strengthening and embossment of final shape in niti shape memory alloys (sma)

5
± [1] M. Tokita, J. Soc. Powder Tech. (JPN) 1993, 30, 790. [2] S. H. Risbud, J. R. Groza, Philosophical Magazine B 1994, 69, 525. [3] a) S. J. Glass, K. G. Ewsuk, MRS Bulletin 1997, 22, 24. b) J. J. Lannutti, MRS Bulletin 1997, 22, 38. c) I. Aydin, B. J. Briscoe, and N. Ozkan, MRS Bulletin 1997, 22, 45. [4] K. M. Hurysz, J. L. Clark, A. R. Nagel, C. U. Hard- wikke, K. J. Lee, J. K. Cochran, T. H. Sanders, in Mater. Res. Soc. Symp. Proc. Vol. 521 , MRS, Warrendale, PA, 1998, 191. [5] O. Andersen, U. Waag, L. Schneider, G. Stephani, B. Kieback, Adv. Engin. Mater. 2002, 4, 192. [6] S. Kishimoto, and N. Shinya, J. Intelligent Mater. Systems & Structures 2001, 12, 271. [7] S. Kishimoto, N. Shinya, Mater. Design 2000, 21, 575. [8] Z. Song, S. Kishimoto, N. Shinya, J. Alloy Comp. 2003, 355, 166. [9] Z. Song, S. Kishimoto, N. Shinya, J. Mater. Sci. 2003, 38, 4211. Strengthening and Embossment of Final Shape in NiTi Shape Memory Alloys (SMA)** By Erhard Hornbogen* Shape memory alloys transform at low temperature by a martensitic reaction b ® a, which implies formation of a domain structure (similar to ferromagnetic, ferroelectric transformations). This microstructure allows complex pseu- do-plastic deformability (high degree of freedom). Reversion of a into b restores a definite shape, either by heating to T > A f (austenite finish), or by reduction of the external transfor- mational stress (pseudo-elasticity). It is discussed how a de- fined final shape is achieved at temperatures high above A f , at which diffusional processes can take place. In addition maximum strength is required for many SMA applications,- especially a high stability at repeated transformations (fatigue, loss of memory). The origin of the microstructure is discussed, which leads to the desired combination of proper- ties. Special attention is paid to thermo-mechanical treat- ments (TMT), by which a wide range of microstructures can be obtained. A systematic approach is provided for the types of reverse reactions a ® b, which are found between, crystal- ographically reversible (martensitic) and diffusion controlled (combined reactions). Features of optimum microstructures for shaping and desired SM-properties are discussed. Temperature Ranges: There is a wide temperature range in which SMA behave like normal intermetallic compounds with CsCl-structure: M d < D T 1 < T m (Fig. 1). [1] At and below M d martensitic phase transformation can take place. It is com- plete below a temperature designated as M f . Thus we find an intermediate range M f < D T 2 < M d , in which the alloy is transforming, and the range 0 K < D T 3 <M f in which trans- formation is complete. The two upper temperature ranges have to be subdivided further. Diffusion controlled processes will become considerable at T D > 1/3 T m . This amounts to ~ 300 C for NiTi, less than 200 C for CuZn. The martensite transformation temperatures (M s , M f , A s , A f , M d ) should be situated safely below this temperature, if ageing effects are to be avoided. Above T D extends the range in which, for exam- ple, precipitation or creep is occurring. COMMUNICATIONS 214 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/adem.200300571 ADVANCED ENGINEERING MATERIALS 2004, 6, No. 4 ± [*] Prof. E. Hornbogen Ruhr-Universität Bochum, D-44801 Bochum, Germany E-mail: [email protected] [**] This work was supported by the German Science foundation: DFG SFB 459. Thanks are due to Mr. Karl Rittner for his help with developing the test method for acquiring the final shape and for conducting all thermo-mechanical treatments. Fig. 1. Temperature scales for shape memory alloys.

Upload: e-hornbogen

Post on 06-Jun-2016

217 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Strengthening and Embossment of Final Shape in NiTi Shape Memory Alloys (SMA)

���� �� ����� �� ���� ���� ���� ���� ����� ��� ������ �� �� ������ �� �� ������ ������������� ������� � �����

��� ������� �� �� �� ������ � �� !"���� ��� � ��!�� ����� ""� �#�

�� �� �� $�%%�� ��� � ��!�� ����� ""� �&� '� (� )*�%�+� �� +��'�,� �%� -� .���%���� � ��!�� ����� ""� #��

�#� � �� ���*��� �� $� /����� )� �� -�0,�� /� 1� ����2"��,� � �� $,,� �� � /�'3��%� �� �� ��%�,��� % ��!���� ���� �#$�� ���� %��� &"' � ���� 4���,%���,� 5)������ ����

��� .� )%�,��,%� 1� 4��0� $� �'3%,�,�� �� �,63�%�+� ,��'�� (�)� *����� ��!� ��� +� ����

�7� �� �38��� �%� -� �3%*�� �� ,�!�����! ��!� �#�!$�- �! �! � ��� '"� � ��

� � �� �38��� -� �3%*����!� .���� �� "'� � ���&� 9� ��%0� �� �38��� -� �3%*�� �� (���# /�$�� ���

�&&� �77���� 9� ��%0� �� �38��� -� �3%*�� �� ��!� ���� ��� �0�

#����

������������� � �� ��������� ���� ���� ������ ���������� ������ �������

�� ��������������

�3�6, 8,8��* ����*� ��%�:��8 � ��" ,86,����, �* �8��,%�' �,�'�% � � �� "3'3 86�,� :��8��% �: ���8�% ���'��, ;�8��� � :,���8�0%,'� :,���,�,'�'��%�:��8��%��� �3� 8'�����'��, ����"� '�86�,< 6�,�2��26���' �,:��8���* ;303 �,0�,, �: :�,,��8�� �,=,���%�: � %� � �,���,� � �,:%, �3�6,� ,3,� �* 3,�%0 � � >(: ;���,%, :%�3�� �� �* �,��'�% �: 3, ,<,�%�� ��%�:��28��%�� ��,�� ;6�,���2,���'*�� ( � ��'���,� 3�" � �,2:%,� :%�� �3�6, � �'3,=,� � ,86,����,� 303 ���=, ):�� "3'3 �::���%�� 6��',��,� '�% ��, 6��',� (% ����%8�<8�8 ��,%03 � �,?��,� :�� 8�%* ��) �66�'��%��2,�6,'���* � 303 ����* � �,6,�,� ��%�:��8��%�;:�0�,� ���� �: 8,8��*�� �3, ��0% �: 3, 8'�����'��, ���'���,�� "3'3 �,��� � 3, �,��,� '�8�%��% �: 6��6,�2,�� �6,'�� �,%�% � 6�� � 3,�8�28,'3�%'�� �,�2

8,%� ;����� �* "3'3 � "�, ��%0, �: 8'�����'��,� '�%�, ���%,�� ) �*�,8�' �66���'3 � 6��=�,� :�� 3, *6,��: �,=,��, �,�'�%� � � �� "3'3 ��, :��%� �,",,%� '�*���2�0��63'���* �,=,����, ;8��,%�'� �%� �::���% '�%����,�;'�8�%,� �,�'�%��� @,���,� �: �68�8 8'�����'��,�:�� �3�6%0 �%� �,��,� ��26��6,�,� ��, ��'���,��

�$��! �����1 �3,�, � � "�, ,86,����, ��%0, %"3'3 ��) �,3�=, ��, %��8�� %,�8,���' '�86��%��"3 /�/�2���'��,A �� B � �� B �8 ;@0� ������ ) �%� �,��"�� 8��,%�' 63��, ��%�:��8��% '�% ��, 6��',� ( � '�826�,, �,��" � ,86,����, �,�0%�,� ���:� �3�� ", :%� �%%,�8,��, ��%0, �: B � �� B ��� % "3'3 3, ����* ���%�:��8%0� �%� 3, ��%0, � B � �� B �: % "3'3 ��%�2:��8��% � '�86�,,� �3, "� �66,� ,86,����, ��%0,�3�=, � �, ����=�,� :��3,�� C::���% '�%����,� 6��',��,�"�� �,'�8, '�%��,����, � �C > �D� �8� �3� �8��%� �� ��� E/ :�� -�� �,�� 3�% ��� E/ :�� /�9%� �3, 8��,%�,��%�:��8��% ,86,����,� ;��� �:� (�� (:� ��� �3���� �,���,� ��:,�* �,��" 3� ,86,����,� : �0,%0 ,::,'� ��, ��, �=��,�� )��=, �C ,<,%�� 3, ��%0, % "3'3� :�� ,<�826�,� 6�,'6��% �� '�,,6 � �''���%0�

���

�����

�����

��� � ������� ��� ������ ���� � ��� ����� ��� !��� � !" "��"���#�$������%��&'" �(��)��( �)�)��*)�+�,�*�- �##�� �� )�� �

��F� ��2� *� 3��4���

� �56��)��!7! ���� $�.5++0�' ���� $� 8$��#*5$���1 *����3��4���9 �5 ��54��� $��

�FF� ���� ��: ��� � ���!� 4# !� 8$�� ����� 2� ���!���1.;8 �;� +&�� ����:� � � !� �� <�� ��!!� 2� ��� �����!� �)������ !� !�! $!��� 2� ��= ���� !� 2���� ������� 2� ���� �!��� ��� !�$�5$�������� !�!$�!�� ;��� '� �$��! ����� 2� ���� $$�# ����#��

Page 2: Strengthening and Embossment of Final Shape in NiTi Shape Memory Alloys (SMA)

�3, %,�8,��, ;��%�:��8%0� ,86,����, ��%0, � �� �� �, ����=�,� %� 3�,, 6��� "3 ?����=,�* �::,�,%�,3�=���A���

(: B ��) B ��

6���' ���% % � � 6�,',�%0 3, ��%�:��8��%

�� B ��+ B (:� ��%�:��8� ��,��2%��',� %� �

�: B ��/ B ��

� � 6�����* ��%�:��8,�� ,<,�%�� ��,�� %��',� �,��,%2��% �%� ����%�� ��%�:��8��% �: �,����� ��

�3, �66,� �8 :�� ��%0, � ��+ � �,:%,� �*

�F�� G��� ;��

3, ��%�:��8��%�� ��,��� � �,,�8%,� �* � 8��:,�/������ /��6,��% ,?���% ;@0���� � =��� � � > ��A

����

��G���3��

��;��

�F�� � 3, �66,� �8 �: ��,��,� �66�'���, :�� 6�,���2,���'* 5! �%� 6�,���26���'* 55 ;@0� ���

��$�5$�������� ��!$�!�1 �3,�8� 8,'3�%'�� �,�28,%� ��, �: %,�,� % 3�,, �::,�,% ��6,'�A;� �3�6%0 �: �,82:%�3,� 6����'� ;����%0� "�, ���"2

%0��;� )�H��8,% �: ���� 6��6,�,� � �,��,� =���,��

;� @�%��8,%�� ���* �: 3, ,::,' �: 8'�����'��, �%���', �,:,'� �% 3, 8��, �: 3, 8��,%�' ��%�:��8�2�%���I��

4, ��%0��3 3�2:��8%0 % ��%0, � ;���:��8%0� �%�'��� :��8%0 ;8��:��8%0� % ��%0, � ;@0� �����I��

)��:��8%0 %����',� �,:,'� %� ���,%,� "3'3 ��,��%�:,��,� � 8��,%�, ���%0 ����,?�,% '���%0 �� �� B �: ;@0� ��� /�%�,?�,%�* "���3���,%%0 % ���,%2�, ��� J �� � � ��%�:,��,� %� 8��,%�,A

��� J ��� G �F�� � ��� J ��� G �F�� ;��

(: 3, '3,8'�� '�86���% �: 3, ����* ��*� '�%��%�"���3���,%%0 ��, � �,:,'� % ���,%, "�� �,��', 3,8��,%�, ,86,����, ;@0� �'���7�

�� G�� ;�� I � �� ;�6� G��;�� I / �F�� ;#�

���:��8%0 � �8,� �* 3, %3,�,% ���,%,�� �:%,�8,���' '�86��%������ � �3, ��, 6���' �,:��8���*��,� %� �8��% � 8��, 3�% �6 B ��K� C,:��8��%� �:�6 B ��K �,%�,� 3, ����* �%��%�:��8���,� �3� � ��, ������,� �%� %����'�% �: ��', �,:,'� %� 3, ���'��,�: 8��,%�,� /�%�,?�,%�* % 3� ��, 3, ����* ��,� %�

��� ���� #-.�� �.!� � � � $ ����//�� . �0 1� �� -!�2� � )�,� -!�2� +����� �����/ 3-+�4

���

�����

����

�(��)��( �)�)��*)�+�,�*�- �##�� �� )�� � !..25##666���� 7�8� ���$� � ������� ��� ������ ���� � ��� ����� ��� !��� ��$

(a)

(b)

;��� "� ��$�5$�������� !�!$�!�1 �� � �2�$��� ��� 4� $�2�$��� ��� ������

(b) (c)

(a)

microstructure: ausforming

LM

SEM

;��� �� �� �����! �! �2 � �2�$� 4���# ���� &��> �! ? ��5 '�� @/ �����4��� �2�� 4� /�$������ �2 �!�� �!��� � )� �� �� �����!�� �!�!� �� *22�! �2� �2�$��� �� �!��!� ��� $�!���! ��: !$��! �$� &��� �! ?����� � � @/��

Page 3: Strengthening and Embossment of Final Shape in NiTi Shape Memory Alloys (SMA)

�3�" �3�6, 8,8��*� ( 3�� � �, ,826,�,� � �,:��8 3, �263��, �%� �,0�%��%�:��8���* ;@0� #�� �3� "�� ��,6��', � ��+ > ��� E/ ;�,, '3�6,�L4�*� �: � � � �,=,���%M� �%� �,���� � ",��3 �: ��,:�� 8'�����'��,��5�,�,?��, :�� ��� ��2�,�8,%� � 3,6�,�,�=��% �� �,�����% �: 3, �263��, % � ��%�:��8���, '�%��%;@0� ��� �� 3� �3�6, 8,8��* � %� �,2��',��� �&�

�� *$4������ �����1 �3, :%�� �3�6,�"3'3 3, ����* ��"�*� �,8,8�,��� �'�%%,',� "3 3, �263��, ;���,2%,�������� ( 3�� � �, �3�6,� "3�� �����: �,=,����, ��%�:��8���*� �3, �826�,� "�* � �* ���%0 "3 3, �2���'2��,� '��86%0 % � �, "3 3, �,��,��8,%��%�� �%� 3,�%0 ���=, (:� %�3, ,86,����, ��%0, � ��� �3, ������% �� G '�%��� � ��%�:��8,� %�6���' ���% �6 �* �,��<��% �: 3,��,��,� "3'3 ",�, '�,�,� �* '��86%0;@0� 7��

���%0 '�%��%A �� G �, J �6, ;���

�:,� ��� ��%�:��8��%A �� G �, J �6 ;���

:%��� �,��,� �3�6,A �� G �6 ;�'�

5�,�,?��, � 3� 3, 8�,��� "�� ����% 3, ��,��,�"3'3 ��, �,=,��6,� ���%0 3,�%0 � �� > ): ;!?� ���� �,826,����, �%� 8, � �,,�8%,� �* 3, '�,,6 ��, �: 3,�263��,� �3, ��,��

�� G !�;�, J �6,� ;7�

"3'3 3�� �,,% '�,�,� ���%0 3,�%0 �: 3, '��86,� 8�,2��� ;@0�� �%� &� "�� �,��< �%� �� G �6 ;!?� �'� � �,�'3,��C�, � 3, '�,,6 �,���%', �: 3, %,�8,���' -� 3� 6��2',�� � ��3,� ���" �%� %'�86�,,� �� � 3, ���%� "3'3�,��� � 3, �,��,� :%�� �3�6,��3, %�� ��,�� �:,� ��%�:��8��% %� 3, ���,%, � �

�� ;!?� 7�� ( "�� �,��< �* '3�%0%0 ,���' ���%� �, %� 6���2' ���%� �%� �6 G �� � � G �A

��� ���� #-.�� �.!� � � � $ ����//�� . �0 1� �� -!�2� � )�,� -!�2� +����� �����/ 3-+�4

���

�����

�����

��% � ������� ��� ������ ���� � ��� ����� ��� !��� !..25##666���� 7�8� ���$� �(��)��( �)�)��*)�+�,�*�- �##�� �� )�� �

Ni Ti martensite : T < Mf Ni Ti marforming : ε = 41, 4 %

Ni Ti ε = 41, 4 %30'- 200ºC / H2Omarformed plus tempered

Ni Ti ε = 41, 4 %30'- 800ºC / H2Orebatatized

;��� +� �����! �! �2 $�2�$� ��� ��� ����# &��>? �!� ���� �*� $�������� �2 $�2�$��� ��� !$�5����

(a) (b)

;��� &� �� �! �! �� ������ � ��� !�$4���$�! ����� �!�� � � ��!� !���22 ���� !$��! � � +�� @/�� 4� ��2� �!��� �� !� �!��5� �!���5� !$��5! �����$�

Page 4: Strengthening and Embossment of Final Shape in NiTi Shape Memory Alloys (SMA)

� G �� ,<6 ;I!�� ; ��

�3, 8�,���� 6��6,�* � 3, �,��<��% 8, �� 3, ,86,�2���, �,6,%�,%', �: "3'3 � '�%����,� �* �% �'=��%,%,�0* A� (� =���, � '�%����,� �* '�8� �: ����'��%� %3, ��2�,��,� ��, A'�� !=�,%�* � 8�'3 �8���,� :

��,�� �,��<��% ��,� 6��', % � �,:��8,� 8'�����'��,"3'3 �3�"� � '�8�%,� �,'�*�������% �%� ��%�:��8��%�,�'�%� A'� B A'� ;!?� �� ���%0 ,86,�%0�

� G �� ,<6 ;A��� ; ��

�3,�,:��, � :�=������, ��,�%�=, � � %'���, � ��� %�3, 6��',���,� @�� 3� 6��6��, 3, ����* � 8��:��8,�;@0� �� :�� ,<�86�, �* ����%0 �� "�, ���"%0 � �6 G #�K�/�%�,?�,%�* � "���3���,%,�� �� �,%�,�,� ������,�*�%��%�:��8���,� �,�%0 �: 3, '��86,� �6,'8,% �,��� � ��,���� "3'3 � ���6��%0 � 3, :�� �03� �3, ����* ����8,�3, �,��,� �3�6, 8��, 6�,'�,�* � � 8�'3 �3��,� 8,;�,�6,'=,�* ��",� ,86,����,� �� '�86��,� � 3, ��2�,�2�,� ��, ;@0�� #� �%� &��

B�#� �2 � � � �)����1 !=�,%�* ',��% �,�'�%� "3'3�,���, 3, 303 ,86,����, 63��, � ��, �,'�=, :�� 3,��6�* �: 3, �,��<��% 6��',��� @�� 3, ��2�,��,� ��,3� �,=,���% � '�86�,,� � (: � 7� E/� @�� 3, 8��:��8,����%0 '�%��% � ��%�:��8��% ,86,����, % 3, ��%0,�: ���I#�� E/ "�� :��%� �* C�/2�%��*�� ;@0�� #� �%� ���+,",,% 3,�, "� ,<�,8,� 3, :����"%0 �,=,���% �,�'�%���, � �, ,<6,',�� �,6,%�%0 �% ,86,����,� 8,� 3,�%0��,� �%� �8��% �: 8��:��8%0A�� � � � ;:����,����� ��� � ;:���� ��, �%%3��,�� ,::,' �: :�� '*'�,�'� ��� �� ;:���� ��, ��%�:,��,� %� � � 03������ �F� �� �� J �� � ;%�% I��%�:��8���, ���%0 '�%�2

�%�

��� ���� #-.�� �.!� � � � $ ����//�� . �0 1� �� -!�2� � )�,� -!�2� +����� �����/ 3-+�4

���

�����

����

�(��)��( �)�)��*)�+�,�*�- �##�� �� )�� � !..25##666���� 7�8� ���$� � ������� ��� ������ ���� � ��� ����� ��� !��� ��&

(a) (b)

;��� �� �� /��$���� �)�� ��� ����$�� �� ���!��� ��� 2���� ����� 4� �#����� ����� �2 !� ��������# �!����! !�! ��� 2���� ����1'0�@��

;��� >� /� � �2 �!��!� � ��� !� ����!���� !$���� ���� &��> �! ? ����

Page 5: Strengthening and Embossment of Final Shape in NiTi Shape Memory Alloys (SMA)

,� �F�� �� J 5� ; �� J 5 � J � � � J 5� � ;����* 6��%, �6�,'6��%�"3 ��� ��A �� � "3'3 '�%�% �,:,'� ;����'��%��N �F�A � ��,%�,�,� �%��%�:��8���, �* 303 �,:,' '�%',%���%;�8��% �:8��:��8%0�N��A �,'�=,�,��N 5A 6�,'6�, 6��'�,�%� �� � ;-#���N�� �%� �A 8'����6�,< ���'��, ;��6,�6���'�(% @0� ,=�,%�* 3, '�%�,?�,%',� �: �,�'�% ) �%� !

��, �3�"%� �3, '����, :����"%0 �,�'�% ! ���� "3 3, %2�� "���3���,%%0� �3, �,=,��, ��%�:��8��% � %� �%�*6�,',�,� �* �,'�=,�* �: �%��%�:��8���, �F�� �� ���� �* 6�,2'6��% ;5�-#��� "3'3 '���,� '�%��,����, 3���,%%0��3, 8�<8�8 ��,%03 � '�%%,',� "3 "3 3, �%�, �:�,:��8��% �: � �* %�'�,��% �%� 0��"3� �3� � � '�82�%,� 63��, ��%�:��8��% 6��� �,'�*�������% �,�'�%� (%��',� % � %����" ,86,����, ��%0, �% ����:%, ;� J ��8'�����'��, "3'3� ,=�,%�*� �,��� � � 303 '�,,6 ��,;��6,�6���'*� ;@0�� # �%� ����) ��� 303,� ,86,�%0 ,86,����,� � 3�8�0,%,���

�2���'��, :��8�� "3'3 � '�%%,',� "3 �,�66,���%', �:��%�:��8���* �%� �3�6, 8,8��*� C,6,%�%0 �% 3, ����*'�86���% 3, �20��% ���'��, 8�* '�%�% � ��6,���� �:6��'�,� "3'3 '�%���� 0��% 0��"3� (: 6��'�,� �����=, ���� 303,� ,86,����,� ��6� 0��% 0��"3 �%� 0��%���%���* ,8���,8,% "�� ���,�=,��

;�)� �4� /�$4���!���� �2 ���!��1 �3, 0��� 3� :��8%0���* �: 3, ;� J �� 8'����6�,< ���'��, � %� '�%'�,%"3 3, ���'��, "3'3 6��=�,� �68�8 �3�6, 8,8��*6��6,�,�� �,'���, �%�* 6�� �: 3, =���8, ;�� � ��%�:��82���, @0��, ��� �3,�,:��, �:,� ,8����8,% 3, ����* 3�� ��, 3,�,� �%� 3, �263��, 3�� ���66,��,�� +� � 6�,�,�=,�% ����:%, 0��% ��, � :,����, %� � �=,�3,� �%� 3,��6,���� �: 6�,'6�, 6��'�,� 3�=, �����=,�� ��3,� ���8,,� �: 3, 6��'�,� % 3, %�%�28,,� ��%0, �3���� �,��6�,� �,'���, %� �%�* �3�6, 8,8��*� �� ���� 303��,%03 � ��,:��� ( 3�� � �, ��,% %� �''��% 3� 3, 6��2'�,� �::,' 3, 8��,%�' ��%�:��8��% % � �8��� "�* �� "�� ��'���,� :�� ���:��8%0 % !?���% #� (% 3� '��,3�",=,� 3, 8��,%�, ,86,����, 8�* 0� ��"% �� �6��3�

� ��, � 3, :�' 3� 6�,'6��% % � '3�%0,� 3, '3,8'��'�86���% �%� '�%�,?�,%�* 3, 8,�����, ,?�����8,86,����, ��

�7�� �3� ,::,' 8�* �, ��,� :� :�� ,<�86�,� :��8,�'�� �66�'��%�� � �,:%,� ��%�:��8��% ,86,����,� �,?��,���3, �,=,��, �,�'�%�� ���%0 :��8 303�* �,:��8,� �%�

3,�,:��, �,:,' 8��,%�,� 3�=, 3����* �,,% ,<6���,� % ��*�,8�' 8�%%,������ �3,* 6��=�, � �,* :�� �68���% �:��) :�� � "�, ��%0, �: �66�'��%��

���)�1 .�$4 �"� "���

���� �� 4���8�%� C�5 ����� !���2�$�!���� �� ����#��

�6�%0,�� +,��% �������� �� 4� C�,�0� � -� �,��%� C� �O'�,�� *������� ��5

��!� �2 ���� $$�# ����#�� +�,�"��3� $�%��% ������� �� @��%�� !� ���%��0,%� D� �!���:�� ���� 0�� ����#� !� ���%��0,%� �� +�P'�%,�� �� ���,%� D� �!���:��

��� ��� ����� !� ���%��0,%���!� ���� *��� ( ����� ">�E">&� 7����7� !� ���%��0,%� D� �!���:�� ����� >&� #��� � !� ���%��0,%� !� ����� D� �!���:�� ����� 0>� ##���&� C� 4���,����!� ���� *��� ( ����� ">�E">&� 7�#���� !� ���%��0,%� � �%,�� ��:!� �!� ����� �7 � �������� !� ���%��0,%��!� ����� ( ����� '�� �# �

��� ���� #-.�� �.!� � � � $ ����//�� . �0 1� �� -!�2� � )�,� -!�2� +����� �����/ 3-+�4

���

�����

�����

��' � ������� ��� ������ ���� � ��� ����� ��� !��� !..25##666���� 7�8� ���$� �(��)��( �)�)��*)�+�,�*�- �##�� �� )�� �

;��� 0� /�$������ �2 !� $�2�$� ��� ��54!�!��� ����$��� ���$�!��1 �� ������:� �!�! ��F� �!�� ��� �= �� ���� $ �� = ��:�

(a)

(b)

;��� �� �� (���#��� �2 !� !$���� ������ *=� 0� �����! �! �� ���$�!��� �;��� +�� 4� .�/5����#��� �2 !���2�$�!���1 ��22 ���� ���!���� )� ��!��� � �� 1 (2 G +�� @/�