Grain Growth Rate Research Articles

Crystallization and grain growth in impurity-doped colloidal polycrystals

Alloying has long been used to control the properties of crystalline materials. However, the microscopic details of the effects of adding impurities remains poorly understood, as directly imaging these processes is challenging in atomic systems. Here we study how crystallization and grain growth are impacted by impurities in a quenched monolayer of a colloidal polycrystal. The rates of crystallization are unaffected by the impurity concentration and well described by the Johnson-Mehl-Avrami-Kolmogorov model. However, with an increased impurity concentration, more of the system becomes frustrated and does not crystallize. The rate of grain growth is significantly slowed down due to grain boundary pinning. Nevertheless, the evolution of the polycrystalline structure is well described by a single correlation length, and dynamic scaling applies up to relatively large impurity concentrations. Finally, we develop a simple model accounting for both crystallization and grain growth to describe the time evolution of the correlation length, and we find good agreement with our experimental data at all impurity concentrations. Our results shed new light on the interplay between crystallization, grain growth and the presence of impurities in impurity-doped polycrystalline systems.

Comparison of the Microstructure and Superconducting Properties of Eu–Ba–Cu–O and Gd–Ba–Cu–O Single Grain Samples

Bulk Rare Earth–Ba–Cuprate [(RE)BCO] superconductors fabricated in the form of large single grains consisting of a REBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-</sub> δ (RE-123) matrix and RE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> BaCuO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> (RE-211) inclusions can generate trapped magnetic fields that are up to ten times higher than the maximum fields obtainable in conventional Fe-based permanent magnets. The choice of the Rare Earth (RE) element plays a key role in determining the growth rate of single grains, the precise microstructure, mechanical properties and hence the final superconducting properties of the bulk samples, and also the likelihood of RE substitution onto the Ba site which can degrade the performance. In this work, we have studied the growth and microstructure of (RE)BCO single grains with RE = Gd and Eu, where the degree of Ba substitution is known to be very different. We have carried out detailed microstructural characterization of the phase distribution and composition using high resolution electron microscopy to understand the effects of Gd and Eu on the uniformity of the samples, the distribution of the secondary 211 phase, porosity and chemical variations in different regions of the melt-grown single grains.

Dust Formation in the Wind of AGB Stars—The Effects of Mass, Metallicity and Gas-Dust Drift

Dust production in the wind of stars evolving through the asymptotic giant branch is investigated by using a stationary wind model, applied to results from stellar evolution modelling. Results regarding 1–8M⊙ stars of metallicities Z=0.014 (solar) and Z=2×10−3 are compared, to infer the role played by stellar mass and chemical composition on the dust formation process. We find a dichotomy in mass: stars of (initial) mass below ∼3M⊙ produce silicates and alumina dust before they become carbon stars, then carbonaceous dust; the higher mass counterparts produce only silicates and alumina dust, in quantities that scale with metallicity. The presence of drifts with average drift velocities ∼5 Km/s leads to higher dust formation rates owing to the higher growth rates of the dust grains of the different species. However, no significant changes are found in the overall optical depths, because the higher rate of dust formations favours a fast expansion of the wind, that prevents further significant production of dust. As far as oxygen-rich stars are concerned, the presence of drifts makes the main dust component to change from olivine to pyroxene. The release of the assumption that the number density of the seed particles is independent of the dust species considered affects dust formation in the wind of carbon stars: a factor 10 reduction in the density of the seeds of SiC leads to bigger sized SiC grains, and partly inhibits the formation of solid carbon, since the wind is accelerated and the densities in the carbon formation zone are smaller. No substantial differences are found in the winds of oxygen-rich stars.

Microstructural Evolution and Mechanical Properties of 2219 Aluminum Alloy Deposited by Wire and Arc Additive Manufacturing

Thin‐walled specimens of 2219 aluminum alloy are fabricated at different deposition speeds using the wire + arc additive manufacturing (WAAM) method. The effects of deposition speed on the microstructure, growth rate of columnar grains, and tensile strength of WAAM‐printed Al–Cu alloys are investigated. The fraction of columnar grains decreases from 86.7% to 12.2%, and the average grain size decreases from 147 to 65.3 μm as the deposition speed increased. Also, the fraction of θ phase gradually decreases as the deposition speed increased. Specifically, the growth rate of columnar grains varies from 1.02 × 10−3 to 2.05 × 10−3 m s−1, which possesses two orders of magnitude higher than the growth rate of equiaxed grains. With increasing the loading stress, the cracks first form on the dendritic θ phases located at the grain boundaries, reducing the effective loading area. With the deposition speed increased, the typical dimple‐like structures are presented at the fracture surfaces, attributing to a decrease in Cu content at the grain boundaries and the producing of the spot‐like θ phase inside the matrix. The specimen with a deposition speed of 250 mm min−1 possesses a tensile strength around 274 MPa, and the corresponding elongation reaches to 12.6%.

Microstructure evolution and mechanical properties of Cu-Sn intermetallic joints subjected to high-temperature aging

In this work, full Cu3Sn joints were aged at 500°C, 550°C, and 600°C for various durations. Microstructure evolution and grain morphology of the joints were systematically investigated by OM, SEM, EBSD, and TEM technology. In addition, the mechanical properties of hardness and shear strength for the CuSn intermetallic compounds were studied using a Micro Vickers hardness tester and uniaxial tensile equipment. Upon heating to 500°C, the phase transformation pathway was Cu3Sn–Cu41Sn11–α(Cu); aging at 550°C demonstrated a pathway of Cu3Sn–Cu41Sn11–Cu41Sn11&α(Cu)–α(Cu); and finally, heating to 600°C resulted in a phase transformation pathway of Cu3Sn–Cu20Sn6–Cu20Sn6&α(Cu)–α(Cu). It was found that longer aging times and higher temperatures had effects on grain size and morphology. For the 500°C group, the average grain size of the fully formed Cu41Sn11 phase increased from 1.93 μm at an aging time of 20 min to 4.20 μm at 30 min. The grain sizes of the fully formed Cu41Sn11 phase in joints subjected to 550°C for 11 min was lower than 2.36 μm, which were in turn smaller than joints treated at 500°C for 30 min (4.2 μm). Treatment with higher temperatures resulted in more cores and a higher growth rate of Cu41Sn11 grains formed on the interface of Cu/Cu3Sn, which eventually led to the small grain size of the Cu41Sn11 phase. The grain morphologies of the formed Cu41Sn11 phase and Cu20Sn6 phase were mainly column grain. After an aging time of 11 min for the 550°C group, the grain morphology of α(Cu) included in a two-phase microstructure (Cu41Sn11&α(Cu)) mainly exhibited dendritic properties at the grain boundary of Cu41Sn11, its crack tendency broke the hardenability of single grains for the Cu41Sn11 phase, which resulted in a decline in strength from 107 MPa to 42 MPa for Cu41Sn11&α(Cu) compared to the Cu41Sn11 phase. Nevertheless, for the joints treated at 600°C after an aging time of 7 min, the dispersion of α(Cu) particles mainly followed granular shapes within the one large Cu20Sn6 grain in the two-phase microstructure (Cu20Sn6&α(Cu)). This blocked the extension of dislocation, which finally led to an enhancement in strength for the Cu20Sn6 & α(Cu) phase (51 MPa) compared to the Cu20Sn6 phase (73 MPa).

Zone-specific temperature distribution, densification trajectory and grain-growth kinetics of microwave-hybrid-sintered and conventionally sintered Al2O3 slip casts

ABSTRACT A comparative study on the microwave hybrid sintering and conventional sintering of Al2O3 slip casts is reported to observe temperature distribution, grain-growth kinetics and densification in different regions of samples. It was found that the microwave hybrid sintering resulted in a significantly lower temperature difference between the surface and the center as compared to that in conventional sintering. Remarkably, in the microwave-hybrid-sintered samples, the estimated activation energy for grain growth at the center was approximately 27% lower than that at the surface in the conventionally sintered samples. The grain-growth rate in microwave hybrid sintering was more than three times higher at the sample center ((62.07 ± 0.06) × 10–21 m3/s) than at the sample surface in the conventional sintering ((18.75 ± 0.11) × 10–21 m3/s). The volume diffusion for grain growth was found to be the most effective mechanism in all samples, irrespective of the sintering technique and point of observation. It is suggested that the heat-flux, as well as the microwave effect and influence of surface charge due to the electric field of the field-assisted process were the reasons for these outcomes.

The influence of triple junction kinetics on the evolution of polycrystalline materials during normal grain growth: New evidence from in-situ experiments using columnar Al foil

Abstract During grain growth in 2D systems triple junction kinetics may significantly influence not only the rate of grain growth but also the geometric evolution of the grain boundary network. In this contribution we analyse results from in-situ heating experiments coupled with electron backscatter diffraction analysis using a columnar Al foil. It is shown that (a) the von Neumann– Mullins relation is not always satisfied, (b) there is a marked discontinuity and heterogeneity in TJ motion in space and time and (c) grain boundaries evolve from predominately curved to straight boundaries. To interpret these results we introduce 3 main types of triple junctions Tc, Tp, and Ts, which are made up by at least 2 concave, 2 convex, and 3 straight boundaries, respectively. Analyses show that triple junction drag plays a significant role during grain growth. Data suggest that the drag effect of Tp is higher than that of Tc. In addition, triple junctions with 3 low-angle boundaries are exceptionally stable, while those with at least 2 high-angle boundaries are unstable and tend to disappear during grain growth. Only ~ 20% of grain boundaries exhibit steady state triple junction motion.

Effect of niobium alloying on the austenite grain growth and mechanical properties of ultrahigh-strength stainless steel

In the temperature range of 1000 °C–1150 °C and the holding time range of 30–150 min, the effect of niobium (Nb) on the behavior of grain growth and the evolution pattern of the mechanical properties of a martensitic stainless steel was studied. This study found that the addition of Nb allowed a large amount of undissolved NbC phase to be present in the steel, that the dragging effect of the solute atoms such as solute Nb and Mo reduced the migration rate of the grain boundary , and the pinning effect of NbC hindered the growth of grains, and that the growth rate of grains in 0.11Nb steel was slow in the temperature range of 1000 °C–1080 °C and increased significantly at the temperature range of 1080 °C–1150 °C. Next, the kinetic equations of the grain growth of 0.002Nb steel and 0.11Nb steel were constructed. The second phase strengthening of NbC and the fine grain strengthening jointly increased the yield strength of the steel but reduced the plasticity and ultimate tensile strength (UTS) of the steel. The addition of Nb had a minor effect on the content of retained austenite in the steel, but its refining effect on the hierarchical martensite microstructure increased the number of nucleation sites of retained austenite, reduced their sizes, made their distribution more dispersed, and more effectively hindered crack propagation, thus improving the toughness of the steel.

Stability of immiscible nanocrystalline alloys in compositional and thermal fields

Alloying is often employed to stabilize nanocrystalline materials against microstructural coarsening. The stabilization process results from the combined effects of thermodynamically reducing the curvature-dominated driving force of grain-boundary motion via solute segregation and kinetically pinning these same grain boundaries by solute drag and Zener pinning. The competition between these stabilization mechanisms depends not only on the grain-boundary character but can also be affected by imposed compositional and thermal fields that further promote or inhibit grain growth. In this work, we study the origin of the stability of immiscible nanocrystalline alloys in both homogeneous and heterogeneous compositional and thermal fields by using a multi-phase-field formulation for anisotropic grain growth with grain-boundary character-dependent segregation properties. This generalized formulation allows us to model the distribution of mobilities of segregated grain boundaries and the role of grain-boundary heterogeneity on solute-induced stabilization. As an illustration, we compare our model predictions to experimental results of microstructures in platinum-gold nanocrystalline alloys. Our results reveal that increasing the initial concentration of available solute progressively slows the rate of grain growth via both heterogeneous grain-boundary segregation and Zener pinning, while increasing the temperature generally weakens thermodynamic stabilization effects due to entropic contributions. Finally, we demonstrate as a proof-of-concept that spatially-varying compositional and thermal fields can be used to construct dynamically-stable, graded, nanostructured materials. We discuss the implications of using such concepts as alternatives to conventional plastic deformation methods.

Analysis of the structure and conductance of Mg2+ acceptor-doped CaBi2Nb2-xMgxO9-3x/2 piezoceramics

In this work, Mg2+-doped CaBi2Nb2O9 (CBN-xMg) lead-free piezoceramics were prepared by a common solid-state method to investigate the effects of Mg2+ doping content on crystal structure, electrical resistivity, and dielectric and ferroelectric properties. XRD and Raman spectroscopy show that the Mg atoms enter the B-site to form a solid solution of the pure CBN phase. In addition, the XRD refinement results show that Mg2+ doping increases the distortion of the NbO6 octahedron and simultaneously enhances the total contribution of the spontaneous polarization of each position along the a-axis, and that the Ps increases from -28.678 μC/cm2 for x = 0 to -31.768 μC/cm2 for x = 0.02. However, when x > 0.02, the polarization decreases due to the oxygen vacancy pinning effect. According to SEM analysis, Mg2+ doping strengthened the growth rate of CBN ceramic grains on the a-b plane, resulting in a more obvious plate-like structure. The reduced anti-site defects of the CBN ceramic samples strengthened the structure of (Bi2O2)2+ and improved the resistivity of the samples. The internal dipole moment was also strengthened, resulting in a significant increase in the dielectric constant and a decrease in the dielectric loss. In general, Mg2+ doping significantly improved the comprehensive properties of CBN ceramics, with improved values including a d33 of 11.1 pC/N, Pr of 7.22 μC/cm2, tanδ (600 °C) of 3.0%, and ρdc (600 °C) of 108 Ω•cm.

Effect of nitrogen partial pressure on the TCR of magnetron sputtered indium tin oxide thin films at high temperatures

Indium tin oxide (ITO) is a promising sensitive material for ultra-high temperature thin-film sensors (UTTSs) applied in thermal and mechanical parameters test in hot section parts. However, the instability of the temperature coefficient of resistance (TCR) in the ITO film is still one of the major limiting factors in accuracy improvement of the UTTSs. In this work, different ITO thin film samples were prepared by RF magnetron sputtering with various N2/Ar ratios changing from 10%–40%, and the effect of nitrogen partial pressure (NPP) on the TCR of ITO films in elevated temperature from 500 °C to 1200 °C was studied. The micromorphology, crystallographic structures and electrical performances of ITO films were examined by scanning electron microscope (SEM), X-ray diffraction (XRD) and Hall effect measurement, respectively. Results show that lower crystallinity and smaller grain of ITO films can be observed with the increase of NPP. In addition, we found that the recrystallization is one of the main factors affecting the TCR repeatability in the thermal cycle test. The grain growth rate (GGR) is only 27.0% in the 20%N2 ITO film after the thermal cycle test from 500 °C to 1200 °C, far lower than that of the 40%N2 ITO film (309.6%). Consequently, the 20%N2 ITO film showed the lowest TCR volatility rates (TVR) after the thermal cycle test, which were respectively recorded as only about 0.5% and 2.1% at 800 °C and 1200 °C. The high TCR stability in the 20%N2 ITO film can be attributed to the formation of the stable phase structure during the thermal cycle test. Furthermore, the 20%N2 ITO film also has the smallest TCR compared with other ITO films.

The growth restriction effect of TiCN nanoparticles on Al-Cu-Zr alloys via ultrasonic treatment

Ex situ and in situ synchrotron X-radiography study on Al-Cu-Zr alloys with addition of Al-5Ti-1B and TiCN nanoparticles (TiCNnp) were carried out at different cooling rates. Al-Zr alloy can be effectively refined by TiCNnp via Ultrasonic treatment as compared with Al-5Ti-1B which has Zr poisoning effect. The influence of cooling rate on the nucleation and growth of grains have been studied quantitatively. The results show that the grain size was decreased and the growth rate was increased with the increasing of cooling rate. At the same cooling rate, the grain size with addition of 0.5% TiCNnp was smaller than that with the same addition of Al-5Ti-1B. The blocking factor f of TiCNnp decreases with increasing cooling rate. Based on the free growth model, a new numerical model considering the growth restriction effect of nanoparticles was established. The growth of grain was inhibited by the combining effect of solute and nanoparticles. The growth rate of grain is reduced due to part of the solid/liquid interface coated by nanoparticles. The blocking factor f is linearly decreased with the coverage ratio ω which is proportional to the critical grain radius. The grain size decreases with increasing cooling rate and decreasing f . This study is especially beneficial for Al alloys that have poisoning phenomenon inoculated by traditional refiner.

Statistical behaviour of interfaces subjected to curvature flow and torque effects applied to microstructural evolutions

The movement of grain boundaries in pure metals and alloys with a low concentration of dislocations has been historically proved to follow curvature flow behaviour. This mechanism is typically known as grain growth (GG). However, recent 3D in-situ experimental results tend to question this global picture concerning the influence of the curvature on the kinetics of interface migration. This article explains, thanks to 2D anisotropic full-field simulations, how the torque effects can complicate these discussions. It is then illustrated that neglecting torque effects in full-field formulations can have a significant effect on the overall rate of GG, the shape of grains and grain boundaries as well as their local kinetics. The apparent reduced mobility can be much more complex than expected without necessarily questioning the influence of the curvature on the local kinetic equation.

Lead free single – double perovskite composite towards room temperature multiferroicity

Lead free BaTiO3-La2NiMnO6 (BTO-LNMO) composite sample was prepared via solid-state sintering route. Structural studies based on X-ray diffraction (XRD) patterns indicate BTO and LNMO each retain their respective structure in composite form. Raman spectra of composite inferred no structural modulation after mixing of individual phases of BTO and LNMO. The change in microstructure is observed for composite due to the difference in thermal expansion coefficient as well as the different rate of grain growth of BTO and LNMO phases. BTO-LNMO composite sample is found to be ferromagnetic with non saturation of magnetic moments. Temperature-dependent zero-field cooled (ZFC) and field cooled (FC) curves show large irreversibility (94%) for composite than the pure LNMO phase. The magnetic Curie temperature (Tc) of the composite was observed near room temperature. The dielectric and ferroelectric features of BTO is well maintained in composite at room temperature. This study is an attempt to bring in the multiferroicity (magnetic and ferroelectric order simultaneously) in the proximity of room temperature by incorporating the small percentage of magnetic phase (LNMO) in the ferroelectric (BTO) matrix.

Grain Growth Control of Dielectric and Magnetic Ceramics

The sintering process transported the atoms in the materials by decreasing the total interface energy. The microstructure changes as a result of grain growth and densification under the capillary driving force due to the interface curvature among grains. The grain growth rate is expressed as the product of the interface mobility and the driving force. According to grain growth theories, the mobility of the interface governed by diffusion control is constant but interface mobility is nonlinear when the movement of an interface is governed by interface reaction. As the growth rate is nonlinear for the regime of interface reaction control, the grain growth is nonstationary with annealing time. The microstructure can be controlled by changing the growth rate of an individual grain with the correlation between the maximum driving force and the critical driving force for appreciable growth. The present paper discusses applications of the principle in the fabrication of dielectric and magnetic ceramic materials.

Microcrack healing in zirconia ceramics under a DC electric field/current

Flash event caused by a DC electric field/current was applied to the crack healing in 8 mol % Y2O3 stabilized cubic ZrO2 polycrystals (8Y-CSZ). The flash event, which occurred by applying the DC power higher than a critical value of 100 mW/mm3, successfully healed the microcrack within several minutes without any healing agents at a furnace temperature of 800 °C. As compared to the healing treatment under static annealing, the healing phenomena were accelerated about 2 times under the flash treatment even at the same temperatures, suggesting that the enhanced healing phenomena cannot be explained only by the temperature effect. Since the rate of grain growth was accelerated under the flash treatment, the flash healing would be accelerated through the current-enhanced diffusional processes. This study shows for the first time that the flash event has a potential to apply to the crack healing process in the ceramic materials and composites.

Prediction of Epitaxial Grain Growth in Single-Track Laser Melting of IN718 Using Integrated Finite Element and Cellular Automaton Approach.

The mechanical properties of selective laser melting (SLM) components are fundamentally dependent on their microstructure. Accordingly, the present study proposes an integrated simulation framework consisting of a three-dimensional (3D) finite element model and a cellular automaton model for predicting the epitaxial grain growth mode in the single-track SLM processing of IN718. The laser beam scattering effect, melt surface evolution, powder volume shrinkage, bulk heterogeneous nucleation, epitaxial growth, and initial microstructure of the substrate are considered. The simulation results show that during single-track SLM processing, coarse epitaxial grains are formed at the melt–substrate interface, while fine grains grow at the melt–powder interface with a density determined by the intensity of the heat input. During the solidification stage, the epitaxial grains and bulk nucleated grains grow toward the top surface of the melt pool along the temperature gradient vectors. The rate of the epitaxial grain growth varies as a function of the orientation and size of the partially melted grains at the melt–substrate boundary, the melt pool size, and the temperature gradient. This is observed that by increasing heat input from 250 J/m to 500 J/m, the average grain size increases by ~20%. In addition, the average grain size reduces by 17% when the initial substrate grain size decreases by 50%. In general, the results show that the microstructure of the processed IN718 alloy can be controlled by adjusting the heat input, preheating conditions, and initial substrate grain size.

Effect of Integrated Nutrient Management on Yield Attributes and Yield of Black Gram Cv. Pu-31

Background: The main pulses grown in India are chickpea, arhar, lentil, black gram, mung bean, moth bean, horse gram, pea, khesari, cowpea, etc. Black gram is fourth major pulse crop in India, that contributes 13 and 10 per cent of total area and production respectively. This is annual plant that attains 30-100 cm height and its stem is covered with brown hairs and much branched from the base. The pods are long and cylindrical being 5-6 cm length and 4-10 seed in pods. The seeds are generally black, very dark brown. Methods: The field experiment was conducted in kharif-2019 at research farm of Tirhut College of Agriculture Dholi, to study the effect of integrated nutrient management on growth, yield parameters and the yield of black gram cv-PU-31, by the use different sources of nutrient in a integrated manner such as three level of fertilizer i.e. F1-75, F2-100 and F3-125% RDF and two levels of organic manure i.e. M1-control and M2-FYM @ 5 t ha-1 and three levels of biofertilizer i.e., B1-rhizobium, B2-nutrient mobilizer, B3-rhizobium+ nutrient mobilizer. The treatments were allocated in randomized block design (factorial) and replicated thrice. Result: The results revealed that F3 produced taller plants, more dry matter, crop growth rate (CGR) yield attributes resulting higher yield of grain and straw (10.78, 22.61 q ha-1 respectively) which was statistically at par with plant height, dry matter, crop growth rate, yield attributes and yield of grain, straw and highest harvest index (10.73, 22.20 q ha-1 and 32.58% respectively) to F2. Among addition of organic manure significantly maximum plant height, dry matter and crop growth rate and yield attributes resulting maximum yield of grain, straw and harvest index (11.2, 22.79 q ha-1 and 33.31% respectively) was found in M2 over M1. In biofertilizer treatments, B3 recorded higher plant height, dry matter and crop growth rate, yield attributes resulting in significantly higher yield of grain, straw and harvest index (10.26, 21.90 q ha-1 and 31.92% respectively) over B1 and B2.

Phase field simulation of abnormal grain growth mediated by initial particle size distribution

The uniform initial particle size distribution was considered to be an important condition for the preparation of dense ceramics. With the rapid development of templated grain growth method, it is necessary to add large template particles into small matrix to promote the epitaxial growth of grains. However, abnormal grain growth will inevitably occur in this process. In this work, a phase field method was employed to study the growth behavior of the large grains into the small matrix. The effect of initial particle size distribution on the grain growth kinetics was investigated. Our simulations revealed that the growth rate of large grains slowed down as the initial grain size distribution widened. Regulating the initial grain size distribution will be an effective way to control abnormal growth of grain. It was found that the growth rate of a large grain was proportional to the number of surrounding grains. These results have implications for the design of the functional ceramics with a target grain microstructure.

The Growth Restriction Effect of Ticn Nanoparticles on Al-Zr Alloys: An Integrated Study by in Situ X-Radiography and Numerical Modeling

Ex situ and in situ synchrotron X-radiography study of Al-Zr alloys with addition of Al-5Ti-1B and TiCN nanoparticles (TiCNnp ) were carried out at different cooling rates. Al-Zr alloy can be effectively refined by TiCNnp as compared with Al-5Ti-1B which has Zr poisoning effect. The influence of cooling rate on the nucleation and growth of grains has been studied quantitatively. The results show that the grain size was decreased and the growth rate was increased with the increase of cooling rate. At the same cooling rate, the grain size with addition of 0.5% TiCNnp was smaller than that with the addition of 0.5% Al-5Ti-1B. The blocking factor f of TiCNnp increases with increasing cooling rate. Based on the free growth model, a new numerical model considering the growth restriction effect of nanoparticles was established. The growth of grain was inhibited by the combining effect of solute and nanoparticles. The growth rate of grain is reduced due to part of the solid/liquid interface coated by nanoparticles. The blocking factor f is linearly decreased with the coverage ratio f which is proportional to the critical grain radius. The grain size decreases with increasing cooling rate and decreasing f . This study is especially beneficial for Al alloys that have poisoning phenomenon inoculated by traditional refiner such as Al-Zr, Al-Si and Al-Sc alloys.