Abstract
Introduction Crystallization control is crucial during glass production.In glass crystallization theory,it has been hypothesized that there is a direct relationship between glass-crystal interfacial energy and nucleation rate.Since it is difficult to measure interfacial energy directly,classical nucleation theory is used to obtain it.However,the estimation process is complex;various measurement data such as the nucleation rate,viscosity,and Gibbs free energy barriers between the glass and crystal are required.Overall,estimating the glass-crystal interfacial energy is time-consuming.In this regard,the interfacial energy can be directly obtained using molecular dynamics(MD)simulations.In this study,we implemented an interface model to estimate the glass-crystal interfacial energy based on the theory of Tielemann et al.,which was recently introduced to generate crystal orientation planes using minimum-energy cuts.To the best of our knowledge,this is the first work in which the crystal orientation plane determined based on a minimum-energy cutting process has been used to build a glass-crystal interface in a more realistic environment(i.e.,hypothesizes that a minimum-energy structure may occur during crystal nucleation)and calculate the interfacial energy.To achieve this,we considered stoichiometric alkali(Li,Na,and K)disilicate(2SiO2)glasses and crystals,as some early-stage experimental data have been reported,which are highly beneficial for validating the MD results.The effects of different potential models were also investigated and found that they had a significant impact on the reproduction of the experimental trend.
Methods Simulations were performed using the LAMMPS package.The temperature and pressure were controlled with the Nose-Hoover thermostat and barostat,respectively.After setting up the glass-crystal interface using NPT,we ran MD simulations with NVT for another 200 ps to calculate the interfacial energy.The MD simulations were performed with a time step of 1 fs.Periodic boundary conditions were applied in all directions.Cutoff distances were applied according to references.We used three interatomic potential(SHIK,Du,and Pedone)models to estimate the interfacial energies of Li2O-2SiO2 glass-Li2O-2SiO2(001),Na2O-2SiO2 glass-Na2O-2SiO2(010),and K2O-2SiO2 glass-K2O-2SiO2(001).All three of these potential functions are widely used.The glass structure was fabricated from the crystal structures by simulating a melt-quenching process.First,the Li2O-2SiO2(001),Na2O-2SiO2(010),and K2O-2SiO2(001)crystal structures were prepared.Half the crystal was kept fixed,while the other half was melted at 3500 K with a canonical ensemble(NVT)for 300 ps and then quenched to 300 K at a cooling rate of 5 K/ps.After the melt-quenching process,the crystal part was unfixed and relaxed for 200 ps with a glassy structure using an isobaric-isothermal ensemble(NPT)at a temperature of 300 K.An interfacial model was developed by the theory of Tielemann et al,where the crystal plane was determined through the minimum energy cut in the crystal structure.
Results and discussion We first evaluated the glass density by calculating the local density profile along the z-direction of Li2O-2SiO2 glass-Li2O-2SiO2(001),Na2O-2SiO2 glass-Na2O-2SiO2(010),and K2O-2SiO2 glass-K2O-2SiO2(001).The glass structures show density results comparable to the experimental data.
The calculated interfacial energy values using the SHIK potential show a similar experimental trend,while the Du and Pedone potentials are unable to reproduce the experimental trend.However,the potentials of Du and Pedone show better values of interfacial energy for the glass-crystal interface of Li2O-2SiO2 than the SHIK.Our MD results demonstrate that among the potential models,SHIK is a good candidate for calculating interfacial energy in terms of experimental reproduction.
We analyzed the interfacial coordination number(i.e.,cation-anion)in the contact area between the glass and crystal surfaces.These coordination numbers are difficult to estimate experimentally.Typically,the coordination number is determined in the bulk region of a glass or crystal structure.We found that the interfacial coordination number varies significantly at the glass-crystal interface of Li2O-2SiO2,Na2O-2SiO2,and K2O-2SiO2.Among the interfacial systems,coordination number values of two,three,four,and five were observed,the most frequently observed value was one.The values were significantly lower at four and five for K2O-2SiO2 and Na2O-2SiO2,respectively.Our MD results demonstrated that the cation(Li,Na,and K)-anion environments were not the same in the interfacial domain.For further evaluation,we calculated the bond strength-coordination number.
The bond strength-coordination number has been reported for chalcogenide glasses.In the present work,the bond strength-coordination number is introduced for glass-crystal interface systems.The calculated results of bond strength-coordination number show a decreasing trend in the order Li>Na>K,which is similar to interfacial energy.Overall,analysis revealed that the alkali(Li,Na,and K)—O bond plays a crucial role in the interfacial strength.
Conclusion We developed an interface model using molecular dynamics simulations based on the minimum energy cut of crystals with glassy structures.The minimum energy cut of the crystal was determined by applying Tielemann theory.The modeled interfaces were between glass and crystals in stoichiometric alkali(Li,Na,and K)disilicates.The interface model reproduced the experimental interfacial energy trend of Li>Na>K;the interatomic potential model was found to have a significant effect on reproduction.The MD results indicate that the SHIK-based MD model could reproduce the experimental results better than the other potential models.In addition,the interfacial coordination number was also calculated,which varies depending on the alkalinity of Li,Na,and K.Using the interfacial coordination number,the bond strength-coordination number was estimated,and found that the interfacial energy trend Li>Na>K is related to the bond strength-coordination number.关键词
玻璃-晶体界面能/分子动力学模拟/原子间势函数/界面配位数Key words
glass-crystal interfacial energy/molecular dynamics simulation/interatomic potentials/interfacial coordination number分类
化学化工
