Higgins R.A. Engineering Metallurgy: Applied Physical Metallurgy

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at as low a temperature as possible. In fact a little more incompatibility

would lead to a complete 'divorce' to the extent that the metals would

separate forming a eutectic, probably of two solid solutions. We shall in

fact deal with this type of system in the next case.

Case IV—Two metals mutually soluble in all

proportions in the liquid state but only partially

soluble in the solid state

9.60 This case is in effect intermediate between the two dealt with in

Cases II and III and the thermal equilibrium diagram is, in consequence,

a sort of hybrid of these two. It represents a stage where incompatibility

has exceeded that suggested in Fig. 9.11. As in the cadmium-bismuth

system (where the metals are completely incompatible in the solid state)

a eutectic is formed, but in this case it is a eutectic of two solid solutions

instead of two pure metals. It is in fact the 'general' case and purists may

argue that, as such, it should have been dealt with before either of the

preceding particular cases. The systems have, however, been dealt with in

order of complexity rather than logical classification in order to assist the

student who may be encountering the subject for the first time.

The only new feature of this system, as compared with those foregoing,

is that we have phase boundaries occurring below the solidus, indicating

that phase changes can take place in the solid. On the tin-lead thermal-

equilibrium diagram (Fig. 9.12), which we shall use as an example of this

type of system, such phase boundaries as these are indicated by the lines

BC and FG. A line such as BC or FG is termed a solvus and indicates a

change in solubility of one metal in another in the solid state. Part of the

tin-lead system was used in Chapter 7 as an introduction to equilibrium

diagrams. We will now consider it in its entirety.

9.61 As the diagram shows, we have two solid solutions in the system,

since:

(a) Tin will dissolve up to a maximum of 2.6% lead at the eutectic

temperature, forming the solid solution a.

(b) Lead will dissolve up to a maximum of 19.5% tin at the eutectic

temperature, giving the solid solution (3.

(The different phases present in an alloy series are generally lettered from

left to right across the diagram, using letters of the Greek alphabet for

convenient reference.)

The slope of the phase boundaries BC and FG indicates that both the

solubility of lead in tin (a) and the solubility of tin in lead (|3) decrease as

the temperature falls. This is a normal phenomenon with solid solutions

as it is with liquid solutions. In Fig. 9.13 the solubility of a salt in water at

different temperatures is compared with the solid solubility of one metal

in another at different temperatures. In each case solubility increases as

Fig. 9.12 The tin-lead

equilibrium diagram

The

microstructures indicated

are

those obtained under

non-equilibrium

conditions

solidification.

LIQUID

TIN-RICH SOLID

LEAD-RICH

SOLID

EUTECTIC

CORED

/3 +

'EUTECTIC

ALL EUTECTIC

LIQUID

+• /S>

LIQUID

COMPOSITION

PER

CENT

CORED(^

EUTECTIC

OF U)3

CORED

LIQUID

+ <y.

a + /3

CORED

Fig.

9.13 An analogy between the liquid solubility of salt in water and the partial solid

solubility of one metal in another.

temperature rises

and

saturated solutions

are

formed

in a

similar manner.

and

each represent

mixture which

that temperature

is an

unsatu-

rated solution,

ie it

could dissolve more solute.

As the

temperature falls

(Si) the

solution (liquid

solid) reaches

saturation point

that solid

salt

(or

metal

begin

precipitate.

At T

(Ti)

considerable quantity

(Qi)

solute (either salt

metal

B) is

still

solution

but as the

tempera-

ture falls

to R (Ri)

this

reduced

to a

very small amount

each case—

(Yi) as

salt

(or

metal

B) is

progressively precipitated from solution.

9.62

In the

case

of the

tin-lead alloys

the

sloping boundaries

BC and

FG indicate that changes take place

in the

solid. Thus

as the

temperature

falls:

(i) lead becomes less soluble

solid

tin (a)

along

BC;

(H)

tin

becomes less soluble

solid lead

(|3)

along

FG.

Several different structures

may be

formed, depending upon

the

alloy

composition.

For

example,

let us

consider:

(a)

alloy

composition

(70% lead-30%

tin).

This will begin

solidify when

the

temperature falls

to T

and

dendrites

composition

will deposit.

The

alloy continues

solidify

in the

manner

solid

sol-

ution until

183°C

the

last layer

solid

form will

composition

(80.5%

lead-19.5%

tin) and the

remaining liquid will

be of

composition

(the

eutectic composition with

38%

lead

and

62%

tin).

The remaining liquid

now

solidifies

depositing,

in the

form

of a

eutectic, alternate layers

of a

and

|3,

the

compositions

and

respect-

ively.

this structure

now

cools slowly

room temperature

the

compo-

sitions

of the

solid solutions

a and |3

will follow

the

lines

BC and

FG,

the solid solution

will become progressively poorer

lead

and the

solid solution

will become poorer

in tin,

until

at, say,

100

will

contain less than

lead

and (3

will contain less than

10% tin. The

TEMPERATURE

solubility

curve

solvus

unsaturatcd

solid

solution

(cC)

saturated solid solutionWC)

+ solid

metal

% metal

IOOfcmctalA

undissolved

salt

°A> salt

10O

Yo water

saturated liquid solution

+ solid salt

unsaturatcd

liquid

solution

Plate 9.3 Representative tin-lead alloys in the cast condition, x 100.

(i) 75 tin-25

lead.

Primary crystals of a (light) in a matrix of eutectic consisting of layers of

a (light) and p (dark).

(ii) 62 tin—38

lead.

Completely eutectic in structure—layers of a (light) and P (dark).

(iii) 50 tin-50

lead.

Primary crystals of p (dark) in a matrix a + p eutectic as in (i) and (ii).

Note the small 'islands' of a within the primary |3 crystals in (iii). These were precipitated as

the alloy cooled slowly from 183°C to ambient temperature and the P changed in composition

along the steeply sloping solvus FG (Fig. 9.12).

(iii)

(ii)

(i)

proportions of a and (3 will also vary from EFIEB at 183°C to E'JIE'H

at 100

C. In the same way, provided we assume that the structure cooled

slowly enough to allow the primary dendrites of (3 to reach a uniform

composition F, these dendrites will now alter in composition to / at

100

and in so doing precipitate some a of composition H in order to

adjust their own composition. The a precipitated will join that already

present in the eutectic.

(b) If the alloy contained, say, 95% lead, and was cooled slowly

enough to prevent coring, solidification would be complete at P and a

uniform solid solution |3 would result. On continuing to cool slowly,

further solid changes would begin at Q with the precipitation of small

amounts of a at the grain boundaries of the (3. This a would increase in

amount as the temperature fell, and the |3 became progressively poorer

in tin. Hence the final structure would consist of crystals of uniform (3

containing about 98% lead with small amounts of a precipitated at the

crystal boundaries.

slowly, the structure would remain entirely

throughout, after its solidi-

fication had been completed at R.

9.63 In actual practice it is unlikely that cooling would be slow enough

to prevent some coring from taking place. Since the initial |3 dendrites

would then be relatively rich in lead, this could lead to the formation of

small amounts of a at the (3 grain boundaries in (c) and more than the

expected amount of a in (b). In case (c) this a would be absorbed on

annealing. 'Solution annealing' is an important process used in the treat-

ment of many alloys to absorb some constituent which has been precipi-

tated due to coring. After treatment the alloy will be soft and ductile and

able to receive cold-work. Solution annealing is also an integral part of

most strengthening processes based on precipitation hardening, the prin-

ciples of which will be discussed later (9.92).

Case V—A system in which a peritectic

transformation is involved

9.70 Sometimes in an alloy system two phases which are already present

interact at a fixed temperature to produce an entirely new phase. This is

known as a peritectic transformation. The term is derived from the Greek

'peri',

which means 'around', since, during the transformation process, the

original solid phase becomes surrounded or coated by the transformation

product. Frequently one of the interacting phases is a liquid though this is

not a precondition and sometimes two solids will take part—albeit very

slowly—in a peritecto/d transformation. A peritectic transformation occurs

between the phase 6 and the remaining liquid (producing austenite) in

the iron-carbon system (11.20) but here we will consider the peritectic

transformation which takes place in the platinum-silver system, part of

which is shown in Fig. 9.14.

COMPOSITION (°/o)

Fig.

9.14 The platinum-silver thermal equilibrium diagram.

(i) A slowly cooled alloy containing about 75% silver will first begin to solidify as uniform a

(ii) Below 1185°C these a crystals will become coated with 6 due to peritectic interaction

with the remaining liquid, (iii) The original a will be transformed slowly to 6 as the temperature

falls,

(iv) If cooling is extremely slow all a will be absorbed and the remaining liquid will

solidify as uniform 6. (v) In practice cooling will generally be so rapid as to 'trap' some a

'cores'

in the final structure, producing a non-equilibrium structure.

9.71 If we ignore coring effects, that is, assume a very slow rate of

cooling, the peritectic transformation will occur only in those platinum-sil-

ver mixtures containing between 12 and 69% silver. Let us first consider a

liquid of composition x, ie containing about 25% silver. This will begin to

solidify by depositing dendrites of the solid solution a of composition a. If

the rate of cooling is slow enough for diffusion to remove the effects of

coring, by the time the temperature has fallen to 1185°C the structure will

consist of a dendrites containing 12% silver (composition P) and a remain-

ing liquid containing 69% silver (composition R), since the composition of

a will change as it follows the solidus SP. At this stage:

Weight of a (composition P) X

Weight of remaining liquid (composition R) X

9.72 At 1185°C, the peritectic temperature, the a dendrites begin to

interact with the remaining liquid and form a new solid solution, 6, ie

a + liquid ^ 5

This solid solution b contains 55% platinum-45% silver (composition Q).

However the overall composition of the alloy is x\ (75% platinum-25%

liquid

CC + liquid

liquid

OC + S

liquid

silver) and it follows that not all of the a will be used up, since it is in

excess of that required to produce a structure entirely of 5. Therefore, all

of the liquid is used up and some a remains, so that the final structure will

consist of a containing 12% silver (composition P), and 5 containing 45%

silver (composition Q). These phases will be in a ratio given by:

Weight of a (composition P) X

Weight of 3 (composition Q) X

9.73 Let us now consider a liquid alloy of initial composition y. This

will begin to solidify by depositing crystals of a of composition ai, and if

we again neglect coring, the crystals will gradually change in composition

to P when the temperature has fallen to 1185

C, and again the composition

of the remaining liquid will be R. At this stage—

Weight of a (composition P) ^

Weight of remaining liquid (composition R) y

When the peritectic transformation takes place, we shall find that this time

there is an excess of liquid because yi lies between Q and R. The a will

therefore be completely used up, and just below 1185°C we shall be left

with the new solid solution, 8, and some remaining liquid in the ratio—

Weight of S (composition Q) y

Weight of remaining liquid (composition R) y

As the temperature continues to fall slowly, this remaining liquid will

solidify as 5, which will change in composition along Qy

. At y

solidifi-

cation will be complete and the structure will consist of crystals of uniform

5 of the same composition as that of the original liquid. In practice it is

unlikely that the rate of cooling would be slow enough to permit equilib-

rium being reached. Consequently, though the equilibrium structure is

indicated as being completely b (in the case of alloy y), remnants of the

original a dendrites may be present in the rapidly-cooled structure. The

original a dendrites, produced at temperatures above 1185°C, became

coated with a protective envelope of 8 as the interaction with the liquid

began and subsequent diffusion was far too slow to promote dispersal of

the remaining a.

Case Vl—Systems containing one or more

intermediate phase

9.80 Frequently two metals will not only form limited solid solutions with

each other but, in other suitable proportions, will also interact to form one

or more intermediate phases which may vary in nature from secondary

solid solutions to true intermetallic compounds. The formation of any

intermediate phase further complicates

the

thermal equilibrium diagram

by introducing extra boundary lines

and

since some alloy systems include

a number

intermediate phases, formed

different compositions

of the

two metals,

the

resulting diagram becomes increasingly complex.

9.81

will first examine

the

tin-magnesium system

(Fig. 9.15) as an

example containing

single intermediate phase—in this case

the

intermet-

allic compound Mg

Sn (containing 29.1% magnesium). This system

is rep-

resented

by two

simple equilibrium diagrams joined

at B. The

section

represents

eutectiferous series

of the

substances pure

tin and

Sn.

Here

solid solubility

involved

and

section

AB can

therefore

inter-

preted

in the

manner

Case

II (the

bismuth-cadmium system) dealt with

9.40. The

section

BC is a

eutectiferous series

of the

Case

type (9.60)

involving Mg

and the

solid solution

a. If we

consider

the

complete

system extending from pure

tin to

pure magnesium then, clearly, these

two

sections become joined

shown, forming

single diagram. Since Mg

intermetallic compound

single fixed composition

its

'phase field'

represented

on the

diagram

by a

vertical line

at 29.1%

magnesium.

particularly interesting feature

this diagram

that pure Mg

has a

melting point (778°C) which

higher than those

either

of the

constituent

pure metals. This

is an

indication

of the

stability

and

strong chemical

bonding

this valence-type compound.

9.82

will

now

consider

the

solidification

of a

representative alloy

the

series,

alloy

'x' (60%

tin-40% magnesium). This will begin

solidify when

the

temperature falls

to T and the

tie-line from

cuts

the

next phase boundary

at y

which represents

the

pure intermetallic

com-

liquid

OZ +

liquid

Fig.

9.15 The

tin-magnesium thermal equilibrium diagram, consisting essentially

of two

eutectiferous series—tin-Mg

and

Sn-magnesium.

COMPOSITION

(%>)

pound Mg

Sn. Therefore crystals of Mg

Sn begin to form. Since these

crystals are relatively tin-rich (70.9% tin) the composition of the remaining

liquid moves to the right to 'x{ and as the temperature falls to T\ more

Sn solidifies. Mg

Sn continues to solidify in this way until at 560

C the

remaining liquid contains 63.6% magnesium-36.4% tin—the composition,

E, of the Mg

Sn +a eutectic.

The remaining liquid then solidifies as eutectic at 560

C by depositing

alternate layers of Mg

Sn and the solid solution a, containing 85% mag-

nesium-15%

tin (composition S). When completely solid the structure will

consist of primary crystals of the intermetallic compound Mg

Sn sur-

rounded by a eutectic of Mg

Sn and a. If the solid alloy is then allowed to

cool slowly below 560

C, a will change in composition along the solvus line

SL by depositing particles of Mg

Sn which will join the Mg

Sn constituent

already present in the eutectic.

9.83 The large size of lead atoms compared with those of many other

metals contributes to the fact that lead forms relatively few solid solutions.

Thus lead and gold are to all intents and purposes insoluble in each other

in the solid state but, due to differences in the electrochemical properties

of the metals two intermediate phases, Au

Pb and AuPb

are formed at

the appropriate compositions. These two intermediate phases are produced

as a result of peritectic interactions and the resultant phase diagram is

shown in Fig. 9.16.

9.84 Consider an alloy containing 40% lead. This will begin to solidify

°c

liquid

Au + liquid

Pb + liquid

Fig.

9.16 The gold-lead thermal equilibrium diagram. Two intermediate phases are pro-

duced as a result of peritectic transformations.

COMPOSITION (o/o)

at about 500

C (T) by forming dendrites of gold, but on cooling to 418°C,

the first peritectic temperature, these gold dendrites undergo a peritectic

interaction with the remaining liquid to produce crystals of the intermedi-

ate phase, Au2Pb:

Au + liquid ^ AU2 Pb

These crystals of Au

Pb continue to grow as the temperature falls, but at

254°C a further peritectic interaction occurs resulting in the formation of

another intermediate phase AuPb

Pb + liquid ^± AuPb

During this second transformation all of the liquid is used up first and some

Pb remains along with the new phase AuPb

. Assuming that the system

has cooled slowly to room temperature these two phases will be present

in the ratio:

Weight OfAu

Pb _ BX

Weight of AuPb

~AX

_ 67.8-40

" 40 - 34.4

_27.8

9.85 An alloy containing 70% lead will begin to solidify at about 280

(Ti) by depositing crystals of Au

Pb but at 254°C a peritectic interaction

results in the formation of AuPb

. Here all of the Au

Pb is used up and

the remaining liquid continues to solidify as the new phase AuPb

until at

215°C the remaining liquid is of composition E (85% lead-15% gold). A

eutectic consisting of alternate layers of AuPb

and pure lead is then

formed so that the final structure consists of primary AuPb

in a eutectic

of AuPb

and lead.

In both of these cases it has been assumed that cooling has been slow

enough to permit equilibrium to be attained throughout so that peritectic

transformations proceed to completion. In practice this may not be so.

Thus in the 40% lead alloy more than the indicated quantity of Au

Pb may

be present in the microstructure whilst in the 70% lead alloy some Au

cores may be present even though the diagram indicates a AuPb

-lead

structure.

9.86 Sometimes an intermediate phase is of variable composition. Thus

the phase (3 in the tantalum-nickel phase diagram (Fig. 9.17) is based on

TaNi

but it may be thought of as being able to dissolve either excess

tantalum or excess nickel so that the phase field occupies width on the

diagram.