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

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Page 122

Thus , we can restrict the

Thus , we can restrict the

**force**constants to few near neighbors . In practice , one may have to include the effect of several neighbors because the elastic disturbances in the matrix may extend quite far .Page 132

Equating the coefficients of ki ? in the corresponding elements of the matrices D ( k ) and A ( k ) , we get the following relations between the

Equating the coefficients of ki ? in the corresponding elements of the matrices D ( k ) and A ( k ) , we get the following relations between the

**force**constants and the elastic constants A + 2D = C11 B + 2D = C66 E = C44 F + 2G = C44 ...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

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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 example exist experimental fibers force fracture function given gives grain grain boundaries Group growth growth path illustrated increase indicates 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