Ph.D. thesis (pdf) - dirac

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142 Boson Peak The FEC-model suggests a different picture, namely that the disorder distorts the Debye modes and a way which gives rise to a peak in the rDOS. The inverse intensity of the boson peak is based on data compilations suggested to correlate with fragility (see section 8.3 for details). The origin of this correlation is (evidently) not understood, since neither the fragility nor the boson peak itself are understood. However, it is common for the models for the boson peak that its intensity is related to some notion of “amount of disorder” in the glass. The structure of the glass is the frozen-in structure of the liquid, and could in this sense carry a reminiscent signature of the dynamics in the liquid. In this chapter we present a study of the boson peak measured by inelastic neutron scattering in a number of different systems. A section (8.2) is devoted to analyzing the pressure dependence of the boson peak, particularly in comparison to the pressure dependence of the other vibrational modes of the system, the aim being to shed light on the origin of the boson peak. This part of the study is based on experiments on a PIB-sample, which has a well resolved boson peak. A second section (8.3) is reserved for the discussion of the correlation between the boson peak intensity and fragility. We particularly discuss the role of density versus temperature for this type of correlation in light of the general ideas presented in chapter 3. We have for this purpose studied a set of samples which span a large range in isobaric as well as isochoric fragility. 8.1 Time of flight 8.1.1 Experimentals The experiments were carried out at the time of flight spectrometer IN5 at the ILL. The energy of the scattered neutron is in time of flight measured via the time it takes the neutrons to arrive at the detector. The incoming beam is monochromatic and pulsed, the path length is known. The speed and the energy of the outgoing neutron can therefore readily be calculated. The pulsing and monochromation is in the case of IN5 done with a system of choppers. Monochromation can also be done with crystals (e.g. IN6) and the incoming beam can be intrinsically pulsed if it is generated by a spallation source. The use of choppers gives the possibility of freely adjusting the wavelength of the incoming neutron and hereby the resolution in absolute values. The experiments reported in this chapter were all performed using incoming neutrons with a wave-
8.1. Time of flight 143 length of 5 Å yielding a resolution of FMHW=103 µeV. The resolution function, which is nearly Gaussian, was in all cases measured with the sample at 2 K. The range in angle (2θ) goes from 14.5 ◦ to 132.5 ◦ with each detector covering approximately 1 ◦ . This corresponds to a elastic Q values of 0.4 Å −1 to 2.2 Å −1 , when the incoming neutron has λ=5 Å. The PIB3580 sample (see appendix A for details) was studied in a pressure range from atmospheric pressure to 1.4 GPa and at temperatures ranging from 140 K to 430 K. The experiment was performed using a clamp pressure cell and in situ compression. The sample and the cell were kept in the beam during the entire experiment, which means that all the measurements on PIB3580 were obtained under the exact same conditions with regard to position in the beam and the amount of cell in the beam. The volume of the sample in the beam was also kept constant. However, the number of sample scattering centers depends on the density. The compression of PIB3580 was performed at 430 K and the sample was subsequently cooled along the isobar. This procedure ensured that the compression was performed in the melt even when going to the highest pressure. Cumene was studied at atmospheric pressure and at 1.2 GPa in a temperature range of 100 K to 300 K. The experiment at atmospheric pressure was performed using a standard aluminum cell while the pressure experiment was performed using the clamp cell with in situ pressurization. The pressure was applied at 300 K, which means that the liquid was well below P g when compressed. We moreover studied a set of liquids with very different isobaric and isochoric fragility: PB, sorbitol, m-toluidine, m-fluoroaniline and DBP (see appendix A for details on the samples). These experiments were performed at ambient pressure using aluminum cells in a temperature range from 100 K to T g (in most cases T g ∼ 200 K). The clamp and the aluminum cells used are exactly the same as those used in the back scattering experiments. The description of the cells is given in section 7.1.1. However the sample thickness used for the high pressure experiment was only 0.1 mm in this case. The transmission was ∼95% for the experiments in the aluminum cell and ∼88% for the high pressure experiments. 8.1.2 Corrections The data underwent a standard correction procedure using the ILL program INX. INX converts the data from the measured intensity as a function of angle and time of flight to intensity as a function of angle and energy transfer, I(2θ, ω) corrected for
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THÈSE présentée par Kristine NIS
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Acknowledgement First of all I woul
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Contents Abstract iii Acknowledgeme
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CONTENTS ix 9 Summarizing discussio
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2 Introduction fragility with other
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Résumé du chapitre 2 De manière
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8 Slow and fast dynamics glass. The
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10 Slow and fast dynamics energy in
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12 Slow and fast dynamics increasin
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14 Slow and fast dynamics (linear)
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16 Slow and fast dynamics The dynam
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18 Slow and fast dynamics T > T 2
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20 Slow and fast dynamics as theore
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22 Slow and fast dynamics and sugge
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24 Slow and fast dynamics The boson
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26 Slow and fast dynamics modulus 3
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Chapter 3 What we learn from pressu
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3.2. Empirical scaling law and some
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3.3. Correlations with fragility 37
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3.4. Temperature dependences 39 mea
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3.5. Summary 41 assumption that the
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Chapter 4 Experimental techniques a
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4.2. Dielectric spectroscopy 47 4.1
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4.2. Dielectric spectroscopy 49 fie
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4.3. Inelastic Scattering Experimen
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Résumé du chapitre 5 La relaxatio
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72 Alpha Relaxation the dielectric
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74 Alpha Relaxation Measuring the c
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76 Alpha Relaxation 4 2 0 This work
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78 Alpha Relaxation for the 1 s iso
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80 Alpha Relaxation log10(τ α ) 2
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82 Alpha Relaxation 2 1 0 216.4K th
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84 Alpha Relaxation function has a
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86 Alpha Relaxation 2.5 2.5 2 2 log
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88 Alpha Relaxation 0.4 log 10 Im(
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90 Alpha Relaxation keeping the rel
Page 102 and 103: 92 Alpha Relaxation correlation bet
Page 105 and 106: Chapter 6 High Q collective modes I
Page 107 and 108: 6.1. Inelastic X-ray scattering 97
Page 109 and 110: 6.2. Sound speed and attenuation 99
Page 115 and 116: 6.3. Nonergodicity factor 105 where
Page 117 and 118: 6.3. Nonergodicity factor 107 1 0.9
Page 119 and 120: 6.3. Nonergodicity factor 109 high
Page 121 and 122: 6.4. Nonergodicity factor and fragi
Page 127 and 128: 6.5. Summary 117 d log (e(ρ))/ d l
Page 129: Résumé du chapitre 7 Dans ce chap
Page 132 and 133: 122 Mean squared displacement colle
Page 134 and 135: 124 Mean squared displacement 1.5 I
Page 136 and 137: 126 Mean squared displacement 1.4 1
Page 138 and 139: 128 Mean squared displacement a cen
Page 140 and 141: 130 Mean squared displacement cumen
Page 142 and 143: 132 Mean squared displacement / a
Page 144 and 145: 134 Mean squared displacement I P i
Page 146 and 147: 136 Mean squared displacement as be
Page 149: Résumé du chapitre 8 Le pic de bo
Page 154 and 155: 144 Boson Peak the Qout Q in factor
Page 156 and 157: 146 Boson Peak We are mainly intere
Page 158 and 159: 148 Boson Peak 1.5 x 10−3 ω [meV
Page 160 and 161: 150 Boson Peak comparison of the ev
Page 162 and 163: 152 Boson Peak In figure 8.6 we sho
Page 164 and 165: 154 Boson Peak Predictions/explanat
Page 166 and 167: 156 Boson Peak meaning that the Deb
Page 168 and 169: 158 Boson Peak g(ω)/ω 2 [arb. uni
Page 170 and 171: 160 Boson Peak are equivalent becau
Page 172 and 173: 162 Boson Peak m P /m ρ 2 1.8 1.6
Page 174 and 175: 164 Boson Peak S(ω) [arb.unit] S(
Page 176 and 177: 166 Boson Peak 3 2.5 S(ω) [arb. un
Page 178 and 179: 168 Boson Peak perature effect on t
Page 181 and 182: Chapter 9 Summarizing discussion Wh
Page 183 and 184: 173 temperature in the harmonic app
Page 185: Chapter 10 Perspectives In this wor
Page 188 and 189: 178 BIBLIOGRAPHY Angell, C. A. [199
Page 190 and 191: 180 BIBLIOGRAPHY Casalini, R. and R
Page 192 and 193: 182 BIBLIOGRAPHY Farago, B., Arbe,
Page 194 and 195: 184 BIBLIOGRAPHY Inamura, Y., Arai,
Page 196 and 197: 186 BIBLIOGRAPHY Monaco, A., Chumak
Page 198 and 199: 188 BIBLIOGRAPHY Patkowski, A., Gap
Page 200 and 201: 190 BIBLIOGRAPHY Sekula, M., Pawlus
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Appendix A Details on the samples T
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A.1. Cumene 195 the value found fro
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A.2. PIB 197 The temperature depend
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A.4. DBP 199 peak differently at di
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A.6. Other samples 201 NH 2 tempera
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Appendix B Data compilations B.1 Da
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B.1. Data compilation 205 DHIQ = De
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B.1. Data compilation 207 Triphenyl
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Appendix C Dielectric setup Figure
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Abstract The degree of departure fr
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