THE MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATIONFEDERAL STATE BUDGETARY EDUCATIONAL INSTITUTION OF HIGHER EDUCATION

«GUBKIN RUSSIAN STATE UNIVERSITY OF OIL AND GAS (NATIONAL RESEARCH UNIVERSITY)»

DEPARTMENT OF PHYSICAL METALLURGY AND NON-METAL MATERIALS

S.P. GRIGORIEV, V.P. EROSHKIN, А.P. EFREMOV,B.M. KAZAKOV, G.А. TROFIMOVA

LABORATORY WORK NO 2

THERMAL ANALYSIS OF LEAD-ANTIMONY ALLOYS AND PLOTTING PHASE DIAGRAM

for students of all disciplines

Edited by prof. A.K. PRYGAEVEnglish translation assist. I.O. SELEZNEVA

Moscow – 2016

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Objective

To get familiar with the methods of thermal alloy analysis and practical

plotting phase diagrams.

Task

1. To conduct thermal analysis of lead-antimony alloys having different

component ratios.

2. Determine the critical temperature for each investigated alloy.

3. To plot an approximate phase diagram for lead-antimony alloys.

4. To master the phase and segment rules.

Basic information Alloys are complex substances obtained through fusing two or more

components. The structure of alloy depends on interactions between components

making the alloy. Depending on the type of interaction the three types of alloys can

be formed: mechanical mixtures, solid solutions or chemical compounds. The alloy

of Pb - Sb system belongs to the "mechanical mixture" type. The mechanical

mixture is formed when components forming the alloy are mutually soluble in liquid

state, non-soluble in solid state and do not form chemical compounds. The specificity

of crystallization of alloys of mechanical mixture type can be examined using an

example of Pb-Sb alloys having the following composition:

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1. 5%Sb and 95%Pb

2. 13%Sb and 87%Pb

3. 30%Sb and 70%Рb

Cooling curves of these alloys are shown in Figs. 1, 2, 3.

The cooling curve of alloy containing 5% Sb and 95% Pb consists

of four sections (Fig. 1)

1 - cooling alloy in the liquid state;

2 - crystallization of the excess component (Pb) in the temperature range T1- T2 ;

3 - simultaneous crystallization of lead and antimony at a constant temperature

T2.

4 - - cooling alloy in the solid state.

Crystallization of alloy begins at a temperature of T1 (the upper critical

temperature), and develops at variable temperatures down to T2 (the lower critical

temperature).

In the temperature interval T 1 --- T2 the excess component crystals (Pb)

precipitate from the liquid phase.

If Pb crystals precipitate from the liquid Pb concentration in the liquid

phase decreases, and concentration of Sb in the liquid phase increases. During

the crystallization process concentration of components in the liquid phase tends

to change approaching the concentration (13% Sb and 87% Pb), when both

components (Pb and Sb) precipitate as crystals from the liquid together

simultaneously. The simultaneous crystallization of antimony and lead develops

at a constant temperature.

Both components develop the phase transition simultaneously in the liquid

phase of alloy containing 13% Sb and 87% Pb (Fig. 2). As a result, a

homogenous mechanical mixture is formed. A composition consisting of two or

more solid phases which crystallized simultaneously from a liquid phase is called

eutectic.

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In alloy containing 30% Sb and 70% Pb the crystallization process starts at

temperature T1. The component excessive to that of eutectic concentration starts

crystallizing first; in our case this is Sb (Fig. 3). If crystals of antimony are formed in

the liquid phase then the liquid phase is enriched with lead through the crystallization

process. As soon as the concentration of components in the liquid phase reaches an

eutectic concentration (i.e., 13% Sb and 87% Pb), the joint crystallization of both

components starts at a constant temperature T2.

The cooling curves show that all alloys of Pb - Sb system get finally solidified at a

constant temperature T2. This suggests that the portion of molten alloy solidified at a

constant temperature T2 has a constant composition. This composition corresponds to

alloy containing 13% Sb and 87% Pb. The temperature at the end of crystallization is

independent of alloy concentration for mechanical mixture alloys; it is constant for all

alloys. The onset crystallization temperature varies depending on concentration of

components in alloy.

oC

Т1

Т2

L

L + Рb

L Рb + Sb

Pb + (Pb + Sb)

Time

Fig. 1. Cooling curve plotted for hypoeutectic alloy

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Tem

pera

ture

oC

Тcr

L

L Рb + Sb

(Рb + Sb)

Time

Fig.2. The cooling curve of eutectic alloy

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Tem

pera

ture

L

L + Sb

L Рb + Sb

Sb + (Рb + Sb)

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0С

Т1

Т2

Time

Fig. 3. The cooling curve plotted for hypereutectic alloy

Tem

pera

ture

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Plotting phase diagrams

The diagram is a graphical representation of alloy phase plotted as a function

of the temperature and concentration of components.

The phase diagram can be plotted according to the cooling curves of alloys

having different composition.

Phase diagrams of alloys consisting of two components are developed in

coordinates temperature vs. concentration (Fig. 4). The temperature is plotted along

ordinate. The concentration is plotted on abscissa. The total content of both

components in alloy should equal to 100%. Sb concentration increases in alloy along

abscissa from 0 to 100% therefore the concentration of Pb in the alloy will increase

in direction from right to left. Thus, the extreme ordinates correspond to pure Pb and

Sb components. Values of crystallization temperatures for Pb and Sb corresponding

to pure components are plotted on y-axis. Then, based on the thermal analysis of Pb -

Sb alloys having different content of components the cooling curves are plotted to

determine the crystallization onset temperature T1 and the final crystallization

temperature T2.

Temperatures T1 and T2 are plotted on the vertical axis corresponding to

concentration of the alloy for each alloy. A smooth line is developed to connect

crystallization temperature of pure metals and the crystallization onset temperatures

T2 the curve corresponding to the onset of equilibrium crystallization of alloys is

called liquidus (АСВ).

The curve going through the points corresponding to the end of crystallization

is called solidus (DCE).

Above liquidus alloy is liquid, below solidus it is solid. The alloy containing

13% Sb is eutectic. Alloys having less than 13% Sb are called hypoeutectic; if Sb is

higher than 13% the alloys are referred to as hypereutectic.

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In hypoeutectic alloys the crystallization process starts below AC line and Pb

crystals are formed from the liquid phase; in hypereutectic alloys Sb crystals are

formed below GB line. Consequently, there are two phases existing in CBE area: L +

Pb, in CBE domain there are two phases exist: L + Sb.

The concentration of the liquid phase changes approaching the eutectic one

during crystallization in hypoeutectic and hypereutectic alloys. The liquid phase

having eutectic concentration generates simultaneously Pb and Sb crystals along

DCE line, meaning that eutectic gets crystallized:

Ll Pb +Sb

3Phase diagram Pb-Sb

T0CB 630

L

327 A

T1

CD

bT1

L+Sb

ET2 T1;T2 T2

Pb+Sb

Pb 0 5 10 20 30 40 50 60 70 80 90 100, % SbSb

Pb

L+Pb

13

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Rule of phase

Phase diagrams give an idea of crystallization processes in alloys showing

the region of existence of alloys in liquid and solid states and the crystallization

range enabling to determine the equilibrium composition of liquid and solid

phases at any stage of crystallization.

The crystallization process obeys the phase rule which sets forth the

quantitative relationship between degree of freedom in the system and the

number of phases and components.

A homogeneous part of inhomogeneous system separated from other parts

of the system (phase) by an interface is called a phase; crossing the interface

results in abrupt change in the chemical composition or in structure of

compound.

For the conditions when all transformations occur at a constant pressure

the phase rule is expressed through equation

С= к f + 1

where: С - C is the number of degrees of freedom, i.e.

the number of external (temperature) and internal

(concentration) parameters that can be changed without

changing the number of phases in the system

к - is the number of components;

f - is the number of phases.

From the standpoint of the phase rule the process of crystallization of Pb-

Sb alloys is represented in the following manner. When molten alloy is cooling

there are two degrees of freedom:

C = к f + 1= 2 - 1 + 1 = 2

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This means that the temperature can be changed within a limited range and/or

the concentration of the liquid solution can vary through adding lead or antimony

leaving the alloy in a single phase (liquid solution).

When crystals are formed in the supersaturated solution (between the solidus

and liquidus lines).

С = к f + 1 = 2 - 2 +1= 1.

This means that within certain limits it is admissible to raise or lower the

temperature but the number of phases remains equal to two:

a liquid solution and solid crystals.

When eutectic is formed (solidus line), the number of degrees of freedom is

equal to 0, as:

С = к f + 1= 2 3 + 1= 0,

implying that the eutectic crystallization process develops at a constant

temperature and the concentration of antimony in each phase is strictly constant,

namely in the liquid phase 13% Sb, in solid antimony crystals - 100% Sb, in solid

lead crystals 100% Pb.

Rule of segments

To determine the quantitative ratio of phases and concentration in phases it is

possible to apply the rule of segments (or lever rule).

Consider a phase diagram of Pb-Sb alloy with an initial concentration К. At

temperature Т the alloy is composed of antimony and liquid crystals. To determine

the phase composition a line is drawn through a given point а to intersect the

boundaries of the phase diagram. The projection of point в on the concentration axis

gives the liquid phase composition, and the projection of c point gives the

composition of the solid phase. The diagram shows that when the temperature

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decreases during crystallization the composition of the liquid phase changes along

the liquidus line tending to the eutectic concentration whereas the composition of

the solid phase remains constant.

The phase ratio changes during crystallization: the volume of solid phase

increases, and the volume of liquid phase decreases.

Let’s denote the weight of the liquid phase as Ql, and the weight of the solid

phase as Qs designating the total weight of the liquid and solid phases through Q. If

we write the equation of moments relative to point a, then:

Ql ав = Qs ас; Ql / Qs = ас/ав; Ql / Q = ас/вс ; Ql = ас/вс x 100%;

Qs / Q = ав/вс ; Qs = ав/вс x 100%

Methodology

The workflow methodology is similar to that of work No I. The studies are

carried out using the same experimental installation. The results of the thermal

analysis of each of three alloys are registered in the table.

Table 1

Readout number Galvanometer

readings, mV

Note

5 % Sb 13 % Sb 30 % Sb Readouts are taken every 30

seconds.

1.

2.

3.

etc.

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The results of the thermal analysis are used to build cooling curves in EMF -

time coordinates, where the value of EMF1 (corresponding to the crystallization

onset) and EMF2 (corresponding to the end of crystallization) should be determined.

Using the calibration curve (taken from laboratory work № 1) the EMF value is

used to determine the upper and the lower critical temperature in 0С. These data are

also put down in tabular format (Table 2).

Table 2

Metal

or alloy

Upper critical temperature

Т1

(the beginning of crystallization)

Lower critical

temperature Т2 ,

(completion of

crystallization)

EMF oC EMF oC

0 % Sb (pure lead) 5 %

Sb, 95 % Pb

13 % Sb, 87 % Pb

30 % Sb, 70 % Pb

100 % Sb (pure antimony).

Based on the data given in Table 2 a phase diagram can be developed for the lead-antimony system.

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Report format

The report should provide for the following:

1. The statement on the purpose of work and assignment of implementation.

2. The results of measuring EMF should be provided for all alloys (Table 1).

3. The critical temperature should be assessed for lead, antimony and their alloys (Table 2).

4. The approximate diagram of state should be built based on experimental results for

Pb - Sn alloys.

References

1. Solntsev Y.P., Pryakhin E.I., Voytkun L. Material science. Moscow, MISA, 1999,

477 p. (in Russian).

2. Lakhtin Y.M. Metallurgy and Hot Metal Processing: Moscow, Metallurgy, 1993, 447 p. (in

Russian).