Single-particle Strength Research Articles

Study on single particle compression crushing characteristics of iron ore with five different particle sizes

The mechanical properties of particulate materials are among the main factors affecting the grinding and crushing of ball mills. To quantitatively describe the relationship between the breakage characteristics and the stress intensity of irregular particulate materials, this study takes iron ore particles as the research object. It selects five particle size grades of iron ore particles (−4.75 + 3.35, −6.7 + 4.75, −9.5 + 6.7, −13 + 9.5, and −16 + 13 mm) for single particle strength tests. The results showed that the iron ore particles were irregular with certain slenderness and flatness characteristics. The larger the particle size, the lower the sphericity, and the greater the degree of irregularity. As the size of the iron ore particles increased, the number of peak points on the pressure–displacement curve of the particles increased significantly, and the crushing load increased. The single-particle strength of the iron ore particles followed a Weibull distribution, and the Weibull modulus parameter ranged between 2.03 and 2.49.

Quantifying the influence of single particle shape on crushing characteristics of recycled aggregates: Experimental and numerical insights

Exploring the interplay between shapes and crushing characteristics of recycled aggregates (RA) is pivotal for understanding their macro-mechanical behavior in bulk materials. This investigation quantitatively characterizes the shapes of recycled bricks (RB), recycled concrete (RC), and recycled mortar (RM) particles, and assesses their single-particle crushing characteristic. Key focus areas include the analysis of crushing modes, fractal attributes, strength, and energy, supplemented by a comparative study using discrete element method (DEM) simulations to predict outcomes for particles of specific sphericity. Findings reveal that the shapes of RA particles are mainly disk, block, blade and bar, with particle size showing negligible influence on these forms. Crushing behaviors are categorized into penetrating fracture, corner rupture, and overall fragmentation, closely linked to particle sphericity. Notably, an increase in sphericity leads to a reduction in fractal characteristics of RA, refining the gradation distribution from broad to narrow spectrums. An exponential relationship is identified between the crushing strength of RA and particle sphericity, a pattern also mirrored in the correlation between crushing energy and sphericity, thereby underscoring the significant influence of particle shape. These relationships facilitate predictions regarding the crushing strength and energy based on sphericity. While numerical simulations broadly align with experimental data, discrepancies in the crushing energy of highly spheric particles necessitate adjustments, resulting in a modified predictive equation for crushing energy. This work enriches the understanding of RA crushing behavior, offering invaluable insights for predicting the single-particle strength and deformation characteristics across different sphericities, thus advancing material engineering and recycling practices.

Suppressed electric quadrupole collectivity in 49Ti

Single-step Coulomb excitation of 46,48,49,50Ti is presented. A complete set of E2 matrix elements for the quintuplet of states in 49Ti, centred on the 2+ core excitation, was measured for the first time. A total of nine E2 matrix elements are reported, four of which were previously unknown. 2249Ti27 shows a 20% quenching in electric quadrupole transition strength as compared to its semi-magic 2250Ti28 neighbour. This 20% quenching, while empirically unprecedented, can be explained with a remarkably simple two-state mixing model, which is also consistent with other ground-state properties such as the magnetic dipole moment and electric quadrupole moment. A connection to nucleon transfer data and the quenching of single-particle strength is also demonstrated. The simplicity of the 49Ti-50Ti pair (i.e., approximate single-j0f7/2 valence space and isolation of yrast states from non-yrast states) provides a unique opportunity to disentangle otherwise competing effects in the ground-state properties of atomic nuclei, the emergence of collectivity, and the role of proton-neutron interactions.

Influence of real particle morphology on single particle crushing behavior of rockfill based on FDEM

Particle morphology is critical in affecting the crushing behavior of rockfill materials. In contrast, most current single particle simulations lack satisfactory morphology accuracy, and the resulting crushing modes deviate from observations to some extent. Therefore, we reconstruct the real particle morphology with the spherical harmonic (SH) method and employ the finite-discrete element method (FDEM) to simulate the one-dimensional (1D) compressive crushing process of basalt particles commonly used in rockfill. The influences of four main morphological parameters, i.e. sphericity, aspect ratio, roundness, and convexity, on the single particle strength and the crushing modes are discussed. The results show that with the SH degree set to 15 and a mesh number of 20,480, the FDEM models of reconstructed particles achieve sufficient morphology accuracy and high computational efficiency. Based on the model, the simulation results demonstrate that the aspect ratio has the most significant impact on single particle strength, followed by sphericity. In contrast, roundness and convexity have a weaker effect than the above two parameters. Also, it is revealed that single particle strength decreases with increasing aspect ratio and sphericity, while it increases with higher roundness and convexity. Furthermore, aspect ratio significantly changes the initial crushing position, sphericity dominates post-crushing fragment size and quantity, and roundness mainly affects post-crushing morphology. The model results have been employed in establishing a support vector regression (SVR)-based predicted model, exhibiting good predictive performance and advantages for the optimization of rockfill particles in engineering.

Spectroscopy of deeply bound orbitals in neutron-rich Ca isotopes

The calcium isotopes are an ideal system to investigate the evolution of shell structure and magic numbers. Although the properties of surface nucleons in calcium have been well studied, probing the structure of deeply bound nucleons remains a challenge. Here, we report on the first measurement of unbound states in 53Ca and 55Ca, populated from 54,56Ca(p,pn) reactions at a beam energy of around 216 MeV/nucleon at the RIKEN Radioactive Isotopes Beam Factory. The resonance properties, partial cross sections, and momentum distributions of these unbound states were analyzed. Orbital angular momentum l assignments were extracted from momentum distributions based on calculations using the distorted wave impulse approximation (DWIA) reaction model. The resonances at excitation energies of 5516(41)keV in 53Ca and 6000(250)keV in 55Ca indicate a significant l =3 component, providing the first experimental evidence for the ν0f7/2 single-particle strength of unbound hole states in the neutron-rich Ca isotopes. The observed excitation energies and cross-sections point towards extremely localized and well separated strength distributions, with some fragmentation for the ν0f7/2 orbital in 55Ca. These results are in good agreement with predictions from shell-model calculations using the effective GXPF1Bs interaction and ab initio calculations and diverge markedly from the experimental distributions in the nickel isotones at Z=28.

Neutron-transfer induced breakup of the Borromean nucleus 9Be

We address the problem of evaluating neutron-transfer induced breakup cross sections caused by the Borromean nucleus 9Be, using the reaction 197Au(9Be,8Be)198Au as a test case. This reaction was recently measured over a wide range of incident energies around the Coulomb barrier. To deal with the high density of 198Au states that can be potentially populated in this reaction, we employ the Ichimura, Austern, Vicent model, in which the spectrum of physical states for this system is replaced by the solutions of a complex n+197Au potential, accounting effectively for the fragmentation of single-particle states into physical states. Furthermore, to account for the unbound nature of the emitted 8Be system, we employ a three-body model of 9Be. The calculated stripping cross sections are found to be in good agreement with existing data over a wide range of incident energies. The importance of taking into account the energy spread of the single-particle strength of the outgoing 8Be and the target-like residual nucleus is discussed.

An Evaluation of Treatment Effectiveness for Reclaimed Coral Sand Foundation in the South China Sea

Mega land reclamation projects have been carried out on the coral reefs in the South China Sea. Coral sand was used as a backfill material through hydraulic filling, with fill heights ranging from 6 to 10 m. To enhance foundation stability, vibro-flotation and impact rolling have been employed. However, the uneven distribution of coral sand, irregular particle shape, lower single-particle strength, and paucity of engineering cases for reference have posed challenges in evaluating the effectiveness of these foundation treatments. In this study, the effectiveness of vibro-flotation and impact rolling on the densification and bearing capacity of coral sand foundations has been investigated. In situ tests, including the plate load test, California Bearing Ratio (CBR) test, density measurements, dynamic penetration test (DPT), and settlement monitoring, were conducted at four distinct zones: an untreated zone, a vibro-flotation zone at a 5 m depth, a vibro-flotation zone at a 10 m depth, and an impact rolling zone. The findings suggest that coral sand exhibits promising characteristics for foundation construction. Seepage and self-weight consolidation following land reclamation formation significantly enhance the compaction degree of the coral sand foundation, thereby meeting the requirements for areas with lower bearing capacity demands. Both vibro-flotation and impact rolling techniques could significantly enhance the foundation-bearing capacity, with marginal differences between them. Since the machinery is simple and construction speed is quick, the impact rolling method is considered to be the most efficient for the treatment of coral sand foundation. The DPT results suggest that the reinforcement effect of both vibro-flotation and impact rolling on the deep foundation is not as substantial as the surface layers. This study provides valuable insights into optimizing foundation treatments for land reclamation projects on the coral reefs.

New Perspectives on Spectroscopic Factor Quenching from Reactions.

The evolution of single-particle strengths as the neutron-to-proton asymmetry changes informs us of the importance of short- and long-range correlations in nuclei and has therefore been extensively studied for the last two decades. Surprisingly, the strong asymmetry dependence of these strengths and their extreme values for highly asymmetric nuclei inferred from knockout reaction measurements on a target nucleus are not consistent with what is extracted from electron-induced, transfer, and quasi-free reaction data, constituting a two-decade old puzzle. This work presents the first consistent analysis of one-nucleon transfer and one-nucleon knockout data, in which theoretical uncertainties associated with the nucleon-nucleus effective interactions considered in the reaction models are quantified using a Bayesian analysis. Our results demonstrate that, taking into account these uncertainties, the spectroscopic strengths of loosely bound nucleons extracted from both probes agree with each other and, although there are still discrepancies for deeply bound nucleons, the slope of the asymmetry dependence of the single-particle strengths inferred from transfer and knockout reactions are consistent within 1σ. Both probes are consistent with a small asymmetry dependence of these strengths. The uncertainties obtained in this work represent a lower bound and are already significantly larger than the original estimates.

Multiple Mechanisms in Proton-Induced Nucleon Removal at ∼100 MeV/Nucleon.

We report on the first proton-induced single proton- and neutron-removal reactions from the neutron-deficient ^{14}O nucleus with large Fermi-surface asymmetry S_{n}-S_{p}=18.6 MeV at ∼100 MeV/nucleon, a widely used energy regime for rare-isotope studies. The measured inclusive cross sections and parallel momentum distributions of the ^{13}N and ^{13}O residues are compared to the state-of-the-art reaction models, with nuclear structure inputs from many-body shell-model calculations. Our results provide the first quantitative contributions of multiple reaction mechanisms including the quasifree knockout, inelastic scattering, and nucleon transfer processes. It is shown that the inelastic scattering and nucleon transfer, usually neglected at such energy regime, contribute about 50% and 30% to the loosely bound proton and deeply bound neutron removal, respectively. These multiple reaction mechanisms should be considered in analyses of inclusive one-nucleon removal cross sections measured at intermediate energies for quantitative investigation of single-particle strengths and correlations in atomic nuclei.

Single-particle spectroscopic strength from nucleon transfer reactions with a three-nucleon force contribution

The direct reaction theory widely used to study single-particle spectroscopic strength in nucleon transfer experiments is based on a Hamiltonian with two-nucleon interactions only. We point out that in reactions with a loosely-bound projectile, where clustering and breakup effects are important, an additional three-body force arises due to three-nucleon (3N) interaction between two nucleons belonging to different clusters in the projectile and a target nucleon. We study the effects of this force on nucleon transfer in (d,p) and (d,n) reactions on 56Ni, 48Ca, 26mAl and 24O targets at deuteron incident energies between 4 and 40 MeV/nucleon. Deuteron breakup is treated exactly within a continuum discretized coupled-channel approach. It was found that an additional three-body force can noticeably alter the angular distributions at forward angles, with consequences for spectroscopic factors' studies. Additional study of transfer to 2p continuum in the 25F(p,2p)24O reaction, involving the same overlap function as in the 24O(d,n)25F case, revealed that 3N force affects the (d,n) and (p,2p) reactions in a similar way, increasing the cross sections and decreasing spectroscopic factors, although its influence at the main peak of (p,2p) is weaker. The angle-integrated cross sections are found to be less sensitive to the 3N force contribution, they increase by less than 20%. Including 3N interactions in nucleon removal reactions makes an essential step towards bringing together nuclear structure theory, where 3N force is routinely used, and nuclear direct reaction theory, based on two-nucleon interactions only.

Quenching of Single-Particle Strength in A=15 Nuclei.

Absolute cross sections for the addition of s- and d-wave neutrons to ^{14}C and ^{14}N have been determined simultaneously via the (d,p) reaction at 10 MeV/u. The difference between the neutron and proton separation energies, ΔS, is around -20 MeV for the ^{14}C+n system and +8 MeV for ^{14}N+n. The population of the 1s_{1/2} and 0d_{5/2} orbitals for both systems is reduced by a factor of approximately 0.5 compared with the independent single-particle model, or about 0.6 when compared with the shell model. This finding strongly contrasts with results deduced from intermediate-energy knockout reactions between similar nuclei on targets of ^{9}Be and ^{12}C. The simultaneous technique used removes many systematic uncertainties.

Effect of size and strain rate on particle strength and stress–strain properties of rockfill materials

The stress-strain properties of the rockfill materials under cyclic loading conditions are critical for the seismic safety analysis of dams. However, due to the effect of size and strain rate, the parameters obtained from the scaled laboratory tests may not accurately calculate the earthquake response. In the presented study, a novel approach has been developed to infer the prototype parameters based on the single particle strength. Firstly, a series of particle crushing tests with different sizes and loading rates were conducted. The results show that as the strain rate increases, the particle strength enhances and the size effect on particle strength gradually weakens. According to the established particle strength model, it is assumed that two specimens have homothetic particle size distributions and the same compaction, and is geometrically similar, then the size effect relations on macroscopic stress and strain tensors can be derived, a set of monotonic and cyclic triaxial tests are used to validate the approach. Furthermore, the effect of particle size and strain rate on the equivalent linear model is determined, the small-strain modulus parameter K obtained from the laboratory test should be modified. This study provides a reference to the engineering design and seismic safety evaluation of high rockfill dams.

Effect of CoO–NiO additives on the microstructure and mechanical properties of microcrystalline corundum abrasives with in-situ formed needle-shaped LaAl11O18

It is always challenging to synthesize corundum abrasives with high strength and toughness. In this study, pure α-Al2O3/LaAl11O18 dual-phase corundum abrasives were synthesized by the sol-gel method using pseudo-boehmite as the raw material and CoO–NiO binary additives as a sintering aid. By regulating the molar ratio of CoO and NiO in the sintering additives, dense and fine corundum abrasives were prepared at a low temperature of 1400 °C. We show that the addition of CoO–NiO additives can effectively prevent the abnormal growth of α-Al2O3 grains and facilitate the formation of LaAl11O18 s-particles between α-Al2O3 grain boundaries, resulting in final corundum abrasives consisting of equiaxed α-Al2O3 and needle-shaped LaAl11O18 grains. Moreover, the presence of the needle-shaped LaAl11O18 phase promotes the fracture toughness of corundum abrasives, and the high density of corundum abrasives also makes them retain a relatively higher hardness and strength. When the molar ratio of sintering additive (n (CoO)/n (NiO)) reaches 1: 1, the single-particle strength, Vickers hardness, fracture toughness, and maximum density of our synthetic corundum abrasives are 53.4 N, 18.9 GPa, 4.53 MPa m1/2 and 3.94 g cm−3, respectively. The process route suggested in this study is expected to guide the low-temperature synthesis of corundum abrasives with well-rounded mechanical properties.

Effect of Particle Breakage on Strength Characteristics of Limestone Aggregate

Particle breakage is one of the issues that significantly affect the strength characteristics of aggregate. In this paper, the strength of pre-crushed limestone aggregate was evaluated through investigating the friction angle, stress–strain behaviour, and single-particle strength. The particle breakage phenomenon was studied for samples prepared at different conditions, including non-soaked samples, water-soaked samples, and acid-soaked samples. The purpose of preparing the samples at different conditions was to simulate the effect of environmental factors on the breakage behaviour of limestone aggregate. The test program of this paper consists of two phases of triaxial tests: the initial shearing and second shearing. The test results showed remarkable variations among the samples since limestone aggregate tended to experience more particle breakage after being soaked in water and acid solution. Also, the volume change results exhibited an increase in dilation as the breakage index increases. The test results of this study presented the importance of considering the role of environmental factors in evaluating the particle breakage of limestone aggregate.

Quenching of single-particle strengths of carbon isotopes 9-12,14-20C with knockout reactions for incident energies 43–2100 MeV/nucleon * *Supported by National Natural Science Foundation of China (U2067205,11775013,11775316), Fundamental Research Funds for the Central Universities (2020MS033) and Natural Science Foundation of Shanxi Province, China (202103021223047)

To study the quenching of single-particle strengths of carbon isotopes, a systematic analysis is performed for 9-12,14-20C, with single neutron knockout reactions on Be/C targets, within an energy range from approximately 43 to 2100 MeV/nucleon, using the Glauber model. Incident energies do not show any obvious effect on the resulting values across this wide energy range. The extracted quenching factors are found to be strongly dependent on the proton-neutron asymmetry, which is consistent with the recent analysis of knockout reactions but is inconsistent with the systematics of transfer and quasi-free knockout reactions.

Border of the island of inversion: Unbound states in Ne29

The nucleus $^{29}$Ne is situated at the border of the island of inversion. Despite significant efforts, no bound low-lying intruder $f_{7/2}$-state, which would place $^{29}$Ne firmly inside the island of inversion, has yet been observed. Here, the first investigation of unbound states of $^{29}$Ne is reported. The states were populated in $^{30}\mathrm{Ne}(p,pn)$ and $^{30}\mathrm{Na}(p,2p)$ reactions at a beam energy of around $230$ MeV/nucleon, and analyzed in terms of their resonance properties, partial cross sections and momentum distributions. The momentum distributions are compared to calculations using the eikonal, direct reaction model, allowing $\ell$-assignments for the observed states. The lowest-lying resonance at an excitation energy of 1.48(4) MeV shows clear signs of a significant $\ell$=3-component, giving first evidence for $f_{7/2}$ single particle strength in $^{29}$Ne. The excitation energies and strengths of the observed states are compared to shell-model calculations using the sdpf-u-mix interaction

Effect of Particle Size and Constraint Conditions on Single Particle Strength of Carbonate Sand.

Carbonate sand is often encountered and utilized as construction material in offshore engineering projects. Carbonate sand particles, which are porous and angular, are found to be highly crushable under high stress conditions, whereas the mechanisms and controlling factors for the crushing of carbonate sand particles are not well developed. The crushability and particle strength of around 400 particles from three fractions (5–10 mm, 2–5 mm, and 1–2 mm) of carbonate sand from the South China Sea were investigated via grain-scale single particle crushing tests. Special emphasis was placed on the effect of external constraint conditions (i.e., coordination number) and intrinsic particle morphology characteristics on the particle strength of carbonate soil. The particle strength of carbonate sand was found to be around half of quartz sand in terms of characteristic stress. Negative correlations, which could be depicted by an exponential equation, were found between the particle size and particle strength. Due to elongated particle shape and tensile stress concentration, a higher coordination number may lower the particle strength, which contradicts what was reported for quartz sands. A series of seven fundamental particle dimensions and five particle shape descriptors was characterized, and the aspect ratio was found to be one of the more influential shape descriptors for particle strength. The results enriched the database for the analysis of highly irregular geomaterial and provided insights into controlling factors of particle strength and crushing mechanisms of the carbonate sand.

Quenching of single-particle strengths in direct reactions

A discrepancy in the asymmetry dependence of spectroscopic factors extracted with different reaction probes calls into question whether the corresponding reaction models are properly understood. In this work, we present extracted spectroscopic factors from the Ar46,34(p,d)Ar45,33 transfer reactions in inverse kinematics at a beam energy of 70 MeV/nucleon. The results are consistent with previous measurements of these reactions at a lower beam energy [Lee et al., Phys. Rev. Lett. 104, 112701 (2010)], indicating that the transfer reaction is a reliable probe for the nuclear structure of exotic nuclei across a wide energy range. Results from a large body of transfer reaction measurements, (p,pN) measurements, and theoretical nuclear structure studies make a compelling case for much weaker asymmetry dependence than what is observed with single-nucleon knockout reactions on beryllium or carbon targets.Received 19 June 2020Revised 9 November 2020Accepted 8 June 2021DOI:https://doi.org/10.1103/PhysRevC.104.024608©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDirect reactionsModels & methods for nuclear reactionsNuclear reactionsSpectroscopic factors & electromagnetic momentsTransfer reactionsNuclear Physics

Updated systematics of intermediate-energy single-nucleon removal cross sections

The body of experimental measurements of intermediate-energy reactions that remove a single nucleon from a secondary beam of neutron- or proton-rich nuclei continues to grow. These data have been analyzed consistently using an approximate, eikonal-model treatment of the reaction dynamics combined with appropriate shell-model descriptions of the projectile initial state, the bound final states spectrum of the reaction residue, and single-particle removal strengths computed from their wave-function overlaps. The systematics of the ratio ${R}_{s}$ of the measured inclusive cross section to all bound final states and the calculated cross section to bound shell-model states---in different regions of the nuclear chart and involving both very weakly bound and strongly bound valence nucleons---is important in relating the empirically deduced orbital occupancies to those from the best available shell-model predictions. Importantly, several new higher-energy measurements, for which the sudden-approximation aspect of the dynamical description is placed on an even stronger footing, now supplement the previously analyzed measurements. These additional data sets are discussed. Their ${R}_{s}$ values are shown to conform to and reinforce the earlier-observed systematics, with no indication that the approximately linear reduction in ${R}_{s}$ with increasing nucleon separation energy is a consequence of a breakdown of the sudden approximation.

Core of F25 in the rotational model

In a recent experiment, carried out at RIBF/RIKEN, the $^{25}$F$(p,2p)$$^{24}$O reaction was studied at 270 MeV/A in inverse kinematics. Derived spectroscopic factors suggest that the effective core of $^{25}$F significantly differs from a free $^{24}$O nucleus. We interpret these results within the Particle-Rotor Model and show that the experimental level scheme of $^{25}$F can be understood in the rotation-aligned coupling scheme, with its $5/2^+_1$ ground state as the band-head of a decoupled band. The excitation energies of the observed $1/2_1^+$ and $9/2_1^+$ states correlate strongly with the rotational energy of the effective core, seen by the odd proton, and allow us to estimate its $2^+$ energy at $\approx$ 3.2 MeV and a moderate quadrupole deformation, $\epsilon_2 \approx 0.15$. The measured fragmentation of the $\pi d_{5/2}$ single-particle strength is discussed and some further experiments suggested.