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

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Page 133

The three eigenvalues of the dynamical matrix for a value of k give the

frequencies of the three types of waves , and the

describe the polarization of those three waves . If li denote the three Cartesian

components ( i ...

The three eigenvalues of the dynamical matrix for a value of k give the

frequencies of the three types of waves , and the

**corresponding**eigenvectorsdescribe the polarization of those three waves . If li denote the three Cartesian

components ( i ...

Page 135

... ( k ) = 4K sin kį sin k2 ( 59 ) D22 ( k ) = 2A ( 1 – coska ) + 2B ( 1 - coski ) + 4D ( 1

- cosk , coska ) and D ' ( k ) = 2F ( 2 - cosk , - coską ) + 4G ( 1 – cosk , cosk2 ) ( 60

) The eigenvalue

... ( k ) = 4K sin kį sin k2 ( 59 ) D22 ( k ) = 2A ( 1 – coska ) + 2B ( 1 - coski ) + 4D ( 1

- cosk , coska ) and D ' ( k ) = 2F ( 2 - cosk , - coską ) + 4G ( 1 – cosk , cosk2 ) ( 60

) The eigenvalue

**corresponding**to the element DTM ( k ) is immediately known ...Page 145

... one of the eigenvalues , the one

is given by x2 = 2066 ( 1 - сos k2 ) + C44 k 32 ( 82 ) The eigenvector

perpendicular ...

... one of the eigenvalues , the one

**corresponding**to D * is immediately known . Itis given by x2 = 2066 ( 1 - сos k2 ) + C44 k 32 ( 82 ) The eigenvector

**corresponding**to this eigenvalue is [ 1 , 0 , 0 ] . This wave is always polarizedperpendicular ...

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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