Segregation Enthalpy Research Articles

On the relationship between entropy and enthalpy of grain boundary segregation

An extensive study of anisotropy of grain boundary segregation in α-iron, performed in the last decade, confirmed the existence of a linear relationship between entropy and enthalpy of solute segregation at individual grain boundaries. A thermodynamic analysis of this relationship is performed in the present work. It is shown that this dependence defines a “compensation temperature” and an entropy-like parameter. The compensation temperature is not necessarily connected with a phase transformation, but it represents exclusively a mean temperature at which all boundaries approach to a mean value of the Gibbs free energy of segregation. The most important consequences of this dependence are outlined: a reversed anisotropy of grain boundary segregation at temperatures above the compensation temperature, and a new method for the prediction of the enthalpy and entropy of solute segregation at individual grain boundaries.

Ag grain boundary diffusion and segregation in Cu: Measurements in the types B and C diffusion regimes

Grain boundary (GB) diffusion of 110mAg in polycrystalline Cu was measured under the conditions of the Harrinson's type B (962–675 K) and type C (565–452 K) diffusion regimes. In the B-type diffusion regime, the triple product P= sδD gb ( s is the segregation factor and δ the GB width) was found to follow the Arrhenius law P=(1.4 +0.6 −0.4)·10 −15·exp{−[(69.1±2.5)kJ·mol −1]/ RT} m 3 s −1. The measurements under the C regime conditions directly established the temperature dependence of the GB diffusion coefficient D gb , D gb =(1.7 +0.7 −0.5)·10 −4· exp{−[(108.6±1.9) kJ· mol −1]/RT} m 2 s −1. Combining both results and assuming as usual δ≅5·10 −10 m the segregation factor s was determined to follow an Arrhenius dependence s=s 0 exp(−H s /RT) with the pre-exponential factor s 0=(1.6 +1.4 −1.0)·10 −2 and the segregation enthalpy H s=−39.5±4.0 kJ·mol −1. Experimental conditions were analyzed to figure the factors resulting in the curvature of the radiotracer profiles. Probable non-linear segregation was shown to give only marginal (if any) effect. The initial parts of the profiles are well described by accounting for the GB motion during diffusion anneal. The analysis shows that a hypothetial dislocation-enhanced volume diffusion at low temperatures cannot disturb the C-regime conditions in the present experiments. The very small tracer concentrations applied in the types B and C diffusion measurements indeed allow us to establish equilibrium GB segregation at negligible concentrations of solute atoms. The results are compared with the available literature data obtained by direct measurements with non-negligible solute concentrations.

Ultra-highly doped Si1−xGex(001):B gas-source molecular-beam epitaxy: Boron surface segregation and its effect on film growth kinetics

Si 1−x Ge x (001) layers doped with B concentrations CB between 2×1016 and 2×1021 cm−3 were grown on Si(001)2×1 at Ts=500–700 °C by gas-source molecular-beam epitaxy (GS-MBE) from Si2H6, Ge2H6, and B2H6. Secondary-ion mass spectrometry measurements of modulation-doped structures demonstrate that B doping has no effect on the Ge incorporation probability. Steady-state B and Ge surface coverages (θB and θGe) were determined as a function of CB using in situ isotopically tagged temperature-programmed desorption. Results for Si0.82Ge0.18 layers grown at Ts=500 °C show that θGe remains constant at 0.63 ML while the bulk B concentration increases linearly up to 4.6×1020 cm−3, corresponding to saturation coverage at θB,sat=0.5 ML, with the incident precursor flux ratio ξ=JB2H6/(JSi2H6+JGe2H6). B is incorporated into substitutional electrically active sites over this entire concentration range. At higher B concentrations, CB increases faster than ξ and there is a large decrease in the activated fraction of incorporated B. The B segregation enthalpy during Si0.82Ge0.18(001) growth is −0.42 eV, compared to −0.53 and −0.64 eV during Si(001):B and Ge(001):B GS-MBE, respectively. Measured segregation ratios rB=θB/xB, where xB is the bulk B fraction, range from 15 to 500 with a temperature dependence which is consistent with equilibrium segregation. Film deposition rates RSiGe(CB) decrease by up to a factor of 2 with increasing CB⩾5×1019 cm−3, due primarily to a B-segregation-induced decrease in the dangling bond density. The above results were used to develop a robust model for predicting the steady-state H coverage θH, θB, θGe, and RSiGe as a function of ξ and Ts.

Surface segregation in Ni(W) solid solution

The surface composition of Ni–7%W solid solution equilibrated under UHV in the range 750–1100 K was determined by means of quantitative Auger electron spectroscopy. Only part of the excess tungsten accumulated at the sputter-cleaned surface dissolved upon subsequent annealing, and from the temperature dependence of the residual W equilibrium concentration, quantified for two different in-depth distribution models, segregation enthalpies and excess entropies are derived. The observed tungsten surface segregation tendency indicates dominance of elastic strain release over weakened interatomic bonding driving forces in this solid solution. Tungsten segregation levels are relatively low because of the small net energetic driving force, and due to a suppressing excess entropy effect. Adsorption of oxygen on the alloy surfaces enhances W segregation at elevated temperatures due to preferential WO interactions.

Thermodynamics of phosphorus grain boundary segregation in polycrystalline low-alloy steels

Phosphorus grain boundary segregation in three polycrystalline Cr–Mo–V low-alloy steels was investigated using Auger electron spectroscopy and thermodynamic calculations. Obtained data on polycrystals fit very well with the recently reported linear relationship between enthalpy and entropy of phosphorus segregation at individual grain boundaries of α-iron found in bicrystals of an Fe–Si alloy. Different crystallography seems to be responsible for the scatter of the values of segregation enthalpy for individual low-alloy steels. Copyright © 2000 John Wiley & Sons, Ltd.

Computer study of boron segregation at the Si(100)–2×1 and Si(111)–3×3 surfaces

Energetics of the boron substitution near the Si(100)–2×1 and Si(111)–3×3 surfaces have been studied using the semi-empirical cluster AM1 method at substitutional positions at the Si(100)–2×1 surface. It has been found that in the both cases boron prefers to be in the second layer, that is it occupies substitutional positions that are bonded with dimers of the Si(100)–2×1 surface and S5 sites under adatoms of the Si(111)–3×3 surface. The energies, counting from the fourth bulk-like layer, for the Si(100)–2×1 and Si(111)–3×3 surfaces are −1.3 and −2.1 eV, respectively. These values may be interpreted as corresponding segregation enthalpies.

Segregation in Yttrium Aluminum Garnet: I, Experimental Determination

Single crystals of yttrium aluminum garnet (YAG) that were doped with various cations were annealed in air at different temperatures for varying amounts of time. Dopants were chosen to probe the effect of size, charge, and site occupancy on surface segregation. Of the dopants that were chosen for the study (calcium, silicon, neodymium, chromium, and strontium), calcium was the only one that consistently segregated upon annealing in air. Calcium enrichment to the (111) surface was measured using Auger electron spectroscopy, and the segregation enthalpy was determined to be δHseg≈−32 ± 10 kJ/mol. Enrichment occurred according to variations in valence, as opposed to variations in size; therefore, it is suggested that surface segregation is electrostatically driven. The results indicate that aliovalent substituents could be used for interface property tailoring, whereas isovalent dopants would not be useful.

Grain boundary segregation of antimony in iron base alloys and its effect on toughness

The equilibrium grain boundary segregation of antimony was investigated in iron base alloys (Fe-Sb, Fe-C-Sb, Fe-Ni-Sb) after annealing at temperatures between 550 and 750°C. Utilizing Auger electron spectroscopy (AES) the concentration of antimony at intergranular fracture faces was determined as a function of bulk concentration and equilibration temperature. The segregation of antimony in Fe-Sb alloys with mass contents of between 0.012 and 0.094 % Sb was described by the Langmuir-McLean equation. The evaluation leads to the free enthalpy of segregation ΔG segr = -19 kJ/mol - T 28 J/mol K. The relatively low value for the segregation enthalpy AH = -19 kJ/mol indicates a rather small tendency for grain boundary segregation of Sb. However, its embrittling effect is strong, scanning electron micrographs (SEM) of fractured samples show that the percentage of intergranular fracture strongly increases with an increasing coverage of antimony at the grain boundaries. The data for Fe-0.93% Sb and Fe.1.91% Sb (mass contents) do not fit in the thermodynamic evaluation obviously due to formation of antimonide precipitates in the grain boundaries. The addition of carbon to Fe-Sb alloys results in a higher grain boundary cohesion which is caused by two effects of carbon, displacement of antimony from the grain boundaries by carbon and enhanced grain boundary cohesion. In the Fe-Ni-Sb alloys additional segregation of nickel was found at the grain boundaries but no enhanced antimony segregation, as expected from previous models of other authors, assuming Ni-Sb cosegregation.

Special [100] Tilt Grain Boundaries in Iron: A Segregation Study

A systematic study of solute segregation in numerous bicrystals of an Fe-3.5at.%Si alloy enabled us to find all special [100] tilt grain boundaries. Various plots of segregation enthalpy vs. grain boundary orientation were compared to the grain boundary plane classification. From the correlation obtained we conclude that the {012}, {013} and {015} symmetrical, and (001)/(013) and all (011)/(0kl) asymmetrical grain boundaries are special. All other (001)/(0kl) asymmetrical boundaries exhibit low tendencies to solute segregation and can be considered as vicinal interfaces.

Role of entropy in anistropy of grain boundary segregation

From the viewpoint of existence of linear dependence between entropy and enthalpy of grain boundary segregation, the meaning of the entropy term is discussed. It is suggested that negative values of segregation entropy for silicon segregation at individual grain boundaries in α-iron reflect an ‘ordering’ tendency of the interfaces due to the presence of silicon. On the other hand, positive values of segregation entropy suggest a ‘disordering’ of the structure of these grain boundaries by segregation of carbon and mainly of phosphorus. The effect of ‘disordering’ is especially high for special grain boundaries with compact intrinsic structure, resulting in high values of segregation entropy. The slope of the dependence of enthalpy on entropy of solute segregation at different grain boundaries can be considered as a compensation temperature. Its existence implies that an anisotropy of grain boundary chemical composition will possess a qualitatively different character above and under this temperature. This anisotropy measured above the compensation temperature will be characterized by high values of grain boundary concentration for special boundaries as compared to general boundaries. © 1998 John Wiley & Sons, Ltd.

Cation segregation to yttrium aluminum garnet (111) surfaces

Single crystals of yttrium aluminum garnet doped with various cations were annealed in air at different temperatures for varying amounts of time. Dopants were chosen to probe the effects of size, charge and site occupancy on surface segregation. Of a number of dopants (Ca, Nd, Cr, Si, Sr) Ca was the only dopant observed to consistently segregate upon annealing in air. Ca enrichment at the (111) surface was measured with Auger electron spectroscopy and the segregation enthalpy was determined as Δ H seg=−32.33 kJ mol −1. Since variation in size did not cause segregation while variations in valence did, it is suggested that surface segregation is electrostatically driven. Theoretical calculations explain the noted lack of Si segregation in co-doped samples in terms of the vacancy formation energy dependence of the isoelectric point. It is predicted that an excess of negative charge, on the order of 600 ppm, is required to observe a compositional isoelectric point.

Surface segregation in an Al–4.2 at% Ag alloy

The equilibrium surface composition of a polycrystalline Al–4.2 at% Ag alloy has been measured as a function of temperature using Auger electron spectroscopy. These results indicate that silver segregates to surfaces with an apparent enthalpy of segregation of about −38.5 kJ/mol. The equilibrium average surface composition of the alloy has been calculated as a function of surface orientation using the Lee–Aaronson discrete lattice plane model. A modified regular solution model originally due to Alexander et al. was used to represent the interactions between Al and Ag atoms. While this model successfully described the relevant portion of the Al–Ag phase diagram and the faceting behavior of GP zones in Al rich Al–Ag alloys, it predicted no surface segregation of Ag in the present studies. These results are in contrast to the results obtained experimentally. Possible reasons for the lack of agreement are considered. Finally, the surface segregation of silver measured by AES was compared with that predicted by the Gibbs adsorption isotherm, wherein the latter calculation made use of the results of ultra high vacuum measurements of the bulk composition dependence of the surface tension of α Al–Ag alloys (to be reported elsewhere). Qualitative agreement was found between the two experimental methods, both indicating enrichment of Ag at the free surfaces.

Mechanically Induced Phase Transformation and Surface Segregation in Bismuth‐Doped Tetragonal Zirconia

Compact pressure causes a martensitic transformation of partially stabilized tetragonal bismuth‐doped ZrO2 powders to the monoclinic phase. A similar effect is not observed when pelletization, followed by firing, of amorphous bismuth/ZrO2 is performed. The stress‐induced transition has been monitored via X‐ray diffractometry, Raman spectroscopy, and Fourier transform infrared reflectivity. Surface bismuth segregation, which involves few ionic planes, has been probed by angle‐resolved X‐ray photoelectron spectroscopy. The bismuth segregation enthalpy has been evaluated.

Nickel and selenium grain boundary solute diffusion and segregation in silver

For the first time, the grain boundary (GB) solute diffusion of Ni and Se in Ag polycrystals was investigated systematically by the radiotracer serial sectioning technique using 63Ni and 75Se isotopes. Measurements in the temperature ranges 589–989 K for Ni and 371–877 K for Se were carried out in Harrison's type B regime at high temperatures and in type C regime at low temperatures. In the B regime, the product sδD GB was determined ( s being the solute GB segregation factor, δ the GB width, D GB the GB diffusion coefficient), while in the C-regime D GB values were measured directly. The solid solubility of both solutes, Ni and Se, in Ag is very small. The equilibrium phase diagrams, however, are quite different: Se forms an intermetallic compound whereas Ni does not form any compound with Ag, which indicates dominating Se–Ag and Ni–Ni bonds, respectively. Comparing the solute D GB values with C regime measurements of GB self-diffusion in Ag, a drastic decrease of the Ni diffusivity and an increased activation enthalpy of Ni diffusion, H GB Ni, in Ag GBs is observed. This behaviour is discussed in terms of repulsive Ni-vacancy interactions and decreased jump frequencies of the Ni atoms which are mainly located at low energy positions in the GB. The measured D GB values of Se, on the other hand, are comparatively close to GB self-diffusion, whereas H GB Se is again larger than H GB Ag of GB self-diffusion. This behaviour is explained in terms of the formation of “embryos” of two-dimensional phases at high energy GB sites. Combining the obtained sδD GB and D GB values and assuming δ=0.5 nm, the GB segregation factors and segregation enthalpies of Ni ( H s Ni=−39.7 kJ/mol) and Se ( H s Se=−21.4 kJ/mol) in Ag were evaluated.

Criteria for the Occurrence of the Diffusion-Induced Grain Boundary Migration

Recent experimental data on diffusion-induced grain boundary migration (DIGM) are reviewed. For the case of the coherency strain driving force, quantitative criteria for the occurrence of DIGM are suggested, which establish the relationship between the net driving force for grain boundary migration, the diffusivity in the vicinity of the grain boundary, the enthalpy of the grain boundary segregation, the misfit parameter for the solute atoms in the matrix and the solubility of the diffusing element in the matrix. It is shown that an upper limit for the grain boundary velocity during DIGM exists due to the solute drag effect.

Effects of H coverage on Ge segregation during Si1−xGex gas-source molecular beam epitaxy

The effects of H coverage θH on Ge segregation during Si1−xGex gas-source molecular beam epitaxy (GS-MBE) were investigated using D2 temperature programmed desorption (TPD). Si1−xGex films with x=0.01–0.30 were grown from Si2H6/Ge2H6 mixtures at Ts=450–800 °C, held at the growth temperature for 30 s, cooled to <200 °C, and then exposed to atomic deuterium until saturation coverage. D2 TPD spectra were fit using four peaks corresponding, in order of decreasing activation energy, to desorption from Si monodeuteride, Ge–Si mixed-dimer monodeuterides, Si dideuteride, and Ge monodeuteride. Steady-state Ge surface coverages were determined from the TPD data as a function of Ts and x. In contrast to solid-source MBE films grown in this temperature regime, Ge segregation during GS-MBE decreases with decreasing Ts due to the increasing H coverage. The results were well described by a model accounting for the Si/Ge site exchange and θH. The Ge segregation enthalpy varies from −0.28 eV at Ts⩾800 °C, where the steady-state hydrogen coverage θH approaches zero, to −0.10 eV at Ts⩽450 °C, where θH is nearly saturated.

Si(001):B gas-source molecular-beam epitaxy: Boron surface segregation and its effect on film growth kinetics

B-doped Si(001) films, with concentrations CB up to 1.7×1022 cm−3, were grown by gas-source molecular-beam epitaxy from Si2H6 and B2H6 at Ts=500–800 °C. D2 temperature-programed desorption (TPD) spectra were then used to determine B coverages θB as a function of CB and Ts. In these measurements, as-deposited films were flash heated to desorb surface hydrogen, cooled, and exposed to atomic deuterium until saturation coverage. Strong B surface segregation was observed with surface-to-bulk B concentration ratios ranging up to 1200. TPD spectra exhibited β2 and β1 peaks associated with dideuteride and monodeuteride desorption as well as lower-temperature B-induced peaks β2* and β1*. Increasing θB increased the area under β2* and β1* at the expense of β2 and β1 and decreased the total D coverage θD. The TPD results were used to determine the B segregation enthalpy, −0.53 eV, and to explain and model the effects of high B coverages on Si(001) growth kinetics. Film deposition rates R increase by ⩾50% with increasing CB>̃1×1019 cm−3 at Ts⩽550 °C, due primarily to increased H desorption rates from B-backbonded Si adatoms, and decrease by corresponding amounts at Ts⩾600 °C due to decreased adsorption site densities. At Ts⩾700 °C, high B coverages also induce {113} facetting.

Segregation and corrosion behaviour of incommensurate 45°[100] grain boundaries in an FeSi alloy: The role of grain boundary plane orientation

Measurements of the temperature dependencies of the chemical composition of 45°[100] incommensurate tilt grain boundaries in an Fe-3.55at.%Si alloy revealed large differences between the segregation behaviour of {O kl} symmetrical and (001) (011) asymmetrical grain boundaries. The low negative values of the segregation enthalpies of Si, P and C determined at the latter interface as compared to those of the former one are correlated with the cusps found in the orientation dependencies of the etched groove dimensions at a curved grain boundary and with the effective separation of atomic planes parallel to the boundary. The results disclose the surprising fact that the (001) (011) asymmetrical grain boundary possesses singular character whereas the {O kl} symmetrical interface is of the general type. The conclusion highlights the importance of the orientation of the grain boundary plane to characterize a grain boundary and its resulting properties.

The effect of the real structure of monocrystalline sample on the segregation of carbon in iron

The segregation of carbon in monocrystalline iron has been studied using the AES method. Depending on the carbon concentration in bulk and on the temperature, there are three forms of carbon on the clean iron surface: graphite, molecular carbon and atomic carbon. The results of the segregation kinetics studies have been discussed considering the real mosaic structure of monocrystalline samples. The enthalpy of segregation has been determined. This enthalpy drops with decreasing concentration of carbon in the bulk. At lower carbon concentration in the bulk, the segregation occurs mainly from the defects in the monocrystalline sample to the surface. The contribution of adsorption sites located in defects has been determined on the basis of the relation θ = k√ t as 0.74 and compared with the value obtained using the segregation of sulphur in the same sample.

Pressure-thermodynamic study of grain boundaries: Bi segregation in ZnO

A pressure-thermodynamic study of solid interfaces (grain boundaries) has been conducted. The influence of a high quasi-hydrostatic pressure (∼ 1 GPa) on interfacial segregation of Bi in ZnO has been characterized. At ambient pressure (1 atm) and sub-eutectic temperatures, grain boundaries in Bi-saturated ZnO exhibit near-monolayer levels of Bi segregation characterized by a segregation enthalpy of ∼ 0.67 eV/atom. Under ∼ 1 GPa pressure, however, the segregation is nearly completely suppressed. The segregation and pressure-induced de-segregation are highly reversible, with the source/sink for Bi being a Bi-rich secondary phase located at multiple grain junctions. The secondary phase serves as a reference of known molar volume, from which it is determined that the partial molar volume of Bi 2O 3 as a grain boundary segregant is approximately one third greater than its value in pure α-Bi 2O 3. The greater specific volume due to Bi segregation may be associated with charge-compensating point defects important in creating interface electronic states, and may facilitate rapid grain boundary oxidation in ZnO varistors.