Diffusion of carbon in alpha iron

Homan, C.G.

doi:10.1016/0001-6160(64)90079-3

Cited by 72 publications

(15 citation statements)

References 12 publications

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“…An analogous calculation is possible for vacancies. If Aiic and AAv are calculated, we obtain the values compiled in Table 3 using uD = 9.7 x 10l2 (from the Debye temperature of a-iron) and Sv = lk,(estimated), further Do,c = 0.008 cm2/s and Qc = 0.86 eV [28]. AZ is reverse to the mole fraction of sinks, N,.…”

Section: Aqmentioning

confidence: 99%

“…The discussion of the interaction between vacancies and carbon atoms prevails upon the TIM, too. Whilst for a long time a very high interaction enthalpy H,, of xl eV was assumed, now smaller values (0.1 eV H,, 5 0.65 eV) definitely less than H,, = 0.75 eV [28] are preferred. With this there is a spectrum of different interaction energies due to the experimentally based assumption that there are not only simple C-V complexes but also higher complexes up to C,V and CV,, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Quenching-in of vacancies in pure α-iron

Seydel

Frohberg

Wever

1994

Phys. Stat. Sol. (a)

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Once again an attempt is made to quench‐in vacancies in very pure iron (< 0. 5 at ppm C). This is achieved with a quenching rate of 1.5 × 104 K/s and an iron wire with a diameter of 100 μm. The recovery begins at 380 K and continues up to stage IV. An annihilation in stage III cannot be observed. This result can be interpreted with vacancy–C pairs — formed above 380 K with the residual content of carbon — and a following dissociation of the pairs and an annihilation of the vacancies at sinks up to temperatures of 600 K. Such an interpretation assumes the validity of the “two interstitial model” (TIM) and a formation enthalpy of the V–C pairs of ≧4 eV. The possibility of precipitation of the residual carbon in the form of graphite is discussed.

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Section: Aqmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quenching-in of vacancies in pure α-iron

Seydel

Frohberg

Wever

1994

Phys. Stat. Sol. (a)

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“…To ensure longevity of doped materials, it is essential that the spatial homogeneity and transport dynamics of the dopants within the crystal are well controlled and understood. Although theories and models are abundant [5][6][7][8][9][10][11], it remains unclear how large thermal excitations of the matrix lattice affect the dynamics of dopants. This becomes of particular interest during the processing of doped crystals, where they are heated close to or beyond their melting point.…”

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confidence: 99%

Anomalous dynamics of interstitial dopants in soft crystals

Tauber

Higler

Sprakel

2016

Proc. Natl. Acad. Sci. U.S.A.

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The dynamics of interstitial dopants govern the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically stabilized body-centered cubic (BCC) crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localized and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: (i) The instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and (ii) elastic interactions cause strong dopant-dopant interactions even at low doping fractions. These results illustrate how describing nonclassical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopantdopant interactions into account.anomalous dynamics | doping | crystals D oping pure crystalline solids with small amounts of interstitial impurities is a widely used method to enhance material properties such as heat and electric conductivity (1-4) or to tailor mechanical properties (5). Prototypical examples include the introduction of carbon atoms in iron crystals to make steel or the doping of plastic crystals with Li ions to create solid-state batteries (4). To ensure longevity of doped materials, it is essential that the spatial homogeneity and transport dynamics of the dopants within the crystal are well controlled and understood. Although theories and models are abundant (5-11), it remains unclear how large thermal excitations of the matrix lattice affect the dynamics of dopants. This becomes of particular interest during the processing of doped crystals, where they are heated close to or beyond their melting point. For example in body-centered cubic (BCC) iron doped with carbon, significant deviations from the exponential increase of diffusivity with temperature, expected from Arrhenius' law, are observed close to the melting temperature where lattice excitations are strong (12). Whereas doping is typically performed to tailor material properties at the macroscopic scale, these enhanced properties emerge from the dynamics and interactions between dopants at the scale of individual atoms (13). In classical theories for dopant dynamics, impurity particles are described as hopping through a potential energy landscape that is set by a perfect lattice symmetry, with transition rates governed by the energy barriers between adjacent interstitial sites and their occupancy (6,7,14). In reality, thermal fluctuations of atoms away from their equilibrium lattice positions will randomize the instantaneous potential energy l...

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“…Before each new temperature was investigated, the diffusion affected zone was completely removed by grinding and a new weld was made. As final preparation for the diffusion anneal, the diffusion couples were copper plated to prevent carbon diffusion across the cylindrical surface of the couple (14). The copper plated diffusion couples were then individually vacuum encapsulated in quartz tubes.…”

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confidence: 99%