## Treatise on Materials Science and Technology, Volume 1 |

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Page 122

Thus , we can restrict the

may have to include the effect of several neighbors because the elastic

disturbances in the matrix may extend quite far . However , the number of

neighbors to be ...

Thus , we can restrict the

**force**constants to few near neighbors . In practice , onemay have to include the effect of several neighbors because the elastic

disturbances in the matrix may extend quite far . However , the number of

neighbors to be ...

Page 132

Equating the coefficients of k ; ? in the corresponding elements of the matrices D (

k ) and A ( k ) , we get the following relations between the

elastic constants A + 2D = ( 11 B + 2D = 266 E = C44 F + 2G = C44 ( 50 ) H ...

Equating the coefficients of k ; ? in the corresponding elements of the matrices D (

k ) and A ( k ) , we get the following relations between the

**force**constants and theelastic constants A + 2D = ( 11 B + 2D = 266 E = C44 F + 2G = C44 ( 50 ) H ...

Page 144

First , let us note that the matrix DP is exactly similar to the dynamical matrix of a

two - dimensional square lattice of lattice constant equal to a with nearest and

next nearest neighbor interactions given by the following

...

First , let us note that the matrix DP is exactly similar to the dynamical matrix of a

two - dimensional square lattice of lattice constant equal to a with nearest and

next nearest neighbor interactions given by the following

**force**constant matrices...

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addition alloys analysis angle applied approach associated assumed atoms average becomes bond boundary calculated complex composite concentration consider constants contribution crystal curvature curve decrease defined dependence deposition determined developed direction discussed displacement distance distribution dynamical effect elastic electron elements energy equal equation exist experimental fibers force fracture function given gives grain grain boundaries Group growth growth path illustrated increase indicate interaction interface internal friction interstitial iron laminate lattice layer length material matrix measured mechanism metal microstructural molecules nitrogen normal nucleation observed obtained occur oxygen particles peak phase plane position possible potential present produce properties region reinforcing relaxation respectively shown in Fig shows single Snoek peak solid solution strain strength stress structure substitutional surface Table temperature tungsten unit values volume waves