Volume Size Factor Research Articles

Machine-learning prediction of Vegard's law factor and volume size factor for binary substitutional metallic solid solutions

Vegard's law factor (VLF) and volume size factor (SF) of binary substitutional metallic solid solutions (BSMSS) are crucial in alloy design. However, general models for accurately predicting these structure parameters are still undeveloped. In this work, a kernel ridge regression (KRR) model was developed to predict VLF and SF of BSMSS based on 409 published entries and elemental descriptors. The KRR model achieves an average R2 score of 0.67, an average Pearson coefficient of 0.82 for VLF and an average R2 of 0.80, an average Pearson coefficient of 0.90 for SF among 100 random splits of training/testing dataset. The performances of this KRR model based on training sets without certain solvent/solute elements were also investigated. In addition, an explicit expression was learned by the symbolic transformer, which exhibits prediction efficiency with R2 of 0.8 for VLF and 0.9 for SF. The expression can be interpreted as a physically meaningful 2D descriptor with one component containing size difference between solute and solvent atoms in the pure state while the other one does not. This is helpful to clarify the electronic coupling effect referred in previous studies. The predictions of both ML models are compared with those of density functional theory (DFT) for 37 Fe-based BSMSS (Fe-X). The results show that ML models exhibit higher R2 than that of DFT for the 20 Fe-X with experimental data available, and provide reasonable results for the 17 Fe-X without experimental data.

Machine-Learning Prediction of Vegard's Law Factor and Volume Size Factor for Binary Substitutional Metallic Solid Solutions

Machine-Learning Prediction of Vegard's Law Factor and Volume Size Factor for Binary Substitutional Metallic Solid Solutions

High CO2 permeability in supported molten-salt membranes with highly dense and aligned pores produced by directional solidification

Composite molten salt-ceramic membranes are promising devices for high-temperature CO2 separation. Intensive material properties impact on separation performance as do membrane geometry (thickness) and microstructure (pore volume fraction, size, connectivity, and tortuosity factor). Although controlling pore size is considered somewhat routine, achieving pore alignment and connectivity is still challenging. Here we report the production of the first gas separation membrane using a porous ceramic matrix obtained from a directionally-solidified magnesium-stabilised zirconia (MgSZ) – MgO fibrilar eutectic as the membrane support. MgO was removed from the parent material by acid-etching to create a porous matrix with highly aligned pores with diameters of ~1 μm. X-ray nano-computed tomography of a central portion (~32,000 μm3) of the support identified ~21% porosity, with all pores aligned within 10° and ~76% percolating along the longest sampled length. Employing the matrix as a support for a carbonate molten salt, a high CO2 permeability of 1.41x10-10 mol m-1.s-1.Pa-1 at 815 °C was achieved, among the highest reported for supported molten-carbonate membranes (typically 10-12 to 10-10 mol m-1.s-1.Pa-1 at similar temperatures). We suggest that the high permeability is attributable to the excellent pore characteristics resulting from directional solidification, namely a dense array of parallel, micron-scale pores connecting the feed and permeate sides of the membrane.

Damage analysis of unidirectional Ti hybrid nanocomposites containing nanoparticles

In the present work, a nested micromechanical model is presented to analyze the biaxial initial damage envelopes of unidirectional silicon carbide (SiC) fiber-reinforced titanium (Ti) matrix hybrid nanocomposites containing SiC nanoparticles. Firstly, an effort is made to obtain the elastic modulus, yield strength and coefficient of thermal expansion (CTE) of the nanoparticle-reinforced metal matrix nanocomposites by developing an analytical micromechanical model. Size factor and agglomerated state for the nanoparticles into the metal matrix, generation of dislocations by nanoparticle/matrix thermal mismatch and Orowan strengthening mechanism are considered at the nanoscale. Then, a unit cell-based micromechanical model is proposed to extract the biaxial initial damage envelopes of the SiC nanoparticle/SiC fiber-reinforced metal matrix hybrid nanocomposites. The Fiber/matrix interfacial debonding and matrix yielding are included as the dominant damage modes. Also, thermal residual stress (RS) arisen from the fiber/matrix thermal mismatch during the MMC manufacturing process are considered in the analysis. A reasonable agreement is observed between the results of the present model and available experiments for both of the nanocomposite and hybrid nanocomposite thermomechanical properties. It is shown that the SiC nanoparticles are indeed a very effective strengthening agent for the MMCs which can postpone the deterioration initiation due to the interfacial debonding under transverse tension. The presented model is applied to examine the effects of several parameters, including the nanoparticles volume fraction, diameter, size factor and dispersion type and also the thermal mismatch and fiber/matrix interfacial conditions on the biaxial initial damage behavior of the metal matrix hybrid nanocomposites.

Effect of alloying elements on defect evolution in Ni-20X binary alloys

The effect of alloying elements on radiation-induced microstructural evolution in Ni and Ni-20X (X = Fe, Cr, Mn and Pd) binary alloys was investigated using ion irradiation and cross-sectional transmission electron microscopy. The three-dimensional migration mode is identified to be the dominating migration mechanism for interstitial clusters in these binary alloys, contrary to the one-dimensional mode that dominates in the well-studied dilute alloys. The results reveal that: (1) the average size of defect clusters decreases as the solute atomic volume size factor increases. Smaller void size in Ni-20Cr is attributed to faster vacancy mobility in the near surface region, and weaker vacancy binding energy beyond the irradiation peak than Ni-20Fe. The smaller voids observed in Ni-20Mn and Ni-20Pd beyond the damage peak are due to the stronger Mn/Pd-vacancy binding effect of largely oversized solute atoms. (2) Oversized solutes can act as strong trapping sites for interstitials. The larger the solute atomic volume factor, the stronger the trapping force. This leads to a more significantly sluggish interstitial migration and smaller dislocation loop size. The average dislocation loop size in Ni-20Fe was four times larger than Ni-20Pd (atomic volume factor being 10.6% and 41.3%) but an order of magnitude lower in density. The smaller dislocation loop size in Ni-20Cr is attributed to stronger interstitial binding of Cr-Ni. Overall, the alloying effect on defects is more significant in concentrated binary alloys than in dilute binary alloys, due to the concentration difference of alloying atoms and the interstitial dominant migration mechanisms in the main irradiated region.

Undersize solute element effects on defect structure development in copper under electron irradiation

We conducted systematic experiments of defect structure development in Cu base binary alloys under 1000 kV electron irradiation at temperatures higher than 300 K, using in situ observations with high voltage electron microscopy. This report describes the effects of undersize elements: Co (–3.78%), Ni (–8.45%) and Be (–26.45%). The volume size factors are given in parentheses. The amounts of the respective elements were 2, 0.3, 0.05 at.%, or less. In Cu–Ni and Cu–Co and in the reference Cu, temperature dependence of the number density of interstitial-type dislocation loops had a down peak (i.e. loops hardly formed) at approximately 373 K, attributed to unexpected impurity atoms. Above the down-peak temperature, the addition of Co or Ni increased the loop number density through continuous nucleation of loops, extended the loop formation to higher temperatures, and decreased the apparent activation energy of loop growth rate. The addition of Be for 0.3 at.% or more delayed loop formation after formation of stacking fault tetrahedra (SFTs) around 300 K. The apparent mobility of self-interstitial atoms is expected to be smaller than that of vacancies because of strong binding with Be. Loop formation at temperatures higher than 373 K was enhanced by Be for 0.3 or 2 at.%, although it was suppressed greatly for 0.05 at.% or less. All undersize atoms increased the stability of SFTs under irradiation. Mechanisms of those effects were discussed and were briefly compared with earlier results found for oversize elements in Cu.

Simulation of the effect of volume size factor of solute atoms and their clusters on one dimensional motion of interstitial clusters in Ni binary alloys

The effect of the volume size factor of solute atoms and their clusters on the one-dimensional motion of interstitial clusters was studied by computer simulations. Solute atoms were placed on the migration path of the interstitial clusters, and the change in the migration energy of the interstitial clusters was obtained by the static method. The volume size factor of Au atoms in a Ni-Au binary alloy was systematically changed from −30% to +100%. When the volume size factor of the solute atoms was larger or smaller than Ni atoms, the migration energy of the interstitial clusters increased. The average migration energy required for the interstitial clusters to pass through one, two, three, and four solute atoms (volume size factor: +63.7%) was 0.57, 1.28, 2.09, and 2.47eV, respectively. If the solute atom clusters grow and their density is sufficiently high, the jump frequency of the interstitial clusters is so low that the interstitial clusters cannot move through the solute atom clusters under an irradiation temperature of 573K.

Direct observation of solute–dislocation interaction on screw dislocation in a neutron irradiated modified 316 stainless steel

A three-dimensional atom probe (3DAP) technique was used to observe the three-dimensional solute distribution around screw dislocations in neutron-irradiated modified 316 austenitic stainless steel. Si, Ni, and P were observed to get enriched around the cores of screw dislocations, while Fe, Cr, Mn, and Mo were depleted in the same areas. Si was segregated to a narrow region in the core for which, it was concluded that Si was trapped in the initial stage of segregation. Other enriched elements segregated to some edge features such as kinks and/or jogs formed as a result of Si trapping. The results suggest that solute–dislocation interaction of screw dislocations was similar to radiation-induced segregation, which is affected by the volume size factor of solute atoms.

Scale effects in convoluted thermal/spatial statistics of plasticity initiation in small stressed volumes during nanoindentation

The elastic–plastic transition of crystals at small length scales can be quantitatively evaluated by sudden discontinuities (pop-ins) on nanoindentation load–displacement curves. For defect free crystals under nanocontacts, pop-in stress fluctuations result purely from the thermally activated process of homogeneous dislocation nucleation, while at intermediate contact sizes, fluctuations can arise from the spatial statistics of pre-existing defects. Here, we find that the convolution of the above thermal and spatial effects exhibits a distinct dependence on the stressed volume size, dislocation density and geometric factors that describe crystallography and slip anisotropy. These essential features are captured in a unified model that includes both homogeneous dislocation nucleation and heterogeneous activation of pre-existing dislocations. Our theoretical predictions compare remarkably well with experimental findings. In particular, the model describes the observed strong and complex dependence of pop-in probability on indentation direction in NiAl. Implications for other small scale mechanical tests such as micropillar compression are discussed.

First-principles studies on lattice constants and local lattice distortions in solid solution aluminum alloys

Changes in the lattice constants of 55 Al-based solid solutions, as well as local lattice distortions induced by solute atoms, were studied on the basis of first-principles calculations using 3.70, 3.13, 1.56, and 0.93at.% alloys. The first nearest-neighbor interatomic distances between the solute and the solvent Al atoms were relatively constant for all calculated Al–X systems. The calculated volume size factor and the misfit strain were in good agreement with the experimental data available in the literature. The linear relationship observed between the misfit strain and the volume size factor was explained by using the Eshelby approach. A discussion of the application of the misfit strains to the estimation of increasing yield stress due to the solid solution strengthening was also presented. The calculated extent of solid solution strengthening was in good agreement with the available experimental values.

One-dimensional motion of interstitial clusters in iron-based binary alloys observed using a high-voltage electron microscope

Systematic experiments on one-dimensional (1D) motion of interstitial clusters in iron-based binary alloys were performed by in situ observation with a high-voltage electron microscope to investigate the effects of atomic size factor of solutes on 1D motion. The respective solute elements and their atomic volume size factors were copper (+17.53%), germanium (+16.48%), and silicon (−7.88%). The solute element concentrations were 52–9100appm. 1D motion frequency and distance were measured under electron irradiation at room temperature. Addition of copper or silicon of approximately 50appm reduced the 1D motion frequency and distance. Silicon decreased the 1D motion frequency more strongly than copper. The 1D motion frequency and distance were reduced further with increasing solute concentration, but after several 100appm, they became insensitive to it. Results for the dilute alloys were examined assuming a model by which individual solute atoms trap interstitial clusters and suppress their 1D motion.

Comment on “Dependence of volume changes during solid solution formation and of volume size factor on solute volume, group number and crystalline structure by O. Coreño-Alonso, J. Coreño-Alonso, Intermetallics 2012; 22:142”

We comment on the derivation as well as the applicability of the equation used for the bulk modulus of substitutional alloys in terms of the bulk moduli of the pure end members.

Segregation of Alkali and Alkaline Earth Metals at Σ11(113)[110] Grain Boundary in Aluminum from First-Principles Calculations

13Þ½110� grain boundary were investigated in aluminum using the first-principles calculation. The relationship between the grain boundary segregation energies and the volume size factors were examined to understand the role of elastic strain energy in the grain boundary segregation energy. The grain boundary segregation energy decreased with the increase in the volume size factor. It has been explained that the solute atom larger in size than Al, which stores greater strain energy in the bulk, prefers the looser site at the grain boundary plane rather than in the bulk, to release the elastic strain energy. Furthermore, on the basis of the Rice­Wang model, the effects of grain boundary segregation on the embrittlement at the grain boundary were studied. The embrittlement potency indicates that the Mg, Na, Ca, K and Sr atoms serve as embrittler in the grain boundary. [doi:10.2320/matertrans.M2012108]

Dependence of volume changes during solid solution formation and of volume size factor on solute volume, group number and crystalline structure

This paper describes the dependence of both volume change during primary solid solution formation and that of volume size factor, V sf on solute mean atomic volume. Our research findings demonstrate a direct relationship between V sf or volume change and solute atomic volume. For twenty solvent elements, the average linear correlation coefficient between V sf and solute atomic volume is 0.659. The average correlation coefficient for volume changes is 0.592. Forty-seven systems solute–solvents with the same crystalline structure indicate that the average linear correlation coefficient between V sf and solute atomic volume is 0.780. The average correlation coefficient between V sf and solute atomic volume is 0.907 for solute elements from the same group in the Periodic Table. The average correlation coefficient for volume changes is 0.775. Forty-eight systems were analyzed. For fourteen elements, it was found that elements with the same crystalline structure have an average correlation coefficient between V sf and solvents atomic volume of 0.934. The relationship between volume changes and solvent atomic volume can be expressed with a quadratic model. Then, volume change during primary solid solution depends upon solute volume, group number and crystalline structure.

One dimensional motion of interstitial clusters in Ni–Au alloy

The activation energy for one dimensional motion of the interstitial clusters was calculated in Ni–Au alloy by a static method. An EMT potential was used, which was tuned to fit the experimental volume size factor and heat of solution. The number of interstitials contained within the clusters was 1, 7 and 19. In pure Ni, the activation energies of clusters were less than 0.1 eV, and they increased with the size of the interstitial clusters. After the addition of the oversized solute atoms the activation energies increased from 0.49 eV to 0.97 eV. In neutron irradiated Ni with oversized solute atoms, the defect structures near grain boundaries, and the accumulation and absorption of interstitial clusters along the dislocations can be explained by the interactions between interstitial clusters and the oversized atoms.

Effect of solute elements in Ni alloys on blistering under He + and D + ion irradiation

Effects of solute atoms on microstructural evolution and blister formation have been investigated using Ni alloys under 25 keV He + and 20 keV D + irradiation at 500 °C to a dose of about 4 × 10 21 ions/m 2. The specimens used were pure Ni, Ni–Si, Ni–Co, Ni–Cu, Ni–Mn and Ni–Pd alloys. The volume size factors of solute elements for the Ni alloys range from −5.8% to +63.6%. The formations of blisters were observed in the helium-irradiated specimens, but not in the deuteron-irradiated specimens. The areal number densities of blisters increased with volume size difference of solute atoms. The dependence of volume size on the areal number densities of blisters was very similar to that of the number densities of bubbles on solute atoms. The size of the blisters inversely decreased with increasing size of solute atoms. The formation of blisters was intimately related to the bubble growth, and the gas pressure model for the formation of blisters was supported by this study.

Unit cell volume of intermetallic compounds calculated using volume size factors

Unit cell volumes of intermetallic compounds have been calculated using reported volume size factors. An equation to calculate unit cell volume for intermetallics of any crystalline structure was derived from previously reported expressions for L1 2 and B2 compounds. Average error for 122 analyzed compounds was 3.16%. Errors ranged from 0.00 to 14.01%. Factors that could influence the error value, such as order, structure type, solid solubility, and type of elements forming the compound were evaluated. A combination of solid solubility and type of elements forming the compounds seem to be the most relevant factors influencing the error value.

Detection of interstitial clusters in neutron irradiated Ni–Hf alloy by perturbed angular correlation and positron annihilation lifetime measurements

In order to understand the effect of alloying elements on the damage structure evolution in metals, defect clusters near Hf in Ni were studied using the perturbed angular correlation (PAC) technique and positron annihilation spectroscopy (PAS). The volume size factor of Hf in Ni was determined to be 61% by measuring the lattice parameter. The positron annihilation mean lifetime of Ni–0.5 at.%Hf after neutron irradiation at 473 K up to a dose of 0.0053 dpa was 132 ps. The lifetime decreased with increasing annealing temperature and by annealing at 723 K the recovery was finished. The PAC spectrum of 181Ta (← 181Hf) taken after the irradiation indicated that there were two components. The first component consisted of a Larmor frequency of 534 mega-radian/s (Mrad/s). The second consisted of a very broad range of frequencies which brought destructive interference among them and made the contribution to the spectrum almost zero. The component disappeared with annealing at 873 K. It was concluded that the first component and the second component represent Hf in the regular substitutional site and Hf with defect clusters, respectively. From the difference of annealing out temperature of defect clusters, clusters annihilated by 723 K were assigned as stacking fault tetrahedra (SFTs) and those by 873 K as interstitial clusters.

Volume size factor and lattice parameter in cubic intermetallics with L12 or B2 structure derived from the “Macroscopic Atom” model

Volume size factors and lattice parameters in cubic intermetallics with L12 or B2 structure have been derived from the “Macroscopic Atom” model. In a first step, an equation has been derived to calculate the volume size factor for binary solid solutions of two transition metals. Then, lattice parameters of cubic intermetallics were calculated with equations found in the literature which only make use of volume size factors and partial molar volumes. While large differences can be found between some of the predicted and observed volume size factors, differences between measured and calculated lattice parameters ranged from 0.05 to −5.45%.

Effect of solute atoms on swelling in Ni alloys and pure Ni under He + ion irradiation

The effects of solute atoms on microstructural evolutions have been investigated using Ni alloys under 25 keV He + irradiation at 500 °C. The specimens used were pure Ni, Ni–Si, Ni–Co, Ni–Cu, Ni–Mn and Ni–Pd alloys with different volume size factors. The high number densities of dislocation loops about 1.5×10 22 m −3 were formed in the specimens irradiated to 1×10 19 ions/m 2, and they were approximately equivalent, except for Ni–Si. The mean size of loops tended to increase with the volume size factor of solute atoms. In a dose of 4×10 20 ions/m 2, the swelling was changed from 0.2% to 4.5%, depending on the volume size factors. The number densities of bubbles tended to increase with the absolute values of the volume size factor, and the swelling increased with the volume size factors. This suggests that the mobility of helium and vacancy atoms may be influenced by the interaction of solute atoms with them.