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

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Page 122

Thus , we can restrict the force

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 force

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 169

Using the Set 1 for the elastic

Using the Set 1 for the elastic

**constants**( Section X ) , and p = 2 , E ( 0 ) has been plotted in Fig . 25 using Eq . ( 95 ) with | k ] +0 . We notice from Fig . 25 that the agreement between the calculated and experimental results for ...### What people are saying - Write a review

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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