Fast Grain Boundary Diffusion Research Articles

Cation diffusion in polycrystalline thin films of monoclinic HfO2 deposited by atomic layer deposition

Though present in small amounts and migrating at low rates, intrinsic cation defects play a central role in governing the operational lifetime of oxide-ion conducting materials through slow degradation processes such as interdiffusion, kinetic demixing, grain growth, and creep. In this study, a new experimental approach to characterizing the behavior of such slow-moving, minority defects is presented. Diffusion is probed in samples with a constant cation-defect concentration well above the equilibrium values. This approach is applied to monoclinic hafnium dioxide, m-HfO2. To this end, nanocrystalline thin films of m-HfO2 were prepared by atomic layer deposition. Diffusion experiments with ZrO2 as a diffusion source were performed in the temperature range 1173 ≤ T/K ≤ 1323 in air. The Zr diffusion profiles obtained subsequently by secondary ion mass spectrometry exhibited the following two features: the first feature was attributed to slow bulk diffusion and the second was attributed to combined fast grain-boundary diffusion and slow bulk diffusion. The activation enthalpy of Zr diffusion in bulk HfO2 was found to be (2.1 ± 0.2) eV. This result is consistent with the density-functional-theory calculations of hafnium-vacancy migration in m-HfO2, which yield values of ∼2 eV for a specific path. The activation enthalpy of the grain-boundary diffusion of (2.1 ± 0.3) eV is equal to that for bulk diffusion. This behavior is interpreted in terms of enhanced cation diffusion along space-charge layers.

Grain-boundary diffusion of cations in fluorite-type oxides is faster but not always easier

Cation diffusion in fluorite-type MO2 polycrystals has been observed in diverse experimental studies to occur much faster along grain boundaries than in the bulk phase. The activation enthalpy of grain-boundary diffusion (ΔH gb), relative to the value for bulk diffusion (ΔH b), is, in many cases, seemingly unphysical: specifically, the ratio r = ΔH gb/ΔH b approaches, or even exceeds, unity. In this study, we examined the behaviour of r, assuming that fast cation diffusion arises from the accumulation of cation vacancies in space-charge layers adjacent to grain boundaries. Taking an acceptor-doped MO2 oxide as our model system, we obtained, first, numerical solutions to a Poisson equation for equilibrium space-charge layers; and then, numerical solutions to the diffusion equation for cation diffusion occurring parallel to the interface. The resultant diffusion profiles displayed two features and were analysed according to the standard procedure to obtain the grain-boundary diffusion product. From a detailed analysis of our results, we conclude that, within our model, fast diffusion in space-charge layers can yield values of r that approach but do not exceed unity. In addition, we derive an empirical relationship that allows the grain-boundary diffusion product, the effective grain-boundary width and the grain-boundary diffusivity to be predicted with knowledge of space-charge parameters and the bulk diffusivity. Finally, we demonstrate that this relationship is also applicable to the fast grain-boundary diffusion of cations in acceptor-doped ABO3 perovskites.

Effect of Morphological Change of Ni3Sn4 Intermetallic Compounds on the Growth Kinetics in Electroless Ni-P/Sn-3.5Ag Solder Joint

Recently, the growth kinetics of the intermetallic compound (IMC) Ni3Sn4 related to Ni metallization has been investigated in comparison to Cu6Sn5 growth on Cu metallization. In the literature, Ni3Sn4 growth in liquid Sn was analyzed for IMC morphology, grain coarsening, grain boundary (GB) grooving, and GB diffusion. However, the growth kinetics of Ni3Sn4 on electroless (EL) Ni-P metallization has rarely been investigated. In this study, the morphological change of Ni3Sn4 on EL Ni-P and its effects on growth kinetics were analyzed in detail during a reaction with Sn-3.5Ag at 250 °C for up to 30 minutes and compared with electroplated (EP) Ni. For both cases, the IMC growth kinetics was presumed to be governed by fast GB diffusion accompanied with grain coarsening. The morphology of Ni3Sn4 on EP Ni changed little throughout the reaction. Therefore, a 1/3 power-law could be applicable. However, the aspect ratio (thickness/diameter) of the Ni3Sn4 grains on EL Ni-P decreased with the increasing reaction time, which resulted in a larger time exponent of 4.2. The morphological change from needle to chunk induced a high rate of grain coarsening. Consequently, the IMC growth rate declined according to the reduction of fast diffusion paths (GB area).

Room-Temperature Superplasticity in an Ultrafine-Grained Magnesium Alloy

Superplasticity, a phenomenon of high tensile elongation in polycrystalline materials, is highly effective in fabrication of complex parts by metal forming without any machining. Superplasticity typically occurs only at elevated homologous temperatures, where thermally-activated deformation mechanisms dominate. Here, we report the first observation of room-temperature superplasticity in a magnesium alloy, which challenges the commonly-held view of the poor room-temperature plasticity of magnesium alloys. An ultrafine-grained magnesium-lithium (Mg-8 wt.%Li) alloy produced by severe plastic deformation demonstrated 440% elongation at room temperature (0.35 Tm) with a strain-rate sensitivity of 0.37. These unique properties were associated with enhanced grain-boundary sliding, which was approximately 60% of the total elongation. This enhancement originates from fast grain-boundary diffusion caused by the Li segregation along the grain boundaries and the formation of Li-rich interphases. This discovery introduces a new approach for controlling the room-temperature superplasticity by engineering grain-boundary composition and diffusion, which is of importance in metal forming technology without heating.

Impurity diffusion of Hf and Zr in Gd-doped CeO2

The impurity diffusion of Hf and Zr in Gd-doped CeO2 was examined by means of Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS). Dense, polycrystalline samples with a dopant site fraction of nGd=0.5% were subjected to diffusion anneals in the temperature range 1400≤T/K≤1600 in ambient air. Isothermal values of the bulk diffusion coefficient, Db, were similar for the two isovalent impurity cations. The activation enthalpies of bulk diffusion were also similar, ∆HDb(Zr)=(5.5±0.4) eV and ∆HDb(Hf)=(5.3±0.3) eV. Fast grain-boundary diffusion of Hf was observed (the high background of Zr prevented the analysis of Zr grain-boundary diffusion). The activation enthalpy of the grain-boundary diffusion product, ∆HωDgb(Hf)=(5.9±0.8) eV, is, surprisingly, similar to the activation enthalpies for bulk diffusion. Attention is drawn to possible problems that may arise when using chemical tracers instead of true (stable or radioactive) tracers.

Antimony Diffusion in CdTe

Group V dopants may be used for next-generation high-voltage cadmium telluride (CdTe) solar photovoltaics, but fundamental defect energetics and kinetics need to be understood. Here, antimony (Sb) diffusion is studied in single-crystal and polycrystalline CdTe under Cd-rich conditions. Diffusion profiles are determined by dynamic secondary ion mass spectroscopy and analyzed with analytical bulk and grain-boundary diffusion models. Slow bulk and fast grain-boundary diffusion are found. Density functional theory is used to understand formation energy and mechanisms. The theory and experimental results create new understanding of group V defect kinetics in CdTe.

Phosphorus Diffusion Mechanisms and Deep Incorporation in Polycrystalline and Single-Crystalline CdTe

CdTe solar-cell technology could provide a levelized cost of electricity (LCOE) below that of $a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}y$ conventional source, including silicon photovoltaics and fossil fuels---if only the open-circuit voltage could be increased. The key is to raise the density of holes, for which phosphorus doping seems promising. A combination of experiment and theory reveals the atomistic mechanisms of P diffusion in CdTe, including fast grain-boundary and bulk diffusion paths. This strong physical insight is needed for next-generation applications, even beyond photovoltaics.

Competing descriptions of diffusion profiles with two features: Surface space-charge layer versus fast grain-boundary diffusion

Two different physical processes, (i) fast grain-boundary diffusion (FGBD) of oxygen and (ii) hindered oxygen diffusion in a surface space-charge layer, yield oxygen isotope diffusion profiles in a similar form. Two features are observed, with the short, sharp profile close to the surface being followed by a longer, shallower profile. In this study, we develop a procedure for deciding which of the two descriptions applies to experimentally measured profiles. Specifically, we solve Fick's second law, using finite-element simulations, to obtain oxygen isotope diffusion profiles for the two cases. Each set of profiles is then analysed in terms of the competing description. In this manner, we derive falsifiable conditions that allow physical processes to be assigned unambiguously to the two features of such isotope profiles. Applying these conditions to experimental profiles for SrTiO3 single crystals published in the literature, we find that FGBD is an invalid model for describing the diffusion processes.

Oxide Ion Transport in Donor-Doped Pb(ZrxTi1−x)O3: The Role of Grain Boundaries

Oxygen vacancies play a role in various proposed degradation mechanisms of Pb(ZrxTi1−x)O3 (PZT)-based applications. Hence, 18O tracer diffusion experiments investigated by time-of-flight-secondary ion mass spectrometry were used in order to evaluate oxygen diffusion in donor-doped polycrystalline PZT. The PZT shows fast grain-boundary diffusion for annealing temperatures around 650°C with a strong temperature dependency. 18O intensity images clearly coincide with maps of grain boundaries. Within individual grains, local diffusion profiles could be measured and revealed bulk diffusion as well as evidence of a near-surface space–charge layer. The bulk and grain-boundary diffusion coefficients for the samples annealed at 650°C could be calculated with respect to type B diffusion kinetics. Comparison with electrical measurements showed that oxide ion conduction in grain boundaries significantly contributes to the total conductivity of donor-doped PZT.

Multiphase Field Simulations of Intermetallic Compound Growth During Lead-Free Soldering

A multiphase field simulation of the morphological evolution of the intermetallic compounds (IMCs) formed during the reaction between liquid Sn-based solder and a copper substrate is presented. The Cu-substrate, Cu 3 Sn (∈ phase), and Cu 6 Sn 5 (η phase) layers (or grains), as well as the Sn-liquid phase are considered. Interfaces are defined by the presence of more than one phase at a given point of the computational domain. The interface structure is determined by assuming that all components of coexisting phases within the interfacial region have equal chemical potentials, which are in turn calculated from CALPHAD thermodynamic databases. Fast grain boundary (GB) diffusion in the η IMC layer, η grain coarsening and growth with growth/shrinkage of ∈ grains, and dissolution of Cu from the substrate will be discussed and compared with previous works. The simulation will address the kinetics of the IMC growth during soldering and the influence of fast GB diffusion on the concurrent coarsening of Cu 3 Sn and Cu 6 Sn 5 grains. The kinetic behavior of the substrate/ IMC/solder system as a function of model parameters will also be presented.

Oxygen vacancy kinetics in ferroelectric PbZr0.4Ti0.6O3

Oxygen vacancy kinetics in ferroelectric PbZr0.4Ti0.6O3 were studied by oxygen18 (O18) tracer self-diffusion in epitaxial thin films as well as bulk polycrystalline samples. O18 exchange annealing was carried out at an oxygen partial pressure of 250mbar and temperatures between 250 and 400°C. Isotope depth profiling was performed by secondary ion mass spectrometry as well as neutral secondary mass spectrometry. The observed concentration depth profiles of the polycrystalline samples show two distinct diffusion paths, namely, bulk diffusion and grain boundary (GB) diffusion. It appears to be of type B-kinetics in the investigated temperature range, with DGB∕Dbulk⪢100. Donor doped samples with different levels of Nb5+ (1–4mol.%) were also investigated. The effect on the diffusion depth profiles, however, were negligible and can solely be attributed due to the change in the samples microstructure as induced by the dopants. A diffusion coefficient for the bulk diffusion of the O18 isotope, Dbulk=10±5×10−8cm2∕sexp(−0.87±0.1eV∕kT) was found. The faster GB diffusion process shows an activation enthalpy of only EA=0.66±0.2eV.

Effect of alloy grain size on the high-temperature oxidation behavior of the austenitic steel TP 347

Generally, oxide scales formed on high Cr steels are multi-layered and the kinetics are strongly influenced by the alloy grain boundaries. In the present study, the oxidation behaviour of an austenite steel TP347 with different grain sizes was studied to identify the role of grain-boundaries in the oxidation process. Heat treatment in an inert gas atmosphere at 1050 °C was applied to modify the grain size of the steel TP347. The mass gain during subsequent oxidation was measured using a microbalance with a resolution of 10-5 g. The scale morphology was examined using SEM in combination with energy-dispersive X-ray spectroscopy (EDS). Oxidation of TP347 with a grain size of 4 µm at 750 °C in air follows a parabolic rate law. For a larger grain size (65 µm), complex kinetics is observed with a fast initial oxidation followed by several different parabolic oxidation stages. SEM examinations indicated that the scale formed on specimens with smaller grain size was predominantly Cr2O3, with some FeCr2O4 at localized sites. For specimens with larger grain size the main oxide is iron oxide. It can be concluded that protective Cr2O3 formation is promoted by a high density of fast grain-boundary diffusion paths which is the case for fine-grained materials.

The Effect of Grain-Boundary Diffusion on the Oxidation of Low-Chromium Steels

Even though the oxidation behavior of steels is generally considered as to be widely understood, a closer look reveals some open questions, e.g. regarding the influence of the substrate grain size on the overall oxidation kinetics. At temperatures below 570°C the main constituent of the oxide scale formed on top of low alloy steels is magnetite. As shown by gold marker experiments it grows outward and inward at the same time, the latter exhibiting a gradual transition to the more stable spinel compound FeCr2O4. As indicated by intergranular-oxidation attack below the superficial scale, inward oxide growth seems to be driven by oxygen transport along the grain boundaries serving as fast diffusion paths. This is supported by thermogravimetric oxidation tests in air on low-Cr steels with varying grain size: The smaller the grains the higher the oxidation rate. Recently, a numerical model for the diffusive transport processes based on the finite-difference approach has been developed, which distinguishes between fast grain-boundary diffusion and bulk diffusion. Qualitatively, it is capable to predict the relationship between substrate grain size and inward oxide growth kinetics. Together with the thermodynamic tool ChemApp and in combination with a data set for the Fe-Cr-O system the mechanism-based simulation of the overall oxidation process of low-Cr steels is possible.

Phase field simulations of intermetallic compound growth during soldering reactions

Phase field simulations of the microstructural evolution of the intermetallic compound (IMC) layer formed during isothermal soldering reactions between Sn-Cu solder alloys and a Cu substrate are presented. The simulation accounts for the fast grain boundary (GB) diffusion in the IMC layer, the concurrent IMC grain coarsening along with the IMC layer growth, and the dissolution of Cu from the substrate and IMC layer. The simulation results support the previous suggestions that the growth kinetics of the IMC layer during soldering is predominantly governed by the fast GB diffusion and the concurrent coarsening rate of the IMC grains. The IMC grain coarsening is initiated by a competitive growth of the IMC grains at the solder/IMC interface. It is also shown that the dissolution of Cu into an unsaturated solder reduces the coarsening rate of the IMC grains, consequently decreasing the temporal growth exponent of the IMC layer.

Constrained Sintering of Silver Circuit Paste

Densification kinetics and stress development during constrained sintering of a silver film on a rigid silicon substrate have been studied. Compared with free sintering, the sintering of constrained silver film exhibits a much lower densification and slower densification kinetics. The densification‐controlled mechanism changes from fast grain‐boundary diffusion kinetics for free sintering to slow lattice diffusion kinetics for constrained sintering. The in‐plane tensile stress developed during constrained sintering of silver film, measured using a noncontact laser‐scanning optical system, increases rapidly to a maximum level of 1.0–1.5 MPa initially, gradually decreases, and then becomes constant at 0.8–1.0 MPa. The maximum stress observed increases with increasing sintering temperature as a result of the faster densification rate. It is believed that the retardation of densification kinetics of constrained silver film is caused by a change in densification mechanism and the existence of in‐plane tensile stress.

The influence of alumina addition and its distribution upon grain-boundary conduction in 15 mol.% calcia-stabilized zirconia

The improvement of grain-boundary conduction was studied in 15 mol.% calcia-stabilized zirconia (15CSZ) by adding Al 2O 3 in the forms of fine powder and single crystalline particles sized 4–10 μm as a scavenger for resistive siliceous phase. The addition of 1 mol.% Al 2O 3 improved the grain-boundary conduction when sintered at <1500°C, whereas it deteriorated at >1550°C. The restraining Al 2O 3 dissolution into inter-granular glass phase was a key feature for maximizing the scavenging efficiency. At 1450°C, the addition of single crystalline Al 2O 3 sized 4 and 10 μm enhanced grain-boundary conductivity by a factor of 14–16, whose enhancement was about twice of that by fine Al 2O 3 powder. It can be explained by the combination of the sufficient reaction path assisted by fast grain-boundary diffusion and the restraining glass phase formation by employing coarse and inactive single crystalline Al 2O 3 particles.

Evaluation of amorphous (Mo, Ta, W)SiN diffusion barriers for 〈Si〉|Cu metallizations

Amorphous binary M(= Mo, Ta or W)-Si and ternary MSiN, r.f.-sputtered from M 5Si 3 and WSi 2 targets, are assessed as diffusion barriers between silicon substrates and copper overlayers. By I( V) tests of the metallizations on n + p shallow junction diodes, the ternary MSiN barriers prevent copper from reaching the silicon at 800 °C or higher during a 30 min heat treatment in vacuum. Failure of the metallizations correlates with the crystallization temperature of the barrier, which is presumably a prelude to fast grain-boundary diffusion. Metal-rich MoSiN and WSiN barriers liberate nitrogen during annealing, which poses a limitation to their crystallization temperatures. No reaction products of copper with metal-rich MSi or MSiN barriers are observed, which is in agreement with our recent thermodynamic modelling of the MSiCu ternary systems.

Penetration profiles for fast grain-boundary diffusion by the dissociative mechanism

A modified variant of Fisher’s model is proposed to describe the recently discovered phenomenon of fast impurity diffusion along grain boundaries (GBs) in metals as follows, (i) The fast diffusion is assumed to occur by the dissociative mechanism. Depending on the lattice dislocation density ρ the bulk diffusion of the impurity around GBs is either vacancy controlled [if (Dt)1/2≪ρ−1/2] or interstitial controlled [if (DT)1/2≫ρ−1/2]. In the first case the effective bulk diffusivity D depends on the GB concentration whereas in the second case D=const. (ii) Fast diffusers strongly segregate to GBs. The GB saturation effect is taken into account by introducing McLean’s isotherm of GB segregation. The GB penetration profiles calculated from approximate analytical solutions of the model exhibit two parts: a near-surface part caused by the GB saturation effect and a more deeply penetrating linear segregation part with a much smaller slope. The second part of the profile either shows strong downward curvature (vacancy-controlled D) or demonstrates normal Fisher-like behavior (interstitial-controlled D). Methods of profile treatment for the determination of GB diffusion parameters are presented. Based on the present model the available experimental data are critically considered and ideas of future experiments are discussed.

Computer Simulation of Final‐Stage Sintering: I, Model Kinetics, and Microstructure

A Monte Carlo model for simulating final‐stage sintering has been developed. This model incorporates realistic microstructural features (grains and pores), variable surface difusivity, grain‐boundary diffusivity, and grain‐boundary mobility. A preliminary study of a periodic array of pores has shown that the simulation procedure accurately reproduces theoretically predicted sintering kinetics under the restricted set of assumptions. Studies on more realistic final‐stage sintering microstructure show that the evolution observed in the simulation closely resembles microstructures of real sintered materials over a wide range of diffusivity, initial porosity, and initial pore sizes. Pore shrinkage, grain growth, pore breakaway, and reattachment have all been observed. The porosity decreases monotonically with sintering time and scales with the initial porosity and diffusivity along the grain boundary. Deviations from equilibrium pore shapes under slow surface diffusion or fast grain‐boundary diffusion conditions yield slower than expected sintering rates.

Grain-boundary segregation in aluminium-doped silicon carbide

Scanning transmission electron microscopy (STEM) was used to examine sintered and hot-pressed aluminium-doped silicon carbide. Grain-boundary segregation of Al was observed in both materials. Semi-quantitative analysis was carried out on the Al-saturated hot-pressed material. An estimated heat of segregation between 116 and 174 kJ mol−1 was calculated from the STEM data and equilibrium segregation theory. Strain energy as a driving force was considered negligible. The data are consistent with a segregation model in which the driving force for segregation is the difference in the nature of bonding between the solute and solvent atoms. Fast grain-boundary diffusion of Al was suggested from a loss of Al during heat treatments.