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

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- 20 - known as exchange narrowing. Between unlike nuclei the exchange interaction increases the second moment; termed exchange broadening. 2.2.5 METHOD OF MOMENTS A calculation of the theoretical free precession signal or absorption curve for an assembly of nuclear spins requires a complete knowledge of the energy levels and has only proved possible in a few special cases(15). However, theoretical expressions for the moments of a lineshape may be obtained without prior evaluation of the eigenfunctions and eigenstates(16). The nth moment of the frequency distribution curve f(c') is defined by M (w' )nf (W') di/1 f (w')dw where w' =w- wo If the lineshape is symmetric about w' =0 the odd moments vanish. In practice the wings of any experimental lineshape are relatively poorly defined yet make an increasingly large contribution to the value of the higher moments. Hence usually only the experimental second moment and sometimes the fourth moment are measured and compared to theoretical values. From Abragam, p. 111, these terms are given by M2 2 Tr sec'Ixý2/TrLIX11 M4 ý j4 Tr [`sec' ý`sec'Ixý12/TrýIXI Limiting the total perturbing Hamiltonian to its secular components ensures that the satellite lines at 0,2w0,3w0, etc. produced by (2.17) (2.18)
- 21 - the non-secular terms of the dipolar Hamiltonian (for example) are ignored. For a powdered sample the second moment due to dipolar actions between like nuclei is given by N M2 =5I (I + 1) 4112 1 and between unlike nuclei M2 1SYIYS 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 18: and -7- Vd(t) f(w1)cos w't dw Sao -
Page 19 and 20: -9- where the terms represent the Z
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: - 19 - termed pseudo-dipolar. It is
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
Page 69 and 70: - 53 - the manufacture of which was
Page 71 and 72: PTFE Tape_ FIGURE 4.7 rotors SCALE
Page 73 and 74: 4.4.4 COMMENTS - 55 - For completen
Page 75 and 76: Clamp Pf-£-- SECTION II SECTION 11
Page 77 and 78: 5.1 EQUIPMENT - 58 - CHAPTER 5 EXPE
Page 79 and 80: - 59 - the range ±1 V are digitise
Page 81 and 82:
SCALE 3 cm j Cooling Gas ; tainiess
Page 83 and 84:
Trensmitter EXL, FIGURE 5.3 : The s
Page 85 and 86:
FIGURE $. 4 s The spectrometer prob
Page 87 and 88:
Gas Tuning ransmi tter Input Receiv
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- 64 - phase can then be set so tha
Page 91 and 92:
-66- The transient nuclear signals
Page 93 and 94:
- 68 - 5.7.1 THE SOLID ECHO PULSE S
Page 95 and 96:
- 70 - sequence may be repeated. In
Page 97 and 98:
a° P/'rvu - 72 - p is the resistiv
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- 74 - combined with a low viscosit
Page 101 and 102:
6.2 RESULTS AND DISCUSSION - 76 - A
Page 103 and 104:
IC 1 I. FIGURE 6.2 : Measured T1 va
Page 105 and 106:
- 78 - TABLE 6.1. DEBYE TEMPERATURE
Page 107 and 108:
- 80 - TABLE 6.2. RATIO OF TI VALUE
Page 109 and 110:
- 82 - TABLE 6.3. DEPENDENCE OF T1
Page 111 and 112:
- 84 - provides further evidence th
Page 113 and 114:
- 86 - CHAPTER 7 EXPERIMENTAL RESUL
Page 115 and 116:
- 88 - Lorentzian NMR lineshape of
Page 117 and 118:
- 90 - at the top with epoxy glue.
Page 119 and 120:
- 92 - (c) Bulk Susceptibility Effe
Page 121 and 122:
- 94 - aluminium nuclei in the meta
Page 123 and 124:
FIGURE 7.1 : 27A1 F. I. Ds and corr
Page 125 and 126:
- 97 - TABLE 7.1. COMPUTED SECOND A
Page 127 and 128:
- 99 - and Slichter(104) reported t
Page 129 and 130:
- 101 - of this value would be requ
Page 131 and 132:
N JL I F- 0 z J I0 0123456789 ROTAT
Page 133 and 134:
-103- results obtained at a tempera
Page 135 and 136:
T10 ms 3. O 2.5 2'C H 1"C o.. v 234
Page 137 and 138:
0 - 106 - CHAPTER 8 MEASUREMENTS ON
Page 139 and 140:
- 108 - process for vanadium the me
Page 141 and 142:
- 109 - in the same way to the prec
Page 143 and 144:
Qv == , 2 28 kHz -111- which is sli
Page 145 and 146:
- 113 - from Cerac Inc. (USA). The
Page 147 and 148:
- 115 - 8.4.3 SPIN-LATTICE RELAXATI
Page 149 and 150:
tv D Xm =o N O Ul- X- z N O FIGURE
Page 151 and 152:
which gives K=0.048 an ± 0.002 - 1
Page 153 and 154:
- 118 - Lifetime broadening alone g
Page 155 and 156:
- 120 - cannot be spun at low tempe
Page 157 and 158:
- 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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