Peak temperature, Tp, enthalpy release, ΔH, and glass transition temperature, Tg, of 7Nb and 3Nb powders milled for 48 h, and (Fe50Co50)62Nb8B30 mixture milled for 100 h [55].
\r\n\t
",isbn:"978-1-83969-561-2",printIsbn:"978-1-83969-560-5",pdfIsbn:"978-1-83969-562-9",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"65f2a1fef9c804c29b18ef3ac4a35066",bookSignature:"Dr. Luis Loures",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10756.jpg",keywords:"Urban Processes, Urban Patterns, Redevelopment Strategies, Landscape, Land Transformation, Urban Models, Urban Evolution, Urban Organisation, Legislation, Sustainable Development, Green Infrastructure, Regional Planning",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 23rd 2021",dateEndSecondStepPublish:"March 22nd 2021",dateEndThirdStepPublish:"May 21st 2021",dateEndFourthStepPublish:"August 9th 2021",dateEndFifthStepPublish:"October 8th 2021",remainingDaysToSecondStep:"a month",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Dr. Loures has worked on pioneering research on circular planning applied to post-industrial landscape redevelopment. Since he graduated he has published several peer-reviewed papers at the national and international levels and he has been a guest researcher and lecturer both at Michigan State University (USA) and at the University of Toronto (Canada) where he has developed part of his Ph.D. research with the Financial support from the Portuguese Foundation for Science and Technology (Ph.D. grant).",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"108118",title:"Dr.",name:"Luis",middleName:null,surname:"Loures",slug:"luis-loures",fullName:"Luis Loures",profilePictureURL:"https://mts.intechopen.com/storage/users/108118/images/system/108118.png",biography:"Luís Loures is a Landscape Architect and Agronomic Engineer, Vice-President of the Polytechnic Institute of Portalegre, who holds a Ph.D. in Planning and a Post-Doc in Agronomy. Since he graduated, he has published several peer reviewed papers at the national and international levels and he has been a guest researcher and lecturer both at Michigan State University (USA), and at University of Toronto (Canada) where he has developed part of his Ph.D. research with the Financial support from the Portuguese Foundation for Science and Technology (Ph.D. grant).\nDuring his academic career he had taught in several courses in different Universities around the world, mainly regarding the fields of landscape architecture, urban and environmental planning and sustainability. Currently, he is a researcher both at VALORIZA - Research Centre for Endogenous Resource Valorization – Polytechnic Institute of Portalegre, and the CinTurs - Research Centre for Tourism, Sustainability and Well-being, University of Algarve where he is a researcher on several financed research projects focusing several different investigation domains such as urban planning, landscape reclamation and urban redevelopment, and the use of urban planning as a tool for achieving sustainable development.",institutionString:"Polytechnic Institute of Portalegre",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"8",totalChapterViews:"0",totalEditedBooks:"2",institution:{name:"Polytechnic Institute of Portalegre",institutionURL:null,country:{name:"Portugal"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"10",title:"Earth and Planetary Sciences",slug:"earth-and-planetary-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"205697",firstName:"Kristina",lastName:"Kardum Cvitan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/205697/images/5186_n.jpg",email:"kristina.k@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"7476",title:"Land Use",subtitle:"Assessing the Past, Envisioning the Future",isOpenForSubmission:!1,hash:"5b0c406adac8447ffeb089e29eac8ea9",slug:"land-use-assessing-the-past-envisioning-the-future",bookSignature:"Luís Carlos Loures",coverURL:"https://cdn.intechopen.com/books/images_new/7476.jpg",editedByType:"Edited by",editors:[{id:"108118",title:"Dr.",name:"Luis",surname:"Loures",slug:"luis-loures",fullName:"Luis Loures"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8295",title:"Landscape Reclamation",subtitle:"Rising From What's Left",isOpenForSubmission:!1,hash:"1fb7d9e280708a190a90c3b352c93d45",slug:"landscape-reclamation-rising-from-what-s-left",bookSignature:"Luis Loures",coverURL:"https://cdn.intechopen.com/books/images_new/8295.jpg",editedByType:"Edited by",editors:[{id:"108118",title:"Dr.",name:"Luis",surname:"Loures",slug:"luis-loures",fullName:"Luis Loures"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"5962",title:"Estuary",subtitle:null,isOpenForSubmission:!1,hash:"43058846a64b270e9167d478e966161a",slug:"estuary",bookSignature:"William Froneman",coverURL:"https://cdn.intechopen.com/books/images_new/5962.jpg",editedByType:"Edited by",editors:[{id:"109336",title:"Prof.",name:"William",surname:"Froneman",slug:"william-froneman",fullName:"William Froneman"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"314",title:"Regenerative Medicine and Tissue Engineering",subtitle:"Cells and Biomaterials",isOpenForSubmission:!1,hash:"bb67e80e480c86bb8315458012d65686",slug:"regenerative-medicine-and-tissue-engineering-cells-and-biomaterials",bookSignature:"Daniel Eberli",coverURL:"https://cdn.intechopen.com/books/images_new/314.jpg",editedByType:"Edited by",editors:[{id:"6495",title:"Dr.",name:"Daniel",surname:"Eberli",slug:"daniel-eberli",fullName:"Daniel Eberli"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"42255",title:"Thermal Stability of the Nanostructured Powder Mixtures Prepared by Mechanical Alloying",doi:"10.5772/54151",slug:"thermal-stability-of-the-nanostructured-powder-mixtures-prepared-by-mechanical-alloying",body:'Nanocrystalline materials present an attractive potential for technological applications and provide an excellent opportunity to study the nature of solid interfaces and to extend knowledge of the structure-property relationship in solid materials down to the nanometer regime. Nanocrystalline materials can be produced by various methods such as mechanical alloying, inert gas condensation, sol–gel process, electrodeposition, chemical vapour deposition, heat treatment of amorphous ribbons, high speed deformation, etc. Mechanical alloying is a non-equilibrium process resulting in solid state alloying beyond the equilibrium solubility limit. During the milling process, mixtures of elemental or prealloyed powders are subjected to heavy plastic deformation through high-energy collision from the balls. The processes of fracturing and cold welding, as well as their kinetics and predominance at any stage, depend mostly on the deformation characteristics of the starting powders. As a result of the induced heavy plastic deformation into the powder particles during the milling process, nanostructured materials are produced by the structural decomposition of coarser-grained structure. This leads to a continuous refinement of the internal structure of the powder particles to nanometer scales.
Solid-state processing is a way to obtain alloys in states far-from-equilibrium. The microstructural manifestations of the departures from equilibrium achieved by mechanical alloying can be classified as follows: (i) augmented defect concentrations such as vacancies, interstitials, dislocations, stacking faults, twin boundaries, grain boundaries as well as an increased level of chemical disorder in ordered solid solutions and compounds; (ii) microstructural refinement which involves finer scale distributions of different phases and of solutes; (iii) extended solid solubility; a stable crystalline phase may be found with solute levels beyond the solubility limit at ambient temperature, or beyond the equilibrium limit at any temperature; and (iv) metastable phases which may form during processing like crystalline, quasicrystalline and intermetallic compounds. Chemical reactions can proceed towards equilibrium in stages, and the intermediate stages can yield a metastable phase. In the solid state amorphization reaction, an amorphous alloy can be produced by the reaction of two solid metallic elements. Severe mechanical deformation can lead to metastable states. The deformation forces the production of disturbed configurations or brings different phases into intimate contact promoting solid-state reactions.
The alloying process can be carried out using different apparatus such as planetary mills, attrition mills, vibratory mills, shaker mills, etc. [1]. A broad range of alloys, solid solutions, intermetallics and composites have been prepared in the nanocrystalline, quasicrystalline or amorphous state [2-10]. A significant increase in solubility limit has been reported in many mechanically alloyed systems [11, 12]. Several studies of the alloy formation process during mechanical alloying have led to conflicting conclusions like the interdiffusion of elements, the interactions on interface boundaries and/or the diffusion of solute atoms in the host matrix. Indeed, the alloying process is complex and hence, involves optimization of several parameters to achieve the desired product such as type mill, raw material, milling intensity or milling speed, milling container, milling atmosphere, milling time, temperature of milling, ball-to-powder weight ratio, process control agent, etc. The formation of stable and/or metastable crystalline phases usually competes with the formation of the amorphous phase. For alloys with a negative heat of mixing, the phase formation has been explained by an interdiffusion reaction of the components occurring during the milling process [13]. Even though the number of phases reported to form in different alloy systems is unusually large [14], and property evaluations have been done in only some cases and applications have been explored, the number of investigations devoted to an understanding of the mechanism through which the alloy phase’s form is very limited. This chapter summarizes the information available in this area. The obtained disordered structures by mechanical alloying are metastable and therefore, they will experience an ordering transition during heating resulting in exothermic and/or endothermic reactions. The thermal properties of materials are strongly related to the size of nanocrystals essentially when the radius of nanocrystals is smaller than 10 nm. Hence, an important task of thermal analyses is to find the size-dependent function of the thermodynamic amounts of nanocrystalline materials.
The state of a physical system evolves irreversibly towards a time-independent state in which no further macroscopic physical or chemical changes can be seen. This is the state of thermodynamic equilibrium characterized, for example, by a uniform temperature throughout the system but also by other futures. A non-equilibrium state can be defined as a state where irreversible processes drive the system towards the equilibrium state at different rates ranging from extremely fast to extremely slow. In this latter case, the isolated system may appear to have reached equilibrium. Such a system, which fulfils the characteristics of an equilibrium system but is not the true equilibrium state, is called a metastable state. Both stable and metastable states are in internal equilibrium since they can explore their complete phase space, and the thermodynamic properties are equally well defined for metastable states as for stable states. However, only the thermodynamically stable state is in global equilibrium; a metastable state has higher Gibbs energy than the true equilibrium state.
Thermodynamically, a system will be in stable equilibrium, under the given conditions of temperature and pressure, if it is at the lowest value of the Gibbs free energy:
Where H is enthalpy, T absolute temperature and S entropy. According to equation (1), a system can be most stable either by increasing the entropy or decreasing the enthalpy or both. At low temperatures, solids are the most stable phases since they have the strongest atomic bonding (the lowest H), while at high temperatures the -TS term dominate. Therefore, phases with more freedom of atomic movement, such as liquids and gases are most stable. Hence, in the solid-state transformations, a close packed structure is more stable at low temperatures, while a less close packed structure is most stable at higher temperatures. A metastable state is one in internal equilibrium, that is, within the range of configurations to which there is access by continuous change, the system has the lowest possible free energy. However, if there were large fluctuations (the nucleation of a more stable phase), transformation to the new phase would occur if the change in free energy, ΔG, is negative. A phase is non-equilibrium or metastable if it’s Gibbs free energy is higher than in the equilibrium state for the given composition. If the Gibbs free energy of this phase is lower than that of other competing phases (or mixtures thereof), then it can exist in a metastable equilibrium. Consequently, non-equilibrium phases can be synthesized and retained at room temperature and pressure when the free energy of the stable phases is raised to a higher level than under equilibrium conditions, but is maintained at a value below those of other competing phases. Also, if the kinetics during synthesis is not fast enough to allow the formation of equilibrium phase(s), then metastable phases could form.
During the mechanical alloying process, continuous fracturing, cold welding and rewelding of the powder particles lead to the reduction of grain size down to the nanometer scale, and to the increase of the atomic level strain. In addition, the material is usually under far-from-equilibrium conditions containing metastable crystalline, quasi-crystalline or amorphous phases. All of these effects, either alone or in combination, make the material highly metastable. Therefore, the transformation behaviour of these powders to the equilibrium state by thermal treatments is of both scientific and technological importance. Scientifically, it is instructive to know whether transformations in ball milled materials take place
A schematic DSC curve depicting the different stages during crystallization of an amorphous phase where Tg is the glass transition temperature; Tm the melting temperature, Tx1 and Tx2 are the onset crystallization temperatures [
The values of the peak onset temperature and peak areas depend on the position of the baseline. Therefore, the accurate baseline can be obtained by heating the sample to the desired temperature, then cooled it back to the ambient temperature and then reheated it to higher temperatures. The second DSC scan could be used either as the baseline or subtracted from the first scan to obtain the accurate peak positions and areas. There are two types of transformations: reversible and irreversible. For the former, the product phase will revert back to the parent phase. For example, transformation from one equilibrium phase to another on heating gives rise to an endothermic peak during melting and exothermic peak during cooling. However, during irreversible transformation of metastable phases such as amorphous phases, a peak of the opposite sign is not observed. In fact, there will be no peak at all. Furthermore, because metastable phases are always more energetic than the corresponding equilibrium phases, they often exhibit exothermic peaks in the DSC/DTA curves. If an amorphous alloy powder is heated to higher temperatures, one expects to observe a broad exothermic reaction at relatively low temperatures related to structural relaxation of the amorphous phase, a glass transition temperature as well as one or more exothermic peaks corresponding to crystallization event at higher temperatures. Structural changes that occur during crystallization can be investigated by X-rays diffraction or Mössbauer spectrometry by quenching the sample from a temperature just above the DSC/DTA peak temperature. Transmission electron microscopy investigations can also be conducted to uncover the microstructural and crystal structure changes on a finer scale. In addition, compositional changes can be detected. It may be pointed out, however, that there have not been many detailed crystallization studies of amorphous alloys synthesized by the mechanical alloying process [16].
The crystallization temperature corresponds to the maximum of the exothermic peak,
Where A is a constant and R is the universal gas constant. The activation energy
With:
Isothermal transformation kinetics study at different temperatures can be conducted by the Kolmogorov-Johnson-Mehl-Avrami formalism [22-25] in which the fraction transformed,
Where
Mechanical alloying has received a great interest in developing different material systems. It is a solid state process that provides a means to overcome the drawback of formation of new alloys starting from mixture of low and/or high melting temperature elements. Mechanical alloying is a ball milling process where a powder mixture placed in the vials is subjected to high-energy collisions from the balls. The two important processes involved in ball milling are fracturing and cold welding of powder particles in a dry high energy ball-mill. The alloying process can be carried out using different apparatus such as planetary or horizontal mills, attrition or spex shaker mill. The elemental or prealloyed powder mixture is charged in the jar (or vial) together with some balls. As a result of the induced heavy plastic deformation into the powder particles during the milling process, nanostructured materials are produced by the structural decomposition of coarser-grained structure. This leads to a continuous refinement of the internal structure of the powder particles down to nanometer scales.
Depending on the microstructure, the mechanical alloying process can be divided into many stages: initial, intermediate, final and complete [35]. Since the powder particles are soft in the early stage of milling, so they are flattened by the compressive forces due to the collisions of the balls. Therefore, both flattened and un-flattened layers of particles come into intimate contact with each other leading to the building up of ingredients. A wide range of particle sizes can be observed due to the difference in ductility of the brittle and ductile powder particles. The relatively hard particles tend to resist the attrition and compressive forces. However, if the powder mixture contains both ductile and brittle particles (Fig. 2a), the hard particles may remain less deformed while the ductile ones tend to bind the hard particles together [10, 36]. Cold welding is expected to be predominant in fcc metals (Fig. 2b) as compared to fracture in bcc and hcp metals (Fig. 2c).
During the intermediate stage of milling, significant changes occur in the morphology of the powder particles. Greater plastic deformation leads to the formation of layered structures (Fig. 2d). Fracturing and cold welding are the dominant milling processes. Depending on the dominant forces, a particle may either become smaller in size through fracturing or may agglomerate by welding as the milling process progresses. Significant refinement in particle size is evident at the final stage of milling. Equilibrium between fracturing and cold welding leads to the homogeneity of the particles at the macroscopic scale as shown in Fig. 2d for the Fe50Co50 powder mixture [37, 38]. True alloy with composition similar to the starting constituents is formed at the completion of the mechanical alloying process (Fig. 2e) as evidenced by the energy dispersive X analysis, EDX, (Fig. 2f). The large plastic deformation that takes place during the milling process induces local melting leading to the formation of new alloys through a melting mechanism and/or diffusion at relatively high temperature.
Mechanical alloying is a non-equilibrium process resulting in solid state alloying beyond the equilibrium solubility limit. Several studies of the alloy formation process during mechanical alloying have led to conflicting conclusions such as the interdiffusion of elements, the interactions on interface boundaries and/or the diffusion of solute atoms in the host matrix. Indeed, Moumeni et al. have reported that the FeCo solid solution was formed by the interdiffusion of Fe and Co atoms with a predominance of Co diffusion into the Fe matrix according to the spectrometry results [37]. However, Brüning et al. have shown that the FeCo solid solution was formed by the dissolution of Co atoms in the Fe lattice [39]. Sorescu et al. [40] have attributed the increase of the hyperfine magnetic field to a progressive dissolution of Co atoms in the bcc−Fe phase. Such discrepancies have been attributed to the milling conditions and/or to the fitting procedure of the Mössbauer spectra. The role of grain boundaries, the proportions and the thickness of which are dependent on the milling energy affect thus, the hyperfine structure originating some misinterpretations.
Morphologies of powder particles of the ball-milled Fe75Si15B10 (a), Ni20Co80 (b), Fe57Cr31Co12 (c and d), and Fe50Co50 powders (e) with the corresponding EDX analysis (f).
Diffusion in mechanical alloying differs from the steady state diffusion since the balance of atom concentration at the interface between two different components may be destroyed by subsequent fracturing of the powder particles. Consequently, new surfaces with different compositions meet each other to form new diffusion couples when different powder particles are cold welded together. Large difference in composition at the interface therefore promotes interdiffusion. In addition, the change in temperature during the milling process is very significant due to the exothermic reaction causing local combustion. Two major phenomena can contribute to the increase in milling temperature: friction during collisions and localized plastic deformation. At low temperatures, surface diffusion dominates over grain boundary and lattice diffusion. As the temperature is increased, however, grain boundary diffusion predominates, and at higher temperature lattice diffusion becomes the principal mode of diffusion. The first key factor controlling the formation of new alloys is the activation energy which is related to the formation of defects during balls-powder-balls and/or balls-powder-vials collisions. The second key is the vial temperature which is associated with plastic deformation as well as sliding between powder particles and high energetic balls and powder particles. The third key is the crystallite size that is related to the formation of nanometer crystalline structure during the milling process.
Mechanical alloying process was used to prepare nanocrystalline and/or amorphous alloys such as Fe, Fe-Co, Fe-Co-Nb-B, Fe-P and Ni-P from pure elemental powders in high-energy planetary ball-mills Fritsch Pulverisette P7 and Retsch PM 400/2, and vibratory ball-mill spex 8000. The milling process was performed at room temperature, under argon atmosphere, with different milling conditions such as rotation speed, ball-to-powder weight ratio, milling time and composition. In order to avoid the temperature increase inside the vials, the milling process was interrupted for 15−30 min after each 30−60 min depending on the raw mixture.
Particles powder morphology evolution during the milling process was followed by scanning electron microscopy. Structural changes were investigated by X-ray diffraction in a (
Fe and Fe50Co50 were prepared by mechanical alloying from pure elemental iron and cobalt powders in a planetary ball mill Fritsch P7, under argon atmosphere, using hardened steel vials and balls. The milling intensity was 400 rpm and the ball-to-powder weight ratio was 20:1. A disordered bcc FeCo solid solution is obtained after 24 h of milling (Fig 3), having a lattice parameter, a = 0.2861(5) nm, larger than that of the coarse-grained FeCo phase (a = 0.2825(5) nm). Such a difference in the lattice parameter value may be due to heavily cold worked and plastically deformed state of the powders during the milling process, and to the introduction of several structural defects (vacancies, interstitials, triple defect disorder, etc.).
Rietveld refinement of the XRD pattern of the Fe50Co50 powders milled for 40 h [
With increasing milling time, the crystallite size decreases down to the nanometer scale and the internal strain increases. The double logarithmic plot of the crystallite size versus milling time exhibits two-stage behaviour for both Fe and Fe50Co50 powders (Fig. 4). A linear fit gives slopes of −0.65 and –0.20 for short and extended milling times, respectively, in the case of Fe; and slopes of –0.85 and –0.03, respectively, for short and extended milling times in the case of Fe50Co50 mixture. The critical crystallite size achievable by ball milling is defined by the crossing point between the two regimes with different slopes [43]. Consequently, the obtained critical crystallite sizes are of about 13.8 and 15 nm for Fe and Fe50Co50 powders, respectively. By using different milling conditions (mills type, milling intensity and temperature) to prepare nanostructured Fe powders, Börner et al. have obtained the two-regime behaviour, for the grain refinement by using the Spex mill, with slopes of –0.41 and –0.08 for short and extended milling times, respectively. However, the crystallite sizes show only a simple linear relation with slopes of –0.265 and –0.615 by using the Retsch MM2 shaker and the Misuni vibration mill, respectively. The obtained critical crystallite size value was 19 nm [44].
Double logarithmic plot of the crystallite size against milling time for nanostructured Fe and Fe50Co50 powders [
DSC scans of nanostructured Fe and Fe50Co50 powders milled for 40 h are shown in Fig. 5. The non-equilibrium state is revealed by the broad exothermic reaction for both samples, in the temperature range 100−700°C, which is consistent with the energy release during heating due to recovery, grain growth and relaxation processes. As a result of the cold work during the milling process, the main energy contribution is stored in the form of grain boundaries and related strains within the nanostructured grains which are induced through grain boundary stresses [45]. It has been reported that the stored energies during the alloying process largely exceed those resulting from conventional cold working of metals and alloys. Indeed, they can achieve values typical for crystallization enthalpies of metallic glasses corresponding to about 40% of the heat of fusion, ΔHf [45]. The major sources of mechanical energy storage are both atomic disorder and nanocrystallite boundaries because the transition heats evolving in the atomic reordering and in the grain growth are comparable in value [46].
For the nanostructured Fe powders, the first endothermic peak is linked to the bcc ferro-paramagnetic transition temperature, TC, and the second peak to the bcc→fcc transition
DSC scans of nanostructured Fe and Fe50Co50 powders milled for 40 h [
temperature,
Evolution of the Curie temperature and the lattice parameter of the Fe powders as a function of milling time [
decreased by about 10 K from that of coarse-grained Gd while the magnetic transition is broader [49]. According to both Tc and
The disorder-order phase transformation temperature of the nanostructured FeCo powders which is nearly constant (~724°C) along of the milling process (Fig. 7), is comparable to that of bulk Fe-Co alloys. It is commonly accepted that Fe-Co undergoes an ordering transition at around 730°C, where the bcc structure takes the ordered α’−CsCl(B2)-type structure [50]. The ordering effect in the FeCo nanocrystals has been revealed by the changes in the magnetization upon heating and the temperature variation of the coercivity on heating and cooling [51]. Also, the phase transformation temperature from bcc−α to fcc−γ structure in the Fe50Co50 powders is rather milling time independent (~982°C). The lower resistivity of Fe50Co50 compared to that of pure Fe at 300 K [52] and the higher Curie temperature of Fe50Co50 suggest that there is less scattering of the conduction electrons by the magnetic excitations. Thus, the Curie temperature cannot be clearly observed because there is a phase transformation from the bcc to fcc form at 985°C.
Evolution of the order-disorder,
Nanostructured and disordered structures obtained by mechanical alloying are usually metastable. Depending on the Nb and B contents, the mechanically alloyed Fe-Co-Nb-B powders structure may be partially amorphous either magnetic and/or paramagnetic. Pure elemental powders of iron (6-8 µm, 99.7%), cobalt (45 µm, 99.8%), niobium (74 µm, 99.85%) and amorphous boron (> 99%) were mixed to give nominal compositions of Fe57Co21Nb7B15 and Fe61Co21Nb3B15 (wt. %), labelled as 7Nb and 3Nb, respectively. The milling process was performed in a planetary ball-mill Fritsch Pulverisette 7, under argon atmosphere, using hardened steel balls and vials. The ball-to-powder weight ratio was about 19/2 and the rotation speed was 700 rpm. For the (Fe50Co50)62Nb8B30 mixture, the milling process was performed in a planetary ball-mill Retsch PM400/2, with a ball-to-powder weight ratio of about 8:1 and a rotation speed of 350 rpm. In order to avoid the increase of the temperature inside the vials, the milling process was interrupted after 30 min for 15 min.
Rietveld refinement of the XRD patterns of 7Nb and 3Nb powders milled for 48 and 96 h[
The XRD patterns of 7Nb and 3Nb mixtures milled for 48 h (Fig. 8) are consistent of a large number of overlapping diffraction peaks related to different phases. The Rietveld refinement reveals the formation of a partially amorphous structure of about ~78%, where nanocrystalline tetragonal−Fe2B, tetragonal−Fe3B and bcc−FeCo type phases were embedded for 3Nb powders [53]. Whereas, for 7Nb powders, the milling product is a mixture of amorphous (~73.6%), bcc−Nb(B), tetragonal−Fe2B, orthorhombic−Fe3B and bcc FeCo type phases [54]. Further milling (up to 96 h) leads to the increase of the amorphous phase proportion for 7Nb and the mechanical recrystallization in the case of 3Nb mixture (Fig. 8) as evidenced by the decrease and the increase of the diffraction peaks intensity, respectively. The formation of the amorphous phase is confirmed by the Mössbauer spectrometry results as shown in Fig. 9. After 48 h of milling, the Mössbauer spectra exhibit more or less sharp absorption lines superimposed upon a broadened spectral component assigned to the structural disorder of the amorphous state [55]. For 3Nb powders, the mechanical recrystallization is confirmed by the emergence of sharp sextet related to the primary crystallization of α−Fe and FeCo after 96 h of milling. However, a stationary state is achieved for 7Nb powders. The increase of the average hyperfine magnetic field, <
Room temperature Mössbauer spectra of 3Nb and 7Nb powders milled for 48 and 96 h [
XRD patterns of the (Fe50Co50)62Nb8B30 powders milled for 25 and 100 h.
For the (Fe50Co50)62Nb8B30 powders mixture milled for 25 and 100 h, the best Rietveld refinements of the XRD patterns were obtained with two components: bcc−FeCo and amorphous phase (Fig. 10). The complete transformation of the heavily deformed FeB and bcc FeCo type phases into an amorphous state is achieved, after 125 h of milling, through the mechanically enhanced solid-state amorphization which requires the existence of chemical disordering, point defects (vacancies, interstitials) and lattice defects (dislocations). Indeed, the severe plastic deformation strongly distorts the unit cell structures making them less crystalline. The powder particles are subjected to continuous defects that lead to a gradual change in the free energy of the crystalline phases above those of amorphous ones, and hence to a disorder in atomic arrangement. The Mössbauer spectra confirm the formation of a paramagnetic amorphous structure, where about 3.8% of FeCo and Fe2B nanograins are embedded, after 125 h of milling (Fig. 11).
Nanocrystalline Fe72.5Co7.5Nb5+xB15-x with x=0, 5 and 10 at.% labelled as A, B and C, respectively, were prepared by mechanical alloying from pure elemental powders in a planetary ball-mill Retsch PM400, under argon atmosphere, using stainless steel balls and vials. The ball-to-powder weight ratio was about 8:1 and the rotation speed was 200 rpm [58]. The crystallite size decreases with increasing milling duration to about (7.1 ± 0.3) nm for the B-richest alloy (A). The XRD patterns (Fig. 12) reveal the formation of a bcc Fe-rich solid solution after 80 h of milling having an average lattice parameter of about 0.2871 nm for the three alloys.
Room temperature Mössbauer spectra of the (Fe50Co50)62Nb8B30 powders milled for 25 and 125 h.
XRD patterns of alloys A, B and C milled for 80 h [
Depending on the structural state after each milling time, several exothermic and endothermic peaks appear on heating of the mechanically alloyed Fe-Co-Nb-B powders. Representative DSC scans of 7Nb and 3Nb (Fig. 13) as well as (Fe50Co50)62Nb8B30 powder mixtures (Fig. 14) exhibit different thermal effects (Table 1). For all ball milled powders, the first exothermic peak that spreads over the temperature range 100−300°C can be attributed to recovery, strains and structural relaxation. The important heat release (20.56 J/g) for 3Nb powders might be related to the amount of structural defects. The second exothermic peak (2), at 415°C, can be attributed to the α-Fe and/or α-FeCo primary nanocrystallization. This temperature is smaller than that obtained for the ball-milled 7Nb and (Fe50Co50)62Nb8B30 powders. Such a difference might be attributed to the Nb content since Co usually increases the onset of crystallization by about 20°C because this atom inhibits atomic movement raising the kinetic barrier for crystallization. The small exothermic peaks centred at ~623.5°C (3) and ~675.7°C (4) in the 3Nb powders can be related to the crystallization of Fe-borides.
DSC scans of 3Nb and 7Nb powder mixtures milled for 48 h [
DSC scans of the (Fe50Co50)62Nb8B30 powders milled for 100 and 125 h.
Thermal stability of the nanocrystalline phases was investigated by DSC for alloys A, B and C milled for 160 h at a heating rate of 10 K/min (Fig. 15). The broad exothermic process starting at ~400−420 K is due to early surface crystallization (particle surface) and/or internal stress relaxation [58]. In all alloys, an additional exothermic process was detected with a peak temperature between 713 and 743 K. One observes that the peak temperature increases with increasing Nb content from 5 to 15%. This result agrees with those of the ball-milled 3Nb, 7Nb and (Fe50Co50)62Nb8B30 mixtures.
The endothermic peak at about 286.4, 344.5 and 420°C for 3Nb, 7Nb and (Fe50Co50)62Nb8B30 powders, respectively, that can be attributed to the glass transition temperature, Tg, gives evidence of the amorphous state formation. The glass transition temperature of the (Fe50Co50)62Nb8B30 powders increases rapidly up to 25 h of milling, and then remains nearly constant on further milling time (Fig. 16). The increase of Tg might be correlated to the amorphous phase proportion and/or to the change of its composition. The obtained low values compared to those of the amorphous ribbons with the same composition, can be linked to the heterogeneity of the ball-milled samples. The glass transition is not a first order phase transition but a kinetic event dependent on the rearrangement of the system and experimental time scales. Therefore, the transition would be a purely dynamic phenomenon.
Sample Milling time (h) | ||||
(Fe50Co50)62Nb8B30 (100 h) | 1 | 138.83 | 7.58 | 420 |
7Nb (48 h) | 1 | 136.8 | 2.1 | 344.5 |
3Nb (48 h) | 1 | 198.5 | 20.56 | 286.4 |
3 | 623.5 | 1.4 | ||
4 | 675.7 | 3.9 |
Peak temperature, Tp, enthalpy release, ΔH, and glass transition temperature, Tg, of 7Nb and 3Nb powders milled for 48 h, and (Fe50Co50)62Nb8B30 mixture milled for 100 h [55].
DSC scans at a heating rate of 10 K.min-1 of the ball-milled A, B and C powders for160 h [
Variation of the glass transition temperature and the amorphous phase proportion of the (Fe50Co50)62Nb8B30 powders as a function of milling time.
DSC, which measures heat flow to and from a specimen relative to an inert reference, is the most common thermal analysis method used to measure the glass transition. The heat capacity step change at the glass transition yields three temperature values: onset, midpoint and endset. The midpoint is usually calculated as the peak maximum in the first derivative of heat flow (Fig. 1), although it can be calculated as the midpoint of the extrapolated heat capacities before and after the glass transition. This later is the temperature region where an amorphous material changes from a glassy phase to a rubbery phase upon heating, or
DSC detects the Curie temperature as a change in heat flow and due to the small amount of energy associated with this transition. An endothermic reaction occurs just below the Curie temperature as energy is being absorbed by the sample to induce randomization of the magnetic dipoles. An exothermic event occurs directly after the Curie temperature since no further energy is needed for randomization. Consequently, the line break at about 237°C and 249°C for 3Nb and 7Nb powders (Fig. 13), respectively, can be assigned to the ferro-paramagnetic transition at Curie temperature of the amorphous phase. Those values are comparable to that reported for the amorphous (Fe100-xCox)62Nb8B30 bulk metallic glasses [59], where Tc was found to be 245°C for x=0. Accordingly, one can suppose that the amorphous phase composition is Co-free FeBNb-type. Different Tc values of about (157−167)°C and (87−97)°C have been reported for the as-quenched Fe52Co10Nb8B30 and Fe22Co40Nb8B30 alloys [60], respectively. Tc of the residual amorphous phase exhibits antagonist behaviour for both alloys. It decreases with increasing crystalline fraction for the Co−rich Fe22Co40Nb8B30 alloy, and shifts to higher temperature for the Fe−rich Fe52Co10Nb8B30 alloy. Also, lower Tc values in the temperature range (214−230)°C were obtained for the as-cast state and in nanocrystalline Fe77B18Nb4Cu ribbons annealed at different temperatures [61].
Fig. 17 shows the evolution of Curie temperature of the amorphous phase in the (Fe50Co50)62Nb8B30 powders against milling time. Since the amorphous phase Curie temperature is very sensitive to the chemical composition, therefore the progressive decrease of Tc with increasing milling time can be attributed to the increase of B and/or Nb content in the amorphous matrix. It has been reported that the Curie temperature of the FeCoNbB amorphous alloys increases with the B content in the amorphous matrix [62]. Both the first and the second DSC scans of the powders milled for 100 and 125 h, respectively, display many endothermic peaks (see the inset in Fig. 14) that can be attributed to Curie temperatures of different Fe-boride phases and the residual matrix (t=125 h). For example, the endothermic peak at T=579.8°C can be related to the Curie temperature of Fe3B [63].
The apparent activation energy of the crystallization process in the alloys A, B and C was evaluated by the Kissinger method. The obtained values 2.47±0.07, 2.63±0.05 and 2.71±0.08 eV for alloys A, B and C, respectively, can be associated with grain growth process. The activation energy and the peak temperature variation as a function of Nb content (Fig. 18) reveal that the highest peak temperature and activation energy correspond to the 15%Nb alloy. According to the structural and thermal analysis, it can be concluded that the partial substitution of B by Nb favours the stability of nanocrystalline phase with regard to crystal growth.
Variation of the amorphous phase Tc in the (Fe50Co50)62Nb8B30 powders as a function of milling time.
Apparent activation energy and peak temperature of the crystallization process against Nb content for alloys A, B and C milled for 160 h [
Stability of the nanostructured Fe-Co-Nb-B powders can be followed by the variation of the magnetic properties such as saturation magnetization, Ms, and coercivity, Hc. The hysteresis loops of ball milled 3Nb powders for 48 h and 7Nb powders for 96 h and heat treated up to 700°C (Fig. 19) display a sigmoidal shape which is usually observed in nanostructured samples with small magnetic domains. This can be correlated to the presence of structural distortions inside grains. One notes that both Ms and Hc values of 3Nb powders are higher than those of 7Nb powders. The increase of Hc from 71 to 115.5 Oe, after heat treatment of the ball milled 3Nb powders for 96 h, points out that the FeCo-rich ferromagnetic grains might be separated by Nb and/or B-rich phase with weaker ferromagnetic properties. Another possible origin for this behaviour is the increase of Fe2B boride proportion. Nonetheless, for 7Nb mixture Ms increases slightly while Hc remains nearly constant after heat treatment of the powders milled for 48 h. One can conclude that the nanostructured state is maintained after heat treatment.
Hysteresis loops of 3Nb and 7Nb powders milled for 96 h and 48 h, respectively, and after heat treatment up to 700°C [
Thermal annealing leads, in general, to the relaxation of the introduced stresses during the milling process. The DSC curves of the ball-milled Ni70P30 powders for 3 and 12 h (Fig. 20) display different behaviour on heating at a rate of 10°C.min-1. After the first run up to 700°C (scan a), samples are cooled down to ambient temperature, then reheated in the same conditions. One notes that the DSC signal of the second run (scan b) shows a line without any thermal effect indicating that the phase transformation is achieved during the first run [64]. However, for the first run curve, the enthalpy release spreads over the temperature range (100−650)°C. The large exothermic reactions at temperatures below 300°C can be attributed to recovery and strain relaxation. The DSC curve of the powder milled for 3 h shows a single exothermic peak at 496.4°C. While, after 12 h of milling, the DSC curve reveals several endothermic peaks, and one exothermic peak at 567.6°C. According to the Curie temperature of pure Ni (Tc = 350°C), the endothermic peaks (Fig. 21) can be related to the magnetic transition temperature of dilute Ni(P) solid solutions. However, the exothermic peak might be assigned to a growth process of Ni2P nanophase. The depression of Tc compared to that of pure Ni indicates that the nearest-neighbour coordinates are essentially changed in the magnetic nanocrystallites by the P additions. The reason for the existence of several magnetic phase states and therefore, several Curie temperatures can be attributed to inhomogeneities since the Curie temperature is sensitive to the chemical short range order and subsequently, to the local Ni environment.
DSC plots of the Ni70P30 powders milled for 3 and 12 h at a heating rate of 10°C/min; first (a) and second heating runs (b) [
Enlargement of the low temperature regions of the DSC scan of the Ni70P30 powders milled for 12 h.
The kinetics of Mo dissolution into the α-Fe matrix of the Fe-6Mo mixture has been deduced from the XRD analysis by following the evolution of the (110) diffraction peak intensity of the unmixed Mo as a function of milling time [26]. Since the milling process occurs at room temperature, one can suppose that the temperature is constant. In addition, the milling time can be considered as the necessary time for phase transformation. Consequently, the mixed fraction of Mo which is considered as the fraction transformed, x, can be described by the Johnson-Mehl-Avrami formalism. The double logarithmic plot ln(-ln(1-x)) versus lnt leads to the Avrami parameter n, and the rate constant k. Two stages have been distinguished according to the kinetics parameter values: (i) a first stage with n1= 0.83 and k1= 0.34; and (ii) a second stage with n2= 0.33 and k2 = 0.73. The former proves that the Mo dissolution is very slow even non-existent in the early stage of milling (up to 6 h), while the later can be linked to the increased diffusivity by decreasing crystallite size and increasing the grain boundaries area on further milling time.
Amorphization kinetics of the Fe27.9Nb2.2B69.9 (at. %) powders has been deduced from the Mössbauer spectrometry results by following the variation of the α-Fe transformed fraction as a function of milling time [27]. The amorphization process can be described by one stage with an Avrami parameter of about n~1 (Fig. 22). This value is comparable to those obtained for transformations controlled by the diffusion at the interface and dislocations segregation with 0.45< n < 1.1. This might be correlated to the existence of a high density of dislocations and various types of defects as well as to the crystallite size refinement. Comparable values of the Avrami parameter were obtained for the primary crystallization of the amorphous FeCoNbB alloy prepared by melt spinning [65].
Johnson-Mehl-Avrami plot of the ball-milled Fe27.9Nb2.2B69.9 versus milling time [
Johnson-Mehl-Avrami plot of the ball-milled Fe57Co21Nb7B15 versus milling time [
The mixing kinetics of the Fe57Co21Nb7B15 powders can be described by two stages [27, 66] with different Avrami parameters n = 1.08 and n\' = 0.34 (Fig. 23). The lower values of the Avrami parameter can be ascribed to the presence of both Nb and B which favour the grain size refinement and the formation of a highly disordered state. For the (Fe50Co50)62Nb8B30 mixture, two stages have been obtained with different Avrami parameter values n1 = 1.41 and n2 = 0.34 [2]. The former value is comparable to those obtained for the Finemet and Nanoperm [67]. However, it is higher than that obtained during the crystallization of the amorphous FeCoNbB alloy where α-(Fe,Co) nanocrystals with grain size of 15 nm are distributed in the amorphous matrix [65]. Bigot et al. have obtained a value of n = 1.5 for the nanocrystallization of the Finemet [68]. Comparable kinetics parameters have been obtained in the Ni-15Fe-5Mo (n = 1.049 and k = 0.57) [69]. The important fraction of structural defects which is introduced during the milling process favours the phase formation through the diffusion at the surface which is dominant, at lower temperatures, in comparison to the diffusion by the grain boundaries and the lattice parameter (vacancy’s diffusion).
Thermal analysis is widely used in the reaction study of the mechanically alloyed powder particles because of the obtained metastable disordered structures. Hence, thermal annealing leads to the relaxation of the introduced stresses during the milling process. The heat effects are dependent on the structural and microstructural properties of the ball-milled powders.
Prof. Safia Alleg is grateful to the University of Girona-spain for the financial support as invited professor. Financial support from AECID A/016051/08 and AECID A/025066/09 projects is acknowledged. Financial support from WLI Algeria is acknowledged.
Several image encryption algorithms are being developed today to meet privacy needs in multimedia communications [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]. With the rapid expansion of the Internet, innovative technologies, and cryptanalysis, it has become necessary to build new and appropriate cryptosystems for secured data transfer, especially for digital images. Nowadays, a large quantity of images is produced in various fields and exchanged sometimes with text through different channels, favoring the development of multiple-image encryption (MIE) instead of single-image encryption (SIE). A secure technique to protect the large amounts of data (image and text) exchanged in unsecured communication channels is to combine cryptography and watermarking [26, 27]. These two combined approaches help to produce a two-level security of the text and image, especially when the message is hidden in the image to be encrypted. Various watermarking techniques are proposed in the literature [28, 29, 30, 31, 32], and the most used are discrete wavelet transformation (DWT) and discrete cosine transformation (DCT). For instance, if an information, such as a signature, a logo, or a text is embedded in low- or medium-frequency DCT coefficients, then it may be recovered without any loss; however, only high-frequency DCT coefficients are lost in low-pass filtering.
In literature, many encryption algorithms, such as International Data Encryption Algorithm (IDEA), Advanced Encryption Standard (AES), and Data Encryption Standard (DES) have been proposed [1]. However, these standard algorithms do not seem to be appropriate for image encryption, because of the intrinsic features of images, such as huge data capacity, high redundancy, strong correlation among adjacent pixels, and low entropy [2]. Some basic properties of chaotic systems such as the sensitivity to the initial condition and control parameters, sensitivity to plain text, ergodicity and randomness behavior, meet the requirements for a good cryptosystem. Consequently, several cryptosystems were developed by researchers, based on chaotic systems because the latter provided a good combination of speed, high security, complexity, reasonable computational overheads, and computational power [3]. With these features, chaotic-based cryptosystems have excellent properties of confusion and diffusion, which are desirable in cryptography. Therefore, many techniques involving different chaotic systems have been published [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 23], and we can distinguish one-dimensional (1D) chaotic maps and high-dimensional (HD) chaotic maps.
Among the chaotic encryption algorithms developed, the ones using a one-dimensional (1D) chaotic system like Logistic, May, Tent, and Sine map have proven to have some strengths, such as: high-level efficiency, simplicity, and high-speed encryption. 1D chaotic structures have been widely used [4] due to their simple structures, as opposed to the complex ones of higher dimensional chaotic system (which causes a relative slowness in computation). However, some schemes using the 1D map have been broken due to their weaknesses like nonuniform data output, small key space, periodic data output, and poor ergodicity properties for some ranges of control parameters [5, 6]. To overcome this drawback, some researchers stated that the 1D chaotic map should not be used alone [7, 8]. Others proposed new 1D chaotic systems with better properties like Spatiotemporal chaos in [9], coupled with the 1D chaotic map [6], the Nonlinear Chaotic map Algorithm (NCA) [10], and, more recently, nonlinear combinations of two different 1D chaotic maps [3, 11, 12]. For example, Abanda and Tiedeu [3] combined outputs of Duffing and Colpitts chaotic systems to encrypt gray and color images. Kamdeu and Tiedeu [11] proposed a fast and secured encryption scheme using new 1D chaotic systems obtained from Logistic, May, Gaussian, and Gompertz maps. In [12], Chenaghlu et al. proposed a polynomial combination of 1D chaotic maps for image encryption using dynamic functions generation.
Recently, in order to increase the efficiency of cryptosystems for multiple images, some authors proposed algorithms integrating the concept of fusion or mixing images as a step in the encryption process. Image fusion has been proven to have potential for encryption in both spatial and frequency domains. In the last 8 years, much effort has been devoted to compressing and encrypting images at the same time [13], which is considered as a new tool used to reduce the amount of data to be transmitted and protecting the use of these data against unauthorized access. In particular, the discrete cosine transformation (DCT) is employed as a useful tool for spectral fusion in most of these methods. The widely used application DCT for image compression is mainly based on its energy compaction property, which means that the low-frequency coefficients are located around the top-left corner of its spectral plane [24]. In 2018, Jridi and Alfalou [14] proposed a cryptosystem to improve a Simultaneous Fusion, Compression and Encryption (SFCE) scheme [15] in terms of time consumption, bandwidth occupation, and encryption robustness. In [16], Dongfeng et al. proposed a new scheme for simultaneous fusion, imaging and encryption of multiple target images using a single-pixel detector. This algorithm achieves good performance in terms of robustness as the number of images to multiplex increases, but suffered from reduced key space and poor quality of images recovered. Mehra and Nishchal [17] proposed an image fusion encryption based on wavelets for securing multiple images through asymmetric keys. It offers a large key space, which enhances the security of the system. In 2016, Qin et al. [18] proposed an optical multiple-image encryption scheme in diffractive imaging using spectral fusion and nonlinear operations.
More recently, Zhang and Wang [19, 20] proposed two schemes of multiple-image encryption (MIE): the first algorithm based on mixed image element and permutation, and the second MIE algorithm based on mixed image element and chaos. The cryptosystem shows good performances, but can be improved in terms of compression to reduce the size of the multiplex big image when the number of target images increases. In [21], Zhu and Zhang proposed an encryption algorithm of mixed image element based on an elliptic curve cryptosystem. Experimental results and theoretical analysis show that the algorithm possesses a large key space and can accomplish a high level of security concerning information interaction on the network platform, but the encryption and decryption computational time is long. In 2013, Abdalla and Tamimi [22] proposed a cryptosystem, which combines two or more images of different types and sizes by using a shuffling-substitution procedure. Here, the process of mixing image combines stream cipher with block cipher, on the byte level.
After analyzing most MIE algorithms operating in the spectral domain, the robustness of the cryptosystem increases with the number of input images. Consequently, the quality of decrypted images is degraded. Therefore, it is important to design cryptosystems that can keep a good compromise between a large number of images added to text to encrypt, a small MSE after decryption, and a good performance in terms of robustness and efficiency.
As a result, this chapter suggests a new MIE algorithm based on the spectral fusion of different types of watermarked images of same size using discrete cosine transformation (DCT) associated with a low-pass filter and chaotic maps. The proposed scheme has several strengths: it is robust, combines watermarking and cryptography, which produce a two-level security, uses chaotic maps with good properties, encrypts a large number of watermarked images into two hybrid ciphered images, and the quality of the reconstructed images and text is good (reduced MSE). The encryption process comprises three main steps: in the first step, target images are fused into two images through DCT and low-pass filter; in the second step, the small blocks with the size of (4 × 4) images are permuted in a certain order; and in the last step, which is the diffusion phase, the two scrambled images are fused by a nonlinear mathematical expression based on Cramer’s rule to obtain two hybrid encrypted images. The key generation of the cryptosystem is made dependent on the plain images.
The rest of the chapter is organized as follows: Section 2 presents an overview of chaotic generators used in the cryptosystem and the description of the watermarking process. In Section 3, spectral fusion of plain images is detailed. The proposed encryption/decryption scheme is given in Section 4. In Section 5, experimental results and algorithm analyses are presented, then compared with others in the literature. We end with a conclusion in Section 6.
The equations of 1D Logistic, May, Gaussian, and Gompertz maps are described from Eqs. (1) to (4), respectively [11].
where
where
where
where the control parameter
The chaotic properties of 1D Logistic, May, Gaussian, and Gompertz maps are not suitable to build a secure cryptosystem when they are used alone. To solve this problem, Zhou et al. [23] proposed to combine the different seed maps. Figure 1 shows the new map obtained from a nonlinear combination of two different 1D chaotic maps.
New chaotic scheme.
Its equation is defined by Eq. (5)
where
Eq. (6) defines the May-Gaussian (MG) map
where
It is defined by Eq. (7)
where
Figure 2 illustrates the bifurcation diagram and the Lyaponuv exponent graphics of these maps. Referring to Figure 2, all the previous 1D chaotic systems present a wider chaotic range and a more uniform distribution of their density functions. Furthermore, the maximum Lyaponuv exponent values obtained are respectively 8.1, 5.6, and 2.5. Then, these combined 1D systems are more suitable for secure and high-speed encryption if the encryption algorithm is built around a good algebraic structure. Additively, in order to confirm the good performance of the previous pseudo random number generators, we performed the NIST statistical tests. Analysis of these results (see Table 1) showed that all the 15 tests were congruent for the three chaotic maps.
Bifurcation diagrams and Lyaponuv exponent graphics of combined chaotic maps, (a) and (d) logistic-may, (b) and (e) May-Gaussian, (c) and (f) Gaussian-Gompertz.
Statistical test | Logistic-May map (LM) | May-Gaussian map (MG) | Gaussian-Gompertz map | |||
---|---|---|---|---|---|---|
p-Value | Result | p-Value | Result | p-Value | Result | |
Frequency | 0.98147 | 98/100 | 0.99680 | 100/100 | 0.99438 | 100/100 |
Block-frequency | 0.6929 | 97/100 | 0.69842 | 98/100 | 0.678415 | 97/100 |
Cumulative-sums | 0.78621 | 96/100 | 0.87124 | 97/100 | 0.9014 | 100/100 |
Runs | 0.88052 | 99/100 | 0.92735 | 100/100 | 0.87246 | 98/100 |
Longest-runs | 0.98654 | 99/100 | 0.99815 | 100/100 | 0.97729 | 98/100 |
Rank | 0.54702 | 97/100 | 0.57914 | 98/100 | 0.5873 | 99/100 |
FFT | 0.87531 | 97/100 | 0.89678 | 98/100 | 0.82670 | 98/100 |
Nonoverlapping-templates | 0.78951 | 100/100 | 0.75091 | 99/100 | 0.77856 | 98/100 |
Overlapping-templates | 0.28435 | 99/100 | 0.18942 | 97/100 | 0.25167 | 98/100 |
Universal | 0.38277 | 99/100 | 0.34834 | 98/100 | 0.37051 | 100/100 |
Approximate entropy | 0.45393 | 98/100 | 0.49357 | 99/100 | 0.41560 | 98/100 |
Random-excursions | 0.195257 | 60/60 | 0.192410 | 59/60 | 0.19478 | 59/60 |
Random-excursions Variant | 0.14358 | 58/60 | 0.13871 | 57/60 | 0.15120 | 59/60 |
Serial | 0.42962 | 97/100 | 0.47359 | 99/100 | 0.41757 | 97/100 |
Linear-complexity | 0.08945 | 98/100 | 0.32876 | 100/100 | 0.15762 | 98/100 |
Final result | success | success | success |
Statistical NIST tests results of 1,000,000 bits.
Before multiplexing the target images, a binary information in the form of a logo was inserted in one of the target images. To do this, we used a simple watermarked algorithm, which makes the hidden message imperceptible in the watermarked image. Taking advantage of the benefits of DCT, it is possible to embed an information or watermark (text, logo, image) in low- or medium-frequency DCT coefficients. In fact, DCT decomposes an image into three frequency regions: low, medium, and high frequencies. It is recommended to insert the watermark in the low- and medium-frequency regions of the host image in order to ensure imperceptibility [32]. In this work, we adopted the watermarking technique described in [33] in which the message to hide is added to the medium-frequency region discrete cosine coefficients in selected pixel blocks of size
To illustrate an embedded process, as can be seen in Figure 3, we used a host image of size 512
Results of the watermarked process. (a) Host image (512
In order to protect the watermarked and host image from unauthorized access and noise attack, the watermarked image was encrypted with other images in a mixed process.
In this section,
Spectral fusion of target images.
Then, after all of these target images are grouped together by a way of simple addition, the inverse discrete cosine transformation (IDCT) of the multiplex image is performed. A simple rotation is performed on each of these blocks before spectral multiplexing, to prevent from information overlap. Figure 4 illustrates the description of the process. It is possible to multiplex a large number of target images by selecting a smaller size of the filter. However, in this case, the recovered images will be highly altered. To keep a good quality of reconstructed images while maintaining a large number of target images to encrypt, we chose to group these images in two multiplex images of the same size.
This section presents the proposed cryptosystem, which comprises blocks-permutation and diffusion steps using chaotic generators. Figure 5 illustrates the entire process.
Encryption scheme.
A. Blocks-permutation
The plain image is each of the two multiplex images obtained in Section 3. The plain image is decomposed into small blocks of the same size; let us choose blocks size of (
The permutation of blocks is realized as follows:
Divide the plain image
Use initial condition and control parameters
Repeat step 2 to generate a new sequence, using new initial condition and control parameters
Sort the chaotic sequence
Number all the blocks of the plain image obtained in step 1, and adjust their positions with the previous permutation of step 3. Then, the image obtained is a block image permuted.
The values
where
B. Diffusion of the scrambled images
At this level, the two scrambled images are combined in order to create the final hybrid encrypted images that would be difficult to crack. The May-Gaussian and Gaussian-Gompertz systems in Eqs. (6) and (7) are used as pseudo random generators to generate two chaotic sequences after 2 M × 2 M iterations. These values are arranged in two arrays
where
The arrays
where
In the decryption process, the encrypted images are first decomposed using Cramer’s rule in order to recover the scrambled images. Knowing the fusion keys (
Then, the two multiplex images can be obtained easily by decrypting
Numerical simulation experiments have been carried out to verify the proposed encryption method using MATLAB 2016 b platform on a PC with Core (TM) i7-353U processor of 2.5GHz. We first take eight images with 512 × 512 pixels and 256 gray levels as the target images to be encrypted, which are combined in two multiplex images as shown in Figure 6 (
The size of the filter (
For a well-ciphered image, all the frequencies of pixels must be uniformly distributed. As one can see in Figure 7, the histogram of the multiplex encrypted images is uniform.
Plain and combined images. (a–d) Images combined in multiplex image 1, (e–h) images combined in multiplex image 2, (i) multiplex image 1 before IDCT, (j) multiplex image 1 after IDCT.
Encrypted images and their histograms. (a) Multiplexed image 1, (b) multiplexed image 2.
Plot of correlation coefficients in horizontal, vertical, and diagonal directions of plain and cipher cameraman (512 × 512). (a, c, e) correlation coefficients of plain images in horizontal, vertical, and diagonal directions respectively. (b, d, f) correlation coefficients of ciphered images in horizontal, vertical, and diagonal directions respectively.
A good cryptosystem produces a cipher image with a correlation coefficient close to zero, for two adjacent pixels. Five thousand pairs of adjacent pixels were chosen to calculate the correlation coefficients in horizontal, vertical, and diagonal directions respectively, by using Eq. (17).
where X and Y are the values of two adjacent pixels in the image, C
Imageq | Test | Plain image | Encrypted multiplex image 1 or 2 |
---|---|---|---|
Cameraman | HC | 0.9314 | 0.0023 |
VC | 0.9400 | 0.051 | |
DC | 0.8931 | −0.003 | |
Peppers | HC | 0.9934 | 0.0013 |
VC | 0.9954 | −0.0020 | |
DC | 0.9919 | 0.0044 |
Correlation coefficient.
The information entropy evaluates the level of randomness contained in a sequence
where
Key space size is the total number of different keys that can be used in an encryption algorithm. A good encryption algorithm needs to contain sufficiently large key space to make the brute-force attack infeasible. The high sensitivity to initial conditions inherent to any chaotic system, that is, exponential divergence of chaotic trajectories, ensures high security [11].
In literature, a key space of at least 1030 is required for the system to be robust [19]. The proposed encryption algorithm actually does have some of the following secret keys: the initial values
An excellent encryption algorithm should have the desirable property of spreading the influence of slight change to the plain text over as much of the cipher text as possible. The sensitivity of a cryptosystem is evaluated through Number of Pixel Change Rate (NPCR), see Eq. (19), and Unified Average Change Intensity (UACI), see Eq. (20), criteria, which consist in testing the influence of one-pixel change of a plain image in the resulting cipher image.where
Table 4 gives the measurement of NCPR and UACI between two cipher images of cameraman, Lena and peppers, when a Least Significant Bit (LSB) changed on gray value in the last pixel’s position. We can notice that the values obtained are around the mean of 99.61 for NCPR and 33.49 for UACI. This result shows that a slight change to the original images will result in a great change in all the encrypted images. The results also imply that the proposed algorithm has an excellent ability to resist the differential attack.
Image | Test | |
---|---|---|
Multiplex encrypted image 1 | NCPR | 99.62 |
UACI | 33.54 | |
Multiplex encrypted image 2 | NCPR | 99.63 |
UACI | 33.47 |
NCPR AND UACI measure after a LSB change.
As the number of target images to encrypt increases, the quality of recovered images decreases. In order to reduce the NMSE between plain and decrypted images and enlarge the number of target images, we grouped them into two multiplexed images before encryption. To evaluate quantitatively the quality of decrypted image, we used the normalized mean square error (NMSE) between the original image and the decrypted image. The NMSE is defined as:
where M × N are the size of the image, ID(i, j) and IE(i, j) are the values of the decrypted image and the original image at the pixel (i, j), respectively. Table 5 presents the values of NMSE for a set of different target images of size 512 × 512. From this table, we can observe that for
Number of target images ( | ||||
---|---|---|---|---|
NMSE | 0.00082 | 0.0019 | 0.00376 |
NMSE for a set of different target images.
Table 6 reports a comparison of encryption time by the proposed algorithm with some recent works in literature for different images. The algorithm written under Matlab platform was not optimized. The computer time consumption is 0.27389 s, which is smaller than those of [19, 24].
The performance of the proposed algorithm compared to similar and good standing ones in literature is shown in Table 7. From the table, we can observe that the proposed encryption algorithm has a large key space and can encrypt a large number of target images in a good time compared to others. As for UACI and NPCR, they are about the best values expected (respectively >33.3 for UACI and >99.6 for NPCR) as can be seen in the table. Finally, our cryptosystem exhibits the best correlation value and a reduced normalized Mean Square Error (MSE) after decryption step.
Key space | Average correlation | Entropy | NPCR | UACI | Encryption time (s) | NMSE | |
---|---|---|---|---|---|---|---|
Proposed algorithm | 10135 | 0.0032 | 7.9993 | 99.61 | 33.49 | 0.27389 | 3.7 × 10−3 |
Ref. [19] [2017] | 1060 | 0.003 | 7.9994 | 99.62 | 33.50 | 0.7103 | — |
Ref. [20] [2017] | 1056 | — | 7.8225 | — | — | 0.255 | — |
Ref. [24] [2016] | 1090 | — | — | — | — | 11.66 | 8.448 × 10−3 |
Ref. [14] [2015] | 2260 | 0.0032 | — | 99.92 | — | — | |
Ref. [25] [2018] | 10210 | 0.0031 | 7.9986 | 99.62 | 33.42 | 2.386 | 0.0155 |
Comparison of the proposed cryptosystem with others.
In this chapter, an image encryption algorithm based on spectral fusion of multiple watermarked images and new chaotic generators is proposed. Logistic-May (LM), Gaussian-Gompertz (GG), and May-Gaussian (MG) systems were used as chaotic generators in the processes of confusion and diffusion. The target images were firstly combined in two multiplex images of same size through DCT and a low-pass filter. Secondly, the previous images are scrambled by permuting the blocks size of (
This work was partly supported by ERMIT, Entrepreneurship, Resources, Management, Innovation and Technologies.
The authors declare that they have no conflict of interest.
Supporting women in scientific research and encouraging more women to pursue careers in STEM fields has been an issue on the global agenda for many years. But there is still much to be done. And IntechOpen wants to help.
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