Magnetic particles studied with neutron depolarization and small-angle neutron scattering R. Rosman Stellingen behorende bij het proefschrift "Magnetic particles studied with neutron depolarization and smali-angie neutron scattering" 1. De bewering van \ eider et al, dat strooivelden rond magnetische inhomogenii.eiten de neutronendepolarisatie niet beïnvloeden, is onjuist. - A. Veider, G. Badurek, II. Weinfurter en K. Stierstadt. J.de Phys. C8 49, 1831 (1988). - Hoofdstuk 2 van dit proefschrift. 2. De analyse van kleine-hoek neutronenverstrooiingsmetingen aan media met magne- tische één-domein deeltjes wordt sterk bemoeilijkt doordat magnetische en nucleaire verstrooiing vaak niet te scheiden zijn. Het eventuele gebruik van een gepolariseerde neutronenbundel verandert hier in het algemeen weinig aan. 3. De door Montfrooij opgegeven fouten in de dynamische structuurfactor van helium zijn sterk gecorreleerd en in strijd met de ruwe meetdata. -VV.Th. Montfrooij. Thesis, Kanters, Aiblasserdam (1990). 4. Gezien de sterke invloed van thermische absorbers op de porositeitsindex van de gecompenseerde neutronenlog C.VL verdient het aanbeveling bij porositeilsmetingen meer gebruik te maken van epithermische loginstrumenten. - R.l'. Alger, S. Locke, W.A.Nagel en H. Sherman. SPE :t565 (1971). - D.V. Ellis, C. Flaum, J.E. Calford en H.D. Scott. SPE 16814 (1987). 5. De ombuiging van lopend universitair wetenschappelijk onderzoek naar derde geld- stroom onderzoek getuigt van korte termijn denken en leidt op de lange duur tot een verarming van het onderzoek. 6. Het hanteren van publicatiescores als beoordelingcriterium voor onderzoekers werkt publicatie van wetenschappelijk weinig interessante artikelen in de hand. 7. Di' voortgang van wetenschappelijk onderzoek is sterk afhankelijk van een goede pre- sentatie. Hot is daarom verwonderlijk dat presentatietechnieken geen vast onderdeel vormen van elke universitaire studie. 8. Ken van de kernpunten in de politiek is hoe een rechtvaardige verdeling van de gecreëerde welvaart eruil ziet. De door socialistische partijen vaak gehanteerde leuze "eerlijk delen" verduidelijkt hun standpunt in deze geenszins. 9. De verkeersveiligheid is meer gediend met een a.p.k. van bestuurders dan met een a.p.k. van auto's. Magnetic particles studied with neutron depolarization and small-angle neutron scattering R. Rosman Interfacultair Reactor Instituut, Delft University of Technology me' CIP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HAAG Rosman, Remko Magnetic particles studied with neution depolarization and small-angle neutron scattering / Remko Rosman. (Delft: Interfacultair Reactor Instituut van de Technische Universiteit Delft]. - 111. Thesis Delft. - With ref. - With a summary in Dutch. ISBN 90-73861-02-0 NUGI 812 Subject headings: magnetic particles / neutron depolarization / small-angle neutron scat- tering. Magnetic particles studied with neutron depolarization and small-angle neutron scattering Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus, Prof.drs. P.A. Schenck, in net openbaar te verdedigen ten overstaan van een commissie aangewezen door het College van Dekanen op 23 april 1991 te 16.00 uur door Remko Rosman geboren te Onstwedde ingenieur in de technische natuurkunde Dit proefschrift is goedgekeurd door • de promotor Prof.dr. J.J. van Loef • de toegevoegd promotor dr. M.Th. Rekveldt •I i The research described in the thesis has been performed within the 'po- larized neutron group' of the department Radiation Physics of the Inter- facultair Reactor Instituut, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands. Financial support has been obtained from the 'Delftse Universiteitsfonds'. Contents 1 Introduction 1 2 Neutron depolarization theory in the Larmor and the scattering approach 7 2.1 Introduction 7 2.2 A ND experiment 9 2.3 Neutron depolarization formulas 11 2.3.1 The Larmor approach 11 2.3.2 The scattering approach 15 2.4 ND by single-domain particles 18 2.5 The intrinsic anisotropy 19 2.6 Conclusions 24 A.I The Larmor equation 26 A.2 The relation between the scattering vector and the scattering angle .... 27 3 Neutron depolarization theory in particulate media 29 3.1 Introduction , 29 3.2 ND in particulate media 30 3.2.1 General ND theory 31 3.2.2 The correlation matrix w for magnetically uncorrelated single-domain particles 33 3.2.3 The effect of interparticle correlations on w 40 3.2.4 The influence of variations in the neutron transmission length on <2> 50 3.3 Discussion 52 3.4 Summary and conclusions 54 4 Neutron depolarization by anti-ferromagnetic particles 57 4.1 Introduction 57 4.2 Theory of ND in anti-ferromagnetic particles 58 4.2.1 Depolarization due to Bragg scattering 59 4.2.2 Depolarization due to un compensated planes 60 4.3 Experimental results 61 4.4 Discussion 62 4.5 Summary and conclusions 63 A.I The depolarization by an ensemble of rectangular anti-ferromagnetic particles 65 A.2 The depolarization by an ensemble of ferromagnetic planes 69 5 Magnetic interparticle correlation in ferroxdure, magnetic pigments and micron-size Ni and Fe particles, studied with neutron depolarization 73 5.1 Introduction 74 5.2 Brief review of the ND theory 74 5.3 Experimental 77 5.4 Results and discussion 80 5.4.1 ND measurements on a ferroxdure compact and slurry 82 5.4.2 Magnetic correlations in the magnetization reversal process of the CrO2, 7—Fe2O3 and CoZn-ferrite pigment 91 5.4.3 Correlations effects in mixtures of Co-modified 7—Fe2O3 and Q-Fe2O3 97 5.4.4 The magnetization reversal process in compacts of micron-size Ni and Fe particles 102 5.4.5 Switching volumes in the CrO2, Co-modified 7—Fe2C>3, CoZn-ferrite and Fe pigment 107 5.5 Summary and conclusions 112 A.I The effect of scattering outside the aperture of the detector on the depolar- ization 115 6 Particulate recording tapes studied with neutron depolarization 119 6.1 Introduction 119 6.2 Theory of ND in particulate recording tapes 120 6.2.1 Review of the general ND theory 120 6.2.2 Numerical calculations on ND in recording tapes 123 6.3 Experimental 128 6.4 Results and discussion 129 6.4.1 Example of a ND experiment 130 6.4.2 ND measurements on Philips CrO2 video tapes 134 6.4.3 ND measurements on BASF CrO2 video tapes 137 6.4.4 ND and noise measurements on TDK Co-modified 7-Fe2C>3 audio and video tapes 139 6.5 Summary and conclusions 145 7 Ni containing Kr bubbles studied with neutron depolarization and small-angle neutron scattering 149 7.1 Introduction 149 7.2 ND and SANS theory 150 7.2.1 Review of the ND theory 150 CONTENTS iii 7.2.2 Review of the SANS theory 152 7.3 Experimental 154 7.4 Experimental results 156 7.4.1 ND measurements 156 7.4.2 SANS measurements 160 7.5 Discussion 163 7.5.1 Model calculations on M(r) 163 7.5.2 ND results 168 7.5.3 SANS results 170 7.6 Conclusions 176 8 Interparticle correlations in Fe3O4 ferrofluids studied with small-angle neutron scattering 179 8.1 Introduction 179 8.2 Review of the SANS theory 180 8.3 Experimental 182 8.4 Results 188 8.5 Discussion 188 8.5.1 The scattering functions 195 8.5.2 The anisotropy 196 8.5.3 The structure factors 199 8.6 Conclusions 202 9 General conclusions 207 Summary 211 Samenvatting 217 Dankwoord 223 Curriculum vitae 225 Introduction Materials containing magnetic single-domain particles, referred to as particulate media in this thesis, are object of thorough studies for several reasons. In the first place, they are interesting from a fundamental point of view as they can be used as model systems in the study of magnetic particle interactions. In the second place, particulate media have many applications and therefore a large commercial value. The main applications are as audio and video recording tapes and as ferrofluids. Ferrofluids are stabilized suspensions of magnetic single-domain particles in a carrier fluid. Most of their applications are based upon the possibility of controlling the fluid position by means of magnetic field gradients (e.g. high-vacuum seals around rotating shafts). In order to improve the properties of par- ticulate media, knowledge about the micro-magnetic state is important. Bulk methods to study the micro-magnetic state of particulate media are magnetization, susceptibility and noise measurements. This thesis deals with the application of neutron depolarization and to a lesser extent of small-angle neutron scattering to study the micro-magnetic state of particulate media. In the next paragraphs neutron depolarization and small-angle neutron scattering are in- troduced, the scope of the thesis is described in more detail and the different chapters are indicated. The three-dimensional neutron depolarization (ND) technique is a powerful method to study static and dynamic properties of magnetic structures in the micron and submicron range (e.g. [l]-[7]). In a ND experiment the polarization vector of a polarized neutron beam is analyzed after transmission through a magnetic medium. During transmission the polarization vector is affected by the local magnetization of the medium. A mean mag- netic induction results in a net precessional motion of the polarization vector around the former, while magnetic inhomogeneities result in a shortening of the polarization vector, called depolarization henceforth. A magnetic inhomogeneity is a part of the medium with a mean magnetization different from that of the medium. A ND experiment in general yields the mean size of the magnetic inhomogeneities along the neutron path (the ''mag- netic correlation length'), the mean orientation of the magnetic inhomogeneities (magnetic texture) and the mean magnetization. The range of magnetic correlation lengths which can be measured covers 10 nm up to mm's, making ND to some extent complementary to small-angle neutron scattering (SANS).