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

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Page 129

of 10 - 16 gm . To make the transition from a Born - von Karman solid to a Debye

solid in the z direction we shall use Born ' s method of long waves and expand ...

**Substituting**this estimate in Eq . ( 14 ) we get an estimate of the effective mass mof 10 - 16 gm . To make the transition from a Born - von Karman solid to a Debye

solid in the z direction we shall use Born ' s method of long waves and expand ...

Page 131

... we shall expand the sine and cosine functions in Eqs . ( 32 ) – ( 37 ) , keeping

only up to second - order terms and compare the resulting matrix with the Green -

Christoffel matrix for a solid with tetragonal symmetry .

... we shall expand the sine and cosine functions in Eqs . ( 32 ) – ( 37 ) , keeping

only up to second - order terms and compare the resulting matrix with the Green -

Christoffel matrix for a solid with tetragonal symmetry .

**Substituting**for sin ki = ki ...### 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 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