## Treatise on materials science and technology, Volume 4 |

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Page 182

Let us also introduce the symbol x to denote a departure from

the B-rich side such that X = *b - 0.5 (8) where xB is the atomic fraction of B in the

alloy. If we take one gram-atom of an alloy, i.e., N atoms total, as our basis of

discussion, we will have the atomic distribution on the two sublattices, i.e., a- and

/?-sublattice, respectively, as shown in Table II for x = 0 and X > °- For perfect

order at x = 0, TABLE n Atomic Distributions on the a- and /?-Sublattices for the

CsCl ...

Let us also introduce the symbol x to denote a departure from

**stoichiometry**onthe B-rich side such that X = *b - 0.5 (8) where xB is the atomic fraction of B in the

alloy. If we take one gram-atom of an alloy, i.e., N atoms total, as our basis of

discussion, we will have the atomic distribution on the two sublattices, i.e., a- and

/?-sublattice, respectively, as shown in Table II for x = 0 and X > °- For perfect

order at x = 0, TABLE n Atomic Distributions on the a- and /?-Sublattices for the

CsCl ...

Page 183

At nonstoichiometric compositions, i.e., x > 0- let us assume that all the excess B

atoms, x^, go to the a-sublattices. From Table II, we have w IWY. ' N(U2-X)l(xN)l K

' and (A72)! w>=Umrl (9b) Since only the B atoms are on the /?-sublattice, again

we have only one way of arranging the atoms on this sublattice. Using the

Stirling's formula, Nl = N\dN-N (10) and substituting the result from Eq. (9a) into

Eq. (7) yields the configurational entropy 5c as a function of deviation from

At nonstoichiometric compositions, i.e., x > 0- let us assume that all the excess B

atoms, x^, go to the a-sublattices. From Table II, we have w IWY. ' N(U2-X)l(xN)l K

' and (A72)! w>=Umrl (9b) Since only the B atoms are on the /?-sublattice, again

we have only one way of arranging the atoms on this sublattice. Using the

Stirling's formula, Nl = N\dN-N (10) and substituting the result from Eq. (9a) into

Eq. (7) yields the configurational entropy 5c as a function of deviation from

**stoichiometry**, ...Page 198

From Eqs. (55), (56a), and (56b) we have FAB= -2/?rc/[ZN(l -4X2)] (57) At

of Eqs. (57) and (58) immediately yields the following relationship for the

compositional dependence of the critical transition temperature Tc as rc = (l-4x2)

rc,0 (59) Above equation shows clearly that the critical transition temperature

decreases with increasing deviation from the

be expected.

From Eqs. (55), (56a), and (56b) we have FAB= -2/?rc/[ZN(l -4X2)] (57) At

**stoichiometry**, x = 0. Equation (57) becomes FAB= -2*rc.0/ZN (58) A comparisonof Eqs. (57) and (58) immediately yields the following relationship for the

compositional dependence of the critical transition temperature Tc as rc = (l-4x2)

rc,0 (59) Above equation shows clearly that the critical transition temperature

decreases with increasing deviation from the

**stoichiometric**composition as is tobe expected.

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### Contents

Microstructural Characterization of Thin Films | 2 |

Fundamental Concepts of Diffraction | 4 |

Epitaxial Monocrystalline Films | 10 |

Copyright | |

26 other sections not shown

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### Common terms and phrases

a-sublattice Acta alloys aluminum average beam calculated compaction component compositional dependences compression concentration configurational entropy copper correlation factor crystallites CsCl phases decreases deformation diffraction pattern diffusion coefficient dislocation density disorder parameter effect electron diffraction equations Evans and Flanagan f.c. tetragonal face-centered cubic fiber axis flux forged free energy function Gibbs free energy given increases intermetallic iron powder isostatic jump rate lattice disorder material matrix mechanism nearest neighbor observed obtained occurs oriented partial enthalpy partial entropy Phys plane Poisson ratio polycrystalline probability pure metals random reciprocal lattice relps RHEED shear stress shown in Fig single crystals sintered sintered powder solid solution strengthening solute atoms solute content specimen stacking fault energy stoichiometry stress-strain curve structure sublattice Substituting surface Suzuki TED pattern temperature dependence tetragonal theoretical thermal thermodynamic thermodynamic activities thermodynamic properties thin films tracer jump twin vacancy jumps values variations Vook X-ray yield stress