Phase Diagrams and Heterogeneous Equilibria

by Predel, Bruno; Hoch, Michael J. R.; Pool, Monte

• ISBN13: 9783540140115
• ISBN10: 3540140115
• Format: Hardcover
• Copyright: 2004-07-30
• Publisher: Springer Verlag

Summary

This graduate-level textbook provides an introduction to the practical application of phase diagrams. It is intended for students and researchers in chemistry, metallurgy, mineralogy, and materials science as well as in engineering and physics. Heterogeneous equilibria are described by a minimum of theory illustrated by practical examples and realistic case discussions from the different fields of application. The treatment of the physical and energetic background of phase equilibria leads to the discussion of the thermodynamics of mixtures and the correlation between energetics and composition. Thus, tools for the prediction of energetic, structural, and physical quantities are provided. The authors treat the nucleation of phase transitions, the production and stability of technologically important metastable phases, and metallic glasses. Furthermore, the text also concisely presents the thermodynamics and composition of polymer systems.

Table of Contents

List of Symbols	xiii
1 Fundamental Facts and Concepts	1	(8)
1.1 General	1	(2)
1.2 Vaporization Equilibrium	3	(4)
References	7	(2)
2 Phase Equilibria in One-Component Systems	9	(8)
2.1 General	9	(1)
2.2 Transformation Equilibria in the Solid State	9	(3)
2.3 Monotropic Transformations	12	(3)
References	15	(2)
3 Phase Equilibria in Two-Component Systems Under Exclusion of the Gas Phase	17	(72)
3.1 Definition of the Composition	17	(1)
3.2 Partial Reactions of the Solid-Liquid Transition	18	(3)
3.3 Process of Fusion in a Two-Component System	21	(3)
3.4 Eutectic System	24	(1)
3.5 Eutectic Real Systems	25	(1)
3.6 The Gibbs Phase Rule	26	(2)
3.7 Application of the Phase Rule	28	(1)
3.8 The Lever Rule	29	(1)
3.9 Thermal Analysis	30	(4)
3.10 Light Microscopic and Electronmicroscopic Research Methods to Determine Phase Diagrams	34	(6)
3.11 X-Ray Diffraction Methods	40	(1)
3.12 Other Experimental Methods	41	(1)
3.13 Eutectic Crystallization	41	(5)
3.14 Dendritic Crystallization	46	(1)
3.15 Simple Phase Equilibria with Complete Solubility in the Solid and Liquid Phases	47	(3)
3.16 Phase Equilibria with Complete Solubility in the Solid and Liquid Phases and a Melting Point Minimum or Melting Point Maximum	50	(2)
3.17 Real Phase Diagrams with Complete Solubility in the Solid and Liquid Phases	52	(2)
3.18 Miscibility Gap in the Solid Phase	54	(2)
3.19 Phase Diagram with Peritectic Equilibrium	56	(2)
3.20 Miscibility Gap in the Liquid Phase	58	(4)
3.21 Real Phase Diagrams with a Miscibility Gap in the Liquid Phase and an Upper Critical Point Exclusively	62	(2)
3.22 Phases with a Superlattice	64	(3)
3.23 Systems with a Congruently Melting Compound	67	(4)
3.24 Phase Diagram with a Non-Congruently Melting Compound	71	(2)
3.25 Phase Diagram with a Compound Forming from Two Melts	73	(1)
3.26 Real Diagrams with Compounds	74	(3)
3.27 Transformation Equilibria	77	(4)
3.28 The Iron-Carbon Phase Diagram	81	(5)
References	86	(3)
4 Phase Equilibria in Three-Component Systems and Four-Component Systems with Exclusion of the Gas Phase	89	(66)
4.1 The Composition Triangle	89	(2)
4.2 Lever Rule in Ternary Systems	91	(1)
4.3 Compatibility Triangle	92	(1)
4.4 Four-Phase Equilibria	93	(1)
4.5 Representation of Ternary Phase Diagrams	94	(1)
4.6 A Simple System with a Ternary Eutectic	95	(2)
4.7 Phase Fields in a Ternary Eutectic System	97	(1)
4.8 Cuts at Constant Temperature	98	(2)
4.9 Vertical Cuts	100	(1)
4.10 Temperature-Composition Cut through a Corner of the Composition Triangle	101	(1)
4.11 Temperature-Composition Cut Parallel to One Side of the Composition Triangle	102	(1)
4.12 Simple Real Diagrams with a Ternary Eutectic	103	(2)
4.13 Thermal Analysis and Structure of Simple Ternary Eutectic Systems	105	(3)
4.14 Properties of Neighboring Phase Fields	108	(3)
4.15 Non-Regular Sections	111	(1)
4.16 Critical Point	112	(1)
4.17 Schreinemakers' Rule	113	(1)
4.18 Ternary Systems with Unlimited Solubility in the Solid and Liquid State, and without a Melting Point Minimum or Maximum	114	(1)
4.19 Isothermal Section through a Ternary System with Unlimited Solution Formation	115	(2)
4.20 Temperature-Composition Section through a Ternary System with Unlimited Solid Solution Formation	117	(1)
4.21 System with a Ternary Eutectic and Limited Solid Solution	118	(2)
4.22 Ternary System with a Congruently Melting Binary Compound and a Pseudobinary Section	120	(2)
4.23 Ternary System with a Binary Compound without a Pseudobinary Section	122	(2)
4.24 Isothermal Section and Temperature-Composition Section through a Ternary System with a Binary Compound with no Pseudobinary Section	124	(1)
4.25 Ternary System with Two Binary Compounds	125	(2)
4.26 Ternary Compounds with Melting Point Maxima	127	(1)
4.27 Real Ternary Systems with Binary and Ternary Compounds	128	(1)
4.28 Ternary System with Two Eutectic Bounding Binary Systems with Limited Solubility in the Solid and Complete Miscibility in the Third Bounding Binary System	129	(2)
4.29 Ternary System with Two Peritectic Bounding Systems and Complete Solubility in the Third Bounding System	131	(2)
4.30 Transition between an Univariant Peritectic and an Univariant Eutectic Reaction	133	(1)
4.31 Miscibility Gap in the Liquid Phase	134	(3)
4.32 Monotectic Four-Phase Reaction	137	(1)
4.33 Real Ternary Diagrams with Limited Solubility in the Liquid Phase	138	(3)
4.34 Reaction Schemes	141	(2)
4.35 Four-Component Systems	143	(2)
4.36 Simple Equilibria in Four-Component Systems	145	(1)
4.37 Reciprocal Systems	146	(2)
4.38 Solubility of Reciprocal Salt Pairs in Water	148	(2)
4.39 Comments to the Extent of Higher Order Systems	150	(2)
References	152	(3)
5 Phase Equilibria Including a Vapor Phase	155	(20)
5.1 Vapor-Liquid Equilibrium in a One-Component System	155	(1)
5.2 Phase Equilibria between Liquid and Vapor in Binary Systems without a Miscibility Gap	156	(4)
5.3 Gas-Solid Equilibria in a Binary System	160	(3)
5.4 Phase Equilibria in a Binary System in which Solid, Liquid and Gas can Appear	163	(4)
5.5 Phase Equilibria with Participation of the Gas Phase with Limited Solubility in the Liquid Phase	167	(2)
5.6 Vapor-Solid Equilibria with Solid Solution Formation	169	(1)
5.7 Gas-Solid Equilibria in Systems with Compounds	169	(3)
5.8 Heterogeneous Equilibria at Chemical Transport Reaction	172	(1)
References	173	(2)
6 Thermodynamics	175	(94)
6.1 General	175	(1)
6.2 Basic Thermodynamic Concepts and Definitions	176	(2)
6.3 Integral Quantities of Mixing	178	(3)
6.4 Partial Quantities of Mixing	181	(2)
6.5 The Ideal Solution	183	(1)
6.6 The Model of the Regular Solution	183	(2)
6.7 Real Solutions and Excess Functions	185	(3)
6.8 Analysis of Experimental Thermodynamic Data	188	(1)
6.9 Influence of the Atomic Size Difference	188	(2)
6.10 The Association Model	190	(8)
6.10.1 Basic Formulae of the Association Model	191	(2)
6.10.2 Application to Liquid Binary and Ternary Alloys	193	(5)
6.11 The Hoch-Arpshofen Model	198	(5)
6.12 Difference in Heat Capacity between Liquid and Solid Cp(L-S)	203	(3)
6.13 Calculation of Thermodynamic Functions in Multi-Component Systems	206	(7)
6.14 The Thermodynamic Activity	213	(4)
6.15 General Comments about Experimental Methods to Determine Thermodynamic Mixing Properties	217	(1)
6.16 The High-Temperature Calorimeter	217	(1)
6.17 Partial Vapor Pressure Measurements	218	(3)
6.18 Activity Determination from the EMF of Galvanic Cells	221	(1)
6.19 Fusion Equilibrium in a One-Component System	222	(2)
6.20 Fusion Equilibria in Binary Systems	224	(6)
6.21 Equilibrium between a Binary Liquid and the Crystal of one Component in the Ideal System	230	(3)
6.22 Equilibrium between a Binary Liquid and a Solid Solution in an Ideal System	233	(1)
6.23 Fusion Equilibrium in a Regular System	234	(2)
6.24 Fusion Equilibrium in a Real System	236	(1)
6.25 Melting Point Minimum	236	(2)
6.26 Phase Equilibrium During Demixing	238	(2)
6.27 Calculation of the Miscibility Gap Based on the Regular Solution Model	240	(3)
6.28 Evaluation of Solubility Equilibria	243	(3)
6.29 Evaluation of a Fusion Equilibrium with Small Liquidus Concentrations	246	(2)
6.30 Critical Demixing Temperature in Real Solutions	248	(1)
6.31 The Spinodal	249	(1)
6.32 Calculation of a Simple Ordering Reaction in Solid Solutions	249	(6)
6.33 Degree of Order in a Superlattice as a Function of Temperature	255	(2)
6.34 Comments on the Character of Phase Transformations	257	(1)
6.35 Thermodynamic Properties of Ternary Alloys	258	(5)
6.36 Calculation of Fusion Equilibria in Ternary Systems	263	(4)
References	267	(2)
7 Nucleation During Phase Transitions	269	(14)
7.1 General	269	(1)
7.2 Homogeneous Nucleation Without Change of Composition	269	(3)
7.3 Heterogeneous Nucleation	272	(3)
7.4 Homogeneous Nucleation with Change in Composition	275	(3)
7.5 Spinodal Decomposition	278	(3)
References	281	(2)
8 Metastable Phases	283	(30)
8.1 Energetics of the Nucleation of Metastable Crystalline Phases	283	(2)
8.2 Guinier-Preston Zones in Al-Cu Alloys	285	(3)
8.3 Short Range Order in Liquid Solutions and Their Effect on Solid-Liquid Equilibria	288	(14)
8.3.1 Some Empirical Findings about Short Range Order in Liquid Alloys	288	(6)
8.3.2 The Model of Homogeneous Equilibria for the Quantitative Description of the Short Range Order in Liquid Alloys	294	(2)
8.3.3 The Effect of Homogeneous Equilibria on Fusion Equilibria	296	(1)
8.3.3.1 Liquidus Lines in the Vicinity of the Melting Point of a Congruently Melting Compound	296	(1)
8.3.3.2 Miscibility Gap in a Binary Liquid Alloy with a Strong Compound Forming Tendency	298	(4)
8.4 Metallic Glasses	302	(2)
8.5 Metastable, Non-Crystalline Metallic Phases	304	(3)
8.6 Methods to Obtain Extremely High Cooling Rates	307	(2)
8.7 Crystallization of Glasslike Alloys	309	(2)
References	311	(2)
9 Effect of Diffusion on Phase Transformations	313	(18)
9.1 Distribution of Components During Solidification of Liquids	313	(4)
9.2 Constitutional Undercooling	317	(2)
9.3 Effects of the Constitutional Undercooling	319	(3)
9.4 Purification by Zone Melting	322	(2)
9.5 Precipitation Reactions in the Solid State	324	(5)
References	329	(2)
10 Organic and Polymeric Materials	331	(10)
10.1 Introduction	331	(1)
10.2 Organic Materials	331	(2)
10.3 Phase Diagrams	333	(1)
10.4 Polymer Blends	334	(5)
References	339	(2)
Subject Index	341