B L Zhou/ Materials Science and Engineering C 11 (2000)13-18 aAa 4+gg℃Ho封 Fig. 3. Time process of temperature rise and thermal expansion. (1)Temperature rise, (2)thermal expansion [13, 14]. described [10, 11] may play an important role in guiding parameter, by definition 5=E(x-DsD),T=et, and U the design of fiber structure do/ak is the group velocity of second sound. p, B and The present work was carried out to synthesize are parameters. Knowing the moving velocity of soliton- using benzene as the carbon source, iron as the catalyst, nation of Fig 3 quantitaively sives the theoretical expla- fibers with a fractal-root structure through vapor gr and hydrogen as the carrying gas [12]. Fig. 2 illustrates the morphology of the branched vapor-grown fibers (a)and the structure of a branching point(b) 3.2. Dissipative structure and self-organization process of open system /15, 16/ 3. Possibility of modification and recovery of materials by nonequilibrium biomimetic treatment The theory of dissipative structure by the Prigogine 3.1. Nonequilibrium process under transient heating school [15, 16] can be applied to treat the nonequilibrium 6,13,147 problems in material processing, such Glandorf- development of high technol Prigogine criterion is taken to judge the heat transport and thermochemical process. As soon as the external condition heating rate tends to go higher and higher today. A series changes to a threshold value, the system will turn to an of transient processes will be consequently induced in ordered state of time, space and function from the original solids under extremely short laser pulse heating. Besides disordered state. This new structure under nonequilibrium the transport processes, some of the equilibrium properties condition is called the "dissipative structure".Its general will reveal their nonequilibrium characteristics. behavior is described in Fig. 4 Nonsynchronous change of temperature and thermal The system will lose its steadiness at Ae and transfer to expansion under transient heating was observed as shown an ordered state. It is called nonequilibrium phase transi in Fig. 3. The nonequilibrium localized phonon gas in a tion or self-organizing phenomenon hot spot' is studied using Boltzmann equation, leading to a soliton-like solution as follows [13] nP(s,T) y 5 exp(-iyr) 3.3. Inspiration by living process [17, 18/ (2) The coupled process of both nutrition and consume, where n(E, T) consists in the distribution function of fatigue and rest, as well as injury and healing, are all phonons at position x and time t. Let e be a Table I Fatigue life of four sample groups [20] Group no. Testing process Total life of (c) Frb FT250,000 cycles(cs)-rest-FT again 659, ⅣV(3) >5,044,600 2, 500, 000 CS-EPT-FT again 4. Above the special constraint value Ac, the system will t steady-state dissipative structure from the nonequilibrium steady Number of samples state in case of small perturbation: (a)A< Ac, steady state,(b)unsteady state,(c)A>Ae, new steady state [17, 18] Electropulsing treatmentB.L. ZhourMaterials Science and Engineering C 11 2000 13–18 ( ) 15 Fig. 3. Time process of temperature rise and thermal expansion. 1 Temperature rise, 2 thermal expansion 13,14 . Ž. Ž. w x described 10,11 may play an important role in guiding w x the design of fiber structure. The present work was carried out to synthesize carbon fibers with a fractal-root structure through vapor growth, using benzene as the carbon source, iron as the catalyst, and hydrogen as the carrying gas 12 . Fig. 2 illustrates the w x morphology of the branched vapor-grown fibers a and Ž . the structure of a branching point b . Ž . 3. Possibility of modification and recovery of materials by nonequilibrium biomimetic treatment 3.1. Nonequilibrium process under transient heating [ ] 6,13,14 Owing to the development of high technology, the heating rate tends to go higher and higher today. A series of transient processes will be consequently induced in solids under extremely short laser pulse heating. Besides the transport processes, some of the equilibrium properties will reveal their nonequilibrium characteristics. Nonsynchronous change of temperature and thermal expansion under transient heating was observed as shown in Fig. 3. The nonequilibrium localized phonon gas in a ‘‘hot spot’’ is studied using Boltzmann equation, leading to a soliton-like solution as follows 13 : w x y 1 2 1 2 2g g Ž1. n Ž. Ž . j ,t s sech y j exp yigt j1 ž / ž / ž / r b Ž . 2 Ž1. where n Ž . j ,t consists in the distribution function of j1 phonons at position x and time t. Let ´ be a small Fig. 4. Above the special constraint value l , the system will turn to a c new steady-state dissipative structure from the nonequilibrium steady state in case of small perturbation: aŽ. Ž. l-lc , steady state, b unsteady state, cŽ . l)l , new steady state 17,18 . w x c Ž . 2 parameter, by definition js´ xyÕs s t , ts´ t, and Õ s EvrEk is the group velocity of second sound. r, b and g are parameters. Knowing the moving velocity of soliton￾like wave along the sample, it gives the theoretical expla￾nation of Fig. 3 quantitatively. 3.2. DissipatiÕe structure and self-organization process of open system 15,16 [ ] The theory of dissipative structure by the Prigogine school 15,16 can be applied to treat the nonequilibrium w x problems in material processing, such as Glansdorf– Prigogine criterion is taken to judge the heat transport and thermochemical process. As soon as the external condition changes to a threshold value, the system will turn to an ordered state of time, space and function from the original disordered state. This new structure under nonequilibrium condition is called the ‘‘dissipative structure’’. Its general behavior is described in Fig. 4. The system will lose its steadiness at lc and transfer to an ordered state. It is called nonequilibrium phase transi￾tion or self-organizing phenomenon. 3.3. Inspiration by liÕing process 17,18 [ ] The coupled process of both nutrition and consume, fatigue and rest, as well as injury and healing, are all Table 1 Fatigue life of four sample groups 20 w x a Group no. Testing process Total life of fatigue cycles Ž . b I 3 FT 398,800 Ž . c II 3 EPT –FT 482,200 Ž . III 4 FT250,000 cycles cs –rest–FT again 659,900 Ž. Ž . IV 3 FT250,000 cs–EPT–FT again Ž . )5,044,600 2,500,000 cs–EPT–FT again a Number of samples. b Fatigue test. c Electropulsing treatment