Multiferroics have attracted lots of research interest due to their potential in numerous multifunctional applications. The multiferroic materials could simultaneously exhibit two or more ferroic order parameters, and the coupling effects between ferroelectricity and ferromagnetism are named as magnetoelectric (ME) effect. Recently, with the development of thin film growth techniques, the multiferroics magnetoelectric composite heterostructures exhibit a very promising future prospects. This dissertation focused on the design, fabrication and characterization of new multiferroics magnetoelectric composite heterostructures. First, based on the specific phase architectures in BFO-CFO self-assembled thin films grown on variously oriented STO substrates and the epitaxial film growth knowledge, I designed two kinds of new film heterostructures: (i) I utilized self-assembled BFO nanopillars in a BFO-CFO two phase layer on (111) STO as a seed layer on which to deposit a secondary top BiFeO3 layer. The growth mechanism and multiferroic properties of these new heterostructures were investigated. (ii) I demonstrated the formation of a new quasi-(0-3) heterostructure by alternately growing (2-2) and (1-3) layers within the film. I proposed a new concept to overcome limitations of both the (2-2) and (1-3) phase connectivities and identified an indirect ME effect by the switching the characteristics of the piezoresponse for the new heterostructure. Second, for the option for candidates thin film materials with a high piezoelectric coefficient, which is a critical factor for ME composite films, I utilized the simple compositional BaSn0.11Ti0.89O3 bulk ceramic material as a target to grow films with the large piezoelectric properties. The grown high qualify lead-free epitaxial thin films had a chemical constituent similar to the reported giant piezoelectric ceramics near the MPB and with the QP. Both coherent and incoherent regions were observed in the interface and a larger piezoelectric coefficient d33 was achieved in this film. Finally, with respect to their characteristics and potential, I redirected from two-dimensional thin film materials to one-dimensional nanowire materials. By utilizing vertically aligned templates, I fabricated a new type of coaxial two-phase composite nanowires. Multiferroic properties of these new one-dimensional materials have been investigated. All these multiferroics magnetoelectric composite herterostructures would provide lots of potential in applications. / PHD

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24890号 / 工博第5170号 / 新制||工||1987(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 嶋田 隆広, 教授 平方 寛之, 教授 井上 康博 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The hole-doped perovskite manganese oxide such as Ln1-xAxMnO3 (Ln = La, Nd, Pr, and A = Ca, Sr, Ba, Pb) is one of the most studied topics in the recent years due to the observation of colossal magnetoresistance (CMR). Basically, LaMnO3 has an almost insulating behavior and on antiferromagnetic arrangement. By substituting a divalent cation (A2+) in place of La3+, LaMnO3 can be driven into metallic and ferromagnetic state. Mixed valence of Mn 3+ / Mn4+ is needed for both metallic behavior and ferromagnetism in these materials. The CMR characteristic occurs in the ferromagnetic state. A systematic investigation of the structural, magnetic and electrical properties in the perovskite colossal magnetoresistance materials La0.7-xLnxPb0.3Mn1-yMeyO3 (Ln=Pr, Nd and Y, Me=Fe and Co) has presented in this thesis. By subatituting Nd, Pr, Y for the La and Co, Fe for the Mn, the substitution effects on the crystallographic deformation, magnetotransport behavior and electrical properties in these compounds have been studied. According to the results of this research, crystallographic distortion is induced by the substitution of smaller ions, Pr or Nd, onto the La-site. Powder $x$-ray diffraction patterns show a crystallographic transition from rhombohedral symmetry (R-3c) to orthorhombic (Pbnm) crystal structure as the doping content is increased. The increase of deformation from R-3c to Pbnm decreases the bond angle of Mn3+¡ÐO2-¡ÐMn4+ , increases the cant of Mn spin, weakens the double-exchange interaction and results in decrease of ferromagnetism, low ferromagnetic transition temperature Tc, eg electron bandwidth and conductivity. However, the great quantity of decrease in resistivity by an external field leads to the increase in the magnetoresistance ratio. We also find that the increase of saturation magnetization results from the contribution of magnetic ion of Pr or Nd. In addition. in contrast to substitution La by magnetic ion of Pr and Nd, the saturation magnetization is decreased as Y content is increased. The zero-field-cool (ZFC) and field-cool (FC) magnetic measurements indicate that the range of spin ordering for Y one is shorter than Pr one or Nd one with the same doping content. It is because of the small ionic radius of Y, which results in larger distortion, increases the bond angle of Mn3+¡ÐO2-¡ÐMn4+, and corresponds low ferromagnetic transition temperature. The distortion induced by Mn-site substitution is not obvious due to the similar radius of Mn, Co and Fe. Powder x-ray diffraction patterns show a single phase of rhombohedral symmetry (R-3c) for Co doped ststem and a slight crystallographic transition from rhombohedral (R-3c) to orthorhombic (Pbnm) symmetry for Fe doped system. Values of temperature dependence of magnetization indicate that the ferromagnetic double-exchange interaction is gradually substituted by the superexchange interaction. The ZFC-FC curves also indicate that long-range spin ordering is progressively substituted by the short-range spin ordering. The substitution of Mn by Co and Fe supresses the double-exchange interaction, decreases the ferromagnetism and the ferromagnetic transition temperature. Due to the synthesis of the substitution of Nd, Pr, Y for La and Co, Fe for Mn, the mechanism of substitution effects are proved different. The substitution of Nd, Pr and Y for La distorts the crystal, decreases the Mn3+¡ÐO2-¡ÐMn4+ bond angle, and results in the transition of properties, while the substitution of Co and Fe for Mn decrease the percentage of ferromagnetic Mn3+¡ÐO2-¡ÐMn4+. The purpose of this thesis is to clear up the role functions of all elements in these compounds and properties of these compounds. Based on the knowledge of these compounds, it would be helpful to control the physical mechanism and improve the characteristics on preparing their thin film devices.

This thesis deals with the studies of magnetization and electrical transport properties of iron nanoparticles embedded in the carbon matrix. The synthesis and characteristics of the nanoparticle systems studied, are also presented. Carbon-iron (C-Fe) based systems are of growing interest due to their improved magnetic properties as well as in their potential application as sensors, catalysts, and in various other applications. In particular, nanocomposites of iron carbide, such as the cementite phase Fe3C, are further suited to diverse technological exploitations due to their enhanced mechanical properties and importance in ferrous metallurgy. The recent interest in magnetic nanostructures lies in the emergence of novel magnetic and transport properties with the reduction of size. As the dimension approaches the nanometer length scale, interesting size-dependent properties like enhanced coercivity, enhanced magnetic moment, super paramagnetism etc. are seen. Thermal assisted chemical vapour deposition (CVD) is used to decompose and chemically react the introduced precursors, maleic anhydride and ferrocene. This method provides relative size control over the individual particles by varying C/Fe concentration in precursors and the pyrolysis temperature during the co-deposition process. Ferrocene has been used actively for the production of nanoparticle composites and in the production of nanostructured carbon. The temperature of preparation, reaction rate, and the time duration of annealing directly effects the nanoparticle compositions. The catalytic effect of transitional elements are well documented in literature. This thesis is an effort to understand the growth of ferromagnetic nanocrystallites in carbon matrix, which undergo partial graphitization due to the catalytic effect of transitional elements. The effect of transitional metal on the degree of graphitization of the carbon matrix, morphology of the nanoparticle and the carbon matrix are studied. The phase of the ferromagnetic iron nanoparticles and the structural investigation forms part of the study. Here X-Ray diffraction (XRD) is employed to study the presence of different phases of iron in the partially graphitized carbon matrix. The matrix morphology and the particle size distribution were studied using Transmission Electron Microscopy (TEM) and High-Resolution TEM (HRTEM). The ferromagnetic states of the iron nanoparticles are investigated using Mossbauer spectroscopy. The results from these studies, are used to correlated the macroscopic properties to the microscopic studies. The enhanced magnetization, coercivity and the temperature dependence of the magnetization value is understood within the frame work of ferromagnetic Bloch law and surrounding carbon spins. The logarithmic temperature dependence of conductivity of the nanoparticle composites is analyzed in the framework of interference models as well as the many-body Kondo interaction effect. This thesis contains seven chapters: In chapter 1, a brief introduction to mesoscopic physics and the size-dependent phenomenon are given. Special attention is paid to magnetic nanoparticle and its composites, and the various finite-size effects exhibited by them are discussed in detail. The relevance of carbon matrix and its importance on the growth of iron nanoparticles with high thermal stability is also discussed. The ballistic and diffusive transport phenomena observed in low-dimensional systems are briefly discussed. The interplay of localization and various interaction effects at nanoscale are examined. In disordered metals the low temperature conductivity is dominated by the interference effects. A brief discussion is made on the conductivity in disorder systems, with the presence of magnetic impurities and how the classic many-body Kondo problem, is effected by various interactions. Chapter 2, mainly deals with the experimental techniques employed in the thesis. The thermal-assisted chemical vapour deposition setup used to decompose and chemically react the introduced organometallic precursors, for the preparation of C:Fe composites are discussed and its advantage over other preparation methods are emphasized. The method is optimized to provide relative size control over the nanoparticles composites and the phase compositions by varying C/Fe concentration in precursors and the pyrolysis temperature, during the co-deposition process. The various structural characterization tools used in the present study are summed up concisely in this chapter. The SQUID magnetometer system; its working principle and the various protocol used for the low temperature magnetization measurements are elaborated. Further, details regarding superconducting magnetic cryostat, utilized for the low temperature conductivity and magneto resistance measurements, are discussed. Films of C:Fe composites are grown on substrates to study the effect of disorder and sample size on the conductivity behaviour of the composites at low temperature. Chapter 3, presents the outcome of the structural studies undertaken on the C:Fe composites using XRD, TEM, and HRTEM. X-ray diffraction measurements performed on the powder composites reveal that, in addition to the presence of sharp diffraction peak from nanographite, peaks corresponding to the different phases of Fe are also seen. The effect of preparation temperature on the matrix morphology is revealed from the estimation of degree of graphitization. Iron carbide is the predominant phase in all the prepared composites. For low concentration of iron, iron carbide alone is present but as the percentage of iron in the samples increased other phases of iron are also seen. The microscopic studies on the prepared compositions revealed the presence of nanosized iron particles well embedded in the partially graphitized matrix. Here again, with the increase in iron percentage, agglomeration of ferromagnetic nanoparticles are seen. The kinetics of the particle growth and the filamentous nature of the carbon matrix are also discussed. Mossbauer investigation on C:Fe composites are presented in chapter 4. The measurements revealed the iron atom occupation in the crystal lattice. In the lower Fe concentration samples, the room temperature Mossbauer spectrum revealed the presence of sextet from Fe3C (cementite) phase. As the percentage of iron increased, sextet from α-Fe, Fe3O4 are also seen in some of the prepared compositions. Effect of carbon atoms on the structure and magnetic properties of the nanoparticle species are obvious from the isomer shift measurements. Chapter 5 comprises of the various magnetic properties and interactions present in small particle system such as magnetic anisotropy, coercivity, enhanced magnetization, inter-and intra-particle interactions etc. Magnetization measurements carried out in SQUID magnetometer on the C:Fe composites and carbon flakes (prepared from organic precursor, maleic anhydride alone) are presented. The enhanced magnetic properties of the nanoparticle assembly is discussed in detail. The hysteresis loops trace, with a finite coercivity at room temperature, indicates the ferromagnetic nature of the samples. At room temperature the magnetization value saturates at high magnetic field, indicating negligible effect from super paramagnetic particles on the hysteresis loop. The squareness ratio, saturation magnetization, coercivity and remanence magnetization values are analyzed in detail. The temperature dependence of magnetization shows a combination of Bloch law and Curie-Weiss behaviour, consistent with the picture of ferromagnetic clusters embedded in a carbon matrix. The Bloch’s constant is found to be larger by an order of magnitude compared to the bulk value, implying stronger dependence of magnetization with temperature. Effort to understand the enhanced magnetic moment in the light of magnetism in carbon was taken up. The proximity effect of ferromagnetic metal on the carbon and the hydrogen bonding with the dangling bonds, both studied in detail in literature, in connection with the induced magnetic moments in carbon, are invoked. In chapter 6, the different conductivity regimes are identified, to study the conduction mechanisms in composites and films. For the transport measurements pelletized samples are used for the resistivity and magneto resistance measurements. The conductivity data are analyzed based on the interplay of localization and Kondo effect in the ferromagnetic disordered system. In order to understand the effect of disorder and thickness on the Kondo problem, transport measurements are carried on thin films of C:Fe composites grown on quartz and alumina substrate. Disorder induced metal-insulator transition is observed in the prepared samples. The zero-field conductivity and magneto resistance data is fitted to variable range hopping (VRH) in strong localization regime. Chapter 7 summarizes the thesis and presents some perspectives for the future.

High dielectric constant materials have tremendous impact on miniaturization of devices that are used in various applications like wireless communication systems, microelectronics, global positioning systems, etc. To store electric charge in a very small space necessarily needs a capacitor with very high dielectric constant. Thus, these materials are very important in fabricating capacitors, or metal oxide semiconductor filed effect transistor (MOSFET). Among the existing commercially available devices, silicon-based microelectronic devices are commonly used based on the moderately stable dielectric constants of silicon with low losses and minimal temperature and frequency dependence. However, now-a-days, the perovskite based transition metal oxides have drawn attention that have the ability to fulfill all the requirements for being a good dielectric material in all the industrial applications. In this thesis we have studied a few selected perovskite based transition metal oxide systems in terms of their dielectric and magnetic behaviour. In Chapter 1, we have have given brief introductions about the some application of dielectric materials and the origin of dielectric and magnetic properties in the materials. We have also discussed about the polarisation in the dielectric materials to understand it’s frequency dependence and also to formalise different relaxation behaviour with the help of physical and mathematical explanation. In Chapter 2, we describe the various methodologies adopted in this thesis. In Chapter 3, we have studied the dielectric behaviour of Nd2NiMnO6, a rare earth based double perovskite ferromagnetic insulator. We successfully synthesised and characterised the compounds, settled the valency issues with the help of temperature dependent XAS of the transition metal atom in contrast to the existing controversy available in literature. We have found that this material shows relaxor kind behaviour with a colossal dielectric constant value. We have studied in details the origin of the colossal dielectric constant and the relaxation behaviour along with the a.c and d.c. transport properties. We have shown the origin of the ferromagnetism (TC ∼ 200 K) with a low temperature antiferromagnetic ordering (TN ∼ 55 K) with the help of detailed studies of temperature dependent d.c., a.c. magnetism and their XMCD. We have also investigated the isothermal variation of magnetodielectric and magnetoresistance behaviour as a function of magnetic field and their origin. In Chapter 4,we study the effect of cation anti-site disorder on the magnetic, dielectric and transport properties of another rare earth based ferromagnetic double perovskite insulator La2NiMnO6 by controlling different extent of anti-site disordered. We have confirmed the valency of the transition metal cations using XAS technique and followed by shown, different types of magnetic interaction between the transition metal cations using d.c magnetic, quantitative XMCD analysis and the origin of large dielectric response, a.c. transport & dielectric relaxation using temperature variation dielectric measurement as an experimental evidence in contrast of our previous speculation published in literature. We further have studied, the coupling between the magnetic and electric spin through isothermal magnetodielectric measurement. In Chapter 5, we have successfully synthesised and characterised a solid solution of YMnxIn1−xO3 series via different mol % of In doping in the multiferroic YMnO3 system. YMnO3 is a well known multiferroic material studied rigorously during past few decades. We have seen, YMnO3 which has a antiferromagnetic ordering temperature of ∼ 75 K suppressed with increasing the dopant concentration In. We have figured out the effect of In doping in the suppression of multiferroic phase and extended it to the dielectric properties. We have found that, the temperature dependence of dielectric constant shows an anomaly at the magnetic ordering temperature and studied magnetodielectric coupling. We have also investigated the temperature variation of dielectric relaxation and a.c. transport behaviour as a function of composition. In Chapter 6, we have identified the phase seperation and proposed a phase diagram as function of Gd doping in the Ho2−xGdxCuTiO6 double perovskite, where two end member, namely Ho2CuTiO6 and Gd2CuTiO6 are found to be in two different crystallographic phase as, hexagonal (P63cm) and orthorhombic (Pnmm), respectively. We have characterised the valency of the transition metal cations using XAS.We have seen very less temperature and frequency dependence of dielectric constant in hexagonal phase in compare to the orthorhombic phase and tried to figuring out from experimental analysis by performing temperature dependence dielectric const measurement. We also have shown the effect of doping in the origin of dielectric relaxation, a.c transport and magnetic behaviour of this system. In Chapter 7, we have synthesised and characterised successfully two different rare earth based layered perovskite La3Cu2VO9 and La4Cu3MoO12 compounds are of centrosymmetric space group. We have figured it of the valency of the different atoms present in the compound using XAS. We also do have observed the good temperature stability of dielectric constant of these materials and explored origin of mechanism in the dielectric relaxation, a.c. transport property by performing the temperature dependance dielectric measurement. The magnetic structure also have shown with the help of d.d. magnetic measurements. In Appendix A, we have seen the very stable dielectric constant constant from very low to above room temperature of the 2D nano PbS. The frequency stability of dielectric constant is also remarkable in compare to bulk PbS values available in literature. We have explored the origin of the conductivity and relaxation mechanism performing dielectric constant measurement. In conclusion, we investigate, in this thesis, dielectric properties of different transition metal oxides system and the mechanism of dielectric relaxation, a.c, d.c transport and their origin of magnetic response.

Physical systems having dimensions smaller than, or of the same order of magnitude as, the characteristic length scale relevant to a physical property are referred to as mesoscopic physical systems. Due to the dimensions of the system, several physical properties get affected and this could reveal interesting physics which would other-wise have not been apparent. In the recent times, a lot interesting applications have resulted from such studies. The fundamental length scale in ferromagnetic systems is the exchange length. It is related to the magnetic anisotropy and exchange constants. Other length scales such as the size of a magnetic domain or a domain wall depends on the minimisation of energy associated with this length scale along with other factors such as zeeman energy, magnetostatic, magnetoelastic and anisotropy energies. Ultrathin magnetic films have thickness smaller than the exchange length. In this thickness regime, the surface of the film plays an important role. The magnetic anisotropy energy would get a significant contribution from the surface of the film and if it dominates over the volume contribution, would eventually lead to magnetisation pointing out of the plane of the film as opposed to imposition of demagnetising fields. Examples for such cases are FePt(L10 phase) films and Co(0001) films. Such films are important in memory applications where perpendicularly magnetised recording media are desired. When the lateral dimensions of thin films are reduced, demagnetising fields become even more important. Depending on the anisotropy in the system, certain domain patterns get stabilised in the final structure. This has led to important applications in the field of magnonics. The use of angular momentum transfer from spin polarised electrons to change the configuration of magnetisation of structured magnetic films has led to interesting memory and oscillator applications. The underlying physical parameter that needs to be controlled and carefully studied in all these cases is the magnetic anisotropy. It is favourable to have uniaxial magnetic anisotropy for memory and oscillators. This thesis chiefly deals with Fe/GaAs(001) systems. The choice of the physical system follows interest in spintronics where spin injection is desired into a semiconductor from a ferromagnet. The thesis is organized into chapters as follows. Chapter 1 attempts to introduce the reader to some of the basic concepts of mag-netism and some magnetic phenomena. The characteristic nature of a ferro-magnetic material is its spontaneous magnetisation due to long range ordering below the Curie temperature. But the moment is coupled, through some in-teractions, to spatial co-ordinates which leads to spatial variation of magnetic properties. Such interactions are also responsible for the formation of magnetic domains. The spatial variation of magnetic properties within a ferromagnet is called magnetic anisotropy. A major part of the thesis deals with the study of magnetic anisotropy of Fe thin films grown on GaAs(001) substrates. For a better understanding, the structure of the semiconductor is introduced first before discussing the influence of the structure of GaAs on the growth of Fe. A short description of the uniaxial magnetic anisotropy in Fe films is given before starting on an exploration of some possible reasons for it. Concepts of ferromagnetic resonance, spin torque effect and micromagnetic simulations are given. Chapter 2 gives a brief description of some of the experimental apparatus that was setup during the course of the research along with an overview of the differ-ent sample preparation and characterisation techniques used. The chapter is organised according to the general functionality of the techniques. Some con-cepts such as the use of low energy electrons, nanostructuring etc are introduced along with the corresponding techniques since it is best understood along with the instrumentation. Chapter 3 reports some surprising findings about the in-plane magnetic anisotropy in Fe films grown on an MgO underlayer. Until now, it has been understood that such films should exhibit only a four-fold magnetic anisotropy within the plane of the film. But the Fe/MgO/GaAs(001) films studied here exhibited an in-plane uniaxial magnetic anisotropy(IPUMA). IPUMA is dominant upto about 25 ML of Fe in case of Fe/MgO/GaAs(001) films whereas, in Fe/GaAs(001) films it is dominant only upto about 15 ML. Thus, the presence of the MgO film even appeared to enhance the uniaxial anisotropy as compared to the Fe/GaAs(001) films. In the ferromagnetic resonance (FMR) spectra, as many as three peaks were observed in Fe/GaAs(001) films of thickness 50 ML close to the hard axis of magnetisation. This means that three could be three energy minima possibly due to a competition between the anisotropies involved. Chapter 4 elaborates the investigations of the effect of orientation and doping con-centration of the GaAs substrate on the magnetic anisotropy of Fe/GaAs(001) films. It is found that doping the substrate (n type) reduces the strength of the IPUMA in Fe/GaAs films. In the wake of the long-standing debate of electronic structure v/s stress as the origin of the IPUMA in Ferromagnet/Semiconductor films, this result is important because it implies that the electronic structure of the Fe/GaAs interface influences the magnetic anisotropy. But stress, as a cause of IPUMA cannot be ruled out. The influence of deposition techniques on magnetic anisotropy is also investigated. Chapter 5 presents a way of manipulating magnetic anisotropy, and hence mag-netisation dynamics, by nanostructuring of epitaxial Fe films. It is based on the property that magnetic anisotropy of Fe films is thickness dependent. It is demonstrated that using techniques of nanostructuring, a 2 dimensional mag-netic system with controllable variation of local magnetic anisotropy is created. Such a system could be a potential magnonic crystal. chapter 6 demonstrates the proof of concept of a new memory device where memory is stored in the magnetic domain configuration of a ring in relation to that of a nano-wire. Switching between the memory states is acheived through spin trasfer torque of an electric current passing through the device, whereas read-out of the memory state is through the measurement of resistance of the device. Devices are made using NiFe and Co; it is seen that the behaviour of the devices can be explained taking into account the anisotropic magnetoresistance of the material used. Finally, the various results are summarised and a broad outlook is given. Some possible future research related to the topics dealt within this thesis is discussed.

<p>U ovoj doktorskoj tezi razvijen je postupak za ispitivanje uticaja<br />oklopa na merni transformator bez jezgra sa stanovišta<br />linearnosti transformatora i zaštite transformatora od<br />uticaja elektromagnetske smetnje. Formiran je parametarski model<br />oklopa i mernog transformatora bez jezgra. Izvedena su merenja<br />magnetskih karakteristika feromagnetskih materijala, dat je novi<br />analitički model histerezisa i određene su krive magnetisanja i<br />permeabilnosti materijala. Na osnovu numeričkih i<br />eksperimentalnih rezultata, a u skladu sa definisanim<br />kriterijumom, izvršena je analiza kvaliteta oklapanja za<br />razmatrane tipove oklopa.</p> / <p>In this thesis a method for examining the effects of shielding on a coreless<br />measuring transformer from the standpoint of transformer linearity and EM<br />radiation shielding is developed. A parametric model of the shield and the<br />coreless measuring transformer is constructed. Measurements of magnetic<br />properties of ferromagnetic materials were performed; a new analytical model<br />of hysteresis is developed; magnetization curves and permeability of the<br />materials are determined. Based on numerical and experimental results, and<br />using the defined criterion, the analysis of shielding quality of the considered<br />shield types was performed.</p>

No description available.

The work investigates the selective deposition of cobalt oxide via atomic layer deposition. Methoxysilanes chlorosilane and poly(trimethylsilylstyrene) self-assembled monolayers are utilized to prevent wetting of water and cobalt bis(N-tert butyl, N'-ethylpropionamidinate) from the substrate, thereby controlling nucleation on the substrate and providing a pathway to enable selective deposition of cobalt oxide. Sr and Al are deposited atop the oxide films to scavenge oxygen and yield carbon-free cobalt metal films. Thermal reduction of the oxide layer in the presence of CO and H 2 was also investigated as an alternative. Finally, we demonstrate control over the tunability of the coercivity of the resultant films by controlling the reduction conditions.

No description available.