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

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Page 120

For a particular value of l - l ' , the force constant is a tensor of the second rank

and can be written as a 3 x 3

the

transform ...

For a particular value of l - l ' , the force constant is a tensor of the second rank

and can be written as a 3 x 3

**matrix**. Thus , Eq . ( 7 ) and ( 8 ) can be written inthe

**matrix**form as ° ( I ) = S - 1° ( I ' ) S and ( 10 ) r ( ) = Sr ( l ' ) The Fouriertransform ...

Page 122

We shall assume that the

the disturbance is transmitted through the composite in a series of local

disturbances . Thus , we can restrict the force constants to few near neighbors . In

practice ...

We shall assume that the

**matrix**is stretched or compressed only locally and thatthe disturbance is transmitted through the composite in a series of local

disturbances . Thus , we can restrict the force constants to few near neighbors . In

practice ...

Page 127

However , as we shall see in the next section , in the limit of small c , all of them

do not contribute independently to the dynamical

combinations of the above force constants contribute to the dynamical

However , as we shall see in the next section , in the limit of small c , all of them

do not contribute independently to the dynamical

**matrix**. Only ten independentcombinations of the above force constants contribute to the dynamical

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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