Application of the Self-Organization Phenomenon in the Development of Wear Resistant Materials—A Review <s> The Physical Meaning of the Self-Organization Phenomenon as Applied to Friction <s> It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns onHydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis.The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading. <s> BIB001 </s> Application of the Self-Organization Phenomenon in the Development of Wear Resistant Materials—A Review <s> The Physical Meaning of the Self-Organization Phenomenon as Applied to Friction <s> I Historical Roots: From Heat Engines to Cosmology ::: 1 Basic Concepts and the Law of Gases ::: 2 The First Law of Thermodynamics ::: 3 The Second Law of Thermodynamics and the Arrow of Time ::: 4 Entropy in the Realm of Chemical Reactions ::: ::: II Equilibrium Thermodynamics ::: 5 Extremum Principles and General Thermodynamics Relations ::: 6 Basic Thermodynamics of Gases, Liquids and Solids ::: 7 Thermodynamics of Phase Change ::: 8 Thermodynamics of Solutions ::: 9 Thermodynamics of Chemical Transformations ::: 10 Fields and Internal Degrees of Freedom ::: 11 Thermodynamics of Radiation ::: ::: III Fluctuations and Stability ::: 12 The Gibbs Stability Theory ::: 13 Critical Phenomena and Configurational Heat Capacity ::: 14 Entropy Productions, Fluctuations and Small Systems ::: ::: IV Linear Nonequilibrium Thermodynamics ::: 15 Nonequilibrium Thermodynamics: The Foundations ::: 16 Nonequilibrium Thermodynamics: The Linear Regime ::: 17 Nonequilibrium Stationary State and Their Stability: Linear Regime ::: ::: V Order Through Fluctuations ::: 18 Nonlinear Thermodynamics ::: 19 Dissipative Structures ::: 20 Elements of Statistical Thermodynamics ::: 21 Self-Organization and Dissipative Structures in Nature <s> BIB002 </s> Application of the Self-Organization Phenomenon in the Development of Wear Resistant Materials—A Review <s> The Physical Meaning of the Self-Organization Phenomenon as Applied to Friction <s> Abstract The main advantage of the filtered arc deposition (FAD) technique is a significant grain refinement that leads to the formation of nano-crystalline (grain size approx. 60–80 nm) PVD coatings. This technique improves the wear resistance of FAD TiAlN coatings under high-speed machining conditions when cutting tool oxidation wear is dominant. A study of the surface structure characteristics of the FAD TiAlN coatings using SEM, EDS, TEM, AES, SIMS and EELFS was performed. The microhardness of the coatings were measured. The microstructure of the chips was analyzed. The compression of the chips as well as shear angle was measured. The friction parameter on the rake surface of the tools was determined in-situ. It was shown that the major cause of the high wear resistance of the FAD coatings during high-speed machining was the formation of the thin protective oxide films on the cutting tool surface. The grain size refinement of the coating promotes the formation of protective alumina films. These films are formed at the surface of nano-crystalline FAD TiAlN coating during high-speed machining. They mainly consist of protective alumina, whereas the films that are forming on the surface of TiAlN commercial coatings with coarser grains consist only of non-protective titania. The formation of the protective alumina films, composed of complicated amorphous–crystalline structures, significantly improves the friction and wear performance of coated tools. The tendency of the work piece material to adhere is reduced and considerably more heat is dissipated via chip removal. This is a major cause of the enhanced wear resistance of the FAD coating technique. Tribo-oxidation during cutting is a typical process of the self-organization of TiAlN coatings that results in a quasi-stabilization of cutting tool wear. The self-organization and friction control for coated cutting tools is considered based on a non-equilibrium thermodynamic approach. <s> BIB003 </s> Application of the Self-Organization Phenomenon in the Development of Wear Resistant Materials—A Review <s> The Physical Meaning of the Self-Organization Phenomenon as Applied to Friction <s> Self-organization during friction in complex surface engineered tribosystems is investigated. The probability of self-organization in these complex tribosystems is studied on the basis of the theoretical concepts of irreversible thermodynamics. It is shown that a higher number of interrelated processes within the system result in an increased probability of self-organization. The results of this thermodynamic model are confirmed by the investigation of the wear performance of a novel Ti0.2Al0.55Cr0.2Si0.03Y0.02N/Ti0.25Al0.65Cr0.1N (PVD) coating with complex nano-multilayered structure under extreme tribological conditions of dry high-speed end milling of hardened H13 tool steel. <s> BIB004 </s> Application of the Self-Organization Phenomenon in the Development of Wear Resistant Materials—A Review <s> The Physical Meaning of the Self-Organization Phenomenon as Applied to Friction <s> This article discusses the peculiarities of self-organization behavior and formation of dissipative structures during friction of antifriction alloys for slide bearings against a steel counterbody. It shows that during self-organization, the moment of friction in a tribosystem may be decreasing with the load growth and in the bifurcations of the coefficient of friction with respect to load. Self-organization and the formation of dissipative structures lead to an increase in the seizure load. <s> BIB005
In  self-organization was defined as a process of formation of dissipative structures. Therefore this section discusses the notion of dissipative structures. The term "dissipative structures" was conceived by Prigogine  , who presented dissipative structures as consisting of big fluctuations using the example of a fluid's flow velocity profile. At a deviation from equilibrium fluctuations are not stable around the equilibrium state BIB002  . Formation of fluctuations is accompanied by a growth of free energy or negative production of entropy. After this, the system returns to the state with less free energy. In the tribosystem, thermodynamic equilibrium may only be achieved where there is no friction. In a steady-state with linear dependency of thermodynamic flows on thermodynamic forces production of entropy-according to Prigogine's theorem-is minimal. The terms of Prigogine's theorem can only be achieved under relatively mild friction conditions, i.e., at a low sliding speed, low clamping force, etc. The stationary state of a tribosystem in which Prigogine's theorem applies can be considered as thermodynamically stable. The increase in sliding speed, pressing force or other parameter of friction leads to the removal of the tribosystem from equilibrium. A curve which describes such a state in a phase space depending on the changing parameter is called a thermodynamic branch. If removing of tribosystem from equilibrium is accompanied by the action of the Prigogine's theorem, the states on the thermodynamic branch are thermodynamically stable. However, after a certain critical value of the parameter, the system's state can become unstable. Any negligibly small perturbation can then deviate the system from a thermodynamic branch (a catastrophe). Thermodynamic stability of a nonequilibrium state is determined by the following condition BIB002 : where δ-fluctuation; X n , J n -thermodynamic forces and flows, correspondingly; S-entropy; t-time. The sum in the right hand side of Equation (1) is called excessive production of the entropy. The values δX n and δJ n are fluctuations of the corresponding flows and forces in steady-state conditions. In BIB004 it is shown that as the number of interacting thermodynamic flows increases the probability of a loss of thermodynamic stability of the tribosystem increases. Hence, the probability of self-organization grows. Taking into account only pair interactions of n flows with each other the probability (P) is: If inequality is apparent at the beginning of the disturbance (1), this condition is stable. However, during certain processes or under the influence of various processes, one can get a negative contribution leading to excessive production of entropy which grows as the disturbance grows. In this case this condition can become unstable (positive production of entropy is a sufficient but not mandatory condition of instability). Only after going through instability can the self-organization process begin. The new regime which is installed in the system can correspond to the orderly condition, i.e., it can have entropy which is lower than the chaotic condition one. In this case bifurcation takes place at the critical point (emergence of a new parameter at the critical value for solving the equation). As a result, a new branch of solutions emerges. Prigogine proposed naming such ordered configurations, which emerge outside of the scope of stability of the thermodynamic branch, dissipative structures  . The choice of solution by the system which emerges in the bifurcation point, i.e., the process of formation of dissipative structures, is called as self-organization. Just as any fluctuation dissipative structures are generated spontaneously and in a surge mode. This means that the relevant physical-chemical process characterizing dissipative structures starts as an avalanche. This corresponds to a catastrophe on a thermodynamic branch. A great number of publications have been devoted to the theory, experiments, and description of such structures. This is why here we will not describe any specific structures, but will rather refer to certain general results. Only nonlinear equations can have more than one solution. Therefore bifurcations-and henceemergence of dissipative structures-can only take place in a system in which the processes are governed by nonlinear laws. The analysis of the known processes of self-organization, for example, during the formation of Benar cells BIB002 or Turing structures BIB001 , shows that the formation of dissipative structures is only possible as a result of interaction of two or more processes. The analysis of stability condition validates this (1) . In  it is shown that the loss of stability of tribosystem is impossible when accounting for one process only. Entropy of an equilibrium condition is maximal. If one excludes the factors supporting nonequilibrium condition, then such system will transit to an equilibrium condition. Such a spontaneous transition will feature positive entropy production. Thus, other factors being equal, the entropy of a nonequilibrium condition of the system is less than the entropy of its equilibrium condition. This is true for the formation of dissipative structures. The process of self-organization (formation of dissipative structures) is abrupt, not gradual, therefore the boundary conditions and the flow of entropy are not changed. Hence, as the entropy is reduced so should the production of entropy. This corresponds to the assertion in  that after formation of dissipative structures in the system, production of the entropy is lower than under the same conditions but without self-organization. Production of entropy is reduced due to intensive processes characterized by the increase of free energy, i.e., negative affinity. Such processes feature negative production of entropy. This does not contradict the second law of thermodynamics as the overall production of entropy remains positive. Reduction of production of entropy does not always mean the formation of dissipative structures. For instance, during the formation of a gradient of temperatures in a mixture of two gases the diffusion can take place towards increasing the gradient of concentration. At the same time, the entropy will reduce  . Such a thermodiffusion is a result of linear processes: the variance of concentrations is proportional to the variance of temperatures. The variance of concentrations is formed gradually from the mixture, not as a surge, which is the case of self-organization. Besides, during diffusion molecules move regardless of each other, i.e., the process of diffusion is chaotic in this sense. Thus, thermodiffusion is not a self-organization process. So, why is self-organization interesting for friction processes? According to de Donder  , any change in the entropy in an open nonequilibrium system dS dt consists of the flow of entropy (interface with a medium) and the production of entropy dt (processes inside the system)  : At the same time, the flow of entropy of one body under friction consists of flows of the entropy relating with exchange between energy and substance: where: The negative sign before the flow of entropy relating with wear means that the substances leave the body under friction with their own entropy. Production of the entropy of one body under friction consists of a part connected with dissipation of energy during heat transfer and deformation,  In this case (3) will look as follows: In a steady-state condition ( Entropy is an additive value therefore, other factors being equal, the greater the value of d ew S dt , the higher the intensity of wear. Based on Equation (7) it can be concluded that, other factors being equal, the intensity of wear is reduced as the production of entropy decreases. It was earlier mentioned that during self-organization production of entropy is reduced, hence the intensity of wear is also reduced. Due to this, the phenomenon of self-organization represents interest to tribology. It should be noted that during a self-organization the process with negative entropy production appears as an avalanche. Part of the energy of friction is spent on the processes with negative entropy production Thus, during self-organization, part of the friction energy that could be spent on wear, is spent on the passage of the process with negative entropy production contributing to a reduction of the wear rate. Avalanche-like appearance of such a process leads to a finite value of negative entropy production, the positive part of the production of entropy does not change in this case. If the process with negative entropy production would gradually appear, then at the same time it has increased the positive part of entropy production. Other things being equal, entropy production and the rate of wear at the same time would always be greater than an avalanche-like occurrence. This also differs the self-organization from a gradual process, for example increasing the break-contact area under running-in. Despite the fact that during self-organization the intensity of wear decreases, not every case of the decrease of intensity of wear can be attributed to self-organization. For instance, the decrease of intensity of wear takes place during a "mechanical" run-in process where an area of contact is increased and the pressure in that contact is reduced. Such "mechanical" run-in process is characterized by gradual reduction in the intensity of wear. In case of self-organization the intensity of wear is reduced in an abrupt fashion. The difference between a gradual and abrupt (self-organization) decrease in the intensity of wear is shown using the example of different types of schematic dependencies of wear and wear rate of the friction distance on Figure 1 . Figure In the case where there is no self-organization, the wear ( Figure 1a ) and reduction of the intensity of wear (Figure 1b ) are shown by smooth and gradual curves. In the case where there is selforganization, the wear is shown as a broken curve (Figure 1c) . Reduction in the intensity of wear in the case where there is self-organization is abrupt (Figure 1d ) in the breaking point of the wear curve. For dependencies shown in Figure 1a ,b, the increase of the contact area, reduction of pressure and intensity of wear take place due to the wear and plastic deformation in a gradual manner. At the same time, no new physical and chemical processes emerge. For dependencies shown in Figure 1c ,d, the break on the wear curve (Figure 1c) is caused by the emergence of a new physical and chemical process which, prior to that could only be an unstable fluctuation. This process is accompanied by negative production of the entropy. The abrupt reduction of intensity of wear in Figure 1d points to an avalanche-like emergence of a physical-chemical process with negative entropy production. This process is dissipative structures. Such real broken dependences are described, for example, for cutting tool BIB003  . In BIB003  and in Figure 1c ,d friction conditions allow passage of self-organization, i.e., the thermodynamic stability of the tribosystem may be lost under these conditions. The loss of thermodynamic stability, therefore, and self-organization are stochastic processes (due to the fact that compliance with the conditions of Lyapunov's theorem) is necessary but not sufficient)  . Thus, for tribosystems BIB003  (Figure 1c,d ) the only possibility to lose thermodynamic stability appears. Therefore, in spite of compliance with the necessary conditions of stability loss from the beginning of friction, self-organization (the breaking in the curves) occurs after a sliding distance has been traveled. That is not self-organization since the beginning of friction (Figure 1c,d) shows that on the dependence of the wear (wear rate) on the friction parameter in BIB003  -a cutting rate bifurcation is possible. One branch after the bifurcation point (thermodynamic)-a characteristic dependence In the case where there is no self-organization, the wear ( Figure 1a) and reduction of the intensity of wear (Figure 1b ) are shown by smooth and gradual curves. In the case where there is self-organization, the wear is shown as a broken curve (Figure 1c) . Reduction in the intensity of wear in the case where there is self-organization is abrupt (Figure 1d ) in the breaking point of the wear curve. For dependencies shown in Figure 1a ,b, the increase of the contact area, reduction of pressure and intensity of wear take place due to the wear and plastic deformation in a gradual manner. At the same time, no new physical and chemical processes emerge. For dependencies shown in Figure 1c ,d, the break on the wear curve (Figure 1c) is caused by the emergence of a new physical and chemical process which, prior to that could only be an unstable fluctuation. This process is accompanied by negative production of the entropy. The abrupt reduction of intensity of wear in Figure 1d points to an avalanche-like emergence of a physical-chemical process with negative entropy production. This process is dissipative structures. Such real broken dependences are described, for example, for cutting tool BIB003  . In BIB003  and in Figure 1c ,d friction conditions allow passage of self-organization, i.e., the thermodynamic stability of the tribosystem may be lost under these conditions. The loss of thermodynamic stability, therefore, and self-organization are stochastic processes (due to the fact that compliance with the conditions of Lyapunov's theorem) is necessary but not sufficient)  . Thus, for tribosystems BIB003  (Figure 1c,d ) the only possibility to lose thermodynamic stability appears. Therefore, in spite of compliance with the necessary conditions of stability loss from the beginning of friction, self-organization (the breaking in the curves) occurs after a sliding distance has been traveled. That is not self-organization since the beginning of friction (Figure 1c,d) shows that on the dependence of the wear (wear rate) on the friction parameter in BIB003  -a cutting rate bifurcation is possible. One branch after the bifurcation point (thermodynamic)-a characteristic dependence before the inflection point (Figure 1c,d) . The second branch (dissipative structures) is a characteristic dependence after the inflection point (Figure 1c,d ). An example of physical-chemical process with negative entropy production is precipitation of tin from a solid solution based on copper during the friction of a tin-lead bronze as described in BIB005 . This precipitation of tin from a solid solution based on copper contradicts the equilibrium phase diagram of Cu-Sn. Hence this is not a spontaneous process which is characterized by the negative production of entropy. The friction does not directly initiate precipitation of tin from this solid solution. The friction in this case directly initiates deformation, wear, heating, heat conductivity, etc. Precipitation of tin from the solid solution may be the result of the interaction of these processes. Importantly, precipitation of tin from a solid solution is a probabilistic process, i.e., it may or may not take place under the same conditions (clamping force). If tin is not precipitated the scoring load would amount to 980 N, while in the case of the precipitation of tin it would amount to 1441 N. Thus, bifurcation appears to depend on the friction coefficient of the load. The listed characteristics suggest that the process of the precipitation of tin from a solid solution is a dissipative structure. Despite the fact that instability invariably precedes to self-organization, the reverse assertion is not always true. On the basis of classical works by Prigogine and our experience in research of self-organization during friction the characteristics of self-organization in this case are formulated below: 1 Self-organization can only take place after the tribosystem loses its thermodynamic stability in a nonlinear zone. Various mathematical models of stability loss that are not strictly linear cases are summarized in     . As a result we obtain conditions of loss of thermodynamic stability of the tribosystem with current collection, recommendations on alloying of coating for the cutting tool by relatively heavy elements to reduce seizure, recommendations to alloy coating of the cutting tool with relatively light elements to reduce the wear rate at friction without seizure. 2 In the case of self-organization, a spontaneous, avalanche-like stable and consistent unprompted process emerges abruptly (a process with the negative production of entropy is a process which moves in the direction of increasing free energy). In this process a considerable amount of friction energy was consumed that previously would be spent for wear, so the self-organization usually leads to an abrupt decrease in wear rate. Abruptness can be explained using the Figures 1d and 2. The formation of dissipative structures is accompanied by a sharp decrease in wear rate (Figures 1d and 2 of the "dissipative structures" curve). Curve "dissipative structures" (Figure 2 ) has the highest value (at the bifurcation point), and the lowest value of the wear rate. In the experiments, we were not able to fix the intermediate value of wear rate between the upper and lower value decreasing an increment of the argument (electric current density). With a decrease in increment of the argument, we recorded the highest (at the bifurcation point) or the lowest value of the wear rate. Perhaps the presence of such a "forbidden zone" can serve as a primary criterion of abruptness in the formation of dissipative structures. During running in (Figure 1b) at increasing of the contact area intermediate values between the highest and lowest value of the wear rate can be fixed with a decreasing in the increment of the argument (time).  The process (2) is not initiated directly by friction.  A nonspontaneous process initiated directly by friction is for example, a wear, deformation, heating or heat conductivity.  A process (2) is a result of interaction of the flows of other processes (5). 6 In the case of self-organization, the production of entropy is reduced as compared with the same condition but without self-organization, consequently, the wear rate decreases abruptly when self-organization is observed.