T H O R H O M B I C C \ \

1 1

_{) )} T E T R A G O N A L L ) ) ) ) ( i s s

c c

(: : /

v. .

Classs 2 -Classs m Classs mm2 Classs 4

::

:X

W««

. / / N N \ \ ) ) \ \ (8) ) (10) ) (5) ) {*) {*) 125 5

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TableTable A-l continued Reference Reference Classs 4n : \ \

:x x

. // (3) \ \ / (-) Classoss 43m a n d 23 (0) ) (1) )

Alll moduli vanish

Classs ,32 . // (6) Classs 3m H E X A G O N A L , , (4) ) Classs 6mm / <: samee as class 4mm Classs 6 1111

"Physical properties of crystals. Their representation by tensors and matrices." J. F. Nye. Clarendonn Press. Oxford. Fourth edition, 1995.