Higgins R.A. Engineering Metallurgy: Applied Physical Metallurgy

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COMPOSITION

Fig.

9.5.

This is generally referred to as the Lever Rule since it is as though we

were taking moments about P as the fulcrum. The relationship can be

expressed in more convenient form:

Weight of solid solution (composition X) PY

Weight of liquid solution (composition Y) PX

(d) A phase which does not occupy a field by

itself,

but appears only

in a two-phase field, is either a pure metal or an intermediate phase

TEMPERATURE

liquid

liquid 4- solid

solid

COMPOSITION

Fig.

9.6.

(usually an intermetallic compound) of invariable composition. In fact

the phase 'field' will be infinitely narrow such as is represented by the

100%

bismuth ordinate in Fig. 9.4 or the Mg

Sn ordinate in Fig. 9.15.

(e) If we draw a vertical line on a diagram this will represent the

composition of a given alloy (X in Fig. 9.6). If, on following along this

line,

a phase boundary is crossed (at O) the number of phases will change

by one at this point, ie a phase (|3) will be either precipitated or absorbed.

(In this instance (3 will be absorbed when the alloy X is heated above O

and precipitated again when the alloy X cools below O.)

We will now consider the main types of thermal equilibrium diagram

which are of use in studying metallic alloy systems. Generally a useful alloy

will only be formed when the two metals are completely soluble in each

other in the liquid state; but in some instances the two metals are only

partially soluble as liquids. We will begin with a brief study of one such

case.

Case

I—Two

metals which are only partially

soluble in each other in the liquid state

9.30 Fig. 9.7 represents the phase equilibrium conditions for the zinc-

lead system above 500

C. As in all of these equilibrium diagrams the base

line shows the composition varying between 100% of one component at

one side of the diagram to 100% of the other component at the opposite

side.

In most diagrams the percentages are by weight but in some cases it

is more relevant to indicate percentages in terms of numbers of atoms.

The ordinate represents temperature. Thus point P represents a mixture

consisting of 70% by weight of zinc and 30% by weight of lead at a tempera-

ture of 700

9.31 The diagram (Fig. 9.7) shows that at 500

C molten zinc will dis-

solve no more than 2% lead (point A) giving a single solution of lead in

zinc.

At the same temperature molten lead will dissolve about 5% zinc

(point B) thus giving a single solution of zinc in lead. However, any alloy

at 500

C which has a composition given by some point between A and B

will consist of two separate layers of two different liquid solutions—the

upper layer will be zinc containing 2% dissolved lead (composition A) and

the lower layer will be lead containing 5% dissolved zinc (composition B).

9.32 The slope of the line ADJC indicates that as the temperature rises

lead becomes increasingly soluble in molten zinc. Similarly the slope of

BEC shows that, under similar conditions, the solubility of zinc in molten

lead also increases. These two solubility curves meet at 798°C indicating

that at temperatures above this, the two metals become completely soluble

in each other so that a single liquid phase will be present in the mixture

whatever its overall composition.

9.33 Consider a molten mixture consisting of 70% zinc and 30% lead

(composition H). At 500

C this will consist of a saturated layer of lead in

COMPOSITION {%> by wt.)

Fig.

9.7 The zinc-lead thermal equilibrium diagram above 500

zinc (composition A) floating on top of a saturated layer of zinc in lead

(composition B). That is, it is a two-phase mixture.

If the temperature is now raised the amount of lead which dissolves in

zinc increases as does the amount of zinc which dissolves in lead. Thus at

700

C zinc will now dissolve 20% lead (composition D) whilst lead will

dissolve 20% zinc (composition E). Using the Lever Rule we can calculate

the relative proportions by weight of each layer:

Weight of zinc-rich layer Weight of lead-rich layer

(composition D)xDP

(composition E) x PE

Weight of zinc-rich layer (composition D) PE

Weight of lead-rich layer (composition E) DP

Substituting values from the diagram:

Weight of zinc-rich layer (80%Zn-20%Pb) _ 80-30

Weight of lead-rich layer (80%Pb-20%Zn) ~ 30-20

As the temperature of this 70-30 mixture is raised still further to 752°C

the two liquid phases merge into one, as the two metals become completely

soluble in each other at this composition.

KX)<*>Pb

O°A>Zn

°C

ONE LIQUID

TWO LIQUIDS

Case II—Two metals mutually soluble in all

proportions in the liquid state becoming

completely insoluble in the solid state

9.40 It is extremely doubtful whether such a situation as this really exists

in practice since most solid metals appear to dissolve quantities, however

small, of other metals. However, in the case of bismuth and cadmium the

mutual solid solubility is so small that we can neglect it for the sake of our

argument and assume that the metals are completely insoluble in the solid

state.

Bismuth, a heavy, brittle, slightly pink metal, is one of the least

'metallic' of metals as indicated by its position near to the non-metals in

the Periodic Table. It forms a complex rhombic-type crystal structure in

which the metallic bond is partly replaced by a mixture of covalent bonds

and van der Waals forces. Cadmium on the other hand crystallises as a

normal CPH structure so that it is not surprising that these two metals with

such unlike lattice structures do not form mixed crystals but separate out

almost completely on solidification. The bismuth-cadmium thermal-

equilibrium diagram is shown in Fig. 9.8.

9.41 Let us consider the solidification of an alloy of composition x, ie

containing about 80% cadmium and 20% bismuth. When the temperature

THE BISMUTH-CADMIUM

EQUILIBRIUM DIAGRAM.

LIQUID +

BISMUTH

LIQUID

LIQUID + CADMIUM

BISMUTH + CADMIUM

(Bi + EUTECTIC)

(Cd + EUTECTIC)

COMPOSITION PER CENT

BISMUTH

CADMIUM

EUTECTIC

LIQUID

THE RELATIVE RICHNESS OF THE

LIQUIO PHASE IN CADMIUM IS INDICATED

BY THE DISTANCE APART OF THE

SHADING LINES.

Fig.

9.8 The bismuth-cadmium equilibrium diagram.

falls to T, crystal nuclei of pure cadmium begin to form in accordance with

rule (b) stated in 9.24. (The temperature horizontal or tie-line, T, cuts the

liquidus at the chosen composition, x, and the other phase boundary is the

100%

cadmium ordinate.) Since pure cadmium is deposited, it follows

that the liquid which remains becomes correspondingly richer in bismuth.

Therefore the composition of the liquid moves to the left—say, to x\—

and, as indicated by the diagram, no further deposition of cadmium takes

place until the temperature has fallen to Ti. When this happens more

cadmium is deposited, and dendrites begin to develop from the nuclei

which have already formed. The growth of the cadmium dendrites, on the

one hand, and the consequent enrichment of the remaining liquid in bis-

muth, on the other, continues until the temperature has fallen to 140

The remaining liquid then contains 40% cadmium and 60% bismuth, ie

the eutectic point E has been reached.

At this point the two metals are in equilibrium in the liquid, but, due to

the momentum of crystallisation, the composition swings a little too far

past the point E, resulting in the deposition of a little too much cadmium.

In order that equilibrium shall be maintained, a swing back in composition

across the eutectic point takes place by the deposition of a layer of bismuth.

In this way the composition of the liquid oscillates about E by depositing

alternate layers of cadmium and bismuth, whilst the temperature remains

at 140

C until the remaining liquid has solidified. Thus the final structure

will consist of primary crystals of cadmium which formed between the

temperature T and 140

C, and a eutectic consisting of alternate layers of

cadmium and bismuth which formed at 140

9.42 Had the original liquid contained less than 40% cadmium, then

crystals of pure bismuth would have formed first, causing the composition

of the remaining liquid to move to the right until ultimately the point E

was reached as before, and the final liquid contained 40% cadmium and

60%

bismuth. This remaining liquid would solidify as eutectic in the

manner already described.

9.43 If the original liquid contained exactly 40% cadmium and 60%

bismuth at the outset, then no solidification whatever would occur until

the temperature had fallen to 140

C. Then a structure composed entirely

of eutectic would be formed as outlined above.

9.44 In all three cases mentioned, the eutectic part of the structure will

be of constant composition and will always contain 40% cadmium and 60%

bismuth. Any variation either side of this in the overall composition of the

alloy will be compensated for by first depositing appropriate amounts of

either primary cadmium or primary bismuth, whichever is in excess of the

eutectic composition. It is important to realise that there is no question

of solid solubility existing in any way in the final structure, whatever its

composition. With the aid of a microscope, we can see the two pure metals

cadmium and bismuth as separate constituents in the microstructure. In

other words, this is a case of complete insolubility in the solid state.

COMPOSITION (°/owt.)

Plate

9.1

Part

of the

aluminium-nickel thermal equilibrium diagram which includes

the

eutectic system between aluminium

and the

intermetallic compound

NiAI

The photomicrographs

two representative alloys

in the

cast condition

are

shown.

The 97-

3 alloy contains approximately equal amounts

primary aluminium crystals

(the

light areas)

and eutectic.

The

structure

of the

90-10 alloy consists

primary

NiAI

crystals (dark)

and

eutectic. Note

the

regular 'geometric' shape

of the

primary

NiAI

crystals—this

often

feature

intermetallic compounds.

The light aluminium layers

in the

lamellar eutectic

are

much broader than those

of the

dark

NiAI

because

the

eutectic composition contains only 5.7% nickel.

Case Ill—Two metals, mutually soluble

in all

proportions

in the

liquid state, remain mutually

soluble

in all

proportions

in the

solid state

9.50

number

pairs

metals fulfil these conditions

and are

generally

those

which:

(i)

the two

atoms concerned

are

compatible

terms

of the

atomic

size factor (8.23);

liquid

NiAI

+ liquid-

Al + liquid

(Al + eutectic)

(NiAI

• eutectic)

Al + NiAI

NiAI

(ii) the electrochemical properties of the two metals are very similar;

(iii) the crystal structures of the two pure metals are similar in pattern.

If these conditions are fulfilled it is reasonable to expect atoms of the

second metal to be able to replace atoms of the first in all proportions to

form a disordered solid solution. Such is the case in the alloy systems: Ag-

Au; Ag-Pd; Au-Pt; Bi-Sb; Co-Ni; Cu-Ni; Cu-Pt; Fe-Pt; Ni-Pt;

and Ta-Ti. (In some of these systems further phase changes occur in the

solid state due to polymorphic transformations (3.14)). Since the copper-

nickel alloys are the only ones of the group mentioned above which are of

use in engineering it is proposed to deal with this system. The cop-

per-nickel thermal-equilibrium diagram is shown in Fig. 9.9.

Again this is a simple type of equilibrium diagram, and since, as in the

cadmium-bismuth system, no transformations take place in the solid, the

diagram consists of two lines only—the liquidus and solidus. Above the

liquidus we have a uniform liquid solution for any alloy in the series, whilst

below the solidus we have a single solid solution for any alloy, though in

the cast condition, as we shall see, the solid solution may vary in concen-

tration due to coring. Between the liquidus and solidus both liquid and

solid solutions co-exist.

9.51 Applying the Phase Rule to that portion of the diagram above the

liquidus:

THE COPPER-NICKEL EQUILIBRIUM DIAGRAM.

LIQUID

SOLID

COMPOSITION PER CENT

IOO Ni

OC.

LIQUID

NICKEL RICH

SOLID SOLUTION

COPPER RICH

SOLID SOLUTION

Fig.

9.9 The copper-nickel equilibrium diagram.

The microstructures indicated are those obtained under non-equilibrium conditions of solidi-

fication.

p + F= C+ 1

1+F =2+1

and F = 2

since there are two degrees of freedom both temperature and composition

can be altered over fairly wide limits without upsetting the stability of the

single phase. However, for a point between the liquidus and solidus, ie in

'liquid + solid' field:

2 + F=2+ 1

and F = 1

There is thus one degree of freedom, and if either temperature or compo-

sition are altered independently of the other, then the system becomes

unstable so that some solid will melt or some liquid will solidify. Thus any

alteration in temperature must be accompanied by a change in overall

composition if the proportions of liquid and solid are to remain the same.

9.52 Consider the freezing of an alloy of composition A (Fig. 9.9), ie

containing 60% nickel and 40% copper. Assume that cooling is taking

place fairly rapidly, such as would be the case during the industrial casting

of slab ingots into cast-iron moulds. Above T

C the alloy will exist as a

uniform liquid solution, but as the temperature falls to T

C, dendrites of

solid solution will begin to form. They will not however be dendrites of

composition A but dendrites of composition B. This composition B is

indicated by drawing a tie-line from the liquidus at A (which represents

the composition and temperature of the original liquid) to the solidus,

Plate 9.2 70-30 cupro-nickel in the chill-cast condition, x 80.

This shows a mass of dendrites of heavily cored solid solution. The lighter cores are nickel-

rich whilst the copper-rich infilling has etched a darker colour.

which it cuts at B. Thus the dendrites which form will contain approxi-

mately 75% nickel (composition B) and, since the original liquid contained

only 60% nickel (composition A), it follows that the remaining liquid will

contain an even lower proportion of nickel. Hence its composition will

move to the left, say to A\.

Solidification will continue when the temperature falls further to T

, and

this time a layer of solid of composition B

will be deposited. This is less

rich in nickel than the original seed crystals and, as crystallisation proceeds,

successive layers will contain less and less nickel, and consequently more

and more copper, until ultimately the liquid is used up.

Clearly, then, a non-uniform solid solution is formed, and whilst its

overall composition will be 60% nickel and 40% copper, due to the coring

effect the initial skeleton of a crystal will contain about 75% nickel and its

outside fringes only about 50% nickel.

9.53 The situation is further influenced, however, by diffusion (8.23),

which is taking place simultaneously with crystallisation. Due to the fact

that successive layers of the alloy which deposit are richer in nickel than

the remaining liquid, a concentration gradient is set up which tends to

make copper atoms diffuse inwards towards the centre of the dendrite,

whilst nickel atoms move outwards towards the copper-rich liquid. In the

above case we have assumed very rapid cooling so that little or no diffusion

has been possible, and that under these conditions the structure has been

unable to reach equilibrium so that a heavily cored structure forms. Since

we are dealing with non-equilibrium conditions, only a limited amount of

information can be obtained from the equilibrium diagram—in this case a

guide as to why the cored structure develops. If cooling were slow, dif-

fusion could take place extensively so that coring would be slight in the

final crystals. Annealing at a sufficiently high temperature will also permit

diffusion to proceed (8.24), resulting in the formation of almost completely

uniform solid-solution crystals.

9.54 We will now consider the cooling of the same alloy under con-

ditions which are ideally slow so that complete equilibrium is attained at

each stage of solidification. The liquid (composition A, Fig. 9.10) will begin

to solidify at temperature T by depositing nuclei of composition B. This

causes the composition of the remaining liquid to move to the left, but,

due to the prevailing slow cooling, diffusion is able to keep pace with

TEMPERATURE

LIQUID

LIQUID + SOLID

SOLID

COMPOSITION PER CENT

Fig.

9.10.

solidification

that,

as the

composition

of the

liquid follows

the

liquidus

from

A to A

, the

composition

of the

solid follows

the

solidus from

B to

Thus,

some temperature

Ti, the

composition

of the

uniform solid

solution

given

by B\,

whilst that

of the

remaining homogeneous liquid

in equilibrium with

it is

given

by A\.

Since

the

overall composition

of the

alloy

indicated

by X

(which

is the

same

as A)

then,

by the

Lever Rule:

Weight

solid solution (composition

) XA

Weight

remaining liquid solution (composition

) XB

the

temperature

the

last trace

liquid (composition

) has

just

solidified

at the

crystal boundaries

and, by the

process

diffusion,

its

composition

has

changed

that

of the

remainder

of the

structure which

has adjusted itself

uniform

throughout.

A and B

course represent

the same composition, which

obvious, since

single uniform liquid

sol-

ution

has

been replaced

by a

single uniform solid solution.

9.55 When

two

metals form

substitutional solid solution some distor-

tion

of the

lattice

inevitable

due to

influences such

different atom size.

In some cases

the two

metals

are

only just compatible

and

although they

are still soluble

in all

proportions

in the

solid state

phase diagram

of the

type shown

in Fig. 9.11

results.

minimum melting point (32.8

produced where liquidus

and

solidus

are

congruent.

The

significance

this

minimum point

that

the

metals

are so

incompatible

solid solution that

there

is a

strong tendency

for

them

return

to the

disordered liquid state

liquid solution

liquid

solid

solid solution

liquid

solid

COMPOSITION (^>wt)

Fig.

9.11 The potassium-rubidium thermal equilibrium diagram.