[Robert de Hoff] Thermodynamics in Materials Scien(BookFi.org)

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Thermodynamics in Materials Science

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Second Edition

Thermodynamics in Materials Science Robert DeHoff

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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2006 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20110713 International Standard Book Number-13: 978-1-4200-0585-1 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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 Lu“ \d:\dQ ! 2gd‡…!\dA: A˜…Ab”b )™ A_\b\d!\dQ YA :\JJA…Ad\!_‡ gJ YA :ApAd:Ad –!…\!)_A‡u gd‡\:A… !Q!\d YA Az”!\gd Jg… › Q\–Ad \d ˜!bp_A Luj —\Y \‡ !Ad:!d 2gd‡…!\d‡u d !_A…d!A ‡…!AQ™ Jg… Kd:\dQ YA A˜…Ab”b \d › ‡”)]A2 g YA 2gd‡…!\d\dQ …A_!\gd‡ ” h ”S˜q ™7q – h –S˜q ™7 )AQ\d‡ )™ !^\dQ YA :\JJA…Ad\!_‡ gJ YA J”d2\gd › !d: YA 2gd‡…!\d\dQ Az”!\gd‡7 :› h ” :˜ | ˜ :” | – :™ | ™ :– :” h :˜ | :™ :– h :˜ r :™ _\b\d!A YA :ApAd:Ad :\JJA…Ad\!_‡ )™ ‡”)‡\”\dQ Jg… :” !d: :– \d YA A˜p…A‡‡\gd Jg… :›7 :› h ” :˜ | ˜S:˜ | :™7 | – :™ | ™S:˜ r :™7 g__A2 A…b‡7 :› h S” | ˜ | ™7:˜ | S– | ˜ r ™7:™

jjB

YA…bg:™d!b\2‡ \d !A…\!_‡ 2\Ad2A

A YA 2gAJK2\Ad‡ Az”!_ g ›A…g7 ”|˜|™hœ –|˜r™hœ g ‡g_–A Jg… ˜ !d: ™8 ”‡A YA 2gd‡…!\d\dQ Az”!\gd‡ g A–!_”!A ” !d: –7 S˜ | ™ | j“7 | ˜ | ™ h œ = “˜ | “™ | j“ h œ S˜ r ™ r B7 | ˜ r ™ h œ = “˜ r “™ r B h œ gA Y! YA‡A 2gd:\\gd‡ Jg… YA A˜…Ab”b !…A \:Ad\2!_ —\Y Yg‡A :A…\–A: \d ˜!bp_A Luj !d: —\__ Y”‡ ™\A_: YA ‡!bA ‡g_”\gdu

YA ‡…!AQ™ g”_\dA: \d ˜!bp_A Luj 2!ddg )A !pp_\A: \J YA 2gd‡…!\d\dQ Az”!\gd‡ !…A dg A˜p_\2\8 \uAu8 \J YA™ 2!ddg )A ‡g_–A: A˜p_\2\_™ Jg… ” !d: –u g… A˜!bp_A8 ‡”ppg‡A YA Az”!\gd …A_!\dQ ” g ˜ !d: ™ Y!‡ YA Jg…b7 ˜“ ™” _d ” h j“ Y\‡ Az”!\gd 2!ddg )A ‡g_–A: A˜p_\2\_™ g g)!\d !d A˜p…A‡‡\gd gJ YA Jg…b ” h ”S˜q ™7q g )A ‡”)‡\”A: —YA…A–A… ” !ppA!…‡ \d YA A˜p…A‡‡\gd Jg… ›u YA ‡…!AQ™ p…A‡AdA: \d ˜!bp_A Lu“ 2!d )A !pp_\A:8 A–Ad —YA…A YA 2gd‡…!\d\dQ …A_!\gd‡ !…A \bp_\2\ \d YA :ApAd:Ad –!…\!)_A‡u g… Y\‡ …A!‡gd8 YA ‡…!AQ™ Abp_g™A: Jg… Kd:\dQ 2gd‡…!\dA: b!˜\b! \d YA Ad…gp™ J”d2\gd g g)!\d 2gd:\\gd‡ Jg… Az”\_\)…\”b —\__ )A Y! p…A‡AdA: \d ˜!bp_A Lu“u g— Y! YA b!YAb!\2!_ d!”…A gJ YA p…g)_Ab Y!‡ )AAd p…A‡AdA: \d :A!\_8 \ \‡ pg‡‡\)_A g _!™ g” ! QAdA…!_ ‡…!AQ™ Jg… Kd:\dQ YA 2gd:\\gd‡ Jg… Az”\_\)…\”b \d ! YA…bg:™d!b\2 ‡™‡Ab gJ !…)\…!…™ 2gbp_A˜\™7 ju …\A ! :\JJA…Ad\!_ A˜p…A‡‡\gd Jg… YA 2Y!dQA \d Ad…gp™ Y! YA ‡™‡Ab b!™ A˜pA…\Ad2A —YAd !^Ad Y…g”QY !d !…)\…!…™ p…g2A‡‡8 A˜p_\2\_™ \d2_”:\dQ A…b‡ Jg… !__ pg‡‡\)_A –!…\!\gd‡ \d YA ‡!A gJ YA ‡™‡Abu “u …\A :\JJA…Ad\!_ A˜p…A‡‡\gd‡ Y! :A‡2…\)A YA 2gd‡…!\d‡ Y! !pp_™ g YA ‡™‡Ab )A2!”‡A \ \‡ 2gd‡\:A…A: g )A \‡g_!A: J…gb \‡ ‡”……g”d:\dQ‡u ‘u ‡A YA \‡g_!\gd 2gd‡…!\d‡ g A_\b\d!A :ApAd:Ad –!…\!)_A‡ \d YA :A‡2…\p\gd gJ YA 2Y!dQA \d Ad…gp™ Jg… YA ‡™‡Abu YA …A‡”_\dQ :\JJA…Ad\!_ A˜p…A‡‡\gd Jg… YA 2Y!dQA \d Ad…gp™ !pp_\A‡ A˜p_\2\_™ g YA pg‡‡\)_A 2Y!dQA‡ Y! b!™ g22”… \d !d \‡g_!A: ‡™‡Ab —\Y !__ –!…\!)_A‡ \d:ApAd:Adu Ou A YA 2gAJK2\Ad‡ gJ A!2Y gJ YA :\JJA…Ad\!_‡ \d YA dA— A˜p…A‡‡\gd Jg… : Az”!_ g ›A…gu YA‡A Az”!\gd‡8 —Y\2Y ‡pA2\J™ !d A˜…AbA –!_”A Jg… 8 !…A YA 2gd:\\gd‡ Jg… Az”\_\)…\”b Jg… YA ‡™‡Abu Y\‡ ‡…!AQ™ Jg… Kd:\dQ 2gd:\\gd‡ Jg… Az”\_\)…\”b \‡ \__”‡…!A: Jg… ! ”d!…™ —g[ pY!‡A ‡™‡Ab \d YA dA˜ ‡A2\gdu

z”\_\)…\”b \d YA…bg:™d!b\2 ™‡Ab‡

jje

LuO                        7    [   g2”‡ gd ! ”d!…™ rgdA 2gbpgdAds —g[pY!‡A dgd…A!2\dQ gYA…—\‡A ‡\bp_A ‡™‡Abu YA ‡…!AQ™ Jg… :A!_\dQ —\Y ! —g[pY!‡A ‡™‡Ab \‡ ‡…!\QYJg…—!…:u !2Y gJ YA ‡Ap!…!A pY!‡A‡ 2!d )A …A!A: !‡ ! gdA[pY!‡A ‡™‡Ab —\Y \‡ g—d ‡A gJ A˜Ad‡\–A !d: \dAd‡\–A p…gpA…\A‡u YA !pp!…!”‡ Jg… :A‡2…\)\dQ YA )AY!–\g… gJ ‡”2Y ‡\dQ_A[ pY!‡A ‡™‡Ab‡ —!‡ :A–A_gpA: \d Y!pA… Ou YA :A‡2…\p\gd gJ ! —g[pY!‡A ‡™‡Ab ‡\bp_™ b!^A‡ ”‡A gJ YA J!2 Y!8 Jg… !__ gJ YA A˜Ad‡\–A p…gpA…\A‡ :AKdA:8 YA –!_”A Jg… ! ‡™‡Ab \‡ YA ‡”b gJ YA –!_”A‡ Jg… A!2Y gJ \‡ p!…‡u Y”‡8 Jg… ! —g[pY!‡A ‡™‡Ab A!2Y gJ YA p…gpA…\A‡  † 8  † 8  † 8 † 8  † 8 !d: † \‡ YA ‡”b gJ YA –!_”A‡ gJ YA 2g……A‡pgd:\dQ z”!d\\A‡ Jg… YA ‡Ap!…!A pY!‡A‡u A2!”‡A YA pY!‡A )g”d:!…™ ‡Ap!…!\dQ —g pY!‡A‡ \‡ ! d!”…!_ )g”d:!…™8 \ \‡ dg pg‡‡\)_A g …A‡…\2 YA Mg— gJ b!A… )A—AAd YA pY!‡A‡u 22g…:\dQ_™8 \ \‡ dA2A‡‡!…™ g …A! A!2Y pY!‡A !‡ !d gpAd ‡™‡Ab \d :A‡2…\)\dQ \‡ )AY!–\g…‰ Y! \‡8 g !__g— Jg… YA pg‡‡\)\_\™ Y! YA d”b)A… gJ bg_A‡ gJ A!2Y pY!‡A b!™ 2Y!dQA :”…\dQ !d !…)\…!…™ p…g2A‡‡u YA K…‡ ‡Ap \d !pp_™\dQ YA QAdA…!_ ‡…!AQ™ …Az”\…A‡ !d A˜p…A‡‡\gd Jg… YA 2Y!dQA \d Ad…gp™ A˜pA…\Ad2A: )™ YA ‡™‡Ab —YAd \ \‡ !^Ad Y…g”QY !d !…)\…!…™ p…g2A‡‡u YA Ad…gp™ Jg… YA ‡™‡Ab \‡ YA ‡”b gJ YA Ad…gp\A‡ gJ \‡ p!…‡‰ YA…AJg…A8 YA 2Y!dQA \d Ad…gp™ gJ YA ‡™‡Ab \‡ : †‡™‡ h :S †  |  †  7 h : †  | : † 

SLJjj7

—YA…A YA ‡”pA…‡2…\p  :AdgA‡ YA p…gpA…\A‡ gJ gdA gJ YA pY!‡A‡ r:A‡\Qd!A: YA  pY!‡As !d: ‡”pA…‡2…\p  :A‡\Qd!A‡ p…gpA…\A‡ gJ YA  pY!‡Au  \‡ Y”‡ dA2A‡‡!…™ g 2gbp”A YA 2Y!dQA‡ \d Ad…gp™ A˜pA…\Ad2A: ‡Ap!…!A_™ )™ YA  !d:  p!…‡ gJ YA ‡™‡Ab :”…\dQ !d !…)\…!…™ p…g2A‡‡u g2”‡ K…‡ ”pgd YA )AY!–\g… gJ YA  pY!‡Au ‡ \dA…d!_ AdA…Q™8  † 8 \‡ \d QAdA…!_ ! J”d2\gd gJ \‡ Ad…gp™8  † 8 –g_”bA8  † 8 !d: d”b)A… gJ bg_A‡8 d 7  †  h  †  S †  q  †  q d 7

SLJj“7

…gb YA 2gb)\dA: ‡!AbAd gJ YA K…‡ !d: ‡A2gd: _!—‡ Jg… YA  pY!‡A : †  h   : †  r  : †  | 6 :d Y\‡ Az”!\gd \d…g:”2A‡ YA 2gAJK2\Ad8   K †  6 h Kd  †  q † 

SLJj‘7

SLJjO7

—Y\2Y \‡ 2!__A: YA 2YAb\2!_ pgAd\!_ gJ YA 2gbpgdAd Y! b!^A‡ ”p YA  pY!‡Au Y\‡ z”!d\™ p_!™‡ ! 2Ad…!_ …g_A \d YA :A‡2…\p\gd gJ YA 2YAb\2!_ !‡pA2‡ gJ YA )AY!–\g… gJ b!A…‰ YA 2gd2Ap —\__ )A :A–A_gpA: \d :A!\_ \d Y!pA… B !d: )A™gd:u g… YA p…A‡Ad p”…pg‡A8 —Y\2Y \‡ g \__”‡…!A YA !pp_\2!\gd gJ YA QAdA…!_ ‡…!AQ™ Jg… g)!\d\dQ

j“œ

YA…bg:™d!b\2‡ \d !A…\!_‡ 2\Ad2A

2gd:\\gd‡ Jg… Az”\_\)…\”b8 ! :AKd\\gd8 z”!\gd LujO8 \‡ !__ Y! \‡ …Az”\…A:u A!……!dQ\dQ z”!\gd Luj‘ Q\–A‡ !d A˜p…A‡‡\gd Jg… YA 2Y!dQA \d Ad…gp™ gJ YA  pY!‡A7 : †  h

j  6  † † : | : r :d   

SLJjL7

:Ad\2!_ …A!‡gd\dQ Jg… YA  pY!‡A p…g:”2A‡ YA !d!_gQg”‡ A˜p…A‡‡\gd Jg… YA 2Y!dQA \d Ad…gp™ gJ YA  pY!‡A7 j  6 : †  |  : †  r  :d SLJj‹7     pp_™ z”!\gd Lujj7 YA A˜p…A‡‡\gd Jg… YA 2Y!dQA \d Ad…gp™ gJ YA ‡™‡Ab Y!‡ ‡\˜ A…b‡7 : †  h

: †‡™‡ h : †  | : †  : †‡™‡ h

6 j  : †  |  : †  r  :d     |

SLJjŠ7

j  6  † † : | : r :d   

YA ‡A2gd: ‡Ap \d YA ‡…!AQ™ …Az”\…A‡ A–!_”!\gd gJ YA 2gd‡…!\d‡ \bpg‡A: )™ \‡g_!\dQ YA ‡™‡Abu YA )g”d:!…™ gJ !d \‡g_!A: ‡™‡Ab \‡ …\Q\: r‡g dg —g…^ 2!d )A :gdA gd g… )™ YA ‡™‡Ab ‡\d2A YA Jg…2A :”A g YA A˜A…d!_ p…A‡‡”…A 2!ddg bg–As8 YA…b!__™ \d‡”_!\dQ r‡g dg YA! 2!d )A A˜2Y!dQA: —\Y YA ‡™‡Abs !d: \bpA…bA!)_A r‡g dg b!A… 2…g‡‡A‡ YA )g”d:!…™ gJ YA ‡™‡Absu YA‡A 2Y!…!2A…\‡\2‡ p_!2A YA Jg__g—\dQ 2gd‡…!\d‡ ”pgd YA ‡!A J”d2\gd‡ Y! :A‡2…\)A YA —g[pY!‡A ‡™‡Ab7 A2!”‡A YA…A !…A dg A˜2Y!dQA‡ —\Y YA ‡”……g”d:\dQ‡ YAd8 )™ YA K…‡ _!—8 YA \dA…d!_ AdA…Q™ gJ YA ‡™‡Ab b”‡ …Ab!\d 2gd‡!du Y”‡8 —Y!A–A… p…g2A‡‡A‡ g22”… —\Y\d YA ‡™‡Ab8 : †‡™‡ h :S †  |  †  7 h : †  | : †  h œ

SLJjB7

A2!”‡A YA )g”d:!…™ \‡ …\Q\:8 : †‡™‡ h :S †  |  †  7 h : †  | : †  h œ

SLJje7

A2!”‡A YA )g”d:!…™ \‡ \bpA…bA!)_A8 :d‡™‡ h :Sd | d 7 h :d | :d h œ

SLJ“œ7

Y”‡8 YA :\JJA…Ad\!_‡ \d YA ‡\˜ A…b‡ Y! !…A …Az”\…A: \d z”!\gd‡ LujŠ g :A‡2…\)A YA 2Y!dQA \d Ad…gp™ gJ ! ”d!…™ —g[pY!‡A ‡™‡Ab —YAd \ \‡ !^Ad Y…g”QY

z”\_\)…\”b \d YA…bg:™d!b\2 ™‡Ab‡

j“j

!d !…)\…!…™ p…g2A‡‡ !…A dg \d:ApAd:Ad —YAd YA p…g2A‡‡ \‡ 2!……\A: g” \d !d \‡g_!A: ‡™‡Abu Y…AA Az”!\gd‡ …A_!A YA‡A ‡\˜ –!…\!)_A‡7 z”!\gd LujB g z”!\gd Lu“œu ‡A YA‡A …A_!\gd‡ g A_\b\d!A Y…AA gJ YA ‡\˜ –!…\!)_A‡ \d z”!\gd LujŠ7 : †  h r: † 

SLJ“j7

: †  h r: † 

SLJ““7

:d h r:d

SLJ“‘7

dA…d!_ AdA…Q™8 –g_”bA8 !d: bg_A‡ gJ b!A…\!_ b!™ )A A˜2Y!dQA: )A—AAd YA pY!‡A‡ )” !…A 2gd‡A…–A: Jg… YA \‡g_!A: ‡™‡Abu ”)‡\”A YA‡A A˜p…A‡‡\gd‡ Jg… : † 8 : †  !d: :d  \d z”!\gd LujŠ7 : †‡™‡q\‡g h : †  | : †  6 j  j h  : †  |  : †  r  :d |  Sr: †  7      6 |  Sr: †  7 r  Sr:d 7  

SLJ“O7

g__A2 A…b‡7 : †‡™‡q\‡g

h



{ U { U  j j   6 6 † † r  : | r  : r r  :d SLJ“L7      

Y\‡ Az”!\gd :A‡2…\)A‡ YA 2Y!dQA \d Ad…gp™ !22gbp!d™\dQ !d !…)\…!…™ 2Y!dQA \d ‡!A gJ ! ”d!…™ —g[pY!‡A ‡™‡Ab —YAd \ \‡ \‡g_!A: J…gb \‡ ‡”……g”d:\dQ‡u YA J”d2\gd8  † 8 \‡ dg— A˜p…A‡‡A: \d A…b‡ gJ Y…AA p…gpA…\A‡ Y! !…A \d:ApAd:Ad_™ –!…\!)_A8  † 8  † 8 !d: d u YA 2gd:\\gd‡ Y! :A‡2…\)A YA b!˜\b”b \d Ad…gp™ Jg… ‡”2Y !d \‡g_!A: ‡™‡Ab !…A g)!\dA: )™ ‡A\dQ YA 2gAJK2\Ad‡ gJ A!2Y gJ YA Y…AA :\JJA…Ad\!_‡ \d z”!\gd Lu“L Az”!_ g ›A…g7 j j r  h œ =  h       r h œ =  h   

6 6 r  h œ = 6 h 6   

SYA…b!_ Az”\_\)…\”b7

SLJ“‹7

SbA2Y!d\2!_ Az”\_\)…\”b7

SLJ“Š7

S2YAb\2!_ Az”\_\)…\”b7

SLJ“B7

YAd YA‡A Y…AA 2gd:\\gd‡ Jg… Az”\_\)…\”b !…A bA —\Y\d Y\‡ —g[pY!‡A \‡g_!A: ‡™‡Ab8 \‡ Ad…gp™ —\__ )A ! b!˜\b”b !d: YA 2…\A…\gd Jg… Az”\_\)…\”b ‡!\‡KA:u r…\2_™ ‡pA!^\dQ8 \ \‡ !_‡g dA2A‡‡!…™ g A˜!b\dA YA ‡A2gd: :A…\–!\–A‡ \d YA J”d2\gd g :AA…b\dA Y! YA A˜…Ab”b \‡ ! b!˜\b”b‰ Yg—A–A…8 A˜p_g…!\gd gJ Y\‡

j““

YA…bg:™d!b\2‡ \d !A…\!_‡ 2\Ad2A

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SLJ‘œ7

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SLJ‘j7

YA 2gd‡…!\d‡ Jg… Y\‡ 2…\A…\gd !…A7 : †‡™‡ h : †  | : †  h œ = : †  h r: † 

SLJ‘“7

: †‡™‡ h : †  | : †  h œ = : †  h r: † 

SLJ‘‘7

:d‡™‡ h :d | :d h œ = :d h r:d

SLJ‘O7

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SLJ‘B7

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YA…bg:™d!b\2‡ \d !A…\!_‡ 2\Ad2A

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SLJ‘e7

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SLJOœ7

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SLJOj7

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SLJO“7

z”\_\)…\”b \d YA…bg:™d!b\2 ™‡Ab‡

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