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Hysteresis of Solid-State Reactions: Its Cause and Manifestations

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Hysteresis of Solid-State Reactions: Its Cause and Manifestations American Journal of Condensed Matter Physics 2013, 3(5): 142-150 DOI: 10.5923/j.ajcmp.20130305.05 Hysteresis of Solid-State Reactions: Its Cause and Manifestations Yuri Mnyukh 76 Peggy Lane, Farmington, CT, USA Abstract The aim of this article is to establish the physical origin of hysteresis in solid state reactions. It had not been identified by the conventional science that remained limited by phenomenological modeling. The hysteresis revealed itself in detail as an essential component of the molecular mechanism of phase transitions in our studies of good transparent single crystals by optical microscopy and X-rays. The exclusive cause of hysteresis is nucleation lags and rooted in the nature of the nucleation far from the classical "random fluctuation" model. The nuclei are localized on crystal defects where nucleation lags are encoded. The hysteresis in structural, ferromagnetic and ferroelectric phase transitions, and upon magnetization and polarization results from the underlying role of structural rearrangements in these processes. Formation of structural and magnetic hysteresis loops is analyzed in detail. Ke ywo rds Hysteresis, Structural Hysteresis, Magnetic Hysteresis, Ferroelectric Hysteresis, Phase Transition, Range of Transition, Nucleation, Hysteresis Loops, Magnetization what are the factors that determine their shape? What is the 1. The Phenomenon of Hysteresis relation, if any, between the temperature and ferromagnetic (and ferroelectric) hysteresis? Hysteresis is a lagging to respond when the system is prompted to change by a control parameter. The phenomenon does not depend on the direction of the change 2. Conventional Science: and is not rooted in kinetics. In solid-state reactions we will Phenomenological Modeling call it structural when it relates to change of crystal structure Setting aside empirical data and merely opinions, and magnetic when it relates to change of magnetization (or scientifica lly-founded answers with explanations to the simp ly hysteresis of polarization in relation to electric above questions are not, and cannot be, found in the literature. polarization). The term "hysteresis" in the condensed matter They are hidden in the origin of the hysteresis that has not literature is frequently assumed only the magnetic hysteresis. been identified. Hysteresis is a significant feature of phase transitions and Those who believe in the Landau's theory[1] of other solid-state reactions. The phase transitions caused by second-order phase transitions must also accept that those change of temperature or pressure, or by application of phase transitions are hysteresis-free. This inference is magnetic or electric field, occur not at the point (TO if it is immaterial, however, since sufficiently documented second - temperature) when the equality of free energies of the phases order phase transitions are not found[2,3]. Then hysteresis is is achieved, but after that by a finite value. In technology the a feature of first-order phase transitions only. But is it phenomenon is found useful in some applications and inevitable in all of them? According to generally held views detrimental in others, but that topic is outside the frames of the transition "may or may not occur" at the temperature TO the present article. when the free energies of the two forms become equal. The The following questions are critical when dealing with the actual mechanis m of first-order phase transitions[2,4,5], hysteresis. Are there solid-state reactions without hysteresis? briefly summarized in Section 4, will explain why they were Why it is wide in some cases and narrow in others? Is its incorrect at that point. magnitude a physical constant for a given phase transition? If There is no lack of literature on hysteresis. The observed, can it be reduced? Can it be completely eliminated? three-volume (2160 pages) set The Science of Hysteresis[6] If yes, then how? Why and how its notorious loops form, and published in 2007 is an example. All that science was devoted to mathematical descriptions of its manifestations. A * Corresponding author: more appropriate title would be "The Science of Hysteresis [email protected] (Yuri Mnyukh) Published online at http://journal.sapub.org/ajcmp Modeling" due to absence there of anything about the Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved physical nature of the phenomenon. From practical point of American Journal of Condensed Matter Physics 2013, 3(5): 142-150 143 view the theoretical modeling of hysteresis is useful. But relatively small rather than dominant. The magnetic structure wouldn't it be better to do it while already understanding (the positional and orientational spatial distribution of the its physical origin? Probably some of that modeling would spin carriers and their spins in the crystal lattice) is dictated not be even needed. by the crystal packing, and not, as previously assumed, the The fact that the origin of hysteresis was not identified by other way around. solid state science does not mean it had not been discovered The mechanism of structural rearrangements in solids is a and publicly revealed. It was done already in 1979 in regard nucleation and interface propagation[2,4,5,7]. The structural to the structural hysteresis in a special section "Hysteresis of hysteresis is one of its manifestations which in case of Polymorphic Transitions" in the article Molecular magnetic crystals is inevitably accompanied by the magnetic Mechanism of Polymorphic Transitions[7]. Not one of the hysteresis. ensuing references to it has been related to the above section. It can be seen now that finding the source of magnetic The finding of a nucleation as being the exclusive cause of hysteresis was impossible without the new understanding hysteresis is remaining unknown. The purpose of this article that magnetic phase transitions and magnetization resulted is to fill the void. The structural hysteresis in solids is fro m the crystal-structural rearrangements. The answer to the presented here in more detail and in conjunction with the above question "What causes magnetic hysteresis?" was magnetic hysteresis. given in the book[2] six years prior to the time the question was posed. The answer was: nucleation. Somehow the sixteen authors of[8] missed it. 3. "What Causes Magnetic Hysteresis?" Probably, the most known and consequential is the 4. The Cause of Structural Hysteresis as magnetic hysteresis. Its cause has not been found by the Seen in Optical Microscope current theory. Here the hysteresis modeling dominates as well. The regular International Conferences on Hysteresis As to the cause of structural hysteresis, it will be and Micromagnetic Modeling (the 9th was held in 9013) illuminating to recall the experiments performed many years illustrate this fact. ago[12]. Phase transitions in small (~1 mm) transparent But the sixteen authors of[8] thought it would be single crystals of p-dichlorobenzene (PDB) were beneficial to understand it, pointing out that magnetic investigated by direct observation in optical microscope hysteresis is fundamental to magnetic storage technologies equipped with a heating/cooling stage. Their temperature T0 and a cornerstone to the present information age. They posed = 30.8℃ when the free energy F of its H (above T0) and L a question "What causes magnetic hysteresis?" and stated (below T0) phases are equal, FH(T0) = FL(T0), was convenient that all the "beautiful theories of magnetic hysteresis based to do the observations. Every crystal was subjected to a slow on random microscopic disorder" failed to explain their own heating or/and cooling. Fig. 1 is a photograph of phase data. Their answer to the above question was: "New transition in one of the heating experiments. Here are some advances in our fundamental understanding of magnetic results. Phase transitions start from nucleation after the T0 hysteresis are needed". has been passed. Nucleation is always heterogeneous, No such advances are possible without proper located at the crystal defects. The actual temperature of understanding of ferromagnetic state and phase transitions phase transitions did not − and could not − coincide with T0, first. The insurmountable obstacle to that understanding is considering that no reason exists for the transition to go in the conventional belief that ferromagnetic phase transitions any direction when FH = FL. In other words, the temperature are, according to the common classification, of a "second T0, usually called "phase transition temperature" (and order", in spite of the fact such phase transitions must not sometimes even "critical temperature") is the temperature exhibit hysteresis. (As stated by Vonsovskii[9], the theory of where phase transitions cannot occur. But the possibility to second-order phase transitions provided an "impetus" to occur at any other temperatures, except of a s mall region studies of magnetic phase transitions). The new around T0, is theoretically unlimited. Heterogeneous fundamentals of ferromagnetism and phase transitions nucleation requires a finite energy for activation, which [2,10,11] remove that basic contradiction. They demonstrate ma kes threshold nucleation lags inevitable. If Tn is the actual that the standard exchange field theory of ferromagnetism by temperature of nucleation, the minimum (threshold) Heisenberg, assuming existence of additional extremely overheating in PDB was ∆Tn = Tn - T0 = ~ 1.9℃. The strong spin interaction, has not been successful and was not threshold overcooling was always
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