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April, 2011

A thesis

for the degree ofmaster of science in Materials

Science

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Bragg-Williams model of

ordered B2, L12 and L10type binary intermetalliccompounds containing

point defects By Daniel G.Egziabher Kiflu

Advisor: Dr. Mulugeta Bekele (PhD)

A thesis defenc for the degree of

master of science in Materials Science April, 2011

AddisAbaba, Ethiopia

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Objective

Developing a generalized Bragg-Williams model ofordered B2, L10 and L12 type binary intermetallic

compounds containing point defect.

Modifying the generalized model to the ordered B2 type

binary intermetallic compound type containing four

defect.

presenting the future prospect to apply the model in

studying the property of a certain binary ordered

intermetallic compound by fitting experimental data.

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Outline

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The present thesis presents a model for a binary AmBn

compound that is composed of two

sublattices.

A pair interaction model applying the Bragg-Williams approach is presented. Theformalism is given in a general form for binary ordered compounds with B2, L12 and

L10 crystal structures considering all possible types ofpoint defects.With this general model the essential equations for three common ordered structures (B2,

L10 and L12) can be easily derived.

a) B2 type b) L12 type c) L10 type

Figure 1.1: Structures of three common superlattices in binary

intermetallic phases

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The generalized model we developed can be

modified for a specific ordered structure havinga certain type of defect,

Now let us apply it

-for a specific ordered structure B2 type-for a defect type three defect.

In this case of three defect z = 0 while the other

defect parameters stay the same. On the other handfor B2 type structure the values ofm, n and

coordination number for nearest-neighbour atoms (Z)

will be labeled as m = 1, n = 1 and Z= 8, respectively.

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Accordingly, the form ofH from eq. (2.9)

for B2 type m = 1, n = 1 and Z= 8Thus, for the nearest atoms interaction only eq. (2.9) takes

the form

(1)

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Again from eq. (2.2b) and assumption 8

Substituting z = 0, n = 1 and m = 1 we get

We have eqs. (3.2a) and (3.2c)

(2)

(3)

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After substituting the above eqs. (2) and (3) in addition to eqs. (3.2a)

and (3.2c) in to eq. (1) gives

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for B2 type m = 1, n = 1 and Z= 8Thus, for the nearest atoms interaction only eq. (2.9) takes

the form

(1)

Four defect model for B2 type binary intermetalics

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After substituting the above eqs. (2.2a) and (2.2b) in addition to eqs.

(3.2a), (3.2b) and (3.2c) in to eq. (1) gives

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