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Image

**Published:**27 April 2016

Fig. 13 Isopleths through an isomorphous system. Adapted from Ref 3
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Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006231

EISBN: 978-1-62708-163-4

... Abstract This article describes the liquidus plots, isothermal plots, and isopleth plots used for a hypothetical ternary phase space diagram. It discusses the single-phase boundary (SPB) line and zero-phase fraction (ZPF) line for carbon-chromium-iron isopleth. The article illustrates the Gibbs...

Abstract

This article describes the liquidus plots, isothermal plots, and isopleth plots used for a hypothetical ternary phase space diagram. It discusses the single-phase boundary (SPB) line and zero-phase fraction (ZPF) line for carbon-chromium-iron isopleth. The article illustrates the Gibbs triangle for plotting ternary composition and discusses the ternary three-phase phase diagrams by using tie triangles. It describes the peritectic system with three-phase equilibrium and ternary four-phase equilibrium. The article presents representative binary iron phase diagrams, showing ferrite stabilization (iron-chromium) and austenite stabilization (iron-nickel).

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006240

EISBN: 978-1-62708-163-4

... includes 42 phase diagrams (liquidus projection, solidus projection, isopleths, isothermal section and vertical section). copper ternary system isopleths liquidus projection miscibility gap solidus projection ternary alloy phase diagrams THIS ARTICLE includes systems where copper...

Abstract

This article is a compilation of ternary alloy phase diagrams for which copper (Cu) is the first-named element in the ternary system. The other elements are Fe, Mn, Ni, Pb, S, Sb, Si, Sn, Ti and Zn. The diagrams are presented with element compositions in weight percent. The article includes 42 phase diagrams (liquidus projection, solidus projection, isopleths, isothermal section and vertical section).

Image

**Published:**31 August 2017

Fig. 13 Isopleth Fe-C sections at 3 mass% Si in the (a) stable and (b) metastable diagrams showing the composition-temperature domains for liquid (L), ferrite (α), austenite (γ), graphite (G), and cementite. Source: Ref 25 , 26
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Image

**Published:**31 August 2017

Fig. 17 Isopleth Fe-C sections of the Fe-C-Si-Mn system at 3 mass% Si and 1 mass% Mn. (a) Stable system. (b) Metastable system. Calculations performed with Thermocalc software and the TCFE8 database.
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Image

**Published:**31 August 2017

Fig. 1 (a) Isopleth Fe-C section at 3 mass% Si of the stable Fe-C-Si diagram. (b) Isothermal section at 810 °C (1490 °F) showing the various fields of equilibrium and the tie lines. Calculations performed with Fe-alloys Database (TCFE8) from Thermo-Calc Software AB.
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Image

**Published:**31 August 2017

Fig. 2 (a) Isopleth Fe-C section at 3 mass% Si of the metastable Fe-C-Si diagram. (b) Isothermal section at 790 °C (1450 °F) showing the various fields of equilibrium and the tie lines. Calculations performed with Fe-alloys Database (TCFE8) from Thermo-Calc Software AB.
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Image

**Published:**01 December 2009

Fig. 13 Comparison between the model-calculated isopleth of Mg-Al-Ca-Sr, from Mg-5Al-3Ca (in wt%) to Mg-5Al-3Sr (in wt%), and the measured liquidus and solidus data. Source: Ref 55
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Image

**Published:**27 April 2016

Fig. 5 Isopleth through hypothetical ternary phase diagram at a constant 40% C . Adapted from Ref 1
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Image

**Published:**27 April 2016

Fig. 6 Carbon-chromium-iron isopleth showing single-phase boundary (SPB) lines and zero-phase boundary (ZPB) lines. Source: Ref 2
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Image

**Published:**15 June 2020

Fig. 8 Isopleth for 17-4 PH stainless steel base composition as a function of nitrogen content. MC and M 2 C are the face-centered cubic (fcc) phase and hexagonal close-packed carbides/nitrides, respectively, where “M” represents metal substitutional elements (e.g., chromium, niobium), and “C
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Image

**Published:**01 November 2010

Fig. 2 Calculated isopleth of the quinary Al-Cu-Ni-Ti-Zr system expressed in terms of temperature as a function of titanium concentration (at.%). The composition of titanium at the origin is 0; corresponding to Zr 56.2 Cu 31.3 Ni 4.0 Al 8.5 , the compositions of copper, nickel, and aluminum
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Image

**Published:**31 August 2017

Fig. 6 (a) Schematic of carbon redistribution during ferrite growth in SG irons and (b) relation to the isopleth Fe-C section of the relevant phase diagram. Source: Ref 15
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Series: ASM Handbook

Volume: 1A

Publisher: ASM International

Published: 31 August 2017

DOI: 10.31399/asm.hb.v01a.a0006300

EISBN: 978-1-62708-179-5

... affects the eutectoid reaction in a similar way as the eutectic reaction. Figure 1(a) shows an isopleth Fe-C section of the stable Fe-Si-C phase diagram at 3.0 mass% Si, which has been limited to the eutectoid temperature range. It is seen that silicon leads to the formation of a three-phase field...

Abstract

This article discusses the stable and metastable three-phase fields in the binary Fe-C phase diagram. It schematically illustrates that austenite decomposition requires accounting for nucleation and growth of ferrite and then nucleation and growth of pearlite in the remaining untransformed volume. The article describes the austenite decomposition to ferrite and pearlite in spheroidal graphite irons and lamellar graphite irons. It provides a discussion on modeling austenite decomposition to ferrite and pearlite.

Series: ASM Handbook

Volume: 22A

Publisher: ASM International

Published: 01 December 2009

DOI: 10.31399/asm.hb.v22a.a0005402

EISBN: 978-1-62708-196-2

... triangular paper. Two other common diagrams of a ternary are an isopleth, that is, a temperature-composition section, with one constraint such as keeping the composition of one component constant, and a projection of the liquidus or solidus surface onto a two-dimensional Gibbs triangular paper. However...

Abstract

A phase diagram is a graphical representation of the phase equilibria of materials in terms of temperature, composition, and pressure. This article provides an overview on the background of phase diagram calculation software. It presents an algorithm to calculate binary stable phase equilibria. The article summarizes a rapid method to obtain a thermodynamic description of a multicomponent system. It also provides information on thermodynamically calculated phase diagrams.

Series: ASM Handbook

Volume: 1A

Publisher: ASM International

Published: 31 August 2017

DOI: 10.31399/asm.hb.v01a.a0006295

EISBN: 978-1-62708-179-5

... of the liquidus surface of the Fe-C-Si phase diagram in the iron-rich corner for the stable system. Source: Ref 12 Sectioning the Fe-C-Si three-dimensional diagram at constant silicon content leads to a so-called Fe-C isopleth section. The graphs in Fig. 13 ( Ref 25 , 26 ) allow comparing an isopleth...

Abstract

The control of the solidification process of cast iron requires understanding and control of the thermodynamics of the liquid and solid phases and of the kinetics of their solidification, including nucleation and growth. This article addresses issues that allow for the determination of probability of formation and relative stability of various phases. These include the influence of temperature and composition on solubility of various elements in iron-base alloys; calculation of solubility lines, relevant to the construction of phase diagrams; and calculation of activity of various components. It discusses the role of alloying elements in terms of their influence on the activity of carbon, which provides information on the stability of the main carbon-rich phases of iron-carbon alloys, that is, graphite and cementite. The article reviews the carbon solubility in multicomponent systems, along with saturation degree and carbon equivalent.

Series: ASM Handbook

Volume: 22B

Publisher: ASM International

Published: 01 November 2010

DOI: 10.31399/asm.hb.v22b.a0005521

EISBN: 978-1-62708-197-9

... presented in Ref 19 . It is based on tracking the position with time of an isopleth of a chosen function. In the present case, the function is the signed geometric distance to the solid-liquid interface, and the “0” isopleth of this function is tracked. For that purpose, an expression of the velocity...

Abstract

This article discusses the three different modeling approaches for grain structures formed during solidification of metallic alloys: direct modeling of dendritic structure, direct modeling of grain structure, and indirect modeling of grain structure. The main construction bases, the scale at which it applies, and the mathematical background are presented for each modeling approach. The article concludes with a table that presents a comparison of the main inputs/outputs, approximations, numerical methods, kinetics laws, and applications for the three approaches to modeling of dendritic grain solidification.

Series: ASM Handbook

Volume: 22B

Publisher: ASM International

Published: 01 November 2010

DOI: 10.31399/asm.hb.v22b.a0005511

EISBN: 978-1-62708-197-9

... to decrease rapidly from the quaternary alloy Zr 56.28 Cu 31.3 Ni 4.0 Al 8.5 (at.%) due to the addition of titanium. Further calculation of several isopleths reveals that the liquidus temperature decreased the fastest when zirconium was replaced by titanium and reached the minimum at 4.9 at.% Ti, as shown...

Abstract

This article focuses on the industrial applications of phase diagrams. It presents examples to illustrate how a multicomponent phase diagram calculation can be readily useful for industrial applications. The article demonstrates how the integration of a phase diagram calculation with kinetic and microstructural evolution models greatly enhances the power of the CALPHAD approach in materials design and processing development. It also discusses the limitations of the CALPHAD approach.

Book: Casting

Series: ASM Handbook

Volume: 15

Publisher: ASM International

Published: 01 December 2008

DOI: 10.31399/asm.hb.v15.a0005206

EISBN: 978-1-62708-187-0

...-dimensional representation is necessary. The phase boundaries that are crossed during cooling and the sequence of phase formation can be read from a temperature-concentration section (e.g., an isopleth, a vertical section through Fig. 5 or Fig. 5 ). However, such a section provides only very limited...

Abstract

This article discusses the application of thermodynamic in the form of phase diagrams for visually representing the state of a material and for understanding the solidification of alloys. It presents the derivation of the relationship between the Gibbs energy functions and phase diagrams, which forms the basis for the calculation of phase diagrams (CALPHAD) method. The article also discusses the calculation of phase diagrams and solidification by using the Scheil-Gulliver equation.

Book Chapter

Book: Alloy Phase Diagrams

Series: ASM Handbook

Volume: 3

Publisher: ASM International

Published: 27 April 2016

DOI: 10.31399/asm.hb.v03.a0006221

EISBN: 978-1-62708-163-4

... of two-dimensional horizontal sections ( isotherms ) and vertical sections ( isopleths ) through the solid diagram. See the article “Introduction to Ternary Diagrams” in this Volume for more details. Isothermal Sections Composition values in the triangular isothermal sections are read from...

Abstract

The application of phase diagrams is instrumental in solid-state transformations for the processing and heat treatment of alloys. A unary phase diagram plots the phase changes of one element as a function of temperature and pressure. This article discusses the unary system that can exist as a solid, liquid, and/or gas, depending on the specific combination of temperature and pressure. It describes the accomplishment of conversion between weight percentage and atomic percentage in a binary system by the use of formulas. The article analyzes the effects of alloying on melting/solidification and on solid-state transformations. It explains the construction of phase diagrams by the Gibbs phase rule and the Lever rule. The article also reviews the various types of alloy systems that involve solid-state transformations. It concludes with information on the sources of phase diagram.

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