Thermally-activated Diffusion Research Articles

Thermally-induced phase transitions in Pt/Tb/Fe trilayers

Structural phase formation induced by thermally-activated diffusion processes and intermixing of layered structures is a promising reaction pathway for the synthesis of unexpected (metastable) thin film materials. Furthermore, the sequence of structural phase transitions during annealing can substantially differ from those predicted by corresponding bulk phase diagrams due to the underlying grain boundary diffusion mechanisms as well as surface and interface effects. In this study, phase transitions in Pt/Tb/Fe trilayers occurring during post-annealing up to 620°C were investigated by various techniques including x-ray diffraction, transmission electron microscopy, secondary neutral mass spectrometry, Auger electron spectroscopy depth profiling, and magnetic properties measurements. At an annealing temperature of 215°C pronounced Pt and Tb diffusion intermixing is observed leading to the formation of the binary Pt2Tb phase. Further annealing up to 280 °C is accompanied by the appearance of the chemically disordered A1-FePt phase and significant Tb segregation to the outer surface forming an oxide layer. The chemically ordered L10-FePt phase starts to form in parallel to the disappearance of the Pt2Tb phase at 450°C. The final phase product at 620°C is characterized by the coexistence of two remaining phases, L10-FePt and TbO2. Structural phase transitions have a significant impact on the films magnetic properties – heat treatment leads to an enhancement of the coercive field. This fact is associated with the formation of the hard magnetic L10-FePt phase, which might be accompanied by grain isolation induced by partially Tb/Tb-O grain boundary filling.

Dynamic re-equilibration controlled multi-step transformations in (Mn, Fe)2(P, Si) alloys

In (Mn, Fe)2(P, Si) alloys crystallographic first-order phase transformations enable strong coupling of magnetic and entropic properties, potentially leading to high-efficiency energy generation and refrigeration applications. Although hysteresis losses that limit these applications can be reduced through careful control of alloy composition, compositional tuning can also unfavorably influence transformation temperatures and magnetocaloric coupling strength. Hence, exploration of additional processing variables enabling independent control of transformation properties is crucial. In this work, we investigate the role of thermal history as an additional processing variable, exploiting thermally-activated mechanisms to control properties of non-diffusive transformations in (Mn, Fe)2(P, Si) alloys. In so doing, we report an unusual transformation-splitting phenomenon following annealing at intermediate times, where a single well-defined magneto-structural transformation evolves towards a multi-step transformation with individual steps occurring at multiple distinct temperatures. On longer annealing at the same temperatures, single-step transformation behavior is recovered. Through additional magnetic and crystallographic characterization, we show that the thermal history-controlled multi-step behavior results from sluggish thermally-activated diffusion. The two-step transformation corresponds to non-equilibrium bimodal composition distributions in the transforming phase, and these develop through a dynamic re-equilibration process as the alloy passes relatively slowly between different thermal equilibria. Together, these results suggest that thermal history primarily controls the transformation properties of (Mn, Fe)2(P, Si) alloys indirectly through the composition of one or more transforming phases. Additional investigations are needed to develop thermal history processing for decoupling hysteresis control from other transformation properties.

Direct imaging of thermally-activated grain-boundary diffusion in Cu/Co/IrMn/Pt exchange-bias structures using atom-probe tomography

Magnetic devices are often subject to thermal processing steps, such as field cooling to set exchange bias and annealing to crystallize amorphous magnetic electrodes. These processing steps may result in interdiffusion and the subsequent deterioration of magnetic properties. In this study, we investigated thermally-activated diffusion in Cu/Co/IrMn/Pt exchange biased polycrystalline thin-film structures using atom probe tomography. Images taken after annealing at 400 °C for 60 min revealed Mn diffusion into Co grains at the Co/IrMn interface and along Pt grain boundaries for the IrMn/Pt stack, i.e., a Harrison type C regime. Annealing at 500 °C showed further Mn diffusion into Co grains. At the IrMn/Pt interface, annealing at 500 °C led to a type B behavior since Mn diffusion was detected both along Pt grain boundaries and also into Pt grains. The deterioration of the films' exchange bias properties upon annealing was correlated to the observed diffusion. In particular, the topmost Pt capping layer thickness turned out to be crucial since a faster deterioration of the exchange bias properties for thicker caps was observed. This is consistent with the idea that Pt acts as a getter for Mn, drawing Mn out of the IrMn layer.

Proposal for a new theoretical model of the cutting tool's flank wear

Based on studies of the physical characteristics of wear processes, the conclusion could be drawn that the cutting distance must be considered not only in abrasive and adhesive processes but also in thermally-activated diffusion and oxidation processes. Consequently, it can be proposed that a mathematical model of the rate of flank wear—an autonomous non-linear differential equation that takes into account the wear-accelerating effect of both the technological parameters of cutting and the temperature developing on the tool flank—can be applied. Furthermore, this model may be used to calculate the tool life and the Taylor formula related to any arbitrarily chosen failure criteria. Technological parameters may also change periodically or continuously depending on time. The constants of the wear equation and the apparent activation energy of the process can be determined by cutting experiments and also by measurements of wear performed during factory manufacturing under a variety of technological parameters. The complex wear equation was validated by the cutting tests performed with P20 carbide on AISI1045 carbon steel. The adverse effect of rapidly changing cutting speed on the wear of the tool during vibration could be modelled.

Controllable magnetic doping of the surface state of a topological insulator.

A combined experimental and theoretical study of doping individual Fe atoms into Bi(2)Se(3) is presented. It is shown through a scanning tunneling microscopy study that single Fe atoms initially located at hollow sites on top of the surface (adatoms) can be incorporated into subsurface layers by thermally activated diffusion. Angle-resolved photoemission spectroscopy in combination with ab initio calculations suggest that the doping behavior changes from electron donation for the Fe adatom to neutral or electron acceptance for Fe incorporated into substitutional Bi sites. According to first principles calculations within density functional theory, these Fe substitutional impurities retain a large magnetic moment, thus presenting an alternative scheme for magnetically doping the topological surface state. For both types of Fe doping, we see no indication of a gap at the Dirac point.

Thermodynamic Origin of the Vitreous Transition.

The vitreous transition is characterized by a freezing of atomic degrees of freedom at a temperature Tg depending on the heating and cooling rates. A kinetic origin is generally attributed to this phenomenon instead of a thermodynamic one which we develop here. Completed homogeneous nucleation laws reflecting the energy saving due to Fermi energy equalization of nascent crystals and their melt are used. They are applied to bulk metallic glasses and extended to inorganic glasses and polymers. A transition T*g among various Tg corresponds to a crystal homogeneous nucleation temperature, leading to a preliminary formation of a cluster distribution during the relaxation time preceding the long steady-state nucleation time of crystals in small samples. The thermally-activated energy barrier ΔG*2ls/kBT at T*g for homogeneous nucleation is nearly the same in all glass-forming melts and determined by similar values of viscosity and a thermally-activated diffusion barrier from melt to cluster. The glass transition T*g is a material constant and a linear function of the energy saving associated with charge transfers from nascent clusters to the melt. The vitreous transition and the melting temperatures alone are used to predict the free-volume disappearance temperature equal to the Vogel-Fulcher-Tammann temperature of fragile glass-forming melts, in agreement with many viscosity measurements. The reversible thermodynamic vitreous transition is determined by the disappearance temperature T*g of the fully-relaxed enthalpy Hr that is not time dependent; the observed specific heat jump at T*g is equal to the proportionality coefficient of Hr with (T*g − Ta) for T ≤ T*g as expected from the enthalpy excess stored by a quenched undercooled melt at the annealing temperature Ta and relaxed towards an equilibrium vitreous state. However, the heat flux measurements found in literature over the last 50 years only gave an out-of-equilibrium Tg since the enthalpy is continuous at T*g without visible heat jump.

Filament diffusion model for simulating reset and retention processes in RRAM

Resistive switching memory (RRAM) devices are attracting an increasing interest as a possible future technology for ultra-scaled, high-density nonvolatile/dynamic memory. Although the RRAM concept is promising from the integration and scaling viewpoints, the switching mechanism and its controllability are still under debate. This paper addresses the modeling of reset and retention processes in unipolar resistive-switching memory devices. Reset transition and data loss are described in terms of the dissolution of a conductive filament, which is modeled by thermally-activated diffusion of defects/dopants. Carrier transport, Joule heating and diffusion of oxygen ions/vacancies during the electrical pulse and/or the annealing are modeled within a 3D numerical solver. The model can account for the observed dependence of reset voltage on the width of the applied triangular pulse and on the initial resistance for NiO-based RRAM devices. Retention simulations as a function of annealing temperature also agree with available data. The model provides a first example of device simulation tool for the design and the exploration of scaling and performance of RRAM cells.

Effects of thermally-activated diffusion on 72 keV Ni ion implantation into Cu targets at elevated temperatures

This work experimentally and theoretically investigates the effects of thermally-activated diffusion on the depth profiles of nickel atoms in copper. Nickel ions of 72keV and 5×1015ions/cm2 were implanted into copper targets at elevated temperatures of 200, 400 and 500°C, respectively. The experimental nickel depth profiles were obtained by the secondary ion mass spectrometry (SIMS). The calculated profiles were obtained using a thermally-activated diffusion model in which both the radiation-enhanced diffusion (RED) and radiation-induced segregation (RIS) are considered. Furthermore, lattice dilation and preferential sputtering were taken into account by means of an appropriate coordinate transformation. The results indicated a strong temperature-dependence of nickel depth profiles. In addition, the nickel depth profiles tend to broaden and surface concentration increase with temperatures.

Laser Heating Dynamics of Poly(methyl methacrylate) Films Doped with Aromatic Molecules as Revealed by Analysis of Diffusion of Triplet States

Abstract The 248 nm laser heating dynamics of poly(methyl methacrylate) (PMMA) doped with biphenyl or p-terphenyl was studied quantitatively by the analysis of temperature-dependent T1-T1 annihilation, which is a result of the thermally-activated diffusion of the dopants. The values of the second-order rate constant k2 (M−1 s−1) for the annihilation were obtained at several temperatures (293–363 K) under weak laser excitation (2–4 mJ cm−2). Arrhenius plots of k2 for both films resulted in straight lines that were used to estimate the rate constant at higher temperatures for the simulation of T1-T1 annihilation. Under intense excitation (100–190 mJ cm−2), the T1 decays of both films occurred faster with increased laser fluence. The comparison between these observed T1 decays and the simulated ones revealed the following: (1) most of the absorbed photon energy, at least 70%, is used to increase the temperature of the polymer, (2) the cooling of the polymer, mainly due to heat transfer into the quartz substrate, slows down the diffusion of the dopants and, accordingly, the T1-T1 annihilation, and (3) the temperature at the polymer-quartz interface after laser excitation remains almost constant up to at least a few microseconds.

Temperature dependence of gamma ray induced luminescence in toluene based liquid scintillator between 220 and 290 K

The fluorescence of toulene based liquid scintillator (toulene +6 g/l butyl-PBD +0.1 g/l POPOP) has been studied as a function of temperature in the range 220 to 290 K. It has been observed that under gamma excitation the light output increases with decrease in temperature by a factor of 1.43. The data are well encompassed by an Arrhenius relation, in which the activation energy of rate process (0.21 eV) is compatible with thermally-activated diffusion mechanism.

Fission-product transport and the diffusion approximation

Abstract An analytical treatment has been used to model the diffusional release of short-lived fission products from UO2 fuel. The model considers a more general framework based on transport theory and the diffusion approximation. This analysis leads naturally to a microscopic description of the diffusion coefficient where fission-product transport in the solid takes place by isotropic jumps of fixed length in accord with random walk theory. The diffusion equation is solved for an equivalent grain sphere using a more physical “zero-inward current” boundary condition. Following techniques used in nuclear reactor analysis, the concept of a linearly-extrapolated concentration at the free surface is introduced. It is demonstrated that the “extrapolation length” is negligible compared to the radius of the grain sphere for thermally-activated diffusion at high temperatures and for radiation-enhanced (athermal) diffusion at low temperatures. As such, the present boundary condition is shown to reduce to a more familiar one of a zero-concentration at the free surface. As expected, a traditional λ −1 2 dependence for the R B ratio is obtained.

Reaction of hydrogen atoms produced by radiolysis and photolysis in solid phase at 4 and 77 K

The behavior of H atoms in the solid phase has been reviewed with special attention to comparison of H atoms produced by radiolysis with those produced by photolysis. The paper consists of three parts. I—Production of H atoms: (1) the experimental results which indicate H-atom formation in the radiolysis of solid alkane are summarized; (2) ESR saturation behavior of trapped H atoms depends upon the method of H-atom-production, i.e. photolysis or radiolysis, and upon the initial energy of H atoms in the photolysis. II—Diffusion of H atoms: (1) activation energies for thermally-activated diffusion of H atoms are shown; (2) quantum diffusion of H atoms in solid H 2 is explained in terms of repetition of tunneling reaction H 2+H→H+H 2. III—Reaction of H atoms: (1) reactions and trapping processes of hot H atoms have been shown in solid methane and argon by use of hot H atoms with specified initial energy; (2) when H atoms are produced by the radiolysis of solvent alkane or by the photolysis of HI in the alkane mixtures at 77K, the H atoms react very selectively with solute alkane at low concentration. The selective reaction of the H atoms has been found in eight matrices; (3) activation energy for a hydrogen-atom-abstraction reaction by thermal H atoms at low temperatures is less than several kJ mol -1 because of quantum tunneling. The absolute rate constants for H 2(D 2, HD) + H(D) tunneling reactions have been determined experimentally in solid hydrogen at 4.2K; (4) theoretical studies for tunneling reactions H 2(D 2, HD) + H(D) at ultralow temperatures were reviewed. The calculated rate constants were compared with the rate constants obtained experimentally.

Modelling of epitaxial thin-film growth on fcc(100) substrates at low temperatures

Long-lived diffracted intensity oscillations have been observed experimentally during thin-film deposition in several systems at temperatures below which thermally-activated diffusion is thought operative. Several models are presented for growth on fcc(100) substrates which can account for these observations. The requirement of a four-fold hollow, rather than atop, adsorption site dramatically influences film structure. Distinct, but short-lived, oscillations are found here even for random immobile adsorption. The prescription of deposition dynamics is also fundamental. Introducing a ‘downward funneling’ propensity, very short-range ‘transient mobility’ after deposition, or ‘knockout mechanisms’ greatly enhances the quasi-steady nature of film growth. The latter is reflected in a slowly-increasing or quasi-periodic film interface width. Long-lived intensity oscillations are also produced, despite the absence of any long-range mobility.

Release of short-lived fission products from UO 2 fuel: Effects of operating conditions

To support accident “source-term” studies, we have carried out a series of in-reactor tests to determine the behaviour of short-lived fission products (Xe, Kr, I) in operating UO 2 fuel under a variety of conditions. The linear power range examined was 1762 kW/m to a maximum burnup of about 220 MW. h/kg U. Under normal operating conditions, release of the short-lived xenons and kryptons was described by a λ(decay constant) −0.5 relationship, characteristic of diffusion; there was a strong temperature-dependence of release in the thermally-activated diffusion range. Release during shutdown and startup transients was dependent on prior operating temperature, while under oxidizing conditions enhancement of release up to a factor of 4.5 was observed. Under loss-of-coolant conditions, release was described by a λ −1 relationship, characteristic of movement of stored inventory. Most release accompanied the re-wet portion of the transient, consistent with enhancement due to fuel cracking. No iodines exited from the fuel elements under normal, oxidizing or loss-of-coolant conditions.

LPE growth kinetics of CaGe-Substituted EuTm 2Fe 5O 12 garnet films

The diffusion-reaction growth melts fluxed with PbO-B 2O 3-Fe 2O 3, has been extended to include a thermally-activated diffusion term. The fluxed melt had a lower PbO : B 2O 3 ratio (11 : 1) than that generally used (≈16 : 1) for garnet LPE films. Measured growth rates for LPE films, produced from melts with four different concentrations of CaGe-Substituted EuTm 2Fe 5O 2 garnet, fit the model with: diffusivity, D (cm 2/s) = 0.06 exp( -1.0 eV kT ) ; reactivity, K (cm/s) = 8000 exp( -1.61 eV kT ) ; viscosity, v ( cm 2 s ) = 0.01 ; and concentration, c e ( g cm 3 ) = 4220 exp − 1.0678 eV kT for rotation rates ω ( rpm) = 36 to 196 in the growth temperature range 890 to 965°C. It is shown that the garnet melt concentration terms are the most critical ones in determining the growth rate, hence the activation energy (heat of solution) for the equilibruim concentration is reported to five significant figures. Evaluating the D and the K effects by both a numerical (results given above) and an analytic method demonstrates that these parameters are least critical in determining the growth rate in this case.