Spinodal decomposition in Fe-Cr alloys: Experimental study at the atomic level and comparison with computer models—I. Introduction and methodology

Miller, M.K.; Hyde, J.M.; Hetherington, M.G.; Cerezo, A.; Smith, George Adam; Elliott, Charles M.

doi:10.1016/0956-7151(95)00040-3

Cited by 204 publications

(78 citation statements)

References 27 publications

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“…Although the detailed structure and ordering mechanism remained unclear in this study, the island morphology might well result from a spinodal decomposition mechanism. Additionally, the typical wavelength found for the (threedimensional) decomposition of alloys is also in the range of about 5 nm [16]. This is conceivable since both the lattice parameters and the approximate magnitude of the particle interaction energies in alloy systems are of the same order of magnitude as in our surface system.…”

Section: P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 68%

Two-Dimensional Nanoscale Self-Assembly on a Gold Surface by Spinodal Decomposition

et al. 2003

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The structure formation upon spinodal decomposition of a two-dimensional model system, a Au adatom gas on a Au(111) surface, was observed in situ by scanning tunneling microscopy (STM). A thermodynamically unstable state was prepared by applying microsecond voltage pulses to the STM tip in an electrochemical system, causing the random dissolution of Au atoms from the uppermost monolayer. Interconnected, labyrinthine island patterns were formed at Au coverages between 0.4 and 0.9 monolayer with dominating length scales m of the order of a few nanometers. DOI: 10.1103/PhysRevLett.91.066101 PACS numbers: 64.75.+g, 05.70.-a, 68.37.Ef, 82.45.Qr The evolution of structure out of a homogeneous system undergoing phase separation is a common phenomenon, encountered upon the condensation of water droplets in clouds [1] as well as upon metal deposition on surfaces [2]. From experience such first order phase transitions are mostly governed by the formation of compact shapes with minimized phase boundary energy, as a consequence of the formation of stable nuclei and their subsequent growth. However, as already pointed out by Gibbs, upon penetrating deeply enough into the coexistence region, the activation barrier against the formation of stable nuclei vanishes and the system becomes unstable. Because of the absence of any activation barrier the instantaneous, i.e., spinodal, decomposition of the system proceeds very fast, with density fluctuations of a certain wavelength growing exponentially with time [3]. This wavelength is determined solely by the thermodynamic properties of the system [4]. When the volume fractions of the phases of the heterogeneous system are close to 50%, labyrinthine interconnected patterns evolve, distinctively different from the morphologies expected upon nucleation and growth.In this Letter we demonstrate how the thermodynamic stability of a surface system can be employed to steer the morphology of resulting patterns from growth of compact islands to labyrinthine interconnected structures on the nanoscale. Phase transitions in a two-dimensional (2D) model system, a gas of Au adatoms on a Au(111) surface, are induced by electrochemical, randomly distributed dissolution of Au atoms out of the topmost layer of a single crystal surface. This process occurs during a voltage pulse of only microsecond duration applied to the tip of an electrochemical scanning tunneling microscope (STM) facing the sample surface. This period is short enough to avoid significant diffusion and ordering already during the change of the state of the system. The resulting atomic-scale morphology is then imaged in situ by STM. The simplicity of the system justifies its description by a 2D lattice gas model with pairwise nearest neighbor interactions. Therefore, the system comes close to the models considered in the very first theoretical treatments of spinodal decomposition by Cahn and Hilliard [4,5] and the evolving structures can be directly compared to the theoretical predictions, derived explicitly for lattice model syst...

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Section: P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 68%

Two-Dimensional Nanoscale Self-Assembly on a Gold Surface by Spinodal Decomposition

et al. 2003

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“…The decomposition process in Fe-Cr is typically investigated by transmission electron microscopy (TEM), 1 M€ ossbauer spectroscopy, 2,3 atom probe tomography (APT), 4,5 or smallangle neutron scattering (SANS). [6][7][8] While each technique has its specific advantages, only SANS readily offers the possibility to perform time-resolved in-situ measurements at elevated temperatures.…”

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confidence: 99%

Early stages of spinodal decomposition in Fe–Cr resolved by in-situ small-angle neutron scattering

Hörnqvist

Thuvander

Steuwer

et al. 2015

Applied Physics Letters

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In-situ, time-resolved small-angle neutron scattering (SANS) investigations of the early stages of the spinodal decomposition process in Fe-35Cr were performed at 773 and 798 K. The kinetics of the decomposition, both in terms of characteristic distance and peak intensity, followed a power-law behaviour from the start of the heat treatment (a 0 ¼ 0.10-0.11 and a 00 ¼ 0.67-0.86). Furthermore, the method allows tracking of the high-Q slope, which is a sensitive measure of the early stages of decomposition. Ex-situ SANS and atom probe tomography were used to verify the results from the in-situ investigations. Finally, the in-situ measurement of the evolution of the characteristic distance at 773 K was compared with the predictions from the Cahn-Hilliard-Cook model, which showed good agreement with the experimental data (a 0 ¼ 0.12-0.20 depending on the assumed mobility). Spinodal decomposition of the bcc phase in Fe-Cr alloys into an Fe-rich and a Cr-rich phase is a widely studied phenomenon. The reason is two-fold: First, the system is the basis of the industrially important stainless steel family, where the decomposition of the bcc phase in ferritic, duplex and to some extent martensitic and d-ferrite containing austenitic grades, is partially responsible for degradation of the mechanical properties over time during elevated temperature exposure in service. Second, the Fe-Cr system is ideal to study the fundamentals of the spinodal decomposition process, since it offers a combination of a wide miscibility gap, a rather wide temperature range where the kinetics of the decomposition is suitable for practical measurements and minor coherency strains.The decomposition process in Fe-Cr is typically investigated by transmission electron microscopy (TEM), 1 M€ ossbauer spectroscopy, 2,3 atom probe tomography (APT), 4,5 or smallangle neutron scattering (SANS). [6][7][8] While each technique has its specific advantages, only SANS readily offers the possibility to perform time-resolved in-situ measurements at elevated temperatures. However, so far only very few investigations have taken advantage of this possibility of direct continuous tracking of the kinetics without any specimen-to-specimen variations in composition, starting structure, or isothermal temperature. For the Fe-Cr(-Ni) system, there are only two readily available reports of in-situ SANS experiments, 9,10 although other systems have been investigated more recently, e.g., Fe-Co-Mo. 11 In Refs. 9 and 10, acquisition times of several hours were used, which resulted in poor temporal resolution. Furusaka et al. 12 used in-situ SANS to investigate the critical scattering of Fe-Cr alloys in the vicinity of the Curie temperature, but the subsequent investigations of aged alloys were performed ex-situ.The existence and location of the spinodal in the binary Fe-Cr system are today rather well described, both from thermodynamic modelling and experiments (see, e.g., Ref. 13, and references therein). Direct observations from three dimensional APT investigations have also...

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“…Such an extension was proposed by Cook [15], see also [20,28,29,30,34]. In the physics literature, this model is also known as Model B in the classification of Hohenberg and Halperin [27].…”

Section: Introductionmentioning

confidence: 97%

“…Then there exist paths u n with u n = u n (0) ∈ F and associated control functions c n via (33), which remain in B µ/2 (F) and such that I un T 0 (u n ) → 0 as n → ∞. Together with (34) and (35) this furnishes [39,Theorem 42.12]. On the other hand, the deterministic orbits leave B µ (F) during [0, T 0 ], i.e., one has sup t∈[0,T 0 ] |S λ (t)u n − u n (t)| ∞ ≥ µ/2, which is a contradiction.…”

mentioning

confidence: 99%

Nucleation in the one-dimensional stochastic Cahn-Hilliard model

Blömker¹,

Gawron²,

Wanner³

2010

Discrete &Amp; Continuous Dynamical Systems - A

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Despite their misleading label, rare events in stochastic systems are central to many applied phenomena. In this paper, we concentrate on one such situationphase separation through homogeneous nucleation in binary alloys as described by the stochastic partial differential equation model due to Cahn, Hilliard, and Cook. We show that in the limit of small noise intensity, nucleation can be explained by the stochastically driven exit from the domain of attraction of an asymptotically stable homogeneous equilibrium state for the associated deterministic model. Furthermore, we provide insight into the subsequent nucleation dynamics via the structure of the attractor of the model in the absence of noise.

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Spinodal decomposition in Fe-Cr alloys: Experimental study at the atomic level and comparison with computer models—I. Introduction and methodology

Cited by 204 publications

References 27 publications

Two-Dimensional Nanoscale Self-Assembly on a Gold Surface by Spinodal Decomposition

Two-Dimensional Nanoscale Self-Assembly on a Gold Surface by Spinodal Decomposition

Early stages of spinodal decomposition in Fe–Cr resolved by in-situ small-angle neutron scattering

Nucleation in the one-dimensional stochastic Cahn-Hilliard model

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