## Treatise on Materials Science and Technology, Volume 2 |

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Page 12

where F and V are

system . For solids ( 2 . 15 ) may be approximated by F = min . ( 2 . 16 ) because

of the negligible compressibility mentioned previously . 2 . SOLUBILITY The ...

where F and V are

**respectively**the Helmholtz free energy and the volume of thesystem . For solids ( 2 . 15 ) may be approximated by F = min . ( 2 . 16 ) because

of the negligible compressibility mentioned previously . 2 . SOLUBILITY The ...

Page 32

73 ) where E and u are the Young ' s and the shear moduli ,

present treatment , b , is the spacing of atomic planes perpendicular to the

interface . Hence , by ( 3 . 10 ) , the volume per interfacial atom is 12 = bxb , nb , (

3 .

73 ) where E and u are the Young ' s and the shear moduli ,

**respectively**; in thepresent treatment , b , is the spacing of atomic planes perpendicular to the

interface . Hence , by ( 3 . 10 ) , the volume per interfacial atom is 12 = bxb , nb , (

3 .

Page 97

33 illustrate

of energy E ( units uc / 412 ) in ( B . 30 ) versus misfit 1 / P for Mo = Ma = 104o .

Curves A , B , and C correspond to v = Ho / ( 1 - 20 ) , 0 , and 00 ,

van ...

33 illustrate

**respectively**ENERGY 1 / 15 14 . 20 05 MISFIT I / P - Fig . 33 . Graphof energy E ( units uc / 412 ) in ( B . 30 ) versus misfit 1 / P for Mo = Ma = 104o .

Curves A , B , and C correspond to v = Ho / ( 1 - 20 ) , 0 , and 00 ,

**respectively**(van ...

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angle anisotropy approximation assumed atoms average axis c-sites calculated cations coherent compounds concentration condition considerations constant contribution corresponding crystal curve defect density dependence determined diffusion direction discussed dislocations displacement effect elastic elastic scattering electron energy equation et al exist experimental experiments factor field flux lines follows force function garnet given gives important increasing Inelastic Scattering interaction interface ions lattice length limit magnetic materials measured Merwe metal method misfit mode neutron normal obtained parameter phase phonon Phys plane position potential present properties range rare earth reference region relation resolution resonance respectively sample scattering cross section shown shows single solid solution space strain stress structure substrate superconducting surface Table temperature tetrahedral theory thermal thickness transition unit values vector X-ray