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Under normal reaction conditions [AlCl3 0.28-0.34M and NaOH 2.5M A.Volford et al.] spontaneous spiral and circular travelling precipitate waves were observed. We constructed a phase diagram for the reaction and identified a large controllable region at lower aluminum chloride levels. We show that it is possible to selectively initiate travelling circular waves and other self-organized structures within this controllable region. In previous work initiation was undertaken before adding the outer electrolyte resulting in disorganized waves. However, marking the gel one minute after adding outer electrolyte resulted in cardioid waves. Increasing the time interval to two minutes caused a transition to single circular waves. If the gel is marked sequentially nested circular waves (target waves) are formed. These reactions were used to calculate simple and additively weighted Voronoi tessellations. The fine control of self-organization in precipitation reactions is of interest for the synthesis of novel and functional Materials.

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I n t r o d u c t i o n A l l q u a r t z c r y s t a l u n i t s e x h i b i t a change i n r e s o n a n t f r e q u e n c y w i t h time, t e ed aging. T h i s change may be l e s s t h a n a few p a r t s i n 1 0 I S n p e r month for t h e best r e s o n a t o r s , but can be three or f o u r o r d e r s o f m a g n i t u d e g r e a t e r f o r some low f r e q u e n c y u n i t s . The a g i n g o f most c r y s t a l u n i t s i s now b e l i e v e d t o be d u e m a i n l y t o e i t h e r stress r e c o v e r y , mass s o r pt i o n o r some c o m b i n a t i o n o f t h e s e two mechanisms, I n o r d e r t o o b t a i n a n i n s i g h t i n t o t h e manner i n which t h e s e two mechanisms a f f e c t t h e a g i n g c h a r a c t e r i s t i c s o f a q u a r t z c r y s t a l u n i t , i t i s h e l p f u l t o c o n s i d e r t h e u n i t a s a c o m p o s i t e r e s o n a t o r c o n s i s t i n g o f a q u a r t z p l a t e , a n e l e c t r o d e , and a m o u n t i n g s t r u c t u r e , a l l s u r r o u n d e d by some atmosphere. The r e s o n a n t f r e q u e n c y of t h i s c o m p o s i t e d e v i c e c h a n g e s i n r e s p o n s e t o c h a n g e s i n a n y one of t h e f r e q u e n c y d e t e r m i n i n g p a r a m e t e r s s u c h a s d e n s i t y , mass d i s t r i b u t i o n , e l a s t i c c o n s t a n t s o r s u r f a c e t r a c t i o n s , The i n t e r a c t i o n s o f t h e s e f r e q u e n c y c o nt r o l l i n g p a r a m e t e r s w i t h e a c h member o f t h e c o m p o s i t e r e s o n a t o r v a r y s i g n i f i c a n t l y w i t h t h e t y p e o f r e s o n a t o r . T h i s undoubtedly i s r e s p o n s i b l e f o r t h e w i d e d i f f e r e n c e s i n a g i n g r a t e s o b s e r v e d f o r d i f f e r e n t modes o f motion. I n t h i s p a p e r , t h e a g i n g c h a r a c t e r i s t i c s o f s e v e r a l t y p e s o f q u a r t z r e s o n a t o r s i n c l u d i n g e x t e n s i o n , f l e x u r e , and width a n d t h i c k n e s s s h e a r u n i t s a r e p r e s e n t e d , and a c a u s e and e f f e c t d i s c u s s i o n on some o f t h e f a c t o r s a f f e c t i n g a g i n g i s g i v e n . W a r n e r , F r a s e r , a n d S t o c k b r i d g e ' c o n s i d e r e d t h e i n i t i a l a g i n g o f a q u a r t z r e s o n a t o r a s p o s s i b l y b e i n g c o n t r o l l e d by a stress r e c o v e r y p r o c e s s whose a c t i v a t i o n e n e r g y i s a d e c r e a s i n g f u n c t i o n o f stress.2 The change i n f r e q u e n c y o f a q u a r t z reson a t o r i n r e s p o n s e t o a change i n t h e s u r f a c e t r a c t i o n s a t e i t h e rt h e e l e c t r o d e -q u a r t z i n t e r f a c e or m o u n t i n g s t r u c t u r e -q u a r t z i n t e r f a c e i s extremely complicated and a t p r e s e n t i s n o t w e l l understood.If, however, one p o s t u l a t e s t h a t t h e s t r e s s i n t h e p l a s t i c a l l y r e l a x i n g e l e c t r o d e or m o u n t i n g s ...