HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER’S THESIS Simulation of structure of CaO – P2O5 – SiO2 material system with various ratios of P2O5/CaO NGUYEN MAI ANH anh.nm212446M@sis
Problem Statement
Industrial and radioactive waste management is a critical challenge for many nations Researchers have dedicated decades to finding suitable materials for hazardous waste storage Studies show that glassy materials composed of SiO2 and/or P2O5 are ideal for this purpose, thanks to their excellent chemical properties, durability, and ability to withstand radiation.
Bioglass is an innovative amorphous silicate-based material known for its compatibility with the human body, ability to bond with bone, and capacity to stimulate new bone growth as it gradually dissolves This unique property allows bioglass to effectively restore diseased or damaged bone, facilitating osteogenesis Since its discovery by scientist Larry L Hench in 1969, bioglass has undergone significant development, leading to a diverse range of structures and applications.
The glass structure is composed of network formers, modifiers, and intermediates Network formers, such as SiO2, B2O3, and P2O5, establish the foundational network of glasses In silicate glass, the network is created through the connection of [SiO4] tetrahedrons via Si-O-Si bonds, known as bridging oxygen bonds (BOs) Network modifiers disrupt these BOs, resulting in the formation of non-bridging oxygens (NBOs).
Key metal oxides, including Na, K, Ca, and Mg, as well as intermediates like Al2O3, serve as either network formers or modifiers based on their concentration The degree of polymerization is determined by the number of bridging oxygens (BOs) Consequently, understanding the structure of glasses is crucial for predicting their properties.
This project aims to explore the significant applications of glassy materials in medicine and daily life by examining the fundamental structure of the CaO-P2O5-SiO2 system with varying P2O5 ratios This foundational research will establish a basis for future advancements in the field.
Purpose and Scope of the study
The research thesis aims to simulate the structure of the CaO-P2O5-SiO2 material system, focusing on analyzing and clarifying its structural parameters It will also examine how variations in the P2O5/CaO ratio influence the microstructure of the material.
Research object: CaO-P2O5-SiO2 glass material systems with different ratios of
Scope: The CaO-P2O5-SiO2 models at 3000 K with various P2O5 (5–40 mol%) content
Research methods
This study employs Molecular Dynamics Simulation (MDS) to effectively model the material, complemented by statistical analysis techniques to evaluate key structural parameters These parameters include the radial distribution function, coordination number distribution, angular distribution, and distance distribution, providing a comprehensive understanding of the material's properties.
The scientific and practical significance of the topic
This thesis explores the high-temperature microstructure of CaO-P2O5-SiO2 material systems with varying P2O5 ratios The research focuses on surveying, calculating, and analyzing key microstructural data, including atomic distances, angular measurements, bond order (BO), non-bonding order (NBO) fractions, and tetrahedral clusters The findings from this study provide valuable insights that can advance future research in this field.
This material is crucial for both the high-tech and medical industries, making it essential to comprehend its properties and structure This understanding is particularly important in the research areas of toxic industrial waste and bioactive materials.
New contributions of the thesis
This thesis expands on our previous studies of CaO-P2O5-SiO2 systems by examining how varying component concentrations affect the material's structure Key aspects of this research include analyzing changes in atomic angles and distances, as well as the transformation of tetrahedron clusters.
The structure of the thesis
In addition to the introduction, conclusion and list of references, the thesis is divided into three main parts
OVERVIEW
Hazardous waste storage
Radioactive waste (radwaste) is categorized into three types: low-level, intermediate-level, and high-level waste Low-level waste originates from hospitals, laboratories, and industrial activities, while intermediate-level waste includes resins and chemical sludge High-level waste (HLW), which constitutes only 3% of the total volume of disposed radioactive waste, is primarily composed of spent nuclear fuel rods, reprocessing waste, and materials from decommissioned nuclear weapons, yet it accounts for over 95% of the total radioactivity Much of this high-level waste is temporarily stored in pools or sealed in stainless steel canisters before being disposed of in geological sites Ongoing research aims to identify suitable storage solutions for HLW.
High-level waste (HLW) hosts must meet several critical requirements, including high waste loading, ease of processing, radiation stability, chemical flexibility, durability, and the presence of natural analogues Materials based on P2O5, such as monazite (REE,Th)PO4, demonstrate the ability to combine with various HLW elements Monazite occurs in several natural forms, including brabantite (Ca0.5Th0.5PO4) and huttonite (ThSiO4), as well as synthesized variants like PrPO4 and CePO4 Notably, monazite exhibits radiation resistance and can repair radiation damage at temperatures below 200 °C Research by Seydoux-Guillaume et al on a 540-million-year-old monazite sample from Madagascar revealed that it maintained its crystalline state despite exposure to radiation levels ten times greater than those typically encountered.
Monazite is a stable and erosion-resistant compound, while apatite (Ca5(PO4)3(F,Cl,OH) is notable for its ability to incorporate tri- and tetravalent actinides by substituting Ca(II) with Ac(III, IV) and PO4 with SiO4 Apatite has demonstrated long-term stability, as evidenced by its presence in the two-billion-year-old Oklo natural nuclear reactor in Gabon, where it contains actinides Additionally, apatite remains stable at high temperatures and is resistant to self-irradiation, making it capable of incorporating radioactive Cesium (Ce) and Iodine (Id), which are challenging for monazite and other solids Research has shown that adding apatite to soils can effectively immobilize soluble uranium and actinides through sorption onto its surfaces or via a dissolution-precipitation mechanism.
Melting glass, particularly borosilicate and phosphate glass, serves as a primary material for high-level waste (HLW) storage due to its ability to incorporate various components at low melting temperatures (1050–1150 °C) Since the 1970s, phosphate minerals and glasses have been explored for nuclear waste storage, as they exhibit essential properties such as chemical stability, significant actinide incorporation, and radiation resistance, making them ideal candidates for waste containment By the end of 2000, vitrification facilities had produced approximately 10,000 tons of radioactive glass stored in around 20,000 canisters Research indicates that phosphate-containing glasses can store a higher fraction of radioactive elements compared to phosphate-free alternatives and promote the formation of actinide-containing secondary phosphate compounds Additionally, studies show that Lead-Iron phosphate glass provides stable storage for high-level nuclear waste, with a processing temperature of 1000-2500 °C and lower melting viscosity (8000-10000 °C) compared to borosilicate glass.
A study by Gin et al highlights the creation of glass nuclear waste through the melting of trash and additives at high temperatures, resulting in an amorphous, dense, and homogeneous material composed of various elements Understanding the mathematical model of glass nuclear waste is crucial, as its behavior is influenced by multiple factors, including temperature, pH, fluid composition and renewal rate, and radioactivity over different time and distance scales Researchers agree that the hydrolysis of Si-O-M bonds (where M represents elements like Si, Al, Zr, Fe, and Zn) is key to determining the initial dissolution rate Additionally, there are ongoing debates regarding mechanisms such as the slow transformation of amorphous phases into stable products, variations in local solution concentration, water diffusion into the glass, and transport limitations within a passivation layer.
Bioactive glass in medical applications
Bone grafting is a widely used surgical technique for promoting bone regeneration in orthopedic treatments, with over two million procedures performed annually worldwide Autologous bone grafts are favored for their ability to integrate essential bone characteristics, including formation and resorption However, challenges such as limited donor resources and complications at the donor site persist In North America, nearly one-third of bone grafts are alloy grafts, which are popular among orthopedic surgeons due to their availability in various shapes and quantities Despite this, artificial grafts are associated with risks of infection and lower healing capabilities compared to autologous grafts The demand for conventional autologous tissue transplants remains unmet, especially amid the global challenges posed by obesity and an aging population.
Alternative materials and patient implants have been produced for centuries, according to Hench [10], the first scientist to study and create biomaterials In the first
10 generation, biologically inert materials were investigated with the goal of being as inert as possible to prevent the formation of the callus at the surface and in host tissues
The second generation of tissue replacement materials began with Hench et al.'s discovery of bioglass in 1969, which introduced an alternative material that could effectively bond implants to host tissue This innovation paved the way for third-generation tissue implant materials, which leverage the gene-activating properties of bioglass to enhance tissue regeneration and repair capabilities.
In 1971, Larry L Hench, with funding from the US Military Medical Command, pioneered the development of the first bioglass 45S5, composed of 45% SiO2, 24.5% Na2O, 24.5% CaO, and 6% P2O5 This innovative material features calcium oxide (CaO) and phosphorus pentoxide (P2O5), which release Ca2+ and PO4 3− ions, essential for hydroxyapatite (Ca5(PO4)3OH) synthesis, a key element in bone formation Additionally, sodium oxide (Na2O) and silica (SiO2) are naturally abundant in the human body The material was successfully grafted by Dr Ted Greenlle in a mouse femur, leading to the development of various bioglasses with diverse medical applications today.
Research by Raghad Abdulrazzaq Al-Hashimi highlights that the effectiveness of root canal treatment relies on thorough canal sterilization, proper sealing of the root canal system, and ensuring impermeability Gutta-percha, the commonly used sealing material, is a trans-isomer of isoprene, but it exhibits limitations such as lack of flexibility and vulnerability to degradation from eugenol and other sealant components Additionally, while gutta-percha possesses thermoplastic properties, it does not enhance the strength of endodontically treated teeth, cannot be sterilized via heat, and its sealing capabilities fall short of clinical expectations Consequently, the research focuses on developing improved root canal filling materials.
Carriers offer a root canal filling material that surpasses conventional options due to its numerous advantages Essential requirements for new materials include biocompatibility, non-resorbability, resistance to dissolution by tissue fluids, the ability to provide a hermetic seal, sterilizability, and ease of retrieval when necessary Polymer composites are a promising solution in this context.
11 comprising of 45S5 Bioglass, Low Density Polyethylene (LDPE), SrO have been developed as promising endodontic treatment materials [11]
45S5 Bioglass is widely used in various medical applications, including treatments for periodontitis, bone fillers, and middle ear bone replacement implants However, it presents challenges such as mechanical weakness and low toughness due to its amorphous structure, which can lead to incompatibility with surrounding bone To address these issues, combining bioglass with polymers to create composites has been suggested Additionally, the crystallization of bioglass, which can occur before complete solidification during heat treatment (sintering), may diminish its biological properties and render it inert Despite this, sintering remains essential for forming structural struts; without it, the material risks becoming fragile due to loose particles.
In the study, examples of compounds added to the 45S5 glass system were presented to develop new glass formulations One such formulation involves the complete or partial substitution of SrO for CaO, resulting in materials known as Stronbone, which benefit bone metabolism due to the presence of strontium ions Additionally, research by Shah et al highlights the exploration of fluoride-containing bioactive glass for various bone tissue applications, where CaO in 45S5 Bioglass was partially replaced with CaF2 for dental uses Other oxides have also been incorporated into the Na2O-CaO-P2O5-SiO2 system to enhance its properties.
The incorporation of elements such as Ag, Cu, and Ga into bioactive glass enhances its antibacterial properties Additionally, the variety of substances available for inclusion has significantly increased, surpassing previous limits Key compounds like Al2O3, B2O3, Fe2O3, BaO, ZnO, Li2O, TiO2, CuO, and CoO play a crucial role in this advancement.
30 Therefore, it is essential to comprehend how factors affect the composition and characteristics of bioactive glass.
The parameters of glass systems in previous studies
Ca- and P-based bio-glasses were designed and manufactured for biomaterials
[16] Concentrations of Ca + and [PO4] - in the bloodstream are relatively high (1-5
12 mM) [17] P2O5 is important for determining the properties of bioglass in biomedicine
Increasing phosphate concentration in gel-glass compositions enhances the crystalline phosphate structure and the amorphous silicate (Si-O-Si) structure while reducing pore size and bioactivity Additionally, a higher CaO/P2O5 ratio increases the NBO/BO ratio, leading to a decrease in the polymerization degree between silicon and phosphorus tetrahedra This increase in the CaO/P2O5 ratio also results in higher density and glass transition temperatures Furthermore, a higher CaO/SiO2 ratio leads to a decline in the SOS angle due to the interaction of bridging oxygens with calcium ions Notably, the Si-O coordination number remains unchanged across varying ratios of calcium, phosphorus, and silicon.
Research by Guozheng Fan and Jiang Diao highlights the structural and property characteristics of the CaO-P2O5-SiO2 glass system, particularly with varying P2O5/SiO2 ratios They assert that phosphorus negatively impacts steel quality, prompting the development of methods over the past 30 years in China to effectively remove it during steel production The CaO-P2O5-SiO2 system is crucial in this metallurgical process, facilitating the formation of 2CaO.SiO2 and 3CaO.P2O5 for phosphorus removal Utilizing a simulation with a 41.7±0.2Å cube model and 5000±1 atoms at 1673K, the study reveals that while the Si-O bond distance remains stable with increasing P2O5 ratios, Si-Ca and P-Ca bonds exhibit significant fluctuations in length Additionally, the O-O bond length decreases markedly as the P2O5 ratio rises, indicating underlying similarities within the CaO-SiO2 system.
The study of the Al2O3 system reveals that varying the Al2O3/SiO2 ratio significantly impacts the coordination numbers of Si-O, P-O, and Ca-O Specifically, the average coordination numbers are 4.068 for Si-O, 4.013 for P-O, and 5.755 for Ca-O Notably, an increase in the P2O5 ratio leads to a substantial rise in the Ca-O coordination number, indicating a stronger tendency for Ca²⁺ ions to bond with more oxygen atoms Conversely, the coordination numbers for Si-O and P-O exhibit a slight decrease as the P2O5/SiO2 ratio increases.
13 authors find that the ratio of non-bridging oxygen (NBO) increases, the ratio of O 2- (free oxygen) declines sharply, and the ratio of bridging oxygen (BO) is relatively flat
A study by Nguyen Van Hong et al explores the structural changes in the bioglass system CaO-Al2O3-SiO2 (CAS) by varying the Al2O3 ratio and pressure Utilizing molecular dynamics (MD) simulation with 5175 atoms and the Born-Mayer-Huggins (BMH) interaction potential, the researchers found that at low pressure, some Ca²⁺ ions form non-bridging bonds (NBO), while most are associated with [TOx] units (where T=Si, Al and x=4,5,6) At elevated pressures, the majority of Ca²⁺ ions bind to [TOx] units, resulting in a narrow fluctuation range for the Ca-O distance Notably, the Ca-O distance decreased from 2.34±0.02 Å at 0 GPa to 2.28±0.02 Å at 40 GPa, indicating significant structural adjustments under varying pressure conditions.
As pressure increases, the O and Si-O bonds significantly decrease, while the first peak height of the radial distribution function (RDF) for Ca-O bonds rises The stability of SiOx units surpasses that of AlOx units in a multicomponent oxide system such as MO-Al2O3-SiO2, where metal cations are typically found near the [AlO4] - unit In systems with high metal oxide content, like CaO-Al2O3-SiO2 with elevated CaO levels, the breaking of BO bonds leads to the formation of negatively charged [NBO] - units, indicating that metal cations act as network modifiers The authors propose that incorporating Ca+ cations into the -T-O- network could effectively facilitate the storage of hazardous industrial and nuclear waste within the glass system's network structure.
A study conducted by Kai Zheng, Zuotai Zhang, and Falua Yang investigates the CAS system's response to varying Al2O3/SiO2 ratios The findings indicate that the polymerization of the material system enhances as the ratio increases.
Increasing the Al2O3/SiO2 ratio leads to a rise in viscosity and a notable increase in oxygen triclusters, reaching 24% This increase is characterized by the presence of O-(Al, Al, Al) and O-(Al, Al, Si) configurations, while the NBO ratio decreases and the Q4 ratio increases Additionally, the coordination number (CN) for aluminum also experiences changes.
14 up from 4.02 (in the CAS1 sample) to 4.11 (in the CAS11 sample) In other words, when the unit [SiO4] is replaced by [AlO4], the CN of Al increases
In a study conducted by Jiang Diao, Guozheng Fan, and colleagues, the CPS material system exhibited structural and polymerization coefficient characteristics comparable to those found in numerous prior studies The researchers employed molecular dynamics simulation techniques to analyze these properties effectively.
In a study involving 5000 atoms within the NVT ensemble at a temperature of 1673K, the average bond distances for Si-O and P-O were found to be 1.61 Å and 1.53 Å, respectively, aligning with both experimental and theoretical findings The substitution of P2O5 for SiO2 resulted in a decrease in the Q0 ratio, while other Q i units exhibited an increase Notably, the [SiO4] tetrahedral structures showed significant changes in Q2 and Q3, while the [PO4] tetrahedra displayed alterations in Q1.
The most significant changes are observed in Q2, where the alteration in Q i units for [SiO4] tetrahedrons surpasses that of [PO4] tetrahedrons As P2O5 content increases, there is a notable decline in free oxygen (FO) concentration, with the FO ratio diminishing significantly due to higher P2O5 levels or a lower calcium ratio (NCa/NSi+P) In the 7CaO.3SiO2 system, FO exceeds 15%, but it drops to approximately 5% in the 7CaO.SiO2.2P2O5 system Additionally, non-bridging oxygen (NBO) consistently maintains a much higher ratio.
In the study of FO and BO systems, it is observed that the non-bridging oxygen (NBO) concentration consistently exceeds 75% across all P2O5 ratios Specifically, in the 7CaO.3SiO2 unit, the NBO ratio surpasses 75% and increases with higher P2O5 levels, while in the 7CaO.SiO2.2P2O5 system, the NBO fraction approaches nearly 90% Conversely, the bridging oxygen (BO) ratio remains relatively stable at around 10%.
(equilibrium constants) are 0.55, 1.62, 2.02 and 2.35, respectively Phosphorus ions tend to promote the polymerization of molten phosphorus
A study by Antonio Tilocca focused on the liquid phase 45S5 Bioglass system at 3000K, utilizing ab-initio simulation to detail the material's structural characteristics The model created a cube measuring 11.63 Å, consisting of 116 atoms with a composition of 19SiO2, 10Na2O, 11CaO, and P2O5, aligning with the 45S5 Bioglass standard and exhibiting a density of 2.66 g/cm³ The authors provide extensive data on the bioglass system's structure, highlighting its similarities to established standards.
15 results of other studies RDF shows that the first peak positions of P-O, Si-O and O-
The study reveals that both vitreous (300K) and molten (3000K) states exhibit consistent Si-O distances of 1.63Å The P-O bond length is measured at 1.55Å, while the O-O distance remains relatively stable, showing minimal variation from 2.68Å at 300K to 2.69Å at 3000K Notably, the Na-O distance decreases from 2.3Å to 2.25Å, and the Ca-O bond length also declines from 2.32Å to 2.25Å, whereas the Si-O distance increases from 3.01Å to 3.05Å The full width at half maximum (FWHM) in the molten state is 2-3 times broader than in the glass phase Additionally, the O-T-O angles decrease by 1° to 2° during the transition from glass to molten form The angular distribution function indicates that the peak position of the SOS angle graph shifts down by 8°, with a new shoulder appearing at 90°, corresponding to Si5C (CNSi-O = 5) Consequently, the Si-O bond length rises to 1.9Å, and the O-Si-O angle increases as the coordination number (CN) decreases, with SOS angles recorded at 90° and 108°.
120 o respectively, corresponding to the CNSi-O is 5, 4, 3 In addition, there exists a second peak at 160 o with Si5C (CNSi-O =5) Also, in Si5C it is found that (SOS) angle is less than 100 0
In this thesis, I explored the microstructure of the CaO-P2O5-SiO2 glass system, recognized as the simplest glass system Numerous prior studies have utilized various methods to investigate CPS systems, including the BET (Brunauer–Emmett–Teller) and BJH (Barrett-Joyner-Halenda) methods, as well as techniques such as scanning electron microscopy, energy-dispersive X-ray analysis, and infrared spectroscopy Additionally, molecular dynamics simulation (MDS) has been employed to further understand these systems.
This study explores the structure of CPS systems with varying P/S ratios through the MDS method, focusing on microstructural elements such as RDFs, bond lengths, and angles in SiOx and POx units Additionally, we analyze the types of connections within the CPS material and compare our findings with those of other researchers.
CALCULATION METHOD
Material model and simulation method
Macroscopic samples of materials consist of an immense number of particles, approximately 10^23 atoms and/or molecules The thermodynamic theory posits that the motion of these particles dictates the macroscopic physical properties observed in experiments Simulating these samples is challenging due to the vast number of possible states, making calculations infeasible for current computing power However, recent studies indicate that smaller systems with significantly fewer particles can yield results that closely align with experimental findings For instance, analyzing the energy of just 0.01 mole of oxygen can provide accurate insights without the need to simulate the entire macroscopic sample.
In simple measurements, 10^-6 can be represented as 10^-S, where S equals 3x10^15, allowing for the study of systems with only a few million or even a few thousand particles instead of larger macroscopic samples This principle underpins atomic-level simulation calculations, with molecular dynamics (MD) and Monte-Carlo (MC) simulations being the two most commonly employed techniques Both methods begin with a random or rule-based distribution of particles within a defined space and subsequently shift these particles according to specific rules By repeating these transitions until equilibrium is achieved, valuable insights into the macroscopic physical properties observed in practice can be obtained.
Let the particles move according to a certain rule (the atoms move under the influence of the interaction potential and gradually reach the equilibrium state)
Do many times to move until equilibrium is reached
Calculate and process data to draw general rules
Infer from the information about the macroscopic physical properties
MD simulations are performed using the isothermal-isobaric (NPT) ensemble, starting with an initial configuration created by randomly distributing atoms within a cubic box measuring 53 Å The models utilized in this study encompass over a specified number of components.
The study involves seven models with varying atomic composition ratios of (40-x)CaO.xP2O5.60SiO2, where x takes values of 5, 10, 15, 20, 25, 30, and 40, totaling 5000 atoms (ranging from 5270 to 5520 atoms) Each model is subjected to a constant ambient pressure and initially heated to 5000K for 10^5 time steps to stabilize the configuration Following this, the models are gradually cooled to temperatures of 4500K, 4000K, 3500K, and finally 3000K, allowing for detailed analysis of the atomic behavior at different thermal conditions.
Models at temperatures of 4000K and 3500K reach recovery in approximately 10^5 time steps, while at 3000K, they achieve equilibrium in around 10^6 simulation time steps The structural data of CPS systems is recorded and analyzed at 3000K.
- Material model size (cube) is LxLxL
Figure 2.1: Simulation model of CPS material with 30 mol% P 2 O 5 Blue, black, red, yellow spheres are Ca, P, Si, O atoms respectively
Molecular dynamics (MD) models typically contain far fewer particles than Avogadro's number (NA = 6.023 x 10^23), which can significantly impact material properties Although the surface particles in these models are limited in number, they still influence the overall characteristics of the material The interaction forces between a particle i and its neighboring particles j, particularly those located on the surface, vary due to their distinct positions, leading to inconsistencies in the material's modeled properties.
Solution is using periodic boundary conditions Contiguous models will become the auxiliary model repeat precisely in space
Coordinates of particles with boundary conditions:
Same for 𝑦 𝑖 , 𝑧 𝑖 , The distance between particle i and particle j is
In this MDS CaO-P2O5-SiO2 system, we use Born-Mayer-Huggins (BMH) potential function as following:
The interatomic pair potential, denoted as \( U_{ij}(r) \), is influenced by the charges of ions \( q_i \) and \( q_j \) and the distance \( r_{ij} \) between atoms \( i \) and \( j \) The BMH potential is characterized by parameters \( A_{ij} \), \( B_{ij} \), and \( C_{ij} \) (refer to Table 2.1) This potential consists of three main components: the Coulomb interaction, which accounts for electrostatic forces; a repulsive interaction that occurs at short ranges; and the attractive Van der Waals interaction, which plays a significant role at longer distances.
Table 2.1 BMH potential for CPS system [25]
Coordinates of the (i + 1) th particles are determined through the i th particles after each time δt, force F by Verlet integration:
Visual analysis of material structural properties
Concept: RDF (g(r)) is a quantity that follows statistical rules, is used to determine the microstructure of materials at the atomic level in the simulation of i-j A ij (eV) B ij (1/Å) C ij (eV Å 6 )
In the study of materials in their liquid and amorphous states, the Radial Distribution Function (RDF) is crucial for experimental determination of structural factors RDF enables the analysis of average coordination numbers, bond distances, and mean bond angles Specifically, the function g(r) illustrates how density changes in relation to the distance from a reference particle, providing valuable insights into material properties.
In statistical mechanics, RDF is defined as:
V is volume of material model
N is the number of particle in volume V
𝑟 𝑖𝑗 = 𝑟 𝑖 − 𝑟 𝑗 with ri, rj are the i and j particle coordinates respectively
Integrating over the volume V between r and r+dr and assume the spherical layer is thin enough, after calculation, the number of particles in the layer is
𝑉 average atomic density in the volume V of the material model
𝑁 〈∑ 𝑛 𝑖 𝑖 (𝑟,∆𝑟) 〉4𝜋𝑟 2 ∆𝑟 atomic density at a distance r from the central atom,
In the simulation of the material structure, the RDFs of the system are calculated in the molecular dynamics simulation program as follows
- N is the number of particle in model
- 𝑁 𝛼 , 𝑁 𝛽 are the numbers of particle 𝛼, 𝛽, respectively
- 𝜌 0 is average particle density in the volume
Figure 2.2: RDF of Si-Si in CPS model with 5 mol% P 2 O 5
Coordination number (CN) is the closest number of particles around a particle For an ion, it is the number of ions of the same sign surrounding the nearest opposite ion
CN 𝑍 𝛼𝛽 is determined by the formula:
𝑟 𝑐 is the interrupt radius, it is usually chosen as the minimum position immediately after the first peak of the RDF
𝑍 𝛼𝛽 indicates how many 𝛽 type particles in a sphere centered at position
From the first peak position of the RDF, we can determine the bond lengths of the pairs of particles:
From the first peak position of the RDF 𝑔 𝛼−𝛼 , we infers the nearest neighbor distance between two 𝛼 type particles
Similar to 𝑔 𝛼−𝛽 and the distance of 𝛼 − 𝛽 pairs
Similar to 𝑔 𝛽−𝛽 and the distance of 𝛽 − 𝛽 pairs
The O-T-O angular distribution reveals the bonding of atoms within a basic structural unit, TOx, indicating short-range order (SRO) In contrast, the T-O-T angular distribution illustrates the relationships between these structural units, reflecting intermediate-range order (IRO) By analyzing the angular distributions, one can assess changes in both close order within structural units and intermediate-range order, which are associated with variations in the linkages between these units.
To analyze atomic interactions, we first identify the nearest neighbors of each atom, ensuring that all atoms fall within the break radius of the central atom Next, we assess the angular distribution within these identified sets.
To determine the angle O-T-O or T-O-T, knowing the coordinates of the corresponding atoms, suppose we consider a set of three atoms with corresponding coordinates O1(x1,y1,z1); T(x2,y2,z2); O2(x3,y3,z3) Angle O-T-O is determined by the formula:
Angle T-O-T is determined by the similar method
2.2.4 The bond forms of oxygen atom
Bridge oxygen (BO) refers to oxygen atoms that are bonded to at least two TOx structural units, where T represents Silicon (Si) or Phosphorus (P), forming a network structure In contrast, non-bridge oxygen (NBO) is only bonded to a single TOx structural unit Additionally, free oxygen (FO) is defined as oxygen that is not bonded to any TOx structural unit.
Figure 2.3: (I) Bridging oxygen, (II) Non-bridging oxygen [31]
RESULT AND DISCUSSION
Short range order
We investigate the radial distribution functions (RDFs) of Ca-O, P-O, Si-O, it is presented in Fig.3.1.With parameters of Ca, we only investigate in the range of 5-
At 30 mol% P2O5 and 40 mol% P2O5, calcium (Ca) is absent Overall, while the distances of the first peaks in the Ca-O, P-O, and Si-O graphs remain relatively stable, the peak heights decrease This trend aligns with findings from another study.
The analysis reveals that the heights of the first peaks in the P-O and Si-O radial distribution functions (RDFs) decrease as the P2O5 ratio increases The distances for Ca-O, P-O, and Si-O are approximately 2.28-2.3 Å, 1.56-1.58 Å, and 1.64-1.68 Å, respectively, aligning with previous experimental and simulation findings The sharp peaks in the RDF graphs for P-O and Si-O indicate strong bonding, consistent with observations that O atoms are tightly bound by the Coulombic forces of P and Si ions Notably, the first peak heights of Si-O and P-O RDFs surpass that of Ca-O, suggesting a higher concentration and greater stability in the coordination numbers of Si-O and P-O compared to Ca-O This indicates a minimal effect of the P2O5 ratio on the Si-O and P-O bonds within the CPS material system Additionally, our findings show a similarity in link distance variations when compared to prior studies, with slight shifts observed in the P-O and Si-O distances.
Figure 3.1: Radial distribution function (RDF) of Ca-O, P-O, Si-O with various
P 2 O 5 ratios Table 3.1: Structure characteristics of CaO-P 2 O 5 -SiO 2
Figures 3.2 and 3.3 illustrate the coordination numbers (CN) of calcium (Ca), phosphorus (P), and silicon (Si), revealing that the CNs of Si and P exceed 4 and increase linearly with rising P2O5 concentration Specifically, the CN of Si rises from 4 to 4.27, while P's CN increases from 4 to 4.49, corroborating findings from previous research indicating that the CN of Si-O is nearly 4 and that [SiO4] tetrahedrons exhibit high stability In contrast, the CN of Ca-O shows minor fluctuations between 5.15 and 5.36 as P2O5 concentration increases, with an average CN of approximately 5, consistent with observations in the CPS system Detailed coordination number data can be found in Table 3.2.
Figure 3.2: Coordination number distribution of Ca, P, Si as a function of P 2 O 5 content Table 3.2: Coordination number of MO x (M P, Si) with different P 2 O 5 ratios
The instability of CN CaOx is illustrated in Fig 3.3, where CaOx comprises multiple units of CaO3-CaO8, with CaO5 dominating at over 35% (ranging from 35.99% to 41.67%) The CaO5 content peaks at 20% P2O5 before gradually declining Additionally, CN4 and CN6 represent approximately 20-30%, while CN7 ranges from 6.75% to 14.84% The lesser CN3 and CN8 contribute only a minimal percentage Due to the broad dispersion of CN from 3 to 8, the RDF graph of Ca-O exhibits significantly lower first peaks compared to the RDFs of Si-O and P-O.
Figure 3.3: Distributions of coordination units CaO x , PO x , SiO x as a function of
Figure 3.3 illustrates that the coordination number (CN) distributions for silicon (Si) and phosphorus (P) are quite similar, with CN4 being predominant in both POx and SiOx The CN4 for SiOx ranges between 74.86% and 99.47%, showing a decreasing trend as the P2O5 ratio increases This finding aligns with previous studies indicating that over 80% of Si-O and more than 90% of P-O bonds exhibit 4 coordination, with a slight decline in CNs as the P2O5 ratio rises Conversely, the CN5 and CN6 values in POx increase with higher P2O5 ratios, rising from 0.53% to 23.19% and from 0% to 1.94%, respectively Similarly, the CN4 ratio in POx decreases linearly from 100% to 66.35%, while CN5 and CN6 concentrations steadily increase, reaching less than 20% This significant reduction in the dominant CN4 ratio also corresponds to a decrease in the first peak height of the radial distribution functions (RDFs) for both P-O and Si-O.
3.1.3 Bond angle distributions and Bond distance distributions
The coordination number of POx exists mainly four, the graph of the PO4 BAD and BDD can be seen very clearly with different P2O5 concentrations The number of
CN 5 and 6 is small and exists with the high P2O5 ratio, so we only consider the BADs and BDDs of PO5 and PO6 with a high P2O5 ratio, see Fig 3.4 Fig 3.4 shows that the angle OPO in PO4 is mainly 110 0 -112 0 , compared approximately to the result of Guozheng Fan et al [22] that OPO angle is 109 0 The angle measure is almost constant, but the peak height of the BAD drops gradually as increasing concentration of P2O5 This decreasing tendency emerges because the ratio of [PO4] tetrahedrons ratio declines when increasing P2O5 ratio Correspondingly, the P-O bond length is 1.54-1.56Å and remains steady with a rising ratio of P2O5 (Fig 3.4) With P2O5 ratio of 25-40 mol%, the OPO angle in PO5 is 92 0 -94 0 and the P-O distance is 1.6Å With a high P2O5 ratio (20-40 mol%), the OPO angle in PO6 is 90 0 -92 0 and the corresponding P-O bond is 1.7Å As can be seen, the microstructural parameters related to POx are less affected by the concentration of P2O5
Figure 3.4: Bond angle and distance distribution of PO x (x=4, 5, 6) at different
Figure 3.5 illustrates the Bond Angle Distributions (BADs) and Bond Distance Distributions (BDDs) for SiOx units, specifically for x=4 and 5 SiO4 is the dominant form due to its higher coordination concentration, while SiO5 exists in smaller quantities, particularly at elevated P2O5 ratios Therefore, our analysis focuses on the BADs and BDDs relevant to these conditions In SiO4, the OSiO angle ranges from 108° to 112°, with a Si-O bond distance of 1.64 to 1.66 Å, whereas the OSiO angle for SiO5 is yet to be specified.
In previous studies, the Si-O bond length in various silicate systems ranges from 1.76 to 1.78 Å, with OSiO angles of 108° in SiO4 and 90° in SiO5 Research on the CaO-SiO2-TiO2 system shows OSiO angles between 105° and 110° Comparatively, measurements of a tetrahedral silicon sample from Engelhard Industries reveal a Si-O bond length of 1.62 Å and an OSiO angle of 109.5° These findings indicate that SiOx structures in bioglass systems maintain stability despite changes in network modifiers and formers, with minimal impact from varying P2O5 concentrations on the microstructural parameters of SiOx units.
Figure 3.5: Bond angle and bond distance distribution of SiO x (x=4, 5) at different P 2 O 5 content
The OTO angles in TO4, TO5, and TO6 units are measured at 110°, 90°-94°, and 90°-92°, respectively, as illustrated in Fig 3.6 These measurements are comparable to those of POx and SiOx and exhibit stability despite variations in P2O5 concentration The graph highlights a prominent peak at 110°, a shoulder at 94°, and a minor peak at 174°, with the main peak aligning with the OTO angle of TO4 and the shoulder corresponding to the OTO angle of TO5.
Figure 3.6: Bond angle distribution of TO x (T=Si, P, x=4, 5, 6) with concentrations of P 2 O 5
Intermediate range order
The RDF analysis of Ca-P indicates that the Ca-P bond length ranges from 3.64 to 3.7 Å, with peak heights diminishing as the P2O5 ratio increases Additionally, the Ca-Si distance increases from 3.62 to 3.68 Å, accompanied by a decrease in peak height with higher P2O5 ratios Furthermore, the P-P bond length measures between 3.33 and 3.28 Å, while the P-Si bond length ranges from 3.24 to 3.28 Å.
33 the Si-Si bond length is 3.26-3.2Å The distance of O-O is 2.52-2.66Å, the distance decreases and the height peak increases with P2O5 ratio
The OMy ratio variation is illustrated in Fig 3.7 and Table 3.3, highlighting that OM2 exhibits the highest percentage, increasing from 52.42% to 78.08% at 20 mol% P2O5 before declining to 47.31% Meanwhile, OM3, which holds the second largest percentage, starts at 35.3% with 5 mol% P2O5, drops to a low of 17.03% at 20 mol% P2O5, and subsequently rises to approximately 30%.
OM4 accounts for the lowest percentage, declines from 11.52% to 1.47% (at 20 mol%
As the concentration of P2O5 rises to 14.14%, there is a noticeable increase in the agglomeration of the material system, which is reflected in the similar fluctuations of OM4 and OM3 concentrations.
Figure 3.7: Coordination number distribution of OM x (x=2, 3, 4) as a function of
Table 3.3: OMy units with different P 2 O 5 concentration
The OM2 primarily consists of O-2Si and O-(P, Si), with the O-2Si ratio decreasing from 75.18% to 27.74% as the P2O5 ratio increases Conversely, the O-(P, Si) ratio rises significantly from 11.1% to 59.77% Additionally, O-(2P), O-(1Ca, 1Si), and O-(1Ca, 1P) represent smaller proportions, each remaining below 20%, with minor fluctuations observed in their percentages relative to concentration changes.
The composition of P2O5 has been altered, resulting in the formation of OM3 in the O-(xCa, yP, zSi) structure Notably, the O-(1P, 2Si) component shows a significant increase from 0.08% to 59.58% In contrast, the O-(2Ca, 1Si) component exhibits a linear decrease from 47.85% to 0% Additionally, the O-(2Ca, 1P) component experiences a dramatic rise, peaking at 56.28% from an initial 24.75% at 20 mol%.
The concentration of P2O5 significantly influences the distribution of various OMy units As P2O5 increases, the ratios of O-(1P, 3Si) and O-(2P, 2Si) rise linearly to 45.37%, while O-(3Ca, 1Si) consistently decreases from 68.97% to 0% Additionally, O-(3Ca, 1P) increases from 21.7% to 73.58% at 20 mol% P2O5 before dropping to 0% The variations in OM4 units highlight the critical role of P2O5 concentration in altering the composition of these units.
3.2.2 Distribution of types of linking oxygens
The analysis presented in Fig 3.8 illustrates the relationship between the concentrations of P2O5/CaO and the fractions of network forming (BO) and non-bridging oxygens (NBO) As the concentration of P2O5 rises, the percentage of BO increases significantly from 55.75% at 5 mol% P2O5 to 94.86%, while the NBO ratio experiences a substantial decline from 44.25% to just 5.13% Notably, the fraction of free oxygen (FO) remains nearly negligible, indicating a remarkable increase in the polymerization of the CPS system.
In the study of bonding units (BO), the primary bonds identified are P-O-Si and Si-O-Si, with a minor presence of P-O-P bonds As the concentration of P2O5/CaO increases, the fraction of P-O-P bonds rises from 0% to 18.44% Concurrently, within the same range of P2O5 concentration, the Si-O-Si bond fraction decreases significantly from 87.48% to a low of 42.5% at 20 mol% P2O5, before increasing again to approximately 50% The P-O-Si bond ratio shows an initial increase from 12.46% to a peak of 51.31% at 20 mol% P2O5, subsequently declining to 32.66% This behavior aligns with previous research, indicating that in the range of 0-20 mol% P2O5, the trends in bond types exhibit similar patterns Notably, the proportion of oxygen bonded solely to silicon atoms is high at low P2O5 ratios but drops sharply to 15.21% as the P2O5 ratio increases.
The fraction of bridging oxygen (BO) bonded solely with phosphorus (P) and silicon (Si) significantly increases from 12.88% to 74.1% In contrast, the oxygen bonding exclusively with silicon shows a minimal percentage that rises with higher concentrations of P2O5, ranging from 0.26% to 10.68% Non-bridging oxygen (NBO) units primarily consist of O-(2Ca, 1P), O-(2Ca, 1Si), O-(1P), and O-(1Ca, 1P) Notably, the O-(1P) ratio experiences a dramatic increase from 0.2% to 100% as P2O5 concentration rises from 0 to 40 mol% Other types of NBOs constitute less than 50% and exhibit significant fluctuations with varying P2O5 ratios, as illustrated in Figure 3.8.
Figure 3.8: Fraction of BO and NBO as a function of P 2 O 5 content
The SiO4 cluster distribution is shown in Table 3.4 We find that with 5 mol%
P2O5 exhibits a large atomic cluster, primarily consisting of a single cluster with 3,947 atoms, alongside smaller clusters of just 5 or 9 atoms Notably, as the concentration of P2O5 rises, the size of the largest cluster diminishes, leading to the emergence of the material system CPS in various forms.
Figure : Fraction of BO and NBO with different P2O5 ratios
The study identifies a total of 37 smaller clusters, with the largest cluster containing 123 atoms at 40 mol% P2O5 At 5 mol% P2O5, there are fewer than 10 clusters with 5 atoms, while the number of clusters significantly increases to 124 as the concentration reaches 40 mol% P2O5.
The size of SiO4 tetrahedron clusters is directly linked to the number of bridging oxygens (BOs), as indicated by survey results These findings reveal that smaller atom clusters correspond to a reduced number of bridging oxygens, highlighting a significant structural change in the material system with an increase in P2O5 concentration.
Table 3.4: The SiO 4 cluster distribution (Nc= the number of clusters, Na= the number of atoms of clusters)
Nc Na Nc Na Nc Na Nc Na Nc Na Nc Na Nc Na
As the concentration of P2O5 rises, the size and quantity of PO4 tetrahedron clusters also increase, with most clusters consisting of five atoms Notably, at elevated P2O5 concentrations, clusters exceeding 20 atoms become evident, highlighting a significant change in the distribution of phosphate clusters compared to SiO4 clusters.
BO (POP), mentioned in the previous section We find that with an upward trend of
P2O5 mol%, there are more small clusters of tetrahedron units of P and Si, and the number of atoms in the biggest clusters declines
Table 3.5: The PO 4 clusters distribution
Nc Na Nc Na Nc Na Nc Na Nc Na Nc Na Nc Na
Figure 3.9: Models of PO 4 clusters Black and yellow spheres are O and P atoms respectively Models a, b, c, d, e, f, g are 5, 9, 13, 17, 21, 24, 25 atoms clusters respectively
Figure 3.10: Models of PO 4 clusters distribution Models a, b, c, d are models with
Figure 3.11: Models of PO4 clusters distribution e, f, g models are models with 25,
The bond distances for Ca-O, P-O, and Si-O are measured at 2.28-2.3 Å, 1.56-1.58 Å, and 1.64-1.68 Å, respectively, showing minimal variation with changes in P2O5 concentration As the P2O5 ratio increases, the height of the first peaks in PRDs decreases The coordination numbers (CN) for Ca-O range from 5.15 to 5.35, while P-O and Si-O are approximately 4.00-4.29 and 4.00-4.27, respectively Most phosphorus and silicon atoms are coordinated four-fold by oxygen, forming SiO4 and PO4 units, with the average CN for P-O and Si-O increasing alongside the P2O5 concentration.
The polymerization of the CPS system increases as the P2O5 ratio increases The
Calcium ions (Ca 2+) are primarily found near non-bridging oxygen (NBO) or bridging oxygen (BO) that links SiOx and POx units in the network structure of calcium phosphate silicate (CPS) systems This structure comprises two interlinked networks: the -O-P-O-P-O- and the O-Si-O-Si-O- networks The incorporation of Ca 2+ ions occurs through bridging oxygens connecting phosphate (PO4) units, and the content of calcium oxide (CaO) plays a crucial role in influencing the degree of polymerization within the network structure.
The structure of the material system changes significantly with increasing the