NNR IN RAPIDLY ROTATED METALS By - Nottingham eTheses ...

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2.1 INTRODUCTION -8- CHAPTER 2 SPIN-SPIN AND SPIN-LATTICE INTERACTIONS For an assembly of nuclear spins the (21 + 1) discrete energy levels described by the eigenvalues of the Zeeman Hamiltonian are broadened by internal interactions. The complete Hamiltonian can be written as nt ''int may consist of several different terms but, providing quadrupole effects are not large, it-is generally considered as a perturbation of the Zeeman Hamiltonian. If nt contains diagonal matrix elements between the Zeeman eigenstates it results in shifts and/ or broadening of the nuclear levels with a corresponding structure and broadening of the resonance spectrum. These secular terms commute with The 0. Z. off-diagonal matrix elements of Y connect nt states of different eigenvalue m and hence give rise to transit- ions between energy levels. In this way the non-secular terms are responsible for the relaxation of the spin system to the temperature of the lattice. There are four main secular components of meint' Hence the spin Hamiltonian may be written as Z+ ýL°D -+ Q+, S+ rJ
-9- where the terms represent the Zeeman, dipolar, quadrupole frequency (chemical and Knight) shift and the indirect exchange interactions respectively. We now describe the spin-spin interactions briefly in turn. 2.2 SECULAR INTERACTIONS 2.2.1 DIPOLAR INTERACTION From the classical energy of interaction between dipole moments the dipolar Hamiltonian over N spins can be written as YD 3(Ii. I.. iii rij_j r. aNi Ij _lj 3i - 21 i
Page 1 and 2: NNR IN RAPIDLY ROTATED METALS By R.
Page 3 and 4: I wish to express my thanks to: ACK
Page 5 and 6: quadrupole relaxation. However theo
Page 7 and 8: 2.3.5 Quadrupole Relaxation 26 (i)
Page 9 and 10: 5.9 Sample Preparation 71 5.9.1 Cup
Page 11 and 12: 1.1 BASIC THEORY -i- CHAPTER 1 INTR
Page 13 and 14: -3- Transforming to the rotating fr
Page 15 and 16: -5- lattice and T2 is the spin-spin
Page 17: and -7- Vd(t) f(w1)cos w't dw Sao -
Page 21 and 22: - 11 - If rii = nrij = (Xli + X2j +
Page 23 and 24: - 13 - In powdered samples a weak i
Page 25 and 26: - 15 - This contact term manifests
Page 27 and 28: - 17 - where 0 is the angle between
Page 29 and 30: - 19 - termed pseudo-dipolar. It is
Page 31 and 32: - 21 - the non-secular terms of the
Page 33 and 34: - 23 - to the lattice directly via
Page 35 and 36: - 25 - (2.25), can then be assumed
Page 37 and 38: - 27 - quadrupole moments to produc
Page 39 and 40: - 29 - where En are the Zeeman ener
Page 41 and 42: 3.1 INTRODUCTION - 31 - CHAPTER 3 N
Page 43 and 44: Aý T. B a A"T"B " - 33 - It is a g
Page 45 and 46: (-Ur Ho FIGURE 3.1. : Co-ordinate s
Page 47 and 48: D, (t) = 331 2 + 3YI2 sin 2a 4 - 36
Page 49 and 50: - 38 - X (t) = cos a cos ßp + sin
Page 51 and 52: - 40 - 3.7 THE EFFECT OF ROTATION O
Page 53 and 54: - 42 - observations are inconsisten
Page 55 and 56: - 44 - that it apparently offered n
Page 57 and 58: - 46 - bearings suffer from instabi
Page 59 and 60: SI FIGURE 4.1 SCALE il cm : The con
Page 61 and 62: N to 9 . ýC 8 Ü7 Z w D 06 w ax U.
Page 63 and 64: - 50 - The rotors used in this work
Page 65 and 66: Ip IJýi O 1 t - 1 - 1 p OI ý I ý
Page 67 and 68: - 52 - at rotation speeds around 4
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- 53 - the manufacture of which was
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PTFE Tape_ FIGURE 4.7 rotors SCALE
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4.4.4 COMMENTS - 55 - For completen
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Clamp Pf-£-- SECTION II SECTION 11
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5.1 EQUIPMENT - 58 - CHAPTER 5 EXPE
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- 59 - the range ±1 V are digitise
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SCALE 3 cm j Cooling Gas ; tainiess
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Trensmitter EXL, FIGURE 5.3 : The s
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FIGURE $. 4 s The spectrometer prob
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Gas Tuning ransmi tter Input Receiv
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- 64 - phase can then be set so tha
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-66- The transient nuclear signals
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- 68 - 5.7.1 THE SOLID ECHO PULSE S
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- 70 - sequence may be repeated. In
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a° P/'rvu - 72 - p is the resistiv
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- 74 - combined with a low viscosit
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6.2 RESULTS AND DISCUSSION - 76 - A
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IC 1 I. FIGURE 6.2 : Measured T1 va
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- 78 - TABLE 6.1. DEBYE TEMPERATURE
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- 80 - TABLE 6.2. RATIO OF TI VALUE
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- 82 - TABLE 6.3. DEPENDENCE OF T1
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- 84 - provides further evidence th
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- 86 - CHAPTER 7 EXPERIMENTAL RESUL
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- 88 - Lorentzian NMR lineshape of
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- 90 - at the top with epoxy glue.
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- 92 - (c) Bulk Susceptibility Effe
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- 94 - aluminium nuclei in the meta
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FIGURE 7.1 : 27A1 F. I. Ds and corr
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- 97 - TABLE 7.1. COMPUTED SECOND A
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- 99 - and Slichter(104) reported t
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- 101 - of this value would be requ
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N JL I F- 0 z J I0 0123456789 ROTAT
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-103- results obtained at a tempera
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T10 ms 3. O 2.5 2'C H 1"C o.. v 234
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0 - 106 - CHAPTER 8 MEASUREMENTS ON
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- 108 - process for vanadium the me
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- 109 - in the same way to the prec
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Qv == , 2 28 kHz -111- which is sli
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- 113 - from Cerac Inc. (USA). The
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- 115 - 8.4.3 SPIN-LATTICE RELAXATI
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tv D Xm =o N O Ul- X- z N O FIGURE
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which gives K=0.048 an ± 0.002 - 1
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- 118 - Lifetime broadening alone g
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- 120 - cannot be spun at low tempe
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- 122 - 11. L. E. Orgel, J. Phys. C
Page 159 and 160:
- 124 - 59. P. J. Randall, Ph. D. T
Page 161 and 162:
- 126 - 101. H. R. Khan, J. M. Reyn
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