Understanding Phase Diagrams

Introduction

• When two or more metals combine to form alloys, a range of products can be obtained
• Obtaining these products depends on the temperature and composition of the constituent elements.
• Products may display different structures, and have differing mechanical properties
• Knowing the relationship between these variables and resulting products is imperative for developing alloys with desirable properties
• Phase diagrams (constitutional diagrams) are pictorial representations of relationships and product descriptions
• They describe liquid areas, solid solutions, and intermetallic compounds
• Phase diagrams depict equilibrium phases in an alloy at various temperatures
• Diagrams are based on the slow cooling of an alloy from a molten state to obtain stable phases at room temperature
• Phase diagrams vary depending on the number of constituent elements
• Binary diagrams represent two-element systems
• Ternary diagrams represent three-alloy systems
• Understanding how diagrams are obtained is helpful when seeking to understand and interpret them
• Construction of alloy system diagrams is considered, followed by interpretation,
• Phase diagrams of systems of steel alloys are discussed

Nomenclature, Definitions, Basic Concepts

• A component is a unique chemical species in an alloy (e.g. Fe, C, Cu, B, N, Al2O3, H2O, NaCl)
• A phase is a homogeneous portion of a system with uniform physical and chemical characteristics
• Two distinct phases in a system have distinct physical or chemical characteristics (e.g., water and ice)
• A phase may contain one or more components
• A one-phase system constitutes a homogeneous system
• Multiple phases present makes for a heterogeneous system (a mixture)
• The solvent is the major (host) component in a solution
• The solubility limit of a component in a phase is the maximum amount of component that can be dissolved
• For example, alcohol has unlimited solubility in water, sugar has a limited solubility, and oil is insoluble
• Cu and Ni are mutually soluble in any amount (unlimited solid solubility), while C has a limited solubility in Fe
• When combining elements, the resulting equilibrium structure is affected
• Factors affecting the equilibrium of an alloy include its phases, the make up of phases, and amount of each phase
• This is for a given composition and temperature

Additional Definitions

• Components are elements or compounds that are mixed
• Phases are physically and chemically distinct regions resulting from the mixture
• Composition is the amount of a component that is in a phase

Solubility Limit

• The solubility limit represents the maximum concentration for which only a solution occurs
• The solubility of sugar (C12H22O11) in a sugar-water syrup at 20 °C is about 65%
• For sugar water, If Co < 65% sugar, a syrup is formed
• If Co > 65% sugar a syrup + sugar solid is formed
• Solubility limit increases with temperature, for example, at 100 °C the solubility limit is 80% sugar

Material Properties

• Mechanical properties are influenced by microstructure (i.e texture)
• Alloy properties depend not only on the proportions of the phases but also on the arrangement at the microscopic level
• Microstructure depends on processing and heat treatment
• Phase diagrams are a guide for us when seeking to understand, explain and predict microstructures of materials

Thermodynamics

• In thermodynamics, equilibrium is the state of a system that corresponds to the minimum of thermodynamic function (free energy)
• Under constant conditions, changes are toward a lower free energy
• States of stable thermodynamic equilibrium have the minimum free energy
• Meta-stable systems are trapped in a local minimum of free energy, rather than the global one

Phase Diagrams

• A phase diagram is a graphical representation of the combinations of temperature, pressure, and composition for which specific phases exist at equilibrium
• The borders in diagrams represent solubility limits for each phase

Ice-Salt Phase Diagram Example

• Change in temperature results in a change in number of phases (path from A to B)
• Change in composition results in a change in number of phases (path from A to C)
• A phase diagram can show distinct phases and their conditions with borders representing the solubility limits for each phase

Types of Phase Diagrams

• Classified according to miscibility of constituents in liquid & solid states:
• Components completely soluble/insoluble in liquid state
• Components partially soluble in liquid state

Common Alloy Systems

• The most common and important engineering alloy systems are binary systems exhibiting complete solubility in liquid state
• They may show complete solubility or complete insolubility upon cooling to room temperature

General Rules of Phase Diagrams

• This is for construction and interpretation
• Phase diagrams are based on slow cooling of alloys to obtain thermodynamically stable structures at room temperature
• A condition of equilibrium for an alloy system is determined by a relation between a number of coexisting phases, number of components and number of variables
• Gibb's phase rule states P + F = V + C
  • P = number of phases
  • C = number of components
  • V = number of variables
  • F = degree of freedom
• For the most common case where pressure is constant (atmospheric) and the only variable is temperature (V = 1), the rule becomes P + F = 1 + C
• Weight proportion of various phases in equilibrium at any temperature can be determined by using compositions of a phase
• The overall composition of alloy
• A “lever arm principle” is used in mechanics
• Three phases cannot coexist at a time except at a constant temperature (e.g. eutectic or peritectic)
• Two phases are always apart by a two-phase region

Construction of Phase Diagrams

• When a pure metal is cooled from a liquid state, at a particular temperature, liquid begins to transform to solid and nuclei of solid phase begin to appear
• The temperature at which this happens is called the solidification temperature
• Upon further cooling, the metal temperature does not change, but more solidification occurs
• The heat energy released by the melt is used up in forming larger liquid-solid interfaces, thus more solid grows
• After solidification is complete, further cooling reduces the solid metal temperature
• The solidification in alloys does not take place at a constant temperature, unlike pure metal
• More than one element is involved, the solidification temperatures would be different
• Solidification begins when one of the elements begins to solidify and temperature also continues to drop until solidification is complete

Construction of Phase Diagrams Example (copper-nickel diagram)

• Alloys that contain differing amounts of Cu & Ni will be made
• Each sample is heated until molten and of uniform composition, then it is allowed to cool very slowly
• Change in temperature by time is recorded
• First, pure Cu is cooled, where solidification starts (A) and finishes (B) at a temperature of 1084 °C
• Subsequently, alloys of different Cu-Ni composition are cooled from a liquid state to solidification starting points (L) and solidification finishing points (S)
• Pure Ni is cooled at the same temperature of C & D (1455 °C)
• Then, the temperatures for each composition are plotted on a diagram
• Lines through solidification start and finish temperatures are drawn to fully complete the diagram
• A line joining points where solidification begins from liquid is called liquidus
• A line joining points where solidification is complete is called solidus
• The region between liquidus and solidus lines is in a mixed state where both solid and liquid phases are present
• Solid and liquid phases are separated by a two-phase region

Cu-Ni System

• The Cu-Ni system also shows complete solubility in the vapor state
• Such systems with complete solubility in vapor, liquid and solid states are called isomorphous systems
• Some binary systems having complete liquid and solid solubility lack a continuous region of solid + liquid (e.g. Au-Cu, Au-Ni, Cr-Fe)
• In such systems, solidus & liquidus lines meet tangentially at a minimum temperature ("X" in figure), which is below the melting point of both components
• The alloy corresponding to this temperature is called an azeotropic alloy, which behaves like pure metal during solidification

Interpretation of Phase Diagrams

• Information derived includes phase, compositions, and relevant fractions to Bismuth-Antimony phase diagrams
• Solidification is completed at Ty, and the solid has the same composition as the remaining liquid, which is 93% Bi (point d)
• As cooling continues, the first and the last solids (with 8% and 93% Bi) homogenize with each other due to high temperatures
• A uniform composition of 50% Bi prevails in the solid in ideal conditions, however in practice, areas of segregation of alloying elements can be observed (known as coring)

Cu-Ni System Example

• Binary system with two components (Ni & Cu), which is isomorphous (complete solubility of one component in the other).

Cored Structure vs Equilibrium Structure

• Fast rate of cooling results in cored structure
• Slow cooling results in equilibrium structure

Weight Fractions of Phases

• Relative weight fractions of two phases (liquid & solid) can also be obtained from diagrams at a given temperature with a "lever arm principle (lever rule)”
• A horizontal line (tie line) is drawn at Ti, and a line constructs mn passing through point i
  • mi = Co − CL = 50 − 23 = 27%
  • in = Cα − Co = 73 − 50 = 23%
  • mn = Cα − CL = 73 − 23 = 50%
• Weight fractions are then calculated such that
  • wt % of solid = (in/mn)*100 = 46%
  • wt % of liquid = (mi/mn)*100 = 54%

Systems Insoluble at Solid State

• For binary alloys that are completely insoluble in the solid state, the diagram can depict bismuth-cadmium (Bi-Cd)
• All previously described rules are applicable
• A significant difference is the alloy Y (in figure) behaves like a pure metal as solidification is concerned
• This alloy solidifies at a constant temperature (Tc), just like pure metal
• The solidification product is not a single phase
• Each is a mixture of two phases solid Bi and Ca that are insoluble in each other

Additional Properties of Systems Insoluble at Solid State

• The two phases exist side-by-side with various structures
• Nucleation of Bi produces a plate
• The liquid next to it becomes enriched in Cd since nucleation of Bi changes liquid composition
• The liquid next to Bi solidifies as Cd in the plate form
• The sequence continues until all of the liquid solidifies at a constant temp
• "Eutectic transformation" happens at a "eutectic temperature"
• The alloy Y is is "eutectic alloy"
• At the eutectic point, one phase (liquid) decomposes to produce two phases (Bi & Cd)

Alloy Solidification

• An alloy (other than alloy Y) would solidify to produce either pure-Bi or pure-Cd followed by eutectic lamellar structure
• Alloy X cooling from 300 °C in liquid state it starts to solidify
• Pure-Bi begins to form at point ‘b’
• The liquid composition (point m´) is 30% Cd, then weight fraction of pure-Bi is determined by lever rule
• Liquid that remains cools down to the eutectic composition and solidifies as a lamellar eutectic structure at constant temperature

Systems Partially Soluble at Solid State

• These are the most common alloy systems (involving steel), where two metals are partially soluble in the solid state
• Silver-Copper (Ag-Cu) system is an example
• At temperatures below eutectic, solubility decreases as cooling continues, this can lead to "age (precipitation) hardening”
• These systems have 3 single-phase regions (L, α, β) separated by two-phase regions
• The solubility is limited, partial
  • α is mostly Cu
  • β is mostly Ag
  • The overall system contains α and β mixture
• Transition can be expressed as
  • L =α+β

Lead-Tin Alloy System

• Consisting of 40% Sn and 60% Pb at 150 degrees Celsius
• Exists as a two phase system: α + β
  • C = 40 wt% Sn
  • Cα = 11 wt% Sn
  • Cβ = 99 wt% Sn
• The relative amount is expressed as
  • Wα =67 wt%
  • Wβ = 33 wt%
  • Co (Sn) = CαWa + Cβ Wβ = 0.110.67 + 0.990.33 = 0.40 → 40%
• Consisting of 40% Sn and 60% Pb alloy at 220 degrees Celsius is characterized with
  • Exists as a two phase system: α + L
  • Co = 40 wt% Sn
  • Cα = 17 wt% Sn
  • CL = 46 wt% Sn
  • WA =21 wt%
  • WC =79 wt%

Eutectic Systems

• Lead and Tin
• For alloys with Tin content of less than %2 is at extreme ends of the system with crystal of α
• For alloys with Tin content of between 2% and 18.3% is initially L + α, cooling results in only α in α polycrystal with fine β inclusions
• For alloys with Tin content of Co = CE = 61.9 wt% Sn the eutectic (lamellar) microstructure has alternating layers (lamellae) of α and β crystals

Hypoeutectic & Hypereutectic

• Alloys existing on either side of the eutectic alloy respectively
• In hypoeutectic alloys: Carbon content is below 0.83%
• In hypereutectic alloys: Carbon content is above 0.83%

Isothermal Reactions

• Transformations in (at Tcst) consist of
  • Eutectic: Liquid changes to Solid
  • Eutectoid: Solid changes to Solid
  • Peritectic: Solid changes from Solid/Liquid combination
  • Peritectoid: Solid changes from Solid/Solid combination
  • Monotectic: Liquid changes from Solid/Liquid combination
  • Monotectoid: Solid changes from Solid/Solid combination
  • Syntectic: Liquid changes from Liquid/Liquid combination

Ternary Systems

• An improvement in properties of a binary alloy can be gained by adding a third element
• Two commercial examples include: nickel (Ni) to steel (Fe-C) and adding lead (Pb) to brass(Cu-Zn)
• Alterations do however occur when introducing third elements to the binary phase diagram
• Systems have more complex parameters and valid lever arm principles are employed

Alloy Composition

• Properties may vary depending on the presence of certain key parameters
• How properties are generally secured by following phase diagrams
• Solubility of materials may be improved in hard conditions
• Components exhibited by conductivity may show decreasing activity due to solute atom presence

Iron-Carbon Equilibrium Diagram

• Shows phases such as delta iron and austenite that are BCC and FCC arrangements of Fe, respectively

Iron-Carbon System Solution Example

• The problem is to determine the weight percentages of austenite, ferrite and pearlite upon slow cooling
• As seen the steel only has austenite above 900°C
• Ferrite begins to form upon 800oC cooling at composition levels above .025
• Carbon exists in a composition below cementite with fractions depending on composition level

Example Problem of Component Weight Percentage

• The problem: Determine percentage of carbon in cementite (Fe3C)
• As seen 3 atoms of Fe bond to 1 atom of Carbon thus molecular weight is 3*(56)+12 = 180
• Thus carbon weight percentage is ~6.67%