Lecture 26

NPTEL Phase II : IIT Kharagpur : Prof. R. N. Ghosh, Dept of Metallurgical and Materials Engineering | |

1

Module 26

Common Binary Alloys

Lecture 26

Common Binary Alloys


2

Introduction We are now familiar with binary and ternary phase diagrams. This tells us about the structure

of alloys. This in turn determines its properties. We are also familiar with the limitations of

phase diagram. However the entire concept was introduced with the help of hypothetical

systems except for the case of iron – iron carbide system. Steel which is an iron carbon alloy is

no doubt by far the most commonly used metallic material. However there are several other

commercial alloys as well. In this lecture let us look at a few of these. We shall begin this lecture

with the rules that govern the solubility limits in binary alloys. This to a great extent determines

what kind of phase diagram a binary system is likely to have. There are several binary alloys

belonging to either simple isomorphous or simple eutectics. We shall look at few of these.

Apart from there are systems that have several intermediate phases. In some of the two metals

are present in definite proportions as in a chemical compound. We shall learn the cases where

we expect such intermediate compounds to form.

Limits of solid solubility: There are several examples where the two metals may have unlimited solubility whereas there

are cases where the solubility is very much restricted. There are certain rules that govern the

limits of solubility. These are popularly known as the Hume Rothery rules. Two metals can have

unlimited solubility if they satisfy the following four criteria.

1. The atomic diameters of the two metals should be within ±15%. This known as the size

factor.

2. The two metals must have identical crystal structure.

3. The metals must have the same valance.

4. The difference between the electro‐negativity of the two atoms should not be greater

than 0.4e.u.

There are several examples of metals that satisfy the above set of rules. They have unlimited

solubility in solid state. Such alloys are classified as isomorphous system. Cu‐Ni and Si‐Ge are

common alloys within this system.

In terms of thermodynamic criteria ideal solutions tend to have unlimited solubility. It was

illustrated earlier that if two metals A & B form ideal solutions in both liquid and solid state its

phase diagram corresponds to that of an isomorphous system. In pure metals we only have like

bonds (either AA or BB). When they dissolve or get mixed some of the like bonds are replaced

by unlike bonds. Let the number of these bonds be represented as nAA, nBB and nAB. Consider a

case where . There is no preferential arrangement of atoms. This satisfies the

condition for a random solid solution. In such a case the activity of A (or B) is likely to be equal


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to its atom (mole) fraction and its phase diagram will be similar to that of an isomorphous

system. If . The deviation from ideality is positive. The system would exhibit a

tendency to form clusters. If . The system would exhibit a tendency to form

compounds. Depending on the extent of deviation the type of phase diagram would change.

Figure 1 illustrates how with increasing deviation from ideality an isomorphous system could

transform into a eutectic system.

The sketch on the extreme left of fig 1 shows a typical phase diagram for a system where both

the liquid and the solid exhibit ideal behavior. The central sketch shows the effect of positive

deviation leading to the formation of clusters. This results in a miscibility gap. With increasing

deviation the minimum in the isomorphous portion of the diagram comes down and the peak

temperature of the miscibility gap increases. Finally the two could meet resulting in a eutectic

phase diagram.

Examples of binary isomorphous system: Slide 1 presents the phase diagram of Cu‐Ni system. Both copper & nickel have the same

crystal structure. Their lattice parameters are nearly the same. The atomic diameter of an

elemental solid is directly proportional to its lattice parameter. Therefore size factor appears

favorable for unlimited solubility. They have identical valence (2). The electro‐negativity is

nearly the same. Therefore the two have unlimited solubility in the liquid state.

L

A B

L +

T

% B

L

A B

L +

T

% B

L

A B

L +

T

% B

L + 2

Fig 1


4

Cu – Ni : Cupronickel

Cu Ni

1083

1455

UTS

Ductility

Good strength, ductility, low temp coefficient for resistance & corrosion resistance (marine). Application: heat exchanger,

condenser tubes, thermocouple (Cu 46Ni : constantan)

Cu: fcc: 3.61

Ni: fcc: 3.52

Cu:29 en: 1.90

Ni:28 en:1.91

The strength of metals increases with increasing alloy content. This is known as solid solution

strengthening. The sketch in slide 1 also displays the effect of composition on the UTS (Ultimate

Tensile Strength). It attains the highest value at an intermediate composition. The increase in

strength is accompanied by loss of ductility. The alloy has good corrosion resistance, high

strength, and good ductility. Its electrical resistance is less sensitive to temperature. It is

commonly used in heat exchangers, condenser tubes. The constantan wire in thermocouples is

made of Cu‐46Ni.

Ge-Si

Ge Si

940

1402

Ge: Diamond cubic: 5.66 Si: Diamond cubic: 5.43

Valence = 4 ( IV of periodic table) At No. 32 & 14

Ge & Si both belong to group IV in the periodic table. Their valence is four. Both have diamond

cubic crystal structure. Their lattice parameters are 5.66 & 5.43 Angstrom respectively. Their

Slide 1

Slide 2


5

electro‐negativity is nearly the same. Therefore they too have unlimited solubility. Slide 2 gives

phase diagram of Ge‐Si system.

Cu-Au

Au Cu

1063 1083L

Au3Cu

AuCu

AuCu3

Au: fcc (4.08) At. No. 79 Group IB

Cu: fcc (3.61) at. No. 29 Group IB

Au & Cu have the same crystal structure. They belong to group IB of the periodic table. They

have identical valence. The difference in their atomic diameters is within 15%. Therefore they

have unlimited solid solubility. However at lower temperatures it undergoes an order disorder

transformation. It is an indicator of deviation from the condition for ideal solid solution. Crystal

structure of Au‐Cu alloy is FCC. In the disordered state at higher temperatures the two atoms

occupy lattice sites at random. For example in an alloy corresponding to Au3Cu one may assume

that each lattice point is made of 75%Au and 25%Cu. In ordered Au3Cu, the gold atoms are

located at face centers whereas the copper atoms are at the corner sites. The two sites are in

the ratio 3:1. This satisfies the composition as well. There is an order disorder transformation

at composition corresponding to AuCu3. In this case after the order disorder transformation Cu

atoms occupy the face centers and Au atoms occupy the corner sites. In the case of AuCu there

is a little difference in the way the two sites are occupied. We may assume that one the two

occupies the corner sites and centers of the base. The other occupies the remaining face

centers.

Slide 3


6

Fig 2: Shows how atoms are arranged in disordered and ordered solid solutions. (a) Denotes

disordered structure where each atom may be assumed to be made of partly Au and partly Cu.

(b) Shows how the Au (red) and Cu (blue) atoms are arranged are arranged in ordered Au3Cu.

(c) Shows how the Au (red) and Cu (blue) atoms are arranged are arranged in ordered AuCu.

Binary eutectic:

Pb-Sn: Eutectic: nAB < 0.5(nAA+nBB)

Sn Pb

183

327

232

L

L+L+

Sn: tetragonal (a=5.35 c=3.18) & Pb : fcc 4.95

Atomic no. Sn: 50 Pb: 82 (IV of periodic table)

One of the most common example of a binary eutectic is that of Pb & Sn. Both belong to group

IV of the periodic table. However the crystal structure of lead is FCC (a= 4.95Angstrom) and that

Sn is body centered tetragonal (a= 5.35 & c = 3.18 Angstrom). This is system where the number

of unlike bonds is less than which is expected if atoms are randomly arranged. Therefore it has

a tendency to form cluster. The sketch slide 4 gives a schematic representation of the Pb‐Sn

phase diagram. Note that the composition of the binary eutectic is always nearer to the metal

having lower melting point. Pb‐Sn eutectic is a very popular material for solder.

Slide 4

(a) (b) (c)


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Al-Si Eutectic

Al: fcc (4.05A) At. No. 13 group IIA : soft & ductile

Si: diamond cubic (5.43) At. No. 14 Group IVA Hard & brittle

L

Al Si

577

1412

660

11.6

Aluminum is a soft and ductile metal. It has FCC structure. It belongs to group II of the periodic

table. Si on the other hand is hard and brittle. It belongs to group IVA of the periodic table. Its

crystal structure is diamond cubic. Therefore The two have very limited solubility is the solid

state. The two form a simple binary eutectic system. Slide 5 shows a sketch of the Al‐Si phase

diagram. The eutectic composition is around 11.8% Si. Si is amongst the few elements that

expand of solidification. Therefore hyper eutectic Al‐Si alloys having around 12% Si does not

shrink on solidification. Therefore these are easy to cast. It is one of the most popular cast

aluminum alloys.

Al-Si Eutectic

Eutectic consisting of coarse Si plates in Al matrix isbrittle. This can be modified by adding Na or NaCl.or rapid solidification. This improves its ductility.Useful cast alloy: pump casing, engine manifolds,piston ( with addition of a few other alloy elements)

L

Al Si

577

1412

660

Al–Si eutectic consists of coarse Si plates in Al matrix. Such a structure is brittle. This can be

modified by adding Na or NaCl or by rapid solidification. As a result of modification eutectic

temperature is lowered and the composition of the eutectic shifts towards higher Si content.

This is illustrated with the help of a sketch given in slide 6. This improves its ductility. Useful

Slide 5

Slide 6


8

cast alloy: pump casing, engine manifolds, and pistons (with addition of a few other alloy

elements).

Pb-Sb: Eutectic

Pb: fcc 4.95 & Sb: rhomb 4.51A 57.1

Pb: At no. 82 Group IVASb: 51 Group VA

Pb Sb

327252

11.1

LL+

630

Pb‐Sb forms a binary eutectic. It is given in slide 7. Note the difference in their crystal structure

& valence.

Ni-Cr

Cr Ni

L

1880

1455

CrNi3

Magnetic transformation

Cr: bcc (2.88A) At. No. 24 Group VIB

Ni: fcc (3.52A) At. No. 28 Group VIII

1345

Ni has FCC structure whereas Cr is BCC. They belong to different groups in the periodic table.

Slide 8 gives a sketch of the Ni‐Cr binary phase diagram. Ni‐Cr alloy has very good oxidation

resistance. Nichrome is a 80Ni20Cr alloy. It is used as heating element. Addition of a few other

alloy elements makes it a very attractive alloy for high temperature applications.

Slide 7

Slide 8


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Phase diagrams having intermediate phases:

As-Ga system nAB > 0.5(nAA+nBB)

Inter-metallic compound formation

Ga (31): IIIA & As (33): VA of periodic table

Ga: Orthorhombic As: HCP

Ga AsGaAs

1238

29.5

810 817

29.8

As‐Ga system is an excellent example of a binary alloy having an inter‐metallic compound GaAs.

Note that the melting point of Ga is very low. But the inter‐metallic compound has a melting

point which much higher than those of As & Ga. Slide 9 gives a sketch of the phase diagram.

There is hardly any solid solubility. Here is an alloy where the number of bonds between unlike

atoms is much more than those between like atoms. The slide also indicates the crystal

structures of Ga & As and the groups of the periodic table they belong to.

Mg-Sn: intermetallic

Mg SnMg2Sn

L

650

232

Mg: hcp (3.21, 5.21A) At. No. 12 group IIA

Sn: tetrag. (5.83, 3.18A) At. No. 50 Group IVA

Mg‐Sn is also an excellent example of a binary alloy having an inter‐metallic compound Mg2Sn.

It has two eutectics one between Mg & Mg2Sn and other between Mg2Sn and Sn. Slide 10 gives

Slide 9

Slide 10


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a sketch of the phase diagram. Note that both GaAs & Mg2Sn melt at fixed temperatures very

much like pure metals.

Cu-Zn: Brass

1083

419

Cu Zn

902

423

560

834700600

30 50 60 80

62.5 Cu 37.5 Zn

’

Cu: fcc (3.61A) At. No. 29 Group IB

Zn: hcp (2.66, 4.95A) At. No. 30 group IIB

Cu‐Zn alloys are known as brass. Slide 11 gives the phase diagram of binary Cu‐Zn system. Note

that the melting point of Cu is much higher than that of Zn. The terminal solid solutions are

called & . There are four intermediate phases. The phase and are the products of peritectic reaction. Unlike inter‐metallic compounds like GaAs or Mg2Sn, the and phases do not have fixed composition or melting point. These are known as intermediate

phases. All of them have single phase structure.

% ElongationUTS

0 60% Zn

UT

S

MP

a

40060%

Mechanical properties of brass

Slide 11

Slide 12


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The copper end alloys have reddish color. The single phase alloys are known as alpha brass.

They have good corrosion resistance. They are ductile. They can be cold worked. 70‐30 (70%Cu

30% Zn) and 60‐40 (60%Cu 40% Zn) are the two most common grades of brass. The former is a

single phase alloy. It belongs to the class of alpha brass. As against this 60Cu40Zn is a two

phase alloy. It consists of two phases & . It is yellow in color. It has good machinability but it

cannot be cold worked. It is also known as brass. The sketch in slide 12 gives the effect of % Zn on % elongation and UTS of brass. Note that 70/30 brass has the highest ductility. Beta brass

has the highest strength. Gamma brass is very brittle. It is of little use.

Cu‐Sn alloys are known as bronze. Like zinc, tin too has a very low melting point. Its crystal

structure is different from that of Cu. They also have different valence. This is why solubility of

Sn in Cu is limited.

Cu-Sn: Bronze

Cu3Sn

L L

Cu ~45% SnCu: fcc (3.61A) At. No. 29 Group IB

Sn: Tetrag (5.83, 3.18A) At. No. 50 group IVA

The sketch in slide 13 gives a part of the Cu‐Sn phase diagram. Within this region itself there are

several isothermal reactions involving 3 phase equilibrium involving several intermediate

phases ( etc.). Only one of these () has a fixed composition. Cu‐10% Sn is a popular

grade of bronze. It has a two phase structure. The matrix is ductile but the second phase is hard

and brittle. It has good wear resistance. It makes this a good bearing alloy.

Slide 13


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Ti-Al

Ti Al

1720

660665

1340

1460

1240

Ti: hcp (2.95, 4.68A) / bcc (3.31) , At. No. 22 Group IVB

Al: fcc (4.05A), At. No. 13 group IIIA

Ti-V

Ti V

1720

1900

1620, 0.3

882

L

600

Ti: hcp (2.95, 4.68A) / bcc (3.31) , At. No. 22 Group IVB

V: bcc (3.03A), At. No. 23 Group VB

Titanium has two crystalline forms. The room temperature form of Ti is HCP. However above

882 till its melting point it is BCC. The BCC form of Ti is more amenable to deformation. The

room form has limited slip system. Therefore it has relatively poor ductility. Two of the most

common alloy additions to Ti are Al & V. The sketch in slide 14 gives the phase diagram of Ti‐Al

and the sketch in slide 15 gives the phase diagram of Ti‐V. Al is an alpha stabilizer. It extends

the region in which is stable. As against this V is a beta stabilizer. It extends the region in which is stable.

Slide 14

Slide 15


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Intermediate phases: We are now familiar with the existence of several intermediate phases in various binary phase

diagrams. They may be classified into 4 groups. These are as follows:

1. Electrochemical compound: Mg2(Pb, Sn, Ge, Si), Mg3(Bi,Sb,As)2

2. Size factor compound: Fe3C

3. Laves phase: MgCu2, MgNi2

4. Electron compound: CuZn, Cu9Al4 , CuZn3

Electrochemical compound: It forms when one is electropositive & the other electronegative.

Mg is a group II element. Metals like Pb(82) Sn(50) Ge(32) & Si(14) belong to group IV. The

figures within brackets are the atomic numbers of the elements. The difference in valence

makes Mg electropositive metals like Pb, Sn, Ge & Si electronegative. Therefore it favors

formation of compounds such as Mg2Pb, Mg2Sn, Mg2Ge, & Mg2Si. Metals like Bi(83) Sb(51) &

As(33) belong to group V. In view of the large difference in their valence with respect to that of

Mg they form compounds such as Mg3Bi2, Mg3Sb2, and Mg3As2.

Size factor compound: It forms when the solute atom is small enough to be accommodated

within the interstices of metal. The most common examples are those of carbides and nitrides.

If the ratio of the radius of the interstitial atom to that of the metal is between 0.41 & 0.59 it

forms compounds like MX or M2X, where M stands for metal and X stands for carbon or

nitrogen. Carbides and nitrides of metals like Ti, Zr, Hf, V, Nb, and Ta come under this category.

If the ratio is greater than 0.59 there is more lattice distortion. The structure that forms is more

complex that those of MX or M2X types of compounds. The most common example of such a

compound is Fe3C known as cementite.

Laves phase: This forms when atomic size difference is about 20‐30%. Each A atom has 12 B & 4

A atoms as its neighbor & each B atom has 6 A & 6 B atoms as its neighbor. Average co‐

ordination number is 13.33. This is greater than that of a close packed structure. MgCu2 and

MgNi2 are two examples of such a phase. The former is cubic and the latter is hexagonal.

Electron compounds: This forms at specific electron to atom (e/a) ratio. Metals have free

electrons. In mono‐valent metals the ratio is one. If a metal having higher valence is added the

ratio keeps increasing. For example valence of copper is one. Its e/a ratio is one. When Zn

whose valence is two is added to Cu the e/a ratio would increase. When the e/a ratio becomes

1.5 (3/2) a new intermediate phase called brass forms. This occurs when the alloy has

50atomic % Zn. It corresponds to CuZn. The brass is FCC whereas brass is BCC. The electron


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compounds that form at this e/a ratio is known to have b brass structure. Table 1 give a list of

several other alloy system where such a compound can form.

Table 1

Table 1 also includes examples of two other set of electron compounds. They are known as

gamma and epsilon brass. The former occurs at e/a = 21/13 and the latter occurs at e/a = 7/4.

The table also gives a list of several other examples of electron compounds having the same

crystal structures as those of gamma and epsilon brasses.

Summary: In this lecture we looked at several common binary alloys. Some of these are simple

isomorphous or eutectic while others have several intermediate phases. Some of the solid

solutions have tendency to form cluster whereas some exhibit ordering. Au‐Cu system is an

excellent example where there is transition from ordered to disordered structure as it is

heated. In ordered structures Au & Cu atoms occupy specific sites whereas in disordered state

these are randomly located. We have also talked about four different types of intermediate

phases and their characteristics. The structure of an alloy can be guessed if we know its phase

diagram. There is strong correlation between structure and properties. Therefore looking at

such diagrams we can have an idea about the properties of the alloys. We can say whether it

can be cold worked or to what temperature the alloy is to be heated so that it can withstand

plastic deformation. We shall learn more about these in subsequent lectures.

brass

(e/a = 3/2)

brass

(e/a = 21/13)

brass

(e/a = 7/4)

CuZn Cu5Zn8 CuZn3

Cu3Al Cu9Al4 Cu3Sn

Cu5Sn Cu31Sn8 Cu3Si

NiAl Fe5Zn21 Ag5Al3


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Exercise:

1. Which lead – tin alloy will be ideal for joining electronic assemblies? Give reason.

2. Why is Al‐12% Si alloy a very popular casting material for automotive applications?

3. Cartridge brass is easily cold worked but Muntz metal can not be cold worked. Explain

why it is so.

4. What is the diffrence between disordered & ordered AuCu3 alloy? How is the presence

of ordered structure detected?

Answers:

1. Eutectic composition is ideal. It has 62Sn 38Pb. It melts at a fixed temperature. It flows

easily into tiny gaps which is the essential criteria for joining electronic assemblies.

2. Apart from light weight it has excellent castability. By modification it can be made to

solidify as complete eutectic structure. Most metals (inculdes Al) contract on

solidification. Si exapnds on solidification. Al‐12Si is an optimum combination where

there is little shrinkage on solidification. It is therefore easy to produce defect free

casting with no shrinkage cavity.

3. Cartridge brass has 70%Cu & 30% Zn. A look at Cu‐Zn phase diagram shows that it is a

single phase alloy. Therefore it can be deformed / shaped easily by cold work. Muntz

metal on the other hand had 60%Cu40%Zn. It falls within region of phase diagram.

is relatively brittle at room tem[perature. A two phase structure is always difficult to

cold work. However if heated it goes to a single phase region. This is where it is

amenable to working. (It can be hot worked)

4. In disordered state both Au & Cu atoms are distributed in both cube corners and face

centres in proportion to their respective atomic percent. Virtually each atom could be

assumed to be made of I part of Au & 3 parts of Cu. In ordered state all Au atoms are

located in corner sites & Cu atoms occupy face centres. These sites are in ratio 1:3 in fcc

lattice. This is best detected by powder X‐Ray diffraction technique. Disordered

structure gives reflections corresponding to fcc lattice where as reflection form ordered

structure corresponds to simple cubic lattice. Additional reflections are called super

lattice reflection.


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Appendix

This includes a binary phase diagrams of AlNi and AlFe system having a number of intermediate phases.

AlNi system has an intermediate phase AlNi having a fixed melting point which is higher than that of

pure Ni. However the others do not have a fixed melting point. Aluminides have attractive high

temperature properties. Many of them have ordered structure. This is responsible for the anomalous

temperature dependence of its yield strength. It increases with increasing temperature unlike most

metals and alloys. A dislocation in an ordered structure splits into two pairs of partials separated by an

anti‐phase domain. It is mobile as long as it remains in a plane. However at high temperature as a result

of thermal activation a part of this may climb on to another plane making this immobile. Such a

configuration is known as Kear – Wilsdrof lock. This is why the strength of an inter‐metallic like Ni3Al

increases with temperature. It forms a major constituent in several Ni base super‐alloys used in gas

turbines. Figure A1 gives a schematic binary phase diagram of Al‐Ni system. Table A1 gives the

composition range and crystal structures of various phases that could be present in binary Al‐Ni system.

1638°C

at. % Ni 0 100

AlNi

640°C

854°C

1133°C

1455°C

700°C

L

L

Al Ni

T° C

660°C

1395

1385

Al3Ni Al3Ni2 Al3Ni5 AlNi3

Fig A1: Gives a schematic (not to scale) binary Al‐Ni phase diagram. It has 6 intermediate phases.

These are often called as Nickel Aluminide. One of these is a congruently melting alloy whose

melting point (1638°C) is higher than that of both Al and Ni. Ni3Al has an ordered structure. It is a

major constituent of several high temperature Ni base super‐alloys.


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Table A1: Crystal structure & stability range of various phases in Al‐Ni binary alloy

Phases Crystal structure (Prototype) Composition range (at. % Ni)

Al rich solid solution A1(Cu) FCC Negligible solubility

Al3Ni D011 (Fe3C) (Orthorhombic) 25

Al3Ni2 D513 37 ‐ 40

AlNi B2 (CsCl) 42 ‐ 69

Al3Ni5 Cmmm (Gs3Pt5) 64 ‐ 68

AlNi3 L12 (AuCu3) 73 ‐ 76

Ni rich solid solution A1 (Cu) FCC 80 ‐ 100

Figure A2 gives a schematic binary phase diagram of Fe‐Al system. Table A2 gives the

composition range and crystal structures of various phases that could be present in binary Fe‐Al

system.


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Table A2: Crystal structure & stability range of various phases in Fe‐Al binary alloy

Phases Crystal structure Composition range (at. %)

Fe solid solution BCC 0 ‐ 45

Fe FCC 0 ‐ 1.3

Fe3Al D03 23 ‐ 34

FeAl (2) BCC (Ordered) 23 ‐ 55

Fe2Al3 Complex cubic 58 ‐ 65

FeAl2 Triclinic 66 ‐ 67

Fe2Al5 Orthorhombic 70 ‐ 73

FeAl3 Monoclinic 74.5 – 76.5

Al solid solution FCC 99.998 ‐ 100

1538

1394

910

770

13101215

1092

1171

652

660

11571164

Fe Al at. % Al

Fe

2

Fe

Curie

temperature

L

Coherent

equilibrium

Fe3Al

FeAl2

Fe2Al5

FeAl3

Fig A2: Gives a schematic (not to scale) binary Fe‐Al phase diagram. It has 7 intermediate

phases. These are often called as Iron Aluminide. One of these () is not stable at room


19

Representation of crystal structure: We are familiar with unit cell and Bravais lattice. These are frame work used to represent the

way atoms are arranged in a crystal. In pure metals a lattice point may denote the location of

an atom. However in intermediate phases or in compounds a lattice point may represent a

group of atoms. Most minerals and inorganic chemicals have well developed crystal faces.

Often these are large enough to find their symmetry elements (mirror plane, 2‐6 fold axis of

symmetry, centre of symmetry etc). There are 32 different combinations of symmetry elements

around a point. These are known as point groups. All of them are easily identifiable from the

shape of the crystal. They can be classified into 7 crystal system. However with the introduction

of X‐ray diffraction technique it is now possible to indentify precise locations of atoms in a unit

cell of a crystal. Therefore in order to describe a crystal structure it became necessary to

introduce the concept of space group representing an array of symmetry elements in three

dimensions. A large number of the possible space groups, consists of an array of point groups

around the 14 Bravais lattices. However apart from these, it is necessary to consider additional

microscopic symmetry elements that are not possible in point groups. The inclusion of both

macroscopic and microscopic symmetry elements at all lattice points, gives rise to 230 space

groups to which all crystals must belong. In order to describe the crystal structure several

notations have evolved over the years. These are Strukturbericht symbol, Pearson symbol, and

Space group. Table A3 gives the Stukturbericht designation for a few selected types of crystal

structures. It consists of a letter describing the type of structure followed by a number denoting

specific type within this category. (For details see books on crystal structure: J D Tilley Crystals

and Crystal Structures, John Wiley & Sons Ltd 2006)

Table A3: Strukturbericht designation and names for a few selected crystal structures

Type Chemical symbol Example

A Elements A1: FCC (Al, Cu); A2: BCC (Fe, Mo); A3: HCP (Mg, Zn); A4: Diamond (C)

B AB : compound B1: Halite (NaCl); B2: CsCl; B3: Zinc Blende (ZnS); B4: Wurzite (ZnO)

C AB2 : compound C1: Fluorite (CaF2); C2: Rutile (TiO2)

D AmBn : compound D03 : Fe3Al

L Alloys L12 : AuCu3

Pearson symbol gives successively the crystal structure, the Bravais lattice and the number of

atoms in a unit cell. For example crystal structure of FCC Cu is denoted as cF4 and that of rock

salt (NaCl) is given by cF8. Note that ‘c’ stands for ‘cubic crystal’ and ‘F’ denotes ‘Face centered

lattice’. The numbers 4 & 8 denote the number of atoms in unit cells of Cu and NaCl

respectively. In this nomenclature ‘a’ means triclinic, ‘m’ means monoclinic, ‘o’ means


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orthorhombic, ‘t’ means tetragonal, ‘h’ means hexagonal and ‘c’ means cubic. A capital letter is

used to represent Bravais lattice. ‘F’ denotes face centered, ‘I’ denotes body centered, ‘C’

denotes base centered, ‘R’ denotes rhombohedral and ‘P’ denotes primitive.

Space group notations give an idea of the lattice and the symmetry elements. For example P

denotes simple lattice whereas F denotes a lattice having a point at the centre of all the 6 faces.

The notation begins with a capital letter representing the type of the lattice followed by a set of

symmetry elements. The representation is a little more complex. It is beyond the scope of an

elementary course of physical metallurgy. Interested readers may refer to a book on

crystallography. Table A4 gives a comparison of the three different ways of representing the

structures of various crystalline materials. There are instances where only one of these may not

be sufficient to describe the structure of a crystal.

Table A4: Representation of crystal structure using the above notations

Strukturbericht Prototype Pearson Space group

A1 Cu cF4 Fm3m

A2 W cI2 Im3m

A3 Mg hP2 P63/mmc

B1 NaCl cF8 Fm3m

B2 CsCl cP2 Pm3m

D03 BiF3 cF16 Fm3m

L12 AuCu3 cP4 Pm3m

Many of the intermediate phases or inter‐metallic compounds have attractive properties. For

example aluminides of Ni, Ti & Fe have very good oxidation / corrosion resistance, low density

and high strength & stiffness at elevated temperature. Some of these like Al3Ni have the exact

stoichiometric composition whereas other may be stable over a range of composition. Most of

these have ordered structure. This is responsible for its high strength. A major limitation of

these is poor ductility. Considerable efforts have gone in, to improve its ductility. One of the

possible ways is alloying. The two of the most widely studied inter‐metallics are Ni3Al and NiAl.

The crystal structure of Ni3Al is L12. The corresponding Pearson symbol is cP4. It suggests that

the crystal structure is cubic. P stands for primitive Bravais lattice. ‘4’ denotes the number of

atoms in a unit cell. It is a derivative of face centered cubic (fcc) structure. Figure A3 (a) gives a

sketch of a unit cell of Ni3Al. In an ordered structure Al occupies the corner sites whereas Ni

occupies face centers. The number of corner and face centre sites are in the ratio 1:3. This

corresponds to its exact stoichiometry. It is a major constituent of several commercial Ni base

super‐alloys. Some of these may have as high as 70% Ni3Al. It is often referred to as gamma

prime phase (’).


21

The crystal structure of NiAl is B2. The corresponding Pearson symbol is cP2. It suggests that the

crystal structure is cubic. P stands for primitive Bravais lattice. ‘2’ denotes the number of atoms

in a unit cell. It is a derivative of body centered cubic (bcc) structure. Figure A3 (b) gives a

sketch of a unit cell of NiAl. In an ordered structure Al occupies the corner sites whereas Ni

occupies body centers (or vice versa).

Ni3Al NiAl

Al

Ni

Fig A3: The atomic arrangement within a unit cube of (a) Ni3Al where Al atoms are at the 8

corners and Ni atoms are at the 6 face centers of a unit cube and (b) NiAl where Al atoms

are at the 8 corners whereas Ni atom is at the centre of a unit cube.

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Lecture 26

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