An Analysis of the Structural and Physical Stability of Quenched … · 2014-03-05 · Mustafa...

International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 119

I J E N S IJENS © February 2014 IJENS -IJET-3535-001149

An Analysis of the Structural and Physical Stability of

Quenched Ribbons Pb-Sn-Sb-Ca Alloys for

Electrowinning

Mustafa Kamal, Shalabia Badr and Nermin Ali Abdelhakim* Metal Physics Lab. Physics Department, Faculty of Science –Mansoura University, Egypt

*M.Sc student, Demonstrator, Metal physics, Mansoura University

[email protected] , [email protected]

Abstract-- The object of the present work is to investigate the

effect of rapid cooling from melt on structure ,electrical and

mechanical properties of Pb-5%Sn , Pb-5%Sn-2%Sb , Pb-

5%Sn-2%Sb-0.5%Ca , Pb-5%Sn-2%Sb-1%Ca , Pb-5%Sn-

2%Sb-1.5%Ca , Pb-5%Sn-2%Sb-2%Ca , Pb-5%Sn-2%Sb-

2.5%Ca (in wt%) ,melt spun ribbons for electrowinning. For this

purpose the structure, resistivity, elastic moduli, Debye

temperature and hardness tests were examined by x-ray

diffraction, double bridge circuit, dynamic resonance technique,

and Vickers microhardeness tester respectively. Experimental

results have shown that the total resistivity pronounced minima

at composition of Pb-5wt%Sn-2wt%Sb-1wt%Ca . This

correspond to formation of ordered alloys.

Index Term-- Quenched ribbons, Electrowinning, Resistivity,

Elastic moduli, Debye temperature, Spalling and Microhardness.

I. INTRODUCTION

Lead alloys are used in a battery for grids and for top metal

.Tin in both lead-calcium and lead-antimony alloy has been

the subject of considerable research. They have also been

developed for electric vehicle battery technology [1] . Various

lead alloys have been designed to increase the strength of the

material and reduce the deformations and distortions during

operational life of the anodes without impairing the corrosion

resistance of the base material .The anodes are made from

metals that can resist the evolution of oxygen and corrosive

conditions of the both [2]. So lead and tin based alloys are

widely used as engineering materials in bush bearing

applications. A uniform distribution of a hard SnSb

Intermetallics compound in a ternary eutectic matrix provides

wear resistance of alloy [3]. During the last decades, there

has been a major change in the composition of lead alloys

used for positive grids in automotive batteries and stationary

lead-acid batteries[4]. Grids for automotive batteries have

changed from lead-antimony alloys to lead-calcium and lead-

calcium-tin alloys [5]. Abouhilou et al [6] reported that

recrystallization texture of Pb-Ca-Sn alloy subjected to rolling

room temperature to different final thickness is a retained

deformation texture with an emerging cube component. For

these reasons the interesting marked for maintenance-free

batteries has promoted the development of lead base

containing calcium alloys. These alloys show better

mechanical and electrochemical properties of the anodes in

electrolyses. Although voluminous studies have been

conducted on understanding the properties of lead alloys , the

studies on the mechanical properties and structural analysis

are limited. The aim of the work is to present the results of a series of

studies carried out to evaluate the effect of chill-block melt-

spinning technique on the structural, physical, mechanical and

dimensional quality properties of Pb-Sn-Sb-Ca alloys used for

electrowinning circuit.

II. EXPERIMENTAL METHODS The experiment techniques utilized have been described in

details in refs [7-10] and will be repeated here only briefly. Alloys were prepared

from high-purity elements by conventional melting

techniques; quantities of about 20 mg were then rapidly

solidified from melt and quenched onto the rotating copper

wheels at room temperature, using melt-spinning technique

[11]. The material flow rate Qf has been empirically found to

be an important chill block melt-spinning process variable and

its dependence on readily adjustable apparatus parameters has

been described by Liebermann [12] . In the present study

this parameter is calculated from

Qf =VrW t (1)

Where Vr is the ribbon or substrate velocity, W is the ribbon

width and t the average thickness calculated by dividing the

ribbon mass by length , density and width

(2)

These quenched ribbons were investigate by x-ray diffraction,

using Cu kα radiation. The lattice parameter values were

obtained from forward reflections up to 2θ=90 using the

known reflections of the copper substrate as an internal

standard, the maximum fractional error in the reported lattice

parameters is which corresponds to about

A0

for lattice parameter of lead. All lattice parameter

are given for the quenched ribbons at room temperature.

Electrical resistivity was calculated using the double bridge

mailto:[email protected]%20,%[email protected]



circuit, the hardness measurements were carried out using

vickers microhardness tester. A dynamic resonance circuit was

used to calculate the elastic moduli, internal friction and

thermal diffusivity after determining the resonance frequency

[13-17].

III. RESULTS AND DISCUSSIONS A. X-ray Diffraction Analysis

Rapid quenching of metallic alloys from melt was first carried

out by Pol Duwez et al [18,19]. They found that the rapid

quenching extends the solid solubility limits and produce non-

equilibrium phase or amorphous alloys [20]. Fig ( I ) produces

an x-ray diffraction pattern of Pb pure, Pb-5%Sn ,Pb-5%Sn-

2%Sb , Pb-5%Sn-2%Sb-0.5%Ca , Pb-5%Sn-2%Sb-

1%Ca , Pb-5%Sn-2%Sb-1.5%Ca , Pb-5%Sn-2%Sb-2%Ca ,Pb-

5%Sn-2%Sb-2.5%Ca (in wt%) rapidly quenched from melt

(5000C), the pattern shows the existence of three kinds of

phases ,Pb-phase with face centered cubic structure, Sn-phase

with tetragonal structure and Antimony tin phase with

rhombohedral (hex) structure. A cubic crystal gives diffraction

lines whose sin2

θ values satisfy the following equation,

obtained by combining the Bragg law with the plane-spacing

equation for the cubic system:

Since the sum (h2+k

2+l

2) is always integral and

is a

constant for any one pattern. The problem of indexing the

pattern will yield a constant quotient when divided by one

into the observed sin2θ values . The lattice parameter a,

calculated from the sin2θ value for the highest-angle line,

which indicated in table (I).

Lattice parameter of the Pb-phase is plotted in fig (II) against

composition for the specimens quenched from melt. Slightly

changed in the lattice parameter a and the diffraction intensity

were observed in a month or more after quenching, showing

that the structure is very stable at room temperature.

The number of atoms per unit cell in any metal crystal is

partially dependent on its bravais lattice. The number of

atoms per cell in a face centered lattice must be a multiple of

4. Turning to the crystal structure of compounds of unlike

atoms, it is find that the structure is built on the skeleton of a

Bravais lattice, but that certain other rules must be obeyed,

precisely because these are unlike atoms present [21]. So the

next step is to find the number of atoms per unit cell in lead –

phase in the melt spun-ribbons. To find this number we use

the following equation

∑

(4)

Where ρ =density (gm/cm3), ∑ =sum of the atomic weights

of the atoms in the unit cell and V is the volume of the unit

cell .

0

1000

2000

3000

4000

5000

6000

7000

20 30 40 50 60 70 80 90In

ten

isty

(a.u

)

2

Pb pure

Pb

(11

1)

Pb

(20

0)

Pb

(22

0)

Pb

(31

1)

Pb

(22

2)

Pb

(40

0)

Pb

(33

1)

Pb

(42

0)

2θ(degree)

0

1000

2000

3000

4000

5000

6000

7000

20 30 40 50 60 70 80 90

Inte

nis

ty(a

.u)

2θ(degree)

Pb

(11

1P

b(2

00

)

Sn(2

11

)

Pb

(22

0)

Pb

(31

1)

Pb

(22

2)

Pb

(31

2)

Pb

(42

0)

Pb-5%Sn

Pb

(33

1)

(b)

0

2000

4000

6000

8000

10000

20 30 40 50 60 70 80 90

Inte

nis

ty(a

.u)

2θ(degree)

Pb-5%Sn-2%Sb

SnSb

(20

0)

Pb

(11

1)

Pb

(20

0)

SnSb

(22

0

Pb

(22

0)

Pb

(31

1)

Pb

(22

2)

Pb

(33

1)

Pb

(42

0

SnSb

(42

2

(c)

a of Pb phase

(A0)

Melt-spun ribbons

64;66 Pb-5wt%Sn

64:: Pb-5wt%Sn-2wt%Sb

64;7 Pb-5wt%Sn-2wt%Sb-0.5wt%Ca

64;7 Pb-5wt%Sn-2wt%Sb-1wt%Ca




Table I

(3)

(a)

24

2

222

2sin

alkh

Fig(I)



From the equation (4) we have

∑ =

∑ = n A Where n is the number of atoms per unit cell, A is the

molecular weight. When determined in this way , the number

of atoms per cell is always an integer , within experimental

error . In our experimental work the melt spun ribbons of

Pb-5%Sn , Pb-5%Sn-2%Sb , Pb-5%Sn-2%Sb-0.5%Ca , Pb-

5%Sn-2%Sb-1%Ca , Pb-5%Sn-2%Sb-1.5%Ca , Pb-5%Sn-

2%Sb-2%Ca , Pb-5%Sn-2%Sb-2.5%Ca (in wt%) as indicated

in the table (II) , atoms are simply missing from a certain

fraction of those lattice sites which they would be expected to

occupy , and the result is a nonintegral number of atoms per cell.

0

1000

2000

3000

4000

5000

6000

7000

8000

20 30 40 50 60 70 80 90

Inte

nis

ty(a

.u)

2θ(degree)

Pb-5%Sn-2%Sb-0.5%Ca

SnSb

(20

0

Pb

(11

pb

(20

0Sn

Sb(2

2

Pb

(22

Pb

(31

1)

Pb

(22

2)

SbSn

(42

0

SbSn

(42

Pb

(33

1)

Pb

(42

0)

(d)

0

1000

2000

3000

4000

5000

20 30 40 50 60 70 80 90

Inte

nis

ty(a

.u)

2θ(degree)

SnSb

(20

0)

Pb

(11

1)

Pb

(20

0)

SnSb

(22

0)

SnSb

(22

2)

Pb

(31

1)

Pb

(22

2)

SnSb

(42

0)

SnSb

(42

2)

Pb

(33

1)

Pb

(42

0)

Pb-2%Sn-2%Sb-1%Ca

(e)

0

1000

2000

3000

4000

5000

6000

20 30 40 50 60 70 80 90

Inte

nis

ty(a

.u)

2θ(degree)

SnSb

(20

0)

Pb

(11

1)

Pb

(20

0)

SnSb

(22

0)

SnSb

(22

2

Pb

(31

1)

Pb

(22

2)

Sb(3

00

)

Pb

(33

1)

Pb

(42

0

Pb-5%Sn-2%Sb-1.5%Ca

(f)

0

1000

2000

3000

4000

5000

6000

20 30 40 50 60 70 80 90

Inte

nis

ty(a

.u

2θ(degree)

Pb

(11

1)

Pb

(20

0)

SnSb

(22

2)

Pb

(31

1)

Pb

(22

2)

SnSb

(42

2)

Pb

(33

1)

Pb

(42

0)

Pb-5%Sn-2%Sb-2%Ca

(g)

0

1000

2000

3000

4000

5000

6000

7000

20 30 40 50 60 70 80 90

Inte

nis

ty(a

.u)

2θ(degree)

SnSb

(20

0)

Pb

(11

1)

Pb

(20

0)

SnSb

(22

0)

Pb

(22

0)

Pb

(31

1)

Sb(3

00

)

Pb

(33

1)

Pb

(22

2)

Pb

(42

0)

Pb-5%Sn-2%Sb-2.5%Ca

(h)

n(No of

atoms/unit

cell)

Melt-spun ribbons

548:7 Pb-5wt%sn

44;7: Pb-5wt%Sn-2wt%Sb

44:8 Pb-5wt%Sn-2wt%Sb-0.5wt%Ca

549 Pb-5wt%Sn-2wt%Sb-1wt%Ca



5478 Pb-5wt%Sn-2wt%Sb-2.5wt%Ca

(5)

Table II



0.0 0.5 1.0 1.5 2.0 2.5

4.87

4.88

4.89

4.90

4.91

4.92

4.93

4.94

4.95

4.96a

(A

0)

Calcium content in (wt%)

B. Particle Size and Lattice Disorder

The broadening of an observed diffraction peak can be

characterized by its full width at half maximum (FWHM)

value at a particular 2θ angle. Since the FWHM values are

estimated from peak areas, heights in automatic peak

search, they may not be precise enough to be used to

establish the instrumental FWHM curve. Previous work

[22] suggests that the broadening is produced by either

lattice strains alone, or by lattice strain and small particle

simultaneously. The rapid quenching from the melt of metallic

alloys using spinning technique [11] has been shown to

produce appreciable changes in the intensity distribution of

diffracted x-rays. The most prominent of these effects are

changes in line shape and in integrated intensity [23]. Changes

in integrated intensity have been studied and discussed by Hall

and Williamson [24] and it is object of this section to interpret

and correlate the changes in line shape with the simultaneous

measurements of integrated intensity. Line width B, both

FWHM and integral, were used in a Williamson –hall plot

[25] as illustrated in Fig(III) .

To derive information about the size of crystallite size, Deff

and local distortions in the lead phase

B =

+ Sin

The

and parameters are given in

table (III).

Table III

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.1 0.2 0.3 0.4 0.5

FWH

M

Sin(θ)/λ

Pb pure (a)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.1 0.2 0.3 0.4 0.5

FWHM

FWH

M

Sin(θ)/λ

Pb-5%Sn (b)

1/Deff

(A0-1

)

aof Pb

phase

(A0)

Melt-spun ribbons

0.001025 2422468; 64;66 Pb-5wt%Sn

24223495 24225364 64:: Pb-5wt%Sn-

2wt%Sb

24223339 242248:6 64;7 Pb-5wt%Sn-

2wt%Sb-0.5wt%Ca

24223754 2422598 64;7 Pb-5wt%Sn-

2wt%Sb-1wt%Ca

242233;4 2422444: 64;6 Pb-5wt%Sn-

2wt%Sb-1.5wt%Ca

242233;9 24224;88 64;6 Pb-5wt%Sn-

2wt%Sb-2wt%Ca

242232;8 2422486: 64;7 Pb-5wt%Sn-

2wt%Sb-2.5wt%Ca

(6)

Fig(III)

Fig(II)



It is found that for lead phases in Pb-5%Sn , Pb-5%Sn-

2%Sb ,Pb-5%Sn-2%Sb-0.5%Ca , Pb-5%Sn-2%Sb-1%Ca ,

Pb-5%Sn-2%Sb-1.5%Ca , Pb-5%Sn-2%Sb-2%Ca, Pb-5%Sn-

2%Sb-2.5%Ca (in wt%) is immeasurably low , hinting to a

good crystallization state . Lattice distortions for lead phase in

all the melt-spun ribbons are very low as indicating in the

table ( III ) . This supports the optimum formation of face-

centered cubic structure phase close to the average electron

number per atom (electron concentration) e/a=4 as indicating

0

0.1

0.2

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5 0.6

Pb-5%Sn-2%Sb (c) FW

HM

Sin(θ)/λ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.1 0.2 0.3 0.4 0.5

Pb-5%Sn-2%Sb-0.5%Ca (d)

FWH

M

Sin(θ)/λ

0

0.1

0.2

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5 0.6

Pb-5%Sn-2%Sb-1%Ca (e)

FWH

M

Sin(θ)/λ

0

0.1

0.2

0.3

0.4

0.5

0.1 0.2 0.3 0.4 0.5 0.6

Pb-5%Sn-2%Sb-1.5%Ca (f)

FWH

M

Sin(θ)/λ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.1 0.2 0.3 0.4 0.5

Pb-5%Sn-2%Sb-2%Ca (g)

FWH

M

Sin(θ)/λ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.1 0.2 0.3 0.4 0.5 0.6

Pb-5%Sn-2%Sb-2.5%Ca (h)

FWH

M

Sin(θ)/λ



in the table (IV) ,reflecting to the atoms in the lead-phase are

arranged in ordered manner. Such configuration is inherently

of lower energy and thereby more stable than a purely random

arrangement of atoms [26].

Table IV electron concentration (e/a) of crystalline phases in the Pb-Sn-Sb-Ca melt

spun ribbons

IV. THE ELECTRICAL PROSPERITIES OF Pb-Sn-Sb-Ca

QUENCHED RIBBONS: The electrical conductivities of Pb-Sn-Sb-Ca rapidly solidified

from melt and their dependence on temperature and

composition provided the main challenge to theories of the

metal physics. They continue to be among the central

concerns of a wide range of metalophysicists concerned with

bearing lead alloys and their electrowinning applications. In

this part we shall be concerned with understanding some of

electrical properties of Pb-Sn-Sb-Ca quenched ribbons. The

electronic structure of alloys is the subject of much current

research. The scattering that produce electrical resistivity is

due to some kind of disorder produced by the mixing of two or

more constituents in random arrangements. If, however the

constituents are able to take up an ordered configuration this

should be reflected in the resistivity of Pb-Sn-Sb-Ca rapidly

solidified from melt. In fig (IV) the resistivity of melt-spun

ribbons Pb-5%Sn ,Pb-5%Sn-2%Sb , Pb-5%Sn-2%Sb-0.5%Ca

, Pb-5%Sn-2%Sb-1%Ca , Pb-5%Sn-2%Sb-1.5%Ca , Pb-

5%Sn-2%Sb-2%Ca , Pb-5%Sn-2%Sb-2.5%Ca (in wt%)

shown as a function of calcium content.

0.0 0.5 1.0 1.5 2.0 2.5

2

4

6

8

10

12

14

16

18

Re

sis

tivity(o

hm

.m)

Calcium content in (wt%)

The resistivities here are measured around room temperature

so that the total resistivity pronounced minima at composition

of 1wt%Ca. This corresponds to the formation of ordered

alloys. Moreover, by addition of Ca to Pb-Sn-Sb solid solution

formation causes a pronounced increase of electrical

resistivity. In multiphase alloys the electrical conductivity

tends to change proportionally with composition between the

electrical conductivity of the phases. Factors affecting the

collision processes or as it is usually called the problem of

scattering ,such as static imperfections, lattice vibrations,

magnetic ions or by scattering by more than one mechanism

operate at the same time, all reduce the electrical conductivity

of a metallic alloy , because these imperfections mean that

there are irregularities in the electrical fields within a metal.

Irregularities reduce the mobility of an electron and finally the

electrical conductivities [26] , Table (V) gives a list of

electrical conductivities and other transport parameters for

Pb93-x-Sn5-Sb2-Cax rapidly solidified from melt using the melt

spinning techniques. Values of drift velocity Vd ,electron

mobility𝜇 ,fermi wave vector Kf and the value of relaxation

time 𝜏,for electron collisions are also given.

e/a Melt-spun ribbons

6 Pb-5wt%Sn

64254 Pb-5wt%Sn-2wt%Sb

54;; Pb-5wt%Sn-2wt%Sb-0.5wt%Ca





Fig. IV



Table V

V. HEAT CONDUCTIVITY

The thermal conductivity changes in approximately the same

way as was developed for electrical conductivity of metals.

Whereas both processes are due to electron transport they rely

on different aspects, namely flow of charge and flow of

energy .However, whereas in pure metals the heat

conductivity was related to the electrical conductivity by the

well-known widemann-franz law [27-29 ] is given by

(7)

The constant is termed Lorenz number, and is the thermal

conductivity. In metallic alloys the changes in electrical

conductivity with composition do not follows the changes in

electrical conductivity according to this ratio, the changes

being in the same direction but to a different degree. Some

investigations [30] have shown that there is a definite

relationship between the electrical and thermal conductivity of

metallic alloys, although the wiedeman-franz ratio doesn’t

hold .The relationship for thermal conductivity is that

( )

Where T is the absolute temperature. A tabulation of the Pb-

Sn-Sb-Ca melt spun ribbons with their thermal conductivities

is shown in table (VI).

Table VI

VI. THERMAL DIFFUSIVITY

The importance of thermal conductivity and for thermal

diffusivity in quenched ribbons of Pb-Sn-Sb-Ca using melt-

spinning technique is associated with the need for appreciable

levels of thermal conductance in electrowinning circuits. The

informations on these parameters of Pb-5%Sn , Pb-5%Sn-

2%Sb , Pb-5%Sn-2%Sb-0.5%Ca , Pb-5%Sn-2%Sb-1%Ca ,

Pb-5%Sn-2%Sb-1.5%Ca , Pb-5%Sn-2%Sb-2%Ca , Pb-

5%Sn-2%Sb-2.5%Ca (in wt%) quenched ribbons is necessary

for modeling the optimum conditions during processing , as

well as for an analysis for transport of heat in Pb-Sn-Sb-Ca

melt-spun ribbons during practical applications. Using

dynamic resonance technique and from the frequency 0 , at

which peak damping occurs ,the thermal diffusivity Dth can be

obtained from the

Dth=2t2f0/𝜋 (9)

Where t is the thickness of the quenched ribbons. For Pb-Sn-Sb-1wt%Ca and Pb-Sn-Sb-2wt%Ca quenched

ribbons, the thermal diffusivity is smaller than the other

compositions. Thermal diffusivity Dth is transport coefficient

which is related to microscopic transport of heat. A nonlinear

increase of thermal diffusivities with an increase in calcium

content is observed in all quenched ribbons. It is seen table

(VII) that Pb-5wt%Sn-2wt%Sb-1wt%Ca as quenched ribbons

has smaller value of cm-2

.sec-1

change the value

of thermal diffusivity of the other quenched ribbons except

Pb-5wt%Sn-2wt%Sb-2wt%Ca.

Electron

concentration

(n)

𝜏 (sec )

Kf

(m-1 )

Electron

mobility

(m2.v

-1.sec

-1)

Vd(m/sec) σ( )

Melt-spun ribbons

3.7 342256 246: 3498 5:494 3427 Pb-5wt%Sn

947 34228 24828 3499 5:4;6 4434 Pb-5wt%Sn-2wt%Sb

;45 34224 24873 3498 5:494 448 Pb-5wt%Sn-2wt%Sb-0.5wt%Ca

;4; 34226 24887 34986 5:4:3 449;; Pb-5wt%Sn-2wt%Sb-1wt%Ca

443 34225 245;5 3498 5:494 2479: Pb-5wt%Sn-2wt%Sb-1.5wt%Ca

5496 3422; 246: 34: 5;48 3428 Pb-5wt%Sn-2wt%Sb-2wt%Ca

646 34228 2473 3499 5:4;6 3447 Pb-5wt%Sn-2wt%Sb-2.5wt%Ca

K

(w.m-1

.k-1

)

melt-spun ribbons

1.6 Pb-5wt%Sn




24:: Pb-5wt%Sn-2wt%Sb-1.5wt%Ca



(8)



We assume this fact is caused by smaller aggregation of

calcium particles. The aggregates could improve the heat

transport and improve thermal diffusivity. The value of

thermal diffusivity of quenched ribbons controls the time rate

of temperature change as heat passes through quenched

ribbons. So it is a measure of the rate at which a body with a

nonuniform temperature reaches a state of thermal

equilibrium. The mathematical formula that relates thermal

conductivity (k) and temperature-dependent specific heat at

constant pressure (heat capacity) is

Dth

(10)

where is the temperature-dependent density and is the

temperature-dependent specific heat at constant pressure [31],

so that by knowing the value of thermal conductivity as

indicated in table (VI ) , the specific heat can be calculated

as indicates in the following table (VIII).

Table VIII

VII. MECHANICAL BEHAVIOR OF QUENCHED RIBBONS

Pb93-x -5 wt% Sn -2wt%Sb- x wt%Ca

Mechanical properties of solid materials are intimately

connected with their physical, structural properties and

determine the performance of schemata prepared from

quenched metallic ribbons consequently there is constant

interest in assessing the mechanical properties of melt-spun

ribbons. The mechanical behavior of melt-spun ribbons is an

intellectual power subject for study by engineers and

physicists. The methods used all rest upon the principle that

elastic properties are a measure of the forces between atoms.

The measured values are listed in table (IX) for young`s

modulus E, shear modulus G, and bulk modulus B.

Table IX

Elastic stiffness of melt spun ribbons

The data obtained indicate that the elastic and shear stiffness

of the Pb-5%Sn , Pb-5%Sn-2%Sb , Pb-5%Sn-2%Sb-0.5%Ca ,

Pb-5%Sn-2%Sb-1%Ca , Pb-5%Sn-2%Sb-1.5%Ca ,Pb-5%Sn-

2%Sb-2%Ca , Pb-5%Sn-2%Sb-2.5%Ca (in wt%) are nearly

all the same . Thus the elastic and shear stiffness are not

sensitive to composition. The bulk modulus is relatively

sensitive to composition Clearly changing the calcium content

leads to a marked decreasing in mechanical properties of Pb-

rich phase quenched ribbons .One may conclude ,the calcium

content has a profound influence on the strength and stiffness

of these quenched ribbons from melt . It is also observed that

in most quenched ribbons, that is in all composition G is about

0.35 E . Shear and elastic moduli related to each other and

to Poisson's according to

E=2G (1+ν) (11)

VIII. CALCULATION OF DEBYE TEMPERATURE

Having computed the elastic moduli, one can calculate the

Debye temperature, which is an important fundamental

parameter closely related to many physical properties such as

elastic stiffness, specific heat and melting

temperature .Low temperature specific heat is

represented by a scalar parameter called the thermal

Debye temperature θDt , and the acoustic specific

heat is represented by the acoustic Debye temperature

θD .Thus at temperature near absolute zero,

Dth

(m2.sec

-1)

Melt-spun ribbons

1.544 Pb-5wt%Sn

34:: Pb-5wt%Sn-2wt%Sb






Cp

(j.k-1

.kg-1

)

Melt-spun ribbons

24;:: Pb-5wt%Sn

34;7 Pb-5wt%Sn-2wt%Sb

24938 Pb-5wt%Sn-2wt%Sb-

0.5wt%Ca


3425 Pb-5wt%Sn-2wt%Sb-

1.5wt%Ca

448; Pb-5wt%Sn-2wt%Sb-2wt%Ca

344; Pb-5wt%Sn-2wt%Sb-

2.5wt%Ca

G/E B

(Gpa)

G

(Gpa)

E

(Gpa)

Melt-spun ribbons

2457 79493 9493 4444 Pb-5wt%Sn

2457 9848 324; 5344 Pb-5wt%Sn-2wt%Sb

2457 3444 3498 7425 Pb-5wt%Sn-2wt%Sb-

0.5wt%Ca

2457 4546 546 ;49 Pb-5wt%Sn-2wt%Sb-

1wt%Ca

2457 3:49 4496 94:6 Pb-5wt%Sn-2wt%Sb-

1.5wt%Ca

2458 38 446 8497 Pb-5wt%Sn-2wt%Sb-

2wt%Ca

2457 334; 34: 742; Pb-5wt%Sn-2wt%Sb-

2.5wt%Ca

Table VII



θDt=θD (12)

The expression for the debye temperature θD in terms of the

sound velocities for an isotropic body is given by (13) the

following equation [32-35]

(

)

1/3 (13)

Where h is the plank`s constant , kB is the Boltzmann constant

,NA is Avogadro's number ,Va is the molar volume calculated

from the effective molecular weight and density (i.e

) and Vm

is the mean ultrasonic velocity defined by the relation

(

)

-1/3 (14)

Where Vt and Vl are the transverse and longitudinal wave

velocities in the solid defined by the ralations

√

And √

(15)

Where k is bulk modulus and G is the shear modulus.

Table X

Unfornately, as far as we know , there is no data available in

the literature on Debye temperature for this quenched ribbons.

IX. INTERNAL FRICTION

The internal friction of the Pb-Sn-Sb-Ca melt spun ribbons is

an important characteristic which are indirectly related to their

elastic properties. Since the same technique (dynamic

resonance method) described in the experimental method

can be used to determine the internal friction Q-1

. Generally,

the method of measuring internal friction of quenched ribbons

is divided into the following: Free-vibration method –direct

observation of stress-strain curves –wave propagation method,

and forced-vibration method. With these methods it was

possible to investigate the effect of impurity content on the

elastic properties. So the internal friction measurements have

been quit beneficial and productive for learning about the

behavior of Pb-Sn-Sb-Ca quenched ribbons , where the

internal friction is able to respond to small changes in the

mechanical state of quenched ribbons. It is found that the

anelastic component (the time-dependent elastic behavior) is

small and negligible.

Table XI

X. SPALLING

Spalling generally produces cracks normal to surface

whenever the stresses arise from thermal contraction. Such

cracking most commonly occurs in brittle materials as a result

of thermal contractions. In certain cases either a phase

transformation is an important causative factor. The spalling

behavior of a material is related to several properties other

than the thermal expansion coefficient, these properties

include strength , modulus of elasticity , and thermal

diffusivity [ 36,37] . So it is convenient, to assign an index to

spalling resistance of quenched ribbon , using the following

equation

Spalling Resistance Index (SRI) =

(16)

Where Ts is the tensile strength and 𝛼 is the thermal

expansion.

Having calculated the young`s modulus E, thermal diffusivity

Dth, tensile strength and thermal expansion ,one can calculate

the spalling resistance , which is an important fundamental

parameters closely related to thermal cracking. The calculated

spalling resistance index for Pb-5%Sn , Pb-5%Sn-2%Sb , Pb-

5%Sn-2%Sb-0.5%Ca , Pb-5%Sn-2%Sb-1%Ca , Pb-5%Sn-

2%Sb-1.5%Ca , Pb-5%Sn-2%Sn-2%Ca , Pb-5%Sn-2%Sb-

2.5%Ca (in wt%) quenched ribbons are given in table

( XII).

Vm

(m/

sec)

Vt (m/

sec)

Vl

(m

/sec)

(k)

Melt-spun ribbons

34447 :89 2570 356 Pb-5wt%Sn

4;: 3354 5522 529 Pb-5wt%Sn-2wt%Sb

34645 695 3583 347 Pb-5wt%Sn-2wt%Sb-

0.5wt%Ca

33244 63;47 3432 346 Pb-5wt%Sn-2wt%Sb-

1wt%Ca

3784: 7;9 3932 379 Pb-5wt%Sn-2wt%Sb-

1.5wt%Ca

36244 7554: 3732 367 Pb-5wt%Sn-2wt%Sb-

2wt%Ca

3354: 65544 3443 34; Pb-5wt%Sn-2wt%Sb-

2.5wt%Ca

Q-1

Melt-spun ribbons

0.147 Pb-5wt%Sn

242:; Pb-5wt%Sn-2wt%Sb

2497; Pb-5wt%Sn-2wt%Sb-0.5wt%Ca







Table XII

It is found that particularly important to spalling resistance is

the avoidance of stress concentrations which permit the tensile

strength of the quenched ribbons to be exceeded locally. In the

design of components which will undergo sudden temperature

changes, just as for compounds to be used under impact

loading, sharp corners should be avoided. It is worth noting

that the Spalling resistance Index values are very small and

negligible.

XI. MICROHARDNESS MEASUREMENTS The measured indentation diagonal length and calculated

microhardness values of an applied load 10gf, and dwell time

5 sec, are given in table (XIII), for each quenched ribbons. It

is obvious from the table (XIII) that the apparent hardness

values are composition dependent for all quenched ribbons.

The value of Hv is found to vary from 125 to 285 MPa .But

this variation is not linear in behavior. This type of nonlinear

behavior, it is known as indentation size effects (ISE). The

ISE behavior can be explained qualitatively on the basis of

penetration depth of indenter [38, 39].

Table XIII Hv(Mpa) Melt-spun ribbons

86 Pb-5wt%Sn

4:7 Pb-5wt%Sn-2wt%Sb






XII. CONCLUSIONS

Based on the experimental results of structural and physical

analysis of Pb-Sn-Sb-Ca quenched ribbons, the following

conclusions can be drawn: 1-Lattice distortions for lead phase in all the melt –spun

ribbons are very low , this supports the optimum formation of

face-centered cubic structure phase close to the average

electron concentration e/a=4 , reflecting to the atoms in the

lead –phase are arranged in ordered manner.

2- It was conclude that the total resistivity pronounced minima

at composition of Pb-5wt% Sn-2wt%Sb-1wt%Ca. This also

corresponds to the formation of ordered quenched ribbons.

3- The mechanical data conclude that the calcium content has

a profound influence on the strength and stiffness of these

quenched ribbons from melt. 4- It was also derived the Debye temperature for Pb-Sn-Sb-Ca

rapidly solidified from melt. 5- Based on these observations, rapid quenched processing of

Pb-Sn-Sb-Ca holds great potential for electrowinning

application as well as for battery-grid application.

6- For these reasons it is interesting to reexamine quenched

ribbons, for which the available data seen to be incomplete

and not reliable before drawing an exhaustive picture of the

behavior of this system used in industrial applications.

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SRI

(m.k.sec-2

)

Melt-spun ribbons

4479 Pb-5wt%Sn


439 Pb-5wt%sn-2wt%sb-0.5wt%Ca

3:48 Pb-5wt%Sn-2wt%Sb-1wt%Ca






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