ENCYCLOPEDIA OF
`MATERIALS:
`SCIENCE AND TECHNOLOGY
`
`Volume9
`Re-S
`
`Editors-in-Chief
`
`K. H. JURGEN BUSCHOW
`University of Amsterdam, The Netherlands
`
`ROBERT W. CAHN
`University of Cambridge, UK
`
`MERTON C. FLEMINGS
`Massachusetts Institute of Technology, Cambridge, USA
`
`BERNHARD ILSCHNER
`Swiss Federal Institute of Technology, Lausanne, Switzerland
`
`EDWARD J. KRAMER
`University of California, Santa Barbara, USA
`
`SUBHASH MAHAJAN
`Ariwna State University, Tempe, USA
`
`2001
`ELSEVIER
`
`AMSTERDAM - LONDON - NEW YORK - OXFORD - PARIS - SHANNON - TOKYO
`
`..
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`T it--Lto2-(cid:173)
`, F 5£
`;_ oc0 I
`v . q
`
`Elsevier Science Ltd, The Boulevard, Langford Lane,
`Kidlington, Oxford OX5 1GB, UK
`
`Copyright© 2001 Elsevier Science Ltd
`
`All rights reserved. No part of this publication may be
`reproduced, stored in any retrieval system or transmitted
`in any form or by any means: electronic, electrostatic,
`magnetic tape, mechanical, photocopying, recording or
`otherwise, without permission in writing from the publishers.
`
`Library of Congress Cataloging-in-Publication
`Data
`Encyclopedia of materials : science and technology /
`edited by K.H. Jurgen Buschow ... [et al.].
`p.crn .
`1. Materials--Encyclopedias. I. Buschow, K. H.J.
`
`TA402 .E53 2001
`620. 1' 1 '03--dc2 l
`
`2001046021
`
`British Library Cataloguing in Publication Data
`Encyclopedia of materials : science and technology
`1. Materials - Encylopedias
`I. Buschow , K. H. J.
`620. 1'1
`
`ISBN 0-08-043152-6
`
`9 TM The paper used in this publication meets the minimum requirements of the
`American National Standard for Information Sciences-Permanence of Paper for
`Printed Library Materials, ANSI 239.48- 1984.
`
`Typeset, printed and bound by Cambridge University Press.
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`Contents
`
`Subject Editors
`
`Preface
`
`Introduction
`
`Alphabetical Entries
`
`Thematic Guide
`
`List of Contributors
`
`Subject Index
`
`List of Acronyms
`
`t.lNDA BALL LIBRARY
`KANiAS CITY, MISSOURI
`
`vii
`
`Volume 1
`
`Volume 1
`
`Volumes 1-10
`
`Volume 11
`
`Volume 11
`
`Volume 11
`
`Volume 11
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`V
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`Petitioner Samsung and Google Ex-1017, 0003
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`Steel Production and Re.fining
`
`Future development will be towards increased
`recycling, waste minimization, decreased liquid waste,
`elimination of noxious gases, and decreased vapor and
`dust emissions. The problem of CO2 production is not
`simply solved as no economic reductant, other than
`carbon, is available at this time.
`
`Yamada K 1999 Recent activities on reducing steelmaking slag
`quantity. Proc. 10th Japan- Germany Seminar. ISIJ, Tokyo,
`pp. 17- 23
`Yin H , Shibata H , Emi T, Suzuki M 1997 In situ observation of
`collision, agglomeration and cluster formation of alumina
`inclusion particles on steel melts. ISIJ Int. 37(10), 936--55
`
`Bibliography
`Bizec R F 2000 Steel industry and climate change-constraints
`and opportunities. /CSS 2000 Steel for a Sustainable Society.
`The Iron and Steel Institute of Japan, Tokyo, pp. 3--6
`Chikama H , Shibata H , Emi T, Suzuki M 1996 JIM Mater.
`Trans. 37(4), 620-26
`d'Entremont JC, Guernsey D L, Chipman J 1963 Trans. /ME
`227, 14-17
`Fn1ehan R J 1970 M etall. Trans: 1, 3403-10
`Fruehan R J, Jung S, Nogueira"'l', Molloseau C 2000 Critical
`aspects of recycljng waste oxides in steel making. In: Irons
`GA, Cramb AW (eds.) The Brimacombe Memorial Sym(cid:173)
`posium. CIM, Montreal, Canada, pp. 261 - 74
`Hino M, Nagasaka T 2000 The limits of steel refining. In: Irons
`GA, Cramb AW (eds.) The Brimacombe Memorial Sym(cid:173)
`posium. CIM, Montreal, Canada, pp. 243-59
`Jonsson L 1998 Mathematical modelling of selected ladle
`operations:-towards metallurgical process models based on
`fundamental equations. Ph.D . thesis, Royal Institute of
`Technology, Stockholm
`Jonsson L, Grip C E, Johansson A, Jonsson P 1998 A new
`approach to model sulphur refining in a gas stirred ladle- a
`coupled CFD and thermodynamic model of sulphur refining
`in a gas stirred ladle. ISIJ Int. 38(3), 260--67
`Jonsson L, Jonsson P 1997 Modeling of the fluid conditions
`around the slag metal interface in a gas stirred ladle. /SIJ Int .
`37(5), 484-91
`I
`Kurokawa N, Tanigawa K, Nishida K , Shirota Y, Kikouri S
`1993 Present and future technologies for producing ultra-low
`carbon steel. CAMP-ISIJ 6, 134-37
`Misra P, Chevrier V, Sridhar S, Cramb AW 2000 Observation
`of inclusions at a slag-metal interface. Metall. Trans . B 31(5),
`1135- 39
`Mizoguchi S 1996 A study on segregation and oxide inclusions
`for the control cif steel properties. Ph.D. thesis, University of
`Tokyo
`Novokhatskiy I A, Belov BF 1969 Russian Metallurgy no. 3, pp.
`13-24
`Rastogi R 2000 Nozzle clogging. Ph.D. thesis, Carnegie Mellon
`University
`Sakurai E, Akai S, Watanabe A, Shirayama A, lsawa T,
`Matsuno H 2000 Reduction of slag volume generation by
`ZSP. CAMP-IS/J 13, 52
`Sano N, Ogawa Y 2000 Outlook for the next generation of steel
`making research-Part I. Recent development of refining _
`process and target of research in Japan. In: Irons GA, Cramb
`AW (eds.) The Brimacombe Memorial Symposium. CIM,
`Montreal, Canada, 291-309
`Sheppard CJ R Confocal Laser Scanning Microscopy. Springer,
`Berlin
`Shevtsov VE 1981 Russ. Metall. 1, 52- 7
`Sridhar S, Cramb A W 2000 Kinetics of Al 2O3 dissolution in
`CaO-MgO-SiO 2-Al 2O3 slags: in situ observation and analysis:
`Metall. Trans. B 31, 406--10
`·
`
`8840
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`A. W. Cramb
`
`Steels: Classifications
`
`The beginning point for the classification of steels and
`iron is .the iron-carbon phase diagram (see FerroUJ
`Alloys : Overview and Phase Equilibria in Fe-C, Fe-X,
`Fe-C-X and Fe-C-Xi). All Fe-C alloys containing less
`than about 2.06wt. % carbon would pass through the
`austenite field when cooled slowly from the liquid to
`room temperature. All binary Fe-C alloys containing
`< 2.06 wt.% carbon are classed as steels. All binary
`Fe-C alloys containing > 2.06wt. % carbon arc
`termed cast irons. These distinctions are roughly
`maintained even when the alloys contain large
`. amounts of alloying elements.
`Cast irons typically have carbon levels of about
`2-4 wt.% carbon. There are many types of cast irons.
`Most are the so-called graphitic cast irons but the
`are other high-alloy cast irons designed for w
`resistance, corrosion resistance, and heat resistan
`The graphitic cast irons (see Cast Irons) are alloys wi"
`the above approximate ranges of carbon content b
`which also contain 0.5-3.0wt. % silicon. The purpo
`of the silicon is to promote the formation of graphi
`rather than iron carbide (cementite) on solidificati
`or during heat treatment. Depending on the ex
`composition, cooling rate on solidification, and su
`sequent heat treatment these materials consist
`particles of either cementite or graphite embedded in
`steel matrix which can be entirely ferritic, ferri ·
`pearlitic, martensitic, or austenitic. In white cast iro
`the material consists of cementite in a steel matrix.
`other types of cast irons consist of particles of graphi
`in a steel matrix. There are four different types
`graphitic cast irons, gray, ductile, malleable,
`compacted and these grades differ primarily in
`shape of the graphite particles. In the four types
`graphite shapes are plates, spheres, popcorn sha
`and rods, respectively. The strengths of each ofth
`types of cast irons can; be varied by changing
`nature of the steel matrix.
`For the purpose of this article steels will be regar
`as all ferrous-based alloys with carbon levels in
`·
`range of 0-2 wt.%. The approach taken here is si
`to that adopted by Leslie where almost all of the st
`described here are discussed in greater detail (
`1981).
`The most widely produced steel product is sheet (
`Sheet Steel: Low Carbon). These materials are fe
`with low carbon contents and are often used
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`applications requmng the sheet to be formed into
`complex shapes, such as auto bodies. High formability
`is achieved in these materials by reducing the inter(cid:173)
`stitials, carbon and nitrogen, to very low levels and by
`developing appropriate textures through thermo(cid:173)
`mechanical processing and control of inclusion char(cid:173)
`acteristics (see Nucleation of Ferrous Solid- Solid Phase
`Transformations at Inclusions). Steel sheet can be
`coated in a variety of ways to provide corrosion
`protection and for decorative purposes (see Sheet
`Steel : Coated). These coatings reduce formability.
`By adding carbon pearlite can be introduced (see
`Pearlite) into steels slowly cooled from the austenitiz(cid:173)
`ing temperature. When steels having less than the
`eutectoid carbon content are slowly cooled frpm the
`austenitizing temperature pro-eutectoid ferrite (see
`Proeutectoid Ferrite) is formed as the steel is cooled to
`the eutectoid temperature. Once the steel is cooled
`below the eutectoid temperature the remaining aus(cid:173)
`tenite, now of the eutectoid carbon content, trans(cid:173)
`forms to pearlite; which consists of alternating layers
`of cementite and ferrite. The amount of pearlite in the
`structure increases with increasing carbon content.
`The strength of the steel increases with the amount of
`pearlite and the strength of pearlite can be increased
`by decreasing the spacing between the alternating
`sheets offerrite and cementite. Low carbon sheet steels
`which contain no pearlite are one extreme of the
`ferritic- pearlitic steel spectrum and steels of the
`eutectoid carbon content which are entirely pearlite
`when slowly cooled represent the other extreme of the
`ferritic-pearlitic steel specfrum. Steels of the eutectoid
`carbon content (see Steels : Near Eutectoid) are
`commonly used for railrpad tracks and wheels.
`When an Fe- C alloy .is cooled (quenched) suf(cid:173)
`ficiently rapidly from the austenitizing tempe.rature
`the austenite will not transform to a combination of
`pro-eutectoid ferrite and pearlite, or to bainite (see
`Bainite). Instead the alloy wiH transform to martensite,
`a body-centered-tetragonal phase, in which the carbon
`is in solid solution (see Martensite) . The carbon in
`solid solution in the martensite is much more effective
`in strengthening martensite than is the pearlite in
`strengthening ferritic- pearlitic, steels. For this reason
`martensitic steels are used to achieve high strength
`levels. However, to achieve a martensitic structure one
`must cool the material sufficiently rapidly to avoid the
`formation ofpro-eutectoid ferrite, pearlite, and bainite.
`Alloying additions can be used to delay the start of the
`decomposition of austenite to pro-eutectoid ferrite,
`pearlite, and bainite, and such alloying is said to
`increase the hardenability of the steel. When the
`hardenability is increased one can use slower quench
`rates to achieve a martensitic structure and achieve a
`martensitic structure in pieces of larger section size.
`Low alloy steels which were developed to be used
`primarily as martensitic steels are referred to as heat(cid:173)
`treated steels. A primary concern in these steels is their
`hardenability. These steels are never used in their as-
`
`Steels: Classifications
`
`quenched condition but are tempered. Tempering is
`the heating of a martensitic steel at a temperature
`below that at which austenite forms (see Tempering of
`Martensite). Tempering results in softening of the steel
`due to precipitation of the carbon as cementite and the
`coarsening of the cementite particles. Steels used for
`bearings (see Bearing Steels) are typically low alloy
`quenched and tempered steels. Krauss ( 1980) discusses
`the effects of composition and heat treatment on the
`microstructures and mechanical properties of low
`alloy steels.
`Ferritic- pearlitic steels have very low strength when
`they are purely ferritic and their toughnesses drop
`rapidly as the carbon content and the amount of
`pearlite are increased. While the mariensitic quenched
`and tempered low alloy steels have much better
`toughnesses (see Martensite before and after Tem(cid:173)
`pering, Deformation and Fracture of) at higher strength
`levels than the ferritic- pearlitic steels, the quenched
`and tempered martensitic structure is difficult to
`achieve in many product forms. Costs are also asso(cid:173)
`ciated with the heat treatment involved in obtaining
`the martensitic quenched and tempered microstruc(cid:173)
`ture.
`l:Iigh-strength low-alloy (HSLA) steels are a
`class of steels developed to achieve properties superior
`to those of the ferritic- pearlitic steel and comparably
`to those of low alloy quenched and tempered marten(cid:173)
`sitic steels. HSLA steels are designed to achieve their
`desired mechanical properties by the development of
`microstructures through controlled thermomechan(cid:173)
`ical processing (TMP) and the steel is produced in its
`fiM.l form by a continuous hot deformation process,
`rolling, or forging, which comprise the TMP. Most
`HSLA steels are microalloyed with small additions
`(0.1 wt.%) of niobium, vanadium, and titanium which
`control microstructural evolution during TMP
`through the formation of carbonitride precipitates.
`The above classes of steel have a low alloy content.
`Most other steels have higher alloy content and these
`steels were developed to achieve certain properties,
`often for particular applications.
`·
`The most widely used of the alloy steels are the
`stainless steels. These are steels with high chromium
`content, a minimum of about 11 wt.%. The chromium
`forms an oxide on the surface of the steel which is
`adherent and slows further oxidation or corrosion of
`the alloy. There are many types of stainless steels.
`They can be roughly distinguished on the basis of
`microstructure. The austenitic stainless steels (see
`Austenitic Stainless Steels) are low carbon stainless
`steels which are austenitic at room temperature and
`they normally contain about 18wt.% chromium and
`about 8 wt.% nickel and/ or manganese to stabilize the
`austenite. The austenitic stainless steels are used in
`applications requiring corrosion resistance and at
`elevat~ temperatures when both oxidation and creep
`resistance are required. The martensitic stainless steels
`(see Stainless Steels : Martensitic) are quenched and
`tempered steels and there are two classes of this type of
`
`8841
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`Petitioner Samsung and Google Ex-1017, 0005
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`Steels: Classifications
`
`stainless steel. The first are the medium carbon steels in
`which strength is achieved by the precipitation of alloy
`carbides. These steels were developed primarily for
`elevated temperature service in which oxidation is a
`concern. The duplex stainless steels (see Stainless
`Steels: Duplex) consist of a mixture of ferrite and
`austenite. The ferritic stainless steels (see Ferritic
`Stainless Steels) are stainless steels which are entirely
`ferritic. The duplex and the ferritic stainless steels each
`have applications in which they have better corrosion
`resistance or better stress corrosion cracking resistance
`than the martensitic or austenitic stainless steels. In
`addition to the wrought forms of stainless steel there
`are stainless steels especially made for casting. The cast
`stainless steels (see Stainless Steels : Cast) are of two
`types. One type is designed for corrosion resistance
`and the second type, the so-called heat resistant grades,
`are designed for elevated temperature service.
`A wide variety of steels have been developed
`primarily for use at elevated temperatures. Typical
`tempered martensitic steels used for high tempera(cid:173)
`ture service have compositions (in wt. %) such as
`0. l 5C- l Cr-0.5Mo, 0.20C- l.25Cr-0.5Mo, 0.15C-
`2.25Cr- l Mo, 0.15C- 5Cr-0.5Mo, 0. IC-9Cr- 1Mo,
`and .0. l 5C- 12Cr- Mo(orW). The creep resistance of
`these steels increases with increasing alloy content.
`These alloys find applications as tubes and pipes in
`power plants and petrochemical plants. There has
`been considerable activity over the past few years in
`developing new 9-12 chromium steels for power plant
`applications both in Europe and Japan, with the
`primary goal to achieve improved creep resistance.
`While various austenitic steels have superior creep
`resistance to the martensitic steels the martensitic
`steels have lower coefficients of thermal expansion and
`higher heat conductivities than do the austenitic steels
`and this results in the martensitic steels having better
`fatigue resistance than the austenitics at elevated
`temperatures. Viswanathan (1989) dfscusses the high
`temperature properties of steels.
`Steels developed primarily to achieve high tough(cid:173)
`ness are of two types. The first are alloys developed to
`have very low ductile-to-brittle transition tempera(cid:173)
`tures so that they can be used at very low temperatures.
`The prototype martensitic steel used in cryogenic
`applications are the so called 9-nickel steels (see
`Cryogenic Steels). A variety of methods can be used to
`lower the ductile-to-brittle transition temperature,
`including refinement of grain size, lowering the yield
`strength, adding nickel and introducing austenite of
`the appropriate morphology, and mechanical stability.
`The second are steels designed to achieve high tough(cid:173)
`ness at very high strength levels (see MartensiticNon(cid:173)
`stainless Steels : High Strength and High Alloy). Steels
`of this type are the precipitation strengthened mar(cid:173)
`aging steels and low to medium carbon secondary
`hardening steels which have been developed according
`to methods used by Speich and · co-workers in the
`development of the steel HY 180 (Speich et al. 1973).
`
`8842
`
`A variety of steels have been developed to achieve
`various types of wear resistance. These include the
`Hadfield steels (see Austenitic Steels: Non-stainless),
`tool and die steels (see Tool and Die Steels) and high
`speed steels.
`The Hadfi!!ld steels are medium to high carbon
`steels containing substantial amounts of manganese.
`These alloys are austenitic at room temperature. These
`alloys have excellent wear resistance because the
`austenite transforms to a high carbon martensite when
`the material is subjected to strain (see Effects of Stress
`and De.formation on Martensite Formation) . Thus wear
`results in a very hard surface layer which is resistant to
`further wear.
`Tool Steels (Roberts and Cory 1980) covers three
`classes of steel: tool steels, die steels (both cold-work
`and hot-work), and the high speed steels. Tool steels
`are traditionally divided into three categories. Carbon
`tool steels, low-alloy tool steels, and the special
`purpose tool steels, .of which there are several types.
`There are four types of cold-work die steels, oil
`hardening cold-work die steels, air hardening cold(cid:173)
`work die steels, high carbon- high chromium cold(cid:173)
`work die steels, and wear resistant cold-work die
`steels. There are five classes of hot-work steels,
`3-4wt. % chromium hot-work die steels, chromium(cid:173)
`molybdenum hot-work die steels, chromium- tungsten
`hot-work die steels, tungsten hot-work die steels, and
`molybdenum hot-work die steels. Many of the steels
`contain large amounts of strong carbide-forming
`elements for two reasons. The first is to provide for a
`dispersion oflarger carbides which are in the steel after
`austenitizing and which improve wear resistance. In
`addition, the strong carbide forming elements which
`are in solid solution after austenitizing can combine
`with carbon during tempering and this precipitation of
`alloy carbides
`(secondary hardening) provides
`· strength at room and elevated temperatures.
`High-speed steels are used primarily for the manu(cid:173)
`facture of cutting tools. While there are a number of
`classes of high speed steels they have in common high
`carbon contents (ranging from 0.8wt. % to >3wt.%~
`chromium levels of about 4wt. %, massive amounts of
`strong carbide forming elements (vanadium, tungsten,
`and molybdenum) to provide large carbides which are
`present after austenitizing and which improve wear
`behavior and to provide for secondary hardening on
`tempering. Many high-speed steels also contain large
`amounts of cobalt, which enhances the secondary
`hardening response and the hot hardness of tho
`. secondary hardened microstructure.
`Steels developed primarily for particular electrical,
`magnetic, and physical properties include the silicoa
`steels (see Silicon Steels), magnetic steels (see Magnetil
`Steels) and steels having low coefficients of thermal
`expansion (see Steels: Low Expansion).
`Silicon steels are ferritic alloys of iron and silicoq
`that have magnetic properties which make them useful
`in motors and transformers. The silicon additio
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`Petitioner Samsung and Google Ex-1017, 0006
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`

`

`improve magnetic softness and increase the electrical
`resistivity. They. also have the undesirable effects of
`decreasing the Curie temperature, reducing the satu(cid:173)
`ration magnetization, and of embrittling the alloy
`when the silicon additions exceed about 2 wt.%. The
`embrittling effects of silicon make it difficult to
`produce silicon steels with more than about 3 wt.%
`silicon. The silicon steels are produced in two forms,
`highly textured grain-oriented alloys and alloys in
`which the grains are not oriented. Grain orientation is
`carried out to align the magnetic easy axis.
`There are a large number of iron-based permanent
`magnet alloys. In addition, there are a number ofiron(cid:173)
`based soft magnetic materials in addition to the silicon
`steels. These alloys include Fe-Co alloys, permalloy
`and iron-based amorphous and nanocrystalline soft
`magnetic materials.
`Iron-ba~ed alloys having near-zero or even negative
`expansions on heating in the vicinity of room tem(cid:173)
`perature were first discovered in the late 1900s by the
`Swiss physicist Charles-Edouard Guillaume. The fam(cid:173)
`ily of alloys which possess this characteristic are
`known as "Invar" for length INV ARiant. The first
`In var alloy had a composition of iron with 36 wt.%
`nickel. This alloy has a coefficient of thermal ex(cid:173)
`pansion varying from slightly negative to less than
`10% of that of a normal metal from near absolute zero
`to near the Curie temperature. In Invar there is a
`volume contraction as the alloy transforms from
`ferromagnetic to diamagnetic which almost exactly
`counterbalances the thermal expansion. By varying
`the nickel content and alloying with additional ele(cid:173)
`ments Invar alloys have been developed which match
`the coefficients of thermal expansion of certain glasses
`and of silicon.
`
`Steels: Low Expansion
`
`freezing point to the boiling point of water. Such
`expansion may be of crucial importance. In the late
`1900s, the Swiss physicist Charles-Edouard Guillaume
`was seeking a substitute for the standard platinum
`meter, and found that a Fe-36% Ni alloy showed
`near-zero or even negative expansion in the vicinity of
`room temperature. This alloy was named "Invar," for
`length INVARiant. Unfortunately Invar was found
`to undergo a very slight change in length when held for
`long times at room temperature, which disqualified it
`for use as the meter standard. However, Guillaume
`and his co-workers, working largely with the French
`metals company which was to become Imphy, S. A.,
`took the lead in developing a series of alloys based on
`the Fe-36% Ni Invar composition. Uses for these
`alloys include measuring tapes, metals for glass-metal
`seals, liners for liquid natural gas tankers, materials
`for the electronics industry, and hair springs for pre(cid:173)
`quartz era time pieces.
`
`1. The Alloys
`At room temperature, Fe- 36% Ni is a metastable,
`ferromagnetic solid solution with a Curie point of
`555 K . The coefficient of thermal expansion (CTE), ex,
`is defined as 11L/ L = o:11T where L = length of the
`specimen, 11L = change in length, and 11T = change-in
`temperature. Figure 1 compares
`the expansion
`behavior of a normal metal with that of Invar. The
`CTE of a normal metal is zero near the absolute zero
`and approaches an asymptotic value typically between
`10- 5 K- 1 and 2 x 10- 5 K- 1 at higher temperatures.
`Invar shows a CTE varying from slightly negative to
`
`Bibliography
`Krauss G 1980 Principles of Heat Treatment of Steel. ASM
`International, Metals Park, OH
`Leslie WC 1981 The Physical Metallurgy of Steels. McGraw(cid:173)
`Hill, New York
`Roberts GA, Cary RA 1980 Tool Steels. ASM International,
`Metals Park, OH
`Speich GR, Dabkowski D S, Porter L F 1973 Strength and
`toughness of Fe- lONi alloys containing C, Cr, Mo, and Co.
`Metal!. Trans. 4, 303- 15
`Viswanathan R 1989 Damage Mechanisms and Life Assessment
`of High-Temperature Components. ASM International, Metals
`Park, OH
`
`.._J --(cid:173)
`
`.._J
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`C:
`0
`"iii
`C:
`"' C.
`X w
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`W. M. Garrison Jr
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`lnvar
`
`---------// /
`
`/
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`/
`
`/
`
`/
`
`/ r
`
`/ / - Normal metal
`
`/
`
`/
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`/
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`
`/
`
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`Temperature, K
`
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`~"
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`--
`
`Steels: Low Expansion
`
`· Nearly all materials expand on heating and contract
`on cooling. In the case· of metals, a bar-1 m in length
`will expand about 1- 2 mm when heated from the
`
`Figure 1
`Comparison of the thermal expansion behavior of a
`normal metal with that of an Invar-type Fe- Ni alloy. The
`Invar alloy expands hardly at all between O K and Tc, the
`Curie temperature. Thereafter the expansion behavior is
`comparable with that of the normal metal (afti:r Beranger
`et al. 1996).
`
`'
`
`8843
`
`Petitioner Samsung and Google Ex-1017, 0007
`
`