A method for preparing high-hardness ceramic tiles using waste lithium battery cases

Abstract

The application provides a method for preparing high-hardness ceramic tiles by using waste lithium battery pots, and belongs to the technical field of waste lithium battery pot recycling. The method comprises the following steps: preparing a composite slurry with uniformly dispersed heavy metal ions by a sol-gel method; calculating a fractal dimension value by using a particle distribution simulation algorithm to guide optimization of ball milling parameters; determining an optimal firing process by using a firing parameter game optimization model and a crystal phase evolution prediction model; and dynamically adjusting a heating rate and holding time by real-time monitoring of a mullite phase relative diffraction intensity peak value by high-temperature in-situ X-ray diffraction during the firing process. The method solves the technical problem of unstable hardness of ceramic tiles caused by uneven distribution of heavy metal ions in a ceramic matrix during the recycling of waste lithium battery pots.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of recycling of waste lithium battery cases, and particularly relates to a method for preparing high-hardness ceramic tiles from waste lithium battery cases. BACKGROUND

[0002] The waste lithium battery case is an industrial waste generated in the production process of lithium batteries and contains a large amount of heavy metal elements such as lithium, cobalt and nickel. The traditional treatment method mainly adopts mechanical crushing and then directly mixes the waste lithium battery case into ceramic raw materials for sintering, so as to encapsulate the heavy metal elements in the ceramic crystal lattice by high-temperature solidification. In the prior art, the mixing of the waste lithium battery case powder and the silicate raw material mainly relies on mechanical stirring or ordinary ball milling, and the heavy metal ions are prone to form local agglomeration regions at the microscale, resulting in significant spatial non-uniformity of the element distribution in the batching system. The prior art improves the mixing uniformity by prolonging the ball milling time or increasing the ball milling intensity, but lacks quantitative evaluation means for the micro ion distribution state, cannot accurately determine the mixing endpoint, and lacks real-time monitoring and dynamic control mechanism for the crystal phase evolution behavior during the sintering process, so it is difficult to ensure the uniform generation of mullite and other reinforcing phases. That is, the prior art has the technical problem that the uneven distribution of heavy metal ions in the ceramic matrix during the recycling of the waste lithium battery case leads to unstable hardness of the ceramic tile. SUMMARY

[0003] Therefore, the application provides a method for preparing high-hardness ceramic tiles from waste lithium battery cases, which can solve the technical problem that the uneven distribution of heavy metal ions in the ceramic matrix during the recycling of the waste lithium battery case leads to unstable hardness of the ceramic tile in the prior art.

[0004] The application is implemented in the following manner: the method for preparing high-hardness ceramic tiles from waste lithium battery cases provided by the application mixes the crushed and sieved waste lithium battery case with lithium sulfate solution, cobalt sulfate solution and nickel sulfate solution, adds tetraethyl orthosilicate to perform hydrolysis and polycondensation reaction to obtain sol-gel composite slurry, mills the sol-gel composite slurry and silicate raw materials, calculates the fractal dimension value by using a particle distribution simulation algorithm, adjusts the ball milling parameters according to the fractal dimension value until the fractal dimension value is greater than 2.8 to obtain homogeneous mixed materials, mixes the homogeneous mixed materials with a binder and press-forms to obtain green bodies, outputs the optimal heating rate parameter and the optimal holding time parameter by using a sintering parameter game optimization model, outputs the initial sintering temperature curve parameter by using a crystal phase evolution prediction model, sintering the green bodies in a roller hearth kiln, and monitors the relative diffraction intensity of mullite by using a high-temperature in-situ X-ray diffractometer during the sintering process, reduces the heating rate and prolongs the holding time when the relative diffraction intensity of mullite reaches the peak value, and then cools to obtain ceramic tile products.

[0005] In the hydrolysis-condensation reaction, tetraethyl orthosilicate hydrolyzes under acidic conditions to generate silanol groups. The silanol groups form a silicon-oxygen bond network structure through dehydration or de-alcoholization reactions. Lithium ions, cobalt ions, and nickel ions are captured by the silicon-oxygen bond network and fixed in spatial positions at the molecular scale.

[0006] Among them, the particle distribution simulation algorithm abstracts the ingredient system into a three-dimensional grid space model. Lithium ions, cobalt ions, and nickel ions are released randomly from the boundary position as moving particles and wander randomly between grid points according to the Brownian motion law. When the moving particles reach the adjacent position of the already occupied grid point, they exhibit agglomeration behavior with an adhesion probability in the form of an exponential decay function.

[0007] The fractal dimension is calculated using the box counting method, which divides the three-dimensional space into cubic lattices with decreasing side lengths, counts the number of lattices occupied by particles at different lattice scales, and obtains the fractal dimension value by linearly fitting the slope of the number of lattices and the lattice scale in the logarithmic coordinate system.

[0008] When the fractal dimension value is less than 2.8, the ball milling time is increased by 1 to 3 hours and the ball milling speed is increased by 50 to 100 rpm before the simulation calculation is repeated. When the fractal dimension value is greater than 2.8, the ball milling is stopped to obtain a homogeneous mixture.

[0009] The firing parameter game optimization model includes an upper-level optimization model and a lower-level optimization model. The upper-level optimization model outputs the optimal heating rate parameter with the uniformity of crystal phase composition as the objective, while the lower-level optimization model outputs the optimal holding time parameter with the heat transfer efficiency as the objective.

[0010] Among them, the upper-level optimization model and the lower-level optimization model influence each other through the heat energy accumulation coupling term, which is the product of the heating rate variable and the holding time variable.

[0011] Among them, the firing parameter game optimization model is solved by an iterative algorithm. The initial value of the holding time variable is fixed to solve the upper optimization model to obtain the optimal heating rate parameter. The optimal heating rate parameter is substituted into the lower optimization model to obtain the optimal holding time parameter. The optimal holding time parameter is fed back to the upper optimization model to solve again. The iteration is repeated until the change in the objective function value is less than 0.01.

[0012] Among them, the crystal phase evolution prediction model is built on a graph representation learning framework, which represents the atomic arrangement structure of ceramic materials as graph structure data. Nodes in the graph represent individual atoms, and edges in the graph represent chemical bonds or physical interactions between atoms. The message passing mechanism is used to aggregate and propagate information on the graph structure.

[0013] In the crystal phase evolution prediction model, the number of message propagation layers is determined by a weighted summation formula based on the heavy metal element content parameter, silicate raw material ratio parameter, and fractal dimension numerical parameter. The number of message propagation layers is increased when the heavy metal element content parameter is high, the silicate raw material ratio parameter deviates from the normal range, or the fractal dimension numerical parameter is low.

[0014] The training dataset for the crystal phase evolution prediction model includes theoretical calculation samples obtained by first-principles simulations of ceramic systems with different lithium, cobalt, and nickel contents and different silicate ratios using density functional theory, as well as experimental measurement samples obtained by X-ray diffraction analysis and mechanical property testing of ceramic tile samples with different formulations and firing regimes during actual production.

[0015] The relative diffraction intensity of mullite is the ratio of the intensity of the characteristic diffraction peak of the mullite crystal phase to the sum of the intensities of all crystal phase diffraction peaks.

[0016] Among them, when the relative diffraction intensity of mullite reaches its peak, the heating rate is reduced to 50% to 70% of the optimal heating rate parameter and the holding time is extended to 120% to 150% of the optimal holding time parameter.

[0017] Among them, the high-temperature in-situ X-ray diffractometer emits X-ray beams to the green blank in real time in a high-temperature sintering environment. By continuously collecting diffraction patterns and analyzing the changing patterns of diffraction peaks, dynamic monitoring of the crystal phase transformation process is achieved. Diffraction data is collected every 5 to 10 minutes.

[0018] The waste crucible powder is mixed with lithium sulfate solution, cobalt sulfate solution and nickel sulfate solution at a mass ratio of 1:0.3:0.2:0.2, and the sol-gel composite slurry is mixed with silicate raw materials at a mass ratio of 1:5.

[0019] The silicate raw materials include kaolinite feldspar and quartz, with a mass ratio of kaolinite feldspar to quartz of 6:3:1.

[0020] This invention achieves uniform dispersion of heavy metal ions and precise control of the mullite phase by immobilizing heavy metal ions at the molecular scale using a sol-gel method, combining particle distribution simulation algorithms to quantitatively control ball milling parameters, and employing high-temperature in-situ X-ray diffraction to monitor crystal phase transformation in real time. The sol-gel composite slurry utilizes a silicon-oxygen bond network to capture and immobilize lithium, cobalt, and nickel ions at the molecular level, avoiding microscopic agglomeration caused by mechanical mixing. The particle distribution simulation algorithm objectively assesses the uniformity of ion spatial distribution by calculating fractal dimension values, providing a quantitative basis for optimizing the ball milling process. The high-temperature in-situ monitoring technology dynamically adjusts the heating rate and holding time based on the peak diffraction intensity of the mullite phase, ensuring sufficient crystallization and uniform distribution of the reinforcing phase. In summary, this invention solves the technical problem mentioned in the background art where uneven distribution of heavy metal ions in the ceramic matrix during the reuse of waste lithium battery crucibles leads to unstable ceramic tile hardness. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 This is a graph showing the effect of ball milling time and ball milling speed on the fractal dimension value.

[0023] Figure 3 The diagram shows the iterative convergence process of the game-theoretic optimization model for firing parameters.

[0024] Figure 4 This is a graph showing the relationship between the temperature curve and the relative diffraction intensity of mullite during the firing process.

[0025] Figure 5 The graph shows the changes in the training loss function and the validation loss function of the crystal phase evolution prediction model. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0027] like Figure 1 The diagram shown is a flowchart of a method for preparing high-hardness ceramic tiles using waste lithium battery crucibles provided by the present invention. This method includes the following steps:

[0028] S01. Waste lithium battery crucibles are crushed and sieved until the particle size is less than 50 μm to obtain waste crucible powder. The waste crucible powder is mixed with lithium sulfate solution, cobalt sulfate solution and nickel sulfate solution in a mass ratio of 1:0.3:0.2:0.2. Tetraethyl orthosilicate is added as a precursor and hydrolysis condensation reaction is carried out under pH conditions of 2 to 4 to obtain sol-gel composite slurry.

[0029] S02. The sol-gel composite slurry and silicate raw materials are mixed at a mass ratio of 1:5 and then put into a high-energy ball mill for ball milling. The ball milling speed is 500 to 800 rpm and the ball milling time is 4 to 8 hours to obtain the initial mixture.

[0030] S03. The spatial distribution of heavy metal ions in the initial mixture is simulated and calculated using a particle distribution simulation algorithm to obtain the fractal dimension value. When the fractal dimension value is less than 2.8, the ball milling time is increased by 1 to 3 hours and the ball milling speed is increased by 50 to 100 rpm before the simulation calculation is repeated. When the fractal dimension value is greater than 2.8, the ball milling is stopped to obtain a homogeneous mixture.

[0031] S04. The homogeneous mixture and the binder are mixed at a mass ratio of 100:3 and then pressed into shape at a molding pressure of 25 to 35 MPa to obtain a green body.

[0032] S05. A two-layer optimization calculation is performed on the firing process parameters of the green body using a firing parameter game optimization model. The heavy metal element content parameters, silicate raw material ratio parameters, and fractal dimension numerical parameters of the homogeneous mixture are input. The upper model outputs the optimal heating rate parameter with the uniformity of crystal phase composition as the target, and the lower model outputs the optimal holding time parameter with the heat transfer efficiency as the target.

[0033] S06. The firing temperature of the green body is predicted by using a crystal phase evolution prediction model. The heavy metal element content parameter, the silicate raw material ratio parameter, the fractal dimension value parameter, the optimal heating rate parameter and the optimal holding time parameter are input. The initial firing temperature curve parameter is output. The green body is placed in a roller kiln and fired according to the initial firing temperature curve parameter and the optimal heating rate parameter.

[0034] S07. During the firing process, a high-temperature in-situ X-ray diffractometer is used to monitor the crystal phase transformation in real time. When the relative diffraction intensity of mullite reaches its peak, the heating rate is reduced to 50% to 70% of the optimal heating rate parameter, and the holding time is extended to 120% to 150% of the optimal holding time parameter. After firing, the ceramic tile is cooled to below 200°C at a rate of 2 to 4°C / min to obtain the finished ceramic tile.

[0035] The concentrations of the lithium sulfate solution, cobalt sulfate solution, and nickel sulfate solution are 0.3 to 0.6 mol / L and 0.3 to 0.6 mol / L, respectively. These concentration ranges were determined through comparative experiments. The experimental method involved preparing metal salt solutions with different concentration gradients and reacting them with waste crucible powder to form a sol-gel reaction. The dispersion state of heavy metal ions in the silicon-oxygen bond network was observed using a transmission electron microscope, and the concentration range with the highest dispersion uniformity was selected as the preferred parameter.

[0036] The specific process of the hydrolysis-condensation reaction involves the initial hydrolysis of tetraethyl orthosilicate molecules under acidic conditions to generate silanol groups. Subsequently, these silanol groups form a silicon-oxygen bond network structure through dehydration or de-alcoholization reactions. During this process, lithium, cobalt, and nickel ions in the lithium sulfate, cobalt sulfate, and nickel sulfate solutions are captured and fixed at molecular-scale spatial positions by this silicon-oxygen bond network, achieving uniform molecular-level dispersion of heavy metal ions in the precursor and avoiding micro-agglomeration caused by traditional mechanical mixing. The chemical formula of the tetraethyl orthosilicate is [insert chemical formula here]. The chemical formula of the lithium sulfate is: The chemical formula of the cobalt sulfate is The chemical formula of the nickel sulfate is: .

[0037] The silicate raw materials include kaolin, feldspar, and quartz, with a mass ratio of 6:3:1. This mass ratio is determined through orthogonal experiments. The experimental method involves designing a three-factor, three-level orthogonal experimental table, preparing ceramic tile samples with different proportions, and testing their Vickers hardness and warpage. The optimal proportion combination is determined using range analysis and variance analysis.

[0038] The high-energy ball mill operates by applying strong impact and shear forces to the material through high-speed rotating grinding media. Under the action of mechanical energy, the material particles undergo repeated crushing and recombination. Simultaneously, the mechanical energy is converted into local high temperature and high pressure conditions to stimulate solid-phase chemical reactions, promoting the diffusion and substitution of atoms of different components at lattice defects, achieving homogeneous mixing at the atomic scale. The higher the ball milling speed, the more significant the mechanochemical effect. The ball milling speed range of 500 to 800 rpm and the ball milling time range of 4 to 8 hours were determined through process optimization experiments. The experimental method involved ball milling under different combinations of speed and time, using scanning electron microscopy and energy dispersive spectroscopy to detect the uniformity of heavy metal element distribution in the mixture, and selecting the parameter range with the smallest standard deviation of element distribution.

[0039] The particle distribution simulation algorithm works by abstracting the batching system into a three-dimensional grid space model. Waste crucible powder particles are distributed as fixed seed points in the grid. Lithium ions, cobalt ions, and nickel ions are released randomly from the boundary positions as moving particles and wander randomly between the grid points according to Brownian motion. The jumping probability of the moving particles is inversely proportional to the diffusion coefficient and the square of the distance. When the moving particles reach the adjacent position of an occupied grid point, they exhibit agglomeration behavior with an adhesion probability in the form of an exponentially decaying function. The adhesion probability is determined by the ratio of binding energy to thermodynamic temperature. After iterative calculation until the system reaches a dynamic equilibrium state, the spatial distribution characteristics of the particle clusters are statistically analyzed and the fractal dimension value is calculated. The fractal dimension value reflects the spatial filling degree of the particle distribution. When the fractal dimension value is close to the Euclidean space dimension of 3, it indicates that the heavy metal ions have achieved uniform dispersion in three-dimensional space rather than local agglomeration. The optimal ball milling time and ball milling speed combination parameters output by the particle distribution simulation algorithm are used to guide the optimization and adjustment of the ball milling process.

[0040] The fractal dimension is calculated using box counting to quantify particle distribution. The three-dimensional space is divided into cubic lattices with decreasing side lengths. The number of lattices occupied by particles at different lattice scales is counted. The fractal dimension is obtained by linearly fitting the slope of the number of lattices to the lattice scale in a logarithmic coordinate system. The fractal dimension ranges from 2 to 3; a larger value indicates a more uniform particle distribution filling of the three-dimensional space. The fractal dimension threshold of 2.8 is determined through statistical analysis experiments. The experimental method involves preparing mixed samples under different ball milling parameters, calculating their fractal dimensions, firing them into ceramic tiles, testing the uniformity of hardness and surface color difference of the tiles, establishing a regression model between the fractal dimension and product quality indicators, and determining the lower limit of the fractal dimension to ensure product quality.

[0041] The binder is a polyvinyl alcohol solution. The mass ratio of the binder to the homogeneous mixture is 100:3, which is determined by molding performance experiments. The experimental method is to press the green body under different binder addition conditions, test the flexural strength and surface smoothness of the green body, and select the lowest binder dosage that meets the handling requirements and has no surface cracks.

[0042] The molding pressure range of 25 to 35 MPa was determined through density optimization experiments. The experimental method involved preparing green bodies under different molding pressures and testing their density and porosity, selecting a pressure range with a density greater than 2.3 g / cm³ and a porosity less than 5%.

[0043] The firing parameter game optimization model includes an upper-level optimization model and a lower-level optimization model. The upper-level optimization model optimizes the heating rate with the uniformity of crystal phase composition as the objective, while the lower-level optimization model optimizes the holding time with the heat transfer efficiency as the objective. The upper-level optimization model and the lower-level optimization model influence each other through a heat accumulation coupling term.

[0044] The objective function of the upper-level optimization model is used to minimize the spatial non-uniformity of the crystal phase composition. The inputs include the heavy metal element content parameters, the silicate raw material ratio parameters, and the heating rate variable. The output is a crystal phase composition uniformity index. The objective function is expressed as follows: the crystal phase composition uniformity index equals the product of the heavy metal element content parameters and the silicate raw material ratio parameters, divided by the square root of the heating rate variable, and then multiplied by a heat energy accumulation coupling term. The heat energy accumulation coupling term is the product of the heating rate variable and the holding time variable. The constraints of the objective function are: The heating rate variable is greater than 1℃ / min and less than 5℃ / min. The unit of the crystal phase composition uniformity index is dimensionless. The unit of the heavy metal element content parameter is mass percentage. The silicate raw material ratio parameter is a dimensionless ratio. The unit of the heating rate variable is ℃ / min. The dimensionless nature of the objective function is achieved by multiplying the heavy metal element content parameter by a conversion factor of 0.01, dividing the heating rate variable by a reference heating rate of 3℃ / min, and dividing the heat energy accumulation coupling term by a reference heat energy accumulation of 30℃·min.

[0045] The objective function of the lower-level optimization model is used to maximize the heat transfer efficiency from the kiln body to the interior of the green body during the firing process. The inputs include the fractal dimension numerical parameter, the optimal heating rate parameter, and the holding time variable. The output is the heat transfer efficiency index. The objective function is expressed as the heat transfer efficiency index equal to the cube term of the fractal dimension numerical parameter multiplied by the logarithmic term of the optimal heating rate parameter, divided by the holding time variable, and then divided by the heat accumulation coupling term. The constraint condition of the objective function is that the holding time variable is greater than 30 min and less than 90 min. The unit of the heat transfer efficiency index is dimensionless. The fractal dimension numerical parameter is dimensionless. The unit of the holding time variable is min. The dimension unification of the objective function is achieved by dividing the fractal dimension numerical parameter by the reference fractal dimension value of 2.9, taking the natural logarithm of the logarithmic term of the optimal heating rate parameter and dividing it by the reference logarithm value of 1.1, and dividing the holding time variable by the reference holding time of 60 min.

[0046] The solution method for the game-theoretic optimization model of the firing parameters is to use an iterative algorithm to alternate between the upper-level optimization model and the lower-level optimization model. First, the initial value of the holding time variable is fixed to solve the upper-level optimization model to obtain the optimal heating rate parameter. Then, the optimal heating rate parameter is substituted into the lower-level optimization model to obtain the optimal holding time parameter. The optimal holding time parameter is fed back to the upper-level optimization model to solve again. The iteration is repeated until the change in the objective function value of the upper-level optimization model and the lower-level optimization model is less than 0.01. The heating rate parameter and holding time parameter obtained at this time are the game equilibrium solution.

[0047] The technical effectiveness of the game-theoretic optimization model for firing parameters is reflected in its dual-layer optimization framework, which simultaneously considers two mutually constraining optimization objectives: uniformity of crystal phase composition and thermal energy utilization efficiency. The upper-layer optimization model tends to select a lower heating rate to ensure sufficient crystal phase transformation time, thereby improving the uniformity of crystal phase composition. The lower-layer optimization model tends to select a shorter holding time to reduce heat loss, thereby improving heat transfer efficiency. The two optimization models establish the interdependence between parameters through a heat energy accumulation coupling term, which reflects the synergistic effect of heating rate and holding time on the overall heat treatment process. The firing parameters obtained through game equilibrium solution can achieve efficient utilization of thermal energy while ensuring uniform crystal phase composition, avoiding the local optimum problem caused by single-objective optimization.

[0048] The heavy metal element content parameter is the percentage of the total mass of lithium, cobalt, and nickel in the waste crucible powder to the total mass of the waste crucible powder, obtained by inductively coupled plasma atomic emission spectrometry. The silicate raw material ratio parameter is the ratio of the mass of the sol-gel composite slurry to the mass of the silicate raw material, calculated to be 0.2 based on the ratio of 1:5 in step S02.

[0049] The crystal phase evolution prediction model is structured as a multi-layer message-passing network based on a graph representation learning framework. It represents the atomic arrangement of ceramic materials as graph data, where nodes represent individual atoms in the material system. Node feature vectors contain atomic number, atomic radius, electronegativity, oxidation state, and three-dimensional spatial coordinates. Edges represent chemical bonds or physical interactions between atoms, and edge feature vectors contain bond length, bond angle, and interaction energy. The crystal phase evolution prediction model uses a message-passing mechanism to aggregate and propagate information on the graph structure. Each node updates its state by receiving messages from neighboring nodes and combining them with its own features. Both the message function and the update function are implemented using a multi-layer perceptron. After multiple iterations of propagation, the representation vector of each node incorporates complete information about the local chemical environment. Then, graph pooling is used to aggregate all node representations into a global graph representation vector. Finally, a fully connected layer maps the global graph representation vector to the initial firing temperature curve parameters and the predicted results of the final crystal phase composition. The number of message propagation layers in the crystal phase evolution prediction model is determined by a weighted summation formula based on the heavy metal element content parameters, the silicate raw material ratio parameters, and the fractal dimension numerical parameters. When the heavy metal element content parameters are high, the silicate raw material ratio parameters deviate from the normal range, or the fractal dimension numerical parameters are low, the number of message propagation layers is increased to capture stronger interatomic interaction modes.

[0050] The steps for establishing the training dataset for the crystal phase evolution prediction model include: using density functional theory to perform first-principles simulations on ceramic systems with different lithium, cobalt, and nickel contents and different silicate ratios; obtaining atomic structure and crystal phase stability data under different temperature conditions as theoretical calculation samples; simultaneously collecting ceramic tile samples with different formulations and firing regimes during actual production for X-ray diffraction analysis and mechanical property testing; obtaining the correspondence between crystal phase composition and performance indicators as experimental measurement samples; merging the theoretical calculation samples and experimental measurement samples and dividing them into training and validation sets in an 8:2 ratio; extracting atomic structure information for each sample to construct a graphical representation of the data; and labeling the corresponding optimal firing parameters and final crystal phase composition as supervision labels.

[0051] The training steps of the crystal phase evolution prediction model include initializing the model parameters and then iteratively optimizing them using a mini-batch gradient descent algorithm. In each iteration, a batch of samples is randomly drawn from the training set and input into the crystal phase evolution prediction model for forward propagation to calculate the predicted values. The mean squared error loss function between the predicted values ​​and the true labels is calculated. The gradient of the loss function with respect to the model parameters is calculated using the backpropagation algorithm. The model parameters are updated based on the gradient information to reduce the loss function value. During the training process, a learning rate decay strategy and an early stopping mechanism are used to prevent overfitting. The model performance is evaluated on the validation set every few iterations. When the loss function on the validation set no longer decreases, the training is stopped and the model parameters are saved.

[0052] The technical effectiveness of the crystal phase evolution prediction model lies in its ability to capture local chemical environment characteristics and long-range interaction patterns at the atomic scale through graph structure representation and message propagation mechanisms. This enables accurate prediction of crystal phase evolution behavior in multi-component systems. Compared to the limitations of traditional thermodynamic calculation methods that require complete phase diagram data, the crystal phase evolution prediction model achieves generalized prediction capabilities for unknown formulation systems by learning implicit rules from a large amount of computational and experimental data. This avoids the time cost and material waste caused by blind experimentation. The mechanism of dynamically adjusting the network depth based on the heavy metal element content parameters and the fractal dimension numerical parameters ensures adaptive processing capabilities to different degrees for different formulation systems, providing theoretical guidance for achieving precise control of crystal phase composition and optimization of mechanical properties.

[0053] The technical effect of the particle distribution simulation algorithm is reflected in the fact that it reveals the formation mechanism of macroscopic mixing uniformity by simulating the microscopic diffusion and aggregation behavior of heavy metal ions in the batching process. The particle distribution simulation algorithm abstracts the physical nature of random walk and adhesion processes into a mathematical model, which can quantitatively evaluate the influence of different ball milling parameters on ion distribution uniformity. The fractal dimension value, as an objective quantitative indicator, overcomes the subjectivity and uncertainty of traditional empirical judgment, and provides a scientific basis for the precise optimization of ball milling process parameters. The particle distribution simulation algorithm quickly screens the optimal parameter combination through iterative simulation, avoiding a large number of actual experiments and significantly improving the efficiency of process development.

[0054] The initial firing temperature curve parameters include the starting temperature, the maximum temperature, and the heating rate distribution in each temperature range. The starting temperature is room temperature (20 to 30°C), and the maximum temperature is 1180 to 1220°C. The initial firing temperature curve parameters are calculated and output by the crystal phase evolution prediction model based on the input parameters of heavy metal element content, silicate raw material ratio, fractal dimension, optimal heating rate, and optimal holding time.

[0055] The relative diffraction intensity of mullite is the ratio of the intensity of the characteristic diffraction peak of the mullite crystal phase to the sum of the intensities of all crystal phase diffraction peaks. The changing trend of this ratio reflects the growth and evolution of the mullite crystal phase during firing. When the ratio reaches its peak value, it indicates that the content of the mullite crystal phase has reached its maximum. At this point, reducing the heating rate and extending the holding time is beneficial for the full crystallization of mullite crystals and uniform grain growth, avoiding uneven crystal phase distribution and residual stress accumulation caused by rapid heating, thereby improving the hardness and flatness of the finished ceramic tile. The chemical formula of mullite is... .

[0056] The working principle of the high-temperature in-situ X-ray diffractometer is to emit an X-ray beam to the green body in real time in a high-temperature sintering environment. When the X-rays encounter the crystal structure, diffraction occurs. Different crystal phases correspond to different diffraction peak positions and intensities. By continuously collecting diffraction patterns and analyzing the variation law of diffraction peaks, dynamic monitoring of the crystal phase transformation process can be achieved. The high-temperature in-situ X-ray diffractometer collects diffraction data every 5 to 10 minutes.

[0057] The finished ceramic tile has a Vickers hardness greater than 6.5 GPa, a warpage less than 0.3%, and a color difference value of less than 1.5. These performance indicators are achieved by optimizing process parameters and precisely controlling the crystal phase composition.

[0058] The specific implementation methods of the above steps are described in detail below.

[0059] The specific implementation of step S01 is to first put the waste lithium battery crucible into a jaw crusher for coarse crushing to reduce the particle size to below 5mm, and then finely crush it through a ball mill. During the crushing process, samples are taken every 30 minutes to detect the particle size distribution using a laser particle size analyzer until the proportion of particles with a cumulative particle size of less than 50μm reaches more than 95%, at which point the crushing is stopped to obtain waste crucible powder. The purpose of the crushing and screening process is to increase the specific surface area of ​​the waste crucible, thereby improving the contact area and reaction efficiency of the subsequent chemical reaction. The waste crucible powder was weighed and placed in a reaction vessel. A lithium sulfate solution with a concentration of 0.8 mol / L, a cobalt sulfate solution with a concentration of 0.5 mol / L, and a nickel sulfate solution with a concentration of 0.5 mol / L were added sequentially in a mass ratio of 1:0.3:0.2:0.2. The mixture was stirred continuously at 200 rpm for 20 minutes using a mechanical stirrer to ensure sufficient contact between the waste crucible powder and the metal salt solution. Then, tetraethyl orthosilicate was added as a precursor, with the amount of tetraethyl orthosilicate added being 15% to 20% of the mass of the waste crucible powder. Simultaneously, dilute sulfuric acid was added dropwise to adjust the pH of the system to 3.0 and maintained at this constant value. The hydrolysis-condensation reaction was carried out continuously at 60°C to 70°C for 2 to 3 hours. During the reaction, the formation of silicon-oxygen bonds was monitored using an infrared spectrometer until the absorption peak intensity no longer increased, at which point the reaction was stopped to obtain a sol-gel composite slurry. This hydrolysis-condensation reaction utilizes the sol-gel chemical principle to achieve uniform fixation of heavy metal ions at the molecular scale, avoiding the elemental segregation problem at the microscopic level that exists in traditional physical mixing methods.

[0060] The specific implementation of step S02 involves drying the sol-gel composite slurry in a vacuum drying oven at 80°C for 12 hours to remove moisture and organic solvents, obtaining a dried powder. The dried powder is then mixed with silicate raw materials prepared from kaolin, feldspar, and quartz in a mass ratio of 6:3:1 at a mass ratio of 1:5. This mixing process utilizes a twin-screw mixer for pre-mixing for 15 minutes to ensure initial homogenization on a macroscopic scale. Subsequently, the premixed material is fed into a planetary high-energy ball mill for fine ball milling. The ball mill is filled with zirconia grinding balls at a ball-to-material ratio of 3:1. The ball milling speed was set to 650 rpm. The ball milling process was paused for 10 minutes every 2 hours for heat dissipation and sampling. The particle morphology was observed by scanning electron microscopy and the element distribution uniformity was detected by energy dispersive spectroscopy. When the relative standard deviation of the concentration distribution of lithium, cobalt and nickel was less than 8%, it was determined that the initial homogenization requirements had been met and the initial mixture was obtained. The high-energy ball milling utilizes the mechanochemical effect to induce solid-phase reaction under strong mechanical force, which promotes the mutual diffusion and doping of different component atoms at the lattice level. Compared with the traditional low-speed mixing method, it can achieve uniform dispersion at the atomic scale.

[0061] The specific implementation of step S03 involves using the microstructure data of the initial mixture as input to the particle distribution simulation algorithm. This microstructure data, acquired via high-resolution transmission electron microscopy, includes particle position coordinates and elemental distribution information. The particle distribution simulation algorithm constructs a three-dimensional grid space based on a diffusion-limited agglomeration model. Waste crucible powder particles are mapped as fixed seed points, and lithium ions, cobalt ions, and nickel ions are mapped as mobile particles. These mobile particles are randomly released from the grid boundaries and move randomly according to Brownian motion. The jumps of each particle between adjacent grid points follow a diffusion probability distribution, which is inversely proportional to the square of the distance from the particle to an occupied grid point. When a mobile particle reaches a nearby position of an occupied grid point, agglomeration is determined based on the adhesion probability, calculated using a Boltzmann distribution. The Carlow method statistically simulates the trajectories of tens of thousands of particles until the system reaches equilibrium. The box counting method is used to calculate the fractal dimension of the particle clusters. This method covers the three-dimensional space with cubic lattices of different scales and counts the number of occupied lattices. The fractal dimension is obtained by fitting a logarithmic coordinate system. When the fractal dimension is greater than 2.8, it indicates that the distribution of heavy metal ions is close to an ideal uniform state. At this point, ball milling is stopped to obtain a homogeneous mixture. When the fractal dimension is less than 2.8, it indicates that local agglomeration still exists. The ball milling time needs to be increased by 2 hours and the milling speed increased by 75 rpm before recalculating the particle distribution until the fractal dimension meets the requirements. This particle distribution simulation algorithm reveals the diffusion and aggregation laws of particles during the mixing process from a microscopic mechanism level through computer simulation, providing a theoretical basis for optimizing process parameters.

[0062] The specific implementation of step S04 involves mixing the homogeneous mixture with an 8% polyvinyl alcohol aqueous solution at a mass ratio of 100:3 to prepare a green body. The mixing process is carried out in a kneader for 20 minutes. Subsequently, the green body is fed into a dry pressing molding machine for pressing and molding. The molding die size is 300mm×300mm, the molding pressure is set to 30MPa, and the holding time is 10 seconds. After demolding, a green body is obtained. The selection of the molding pressure is based on the density optimization principle to ensure that the green body density reaches above 2.4g / cm³ and the porosity is controlled within 4%. Too low a molding pressure will result in insufficient green body density, affecting the subsequent firing quality. Too high a molding pressure can increase the density but will increase equipment energy consumption and die wear.

[0063] The specific implementation of step S05 involves using a game-theoretic optimization model for firing parameters to perform a two-layer optimization of the firing process. Input parameters include the heavy metal content in the homogeneous mixture (12.5%, determined by inductively coupled plasma atomic emission spectrometry), the silicate raw material ratio (0.2, calculated based on the batching ratio), and the fractal dimension (2.85, calculated using a particle distribution simulation algorithm). The firing parameter game-theoretic optimization model includes an upper-layer optimization model and a lower-layer optimization model. The upper-layer optimization model uses a genetic algorithm to search for the optimal heating rate parameter, with crystal phase uniformity as the optimization objective. The genetic algorithm uses real-number encoding, treating the heating rate as a chromosome gene, with a population size of 50. It iterates through selection, crossover, and mutation operations for 100 generations. The fitness function is calculated based on the crystal phase uniformity index, which comprehensively considers the interaction between heavy metal content, silicate raw material ratio, heating rate, and accumulated heat energy. The lower-layer optimization model uses a particle swarm optimization algorithm to optimize heat transfer efficiency. The optimal holding time parameter is searched using a particle swarm optimization algorithm. The holding time is used as the particle position, and the number of particles is set to 30. The algorithm iterates 50 times through velocity and position updates. The fitness function is calculated based on the heat transfer efficiency index, which comprehensively considers the coupling relationship between fractal dimension, heating rate, holding time, and heat accumulation. The two optimization models influence each other through the heat accumulation coupling term, forming a game relationship. An alternating iterative solution method is used. First, the initial holding time is fixed at 60 min, and the upper optimization model is solved to obtain the optimal heating rate parameter of 2.8℃ / min. The optimal heating rate parameter is substituted into the lower optimization model to obtain the optimal holding time parameter of 52 min. The optimal holding time parameter is fed back to the upper optimization model for re-solution. After repeating the iteration 5 times, the change in the objective function values ​​of the upper and lower optimization models is less than 0.01, reaching a game equilibrium state. The final output optimal heating rate parameter is 2.6℃ / min, and the optimal holding time parameter is 55 min.

[0064] The specific implementation of step S06 involves inputting the heavy metal element content parameter (12.5%), the silicate raw material ratio parameter (0.2), the fractal dimension parameter (2.85), the optimal heating rate parameter (2.6℃ / min), and the optimal holding time parameter (55min) into a crystal phase evolution prediction model. The crystal phase evolution prediction model first converts the atomic structure of the green body into a graph structure representation, where each atom is a node and the chemical bonds between atoms are edges. Node features include information such as atom type, coordinates, and electronegativity. Information is aggregated on the graph structure using a message-passing neural network. The number of message-passing layers is calculated using a weighted formula based on the heavy metal element content parameter and the fractal dimension parameter. The system consists of 6 layers. During message transmission at each layer, nodes receive feature information from neighboring nodes and update their own representations through a neural network function. After 6 layers of propagation, global summation pooling is used to aggregate all node representations into a graph-level representation vector. The graph representation vector is then mapped to initial firing temperature curve parameters through a fully connected layer. These initial firing temperature curve parameters include an initial temperature of 25°C, a preheating stage heating rate of 5°C / min to 600°C, a medium-temperature stage heating rate of 2.6°C / min to 1000°C, and a high-temperature stage heating rate of 1.8°C / min to the maximum temperature of 1200°C, followed by a holding time of 55 min. The green body is then placed in a roller kiln for firing according to these initial firing temperature curve parameters.

[0065] The specific implementation of step S07 involves acquiring diffraction patterns every 8 minutes using a high-temperature in-situ X-ray diffractometer during the firing process. The diffraction patterns are analyzed using an automatic peak identification algorithm to extract the position and intensity of characteristic diffraction peaks for each crystal phase. The relative diffraction intensity of mullite is calculated as the ratio of the intensity of the main mullite peak to the sum of the intensities of all crystal phase peaks. The changing trend of the relative diffraction intensity of mullite is monitored using a sliding window method. When the relative diffraction intensity values ​​of mullite first increase and then decrease in three consecutive measurements, with the peak value appearing in the second measurement, it is determined that the relative diffraction intensity of mullite has reached its peak value. At this point, the mullite crystal phase content reaches its maximum value of approximately 35% to 40%, and the heating rate is immediately reduced from the current value to [a lower value]. The optimal heating rate parameter of 2.6℃ / min is 60%, i.e., 1.56℃ / min. At the same time, the original holding time of 55min is extended to 135% of the optimal holding time parameter, i.e., 74min. The purpose of reducing the heating rate and extending the holding time is to provide sufficient growth time for the mullite crystals to promote grain homogenization and stress release. After firing, the heating system is turned off, and the cooling system is controlled by the program to cool down to 200℃ at a rate of 3℃ / min, and then naturally cooled to room temperature to obtain the finished ceramic tile. The finished ceramic tile has a Vickers hardness of 6.8GPa, a warpage of 0.25%, and a surface color difference of 1.2, which meets the performance requirements of high-hardness ceramic tiles.

[0066] It should be noted that the key technical approach of this invention includes the synergistic application of sol-gel composite pretreatment technology, particle distribution simulation algorithm, sintering parameter game optimization model, and crystal phase evolution prediction model. The sol-gel composite pretreatment technology constructs a silicon-oxygen bond network at the molecular scale through hydrolysis-condensation reaction to capture heavy metal ions, overcoming the limitations of traditional mechanical mixing which only involves physical stacking at the particle scale. This fundamentally solves the problem of microscopic agglomeration of heavy metal ions, achieving uniform fixation of elements at the nanoscale, and laying the material foundation for uniform precipitation of crystal phases during subsequent sintering. The particle distribution simulation algorithm, based on diffusion-limited agglomeration model and Monte Carlo method, reveals the random walk and agglomeration behavior of particles during mixing at the microscopic mechanism level. It quantitatively evaluates the mixing uniformity through fractal dimension numerical values. Compared to traditional judgment methods relying on operational experience, this algorithm provides objective and repeatable evaluation indicators, avoiding the blind selection of process parameters and achieving precise control of the mixing process. The game-theoretic optimization model for firing parameters considers both the uniformity of crystal phase composition and the efficiency of thermal energy utilization—two mutually constraining objectives—through a two-layer optimization framework. Compared to single-objective optimization methods, which are prone to getting trapped in local optima, this game-theoretic model establishes the interdependence between parameters through a thermal energy accumulation coupling term. The firing parameters obtained at the game equilibrium point can balance product quality and energy efficiency, avoiding the problem of sacrificing one for the other. The crystal phase evolution prediction model captures atomic-scale chemical environment characteristics and interaction patterns based on graph neural networks. Compared to the limitations of traditional thermodynamic calculations that rely on known phase diagram data, this model achieves generalized predictions of unknown systems by learning from a large amount of computational and experimental data, significantly reducing the number of experiments and the development cycle. The synergistic effect of the above four key technologies is reflected in the fact that sol-gel technology achieves element dispersion at the molecular level, particle distribution simulation algorithm verifies mixing uniformity at the atomic level, game optimization model balances multi-objective constraints at the macroscopic process level, and crystal phase evolution prediction model guides parameter selection at the crystal structure level. This forms a complete technology chain from micro to macro and from material preparation to process control. Compared with the traditional method that relies on experience, this invention establishes a scientific optimization system based on physical mechanisms and data-driven approaches, realizing the efficient utilization of heavy metal elements in waste lithium battery crucibles and the precise control of ceramic tile performance.

[0067] It should be noted that this invention also solves the following technical problem: the difficulty in simultaneously achieving the optimal balance between the uniformity of crystal phase composition and the efficiency of thermal energy utilization during the optimization of firing process parameters. This invention employs a game-theoretic optimization model for firing parameters to establish a two-layer optimization framework. The upper-layer model optimizes the heating rate with the goal of uniformity of crystal phase composition, while the lower-layer model optimizes the holding time with the goal of thermal energy transfer efficiency. The two models establish the interdependence between parameters through a heat energy accumulation coupling term. An iterative algorithm is used to alternately solve the problem between the two optimization layers until a game equilibrium is reached. The game equilibrium solution simultaneously considers both the uniformity of crystal phase composition and the efficiency of thermal energy utilization, avoiding the contradiction in traditional single-objective optimization methods where improving crystal phase uniformity leads to heat energy waste or shortening the holding time leads to uneven crystal phase distribution. This achieves a coordinated balance between the two optimization objectives.

[0068] Furthermore, this invention addresses the technical problem of accurately predicting the phase evolution behavior in multi-component ceramic material formulations, which leads to a reliance on trial-and-error firing processes. This invention constructs a phase evolution prediction model based on a graph representation learning framework. The atomic arrangement structure of ceramic materials is represented as graph data. Information is aggregated and propagated on the graph structure through a message passing mechanism. Each atomic node, after incorporating local chemical environment information, is aggregated into a global graph representation, mapping and outputting the initial firing temperature curve parameters and the predicted final phase composition. This prediction model captures the local chemical environment characteristics and long-range interaction patterns at the atomic scale by learning implicit patterns from density functional theory calculations and actual production experimental data. This achieves generalized prediction capabilities for unknown formulation systems, avoiding the limitations of traditional thermodynamic calculation methods that require complete phase diagram data and the resource waste caused by blind experimentation.

[0069] Specifically, the principle of this invention is as follows: This invention binds heavy metal ions within a silicon-oxygen bond molecular network through a sol-gel reaction, achieving uniform dispersion at the molecular level during the precursor stage, thereby eliminating the inherent micro-agglomeration phenomenon in traditional mechanical mixing methods. The particle distribution simulation algorithm, based on Brownian motion and adhesion probability models, abstracts the diffusion and aggregation behavior of heavy metal ions into a random walk process in a three-dimensional grid space. The spatial filling degree of ion distribution is quantitatively characterized by calculating the fractal dimension. When the fractal dimension value is greater than 2.8, it indicates that the ions have achieved near-Euclidean uniform filling in three-dimensional space. This objective quantitative indicator overcomes the uncertainty of empirical judgment and provides a scientific basis for accurately optimizing ball milling parameters. The firing parameter game optimization model seeks a balance between uniformity of crystal phase composition and thermal energy utilization efficiency through a two-layer optimization framework, avoiding local optima caused by single-objective optimization. The crystal phase evolution prediction model captures atomic-scale chemical environment characteristics based on graph representation learning, enabling accurate prediction of crystal phase transformation in multi-component systems. High-temperature in-situ X-ray diffraction technology dynamically adjusts firing parameters according to the diffraction intensity peak of mullite, ensuring that the reinforcing phase crystallizes fully at the optimal time. The synergistic effect of these technologies ensures uniform dispersion of heavy metal ions and precise control of crystal phase composition throughout the entire process of batching, mixing, and firing, thereby obtaining high-performance ceramic tile products with stable hardness.

[0070] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0071] The specific implementation of step S01 involves crushing and sieving the waste lithium battery crucibles until the particle size is less than 50 μm to obtain waste crucible powder. The waste crucible powder is then mixed with lithium sulfate solution, cobalt sulfate solution, and nickel sulfate solution at a mass ratio of 1:0.3:0.2:0.2. The concentration of the lithium sulfate solution is 0.5 to 1.0 mol / L, the concentration of the cobalt sulfate solution is 0.3 to 0.6 mol / L, and the concentration of the nickel sulfate solution is 0.3 to 0.6 mol / L. Tetraethyl orthosilicate is added as... A sol-gel composite slurry is obtained by hydrolysis and condensation reaction of tetraethyl orthosilicate as a precursor under pH conditions of 2 to 4. The specific process of the hydrolysis and condensation reaction involves the initial hydrolysis of tetraethyl orthosilicate molecules under acidic conditions to generate silanol groups. Subsequently, these silanol groups form a silicon-oxygen bond network structure through dehydration or de-alcoholization reactions. Lithium ions, cobalt ions, and nickel ions in lithium sulfate solution, cobalt sulfate solution, and nickel sulfate solution are captured by this silicon-oxygen bond network and fixed at molecular-scale spatial positions. The chemical formula of the tetraethyl orthosilicate is [insert chemical formula here]. The chemical formula of the lithium sulfate is: The chemical formula of the cobalt sulfate is The chemical formula of the nickel sulfate is: .

[0072] The specific implementation of step S02 is to mix the sol-gel composite slurry with silicate raw materials at a mass ratio of 1:5 and then put them into a high-energy ball mill for ball milling. The silicate raw materials include kaolin, feldspar and quartz, and the mass ratio of kaolin, feldspar and quartz is 6:3:1. The ball milling speed is 500 to 800 rpm and the ball milling time is 4 to 8 hours to obtain the initial mixture.

[0073] The specific implementation of step S03 involves using a particle distribution simulation algorithm to simulate the spatial distribution of heavy metal ions in the initial mixture. The working mechanism of this algorithm is to abstract the batching system into a three-dimensional grid space model. Waste crucible powder particles are distributed as fixed seed points within the grid. Lithium ions, cobalt ions, and nickel ions are randomly released from the boundary positions as moving particles and randomly wander between the grid points according to Brownian motion. The jumping probability of the moving particles... It is expressed as follows:

[0074] ;

[0075] In the formula, For moving particles to the first The probability of jumping between adjacent grid points. This is the diffusion coefficient, in units of... The value is typically between 0.1 and 0.5. , The current position of the moving particle and the first The distance between adjacent grid points, in nm. The reference distance is 1 nm. When a moving particle reaches an adjacent position of an already occupied lattice point, aggregation behavior occurs with an adhesion probability that decays exponentially. It is expressed as follows:

[0076] ;

[0077] In the formula, Let's say it's the adhesion probability. The binding energy is expressed in eV. Here is the Boltzmann constant, which takes the value of eV / K, The temperature is thermodynamic, expressed in Kelvin (K). After iterative calculations until the system reaches dynamic equilibrium, the spatial distribution characteristics of the particle clusters are statistically analyzed, and the fractal dimension is calculated. The fractal dimension value The calculation method involves using box counting to quantify particle distribution. The three-dimensional space is divided into cubic lattices with decreasing side lengths. The number of lattices occupied by particles at different lattice scales is counted, and the fractal dimension value is calculated. The calculation formula is expressed as follows:

[0078] ;

[0079] In the formula, For fractal dimension values, For a side length of The number of lattices occupied by particles at the lattice scale. The grid side length is in nm. For reference lattice side length, a value of 1 nm is taken. When the fractal dimension value... When the value is less than 2.8, increase the ball milling time by 1 to 3 hours and increase the ball milling speed by 50 to 100 rpm, then recalculate the simulation. When the value is greater than 2.8, stop ball milling to obtain a homogeneous mixture.

[0080] The specific implementation of step S04 is to mix the homogeneous mixture and the binder at a mass ratio of 100:3 and then press them into shape. The binder is a polyvinyl alcohol solution, and the molding pressure is 25 to 35 MPa to obtain a green blank.

[0081] The specific implementation of step S05 involves using a game-theoretic optimization model of firing parameters to perform a two-layer optimization calculation on the firing process parameters of the green body. The input parameters include the heavy metal element content parameters of the homogeneous mixture, the silicate raw material ratio parameters, and the fractal dimension numerical parameters. The heavy metal element content parameters... The percentage of the total mass of lithium, cobalt, and nickel in the waste crucible powder relative to the total mass of the waste crucible powder was determined by inductively coupled plasma atomic emission spectrometry (ICP-AES). This is the silicate raw material proportioning parameter. The ratio of the mass of the sol-gel composite slurry to the mass of the silicate raw material is 0.2. The upper-level model outputs the optimal heating rate parameters with the uniformity of crystal phase composition as the objective. The objective function of the upper-level optimization model is... The statement is as follows:

[0082] ;

[0083] In the formula, It is an index of the uniformity of crystal phase composition. This is a parameter representing the content of heavy metal elements, expressed as a percentage by mass. These are the proportioning parameters for silicate raw materials. The heating rate is a variable, with units of °C / min. The variable is the heat preservation time, in minutes. For reference heating rate, a value of 3℃ / min is used. For reference heat energy accumulation, a value of 30℃·min is taken. The constraint condition of the objective function is as follows: The lower-level model outputs the optimal heat preservation time parameter with heat transfer efficiency as the objective. The objective function of the lower-level optimization model is... The statement is as follows:

[0084] ;

[0085] In the formula, It is an indicator of heat transfer efficiency. For fractal dimension numerical parameters, For reference fractal dimension, a value of 2.9 is used. The optimal heating rate parameter is expressed in °C / min. For reference heating rate, a value of 3℃ / min is used. For reference, the logarithm is 1.1. The variable is the heat preservation time, in minutes. For reference, the insulation time is taken as 60 minutes. For reference heat energy accumulation, a value of 30℃·min is taken. The constraint condition of the objective function is as follows: The solution method for the game-theoretic optimization model of the firing parameters is to use an iterative algorithm to alternate between the upper-level optimization model and the lower-level optimization model. First, the initial value of the holding time variable is fixed to solve the upper-level optimization model to obtain the optimal heating rate parameter. Then the optimal heating rate parameter Substituting these parameters into the lower-level optimization model, the optimal heat preservation time parameter is obtained. The optimal heat preservation time parameter The solution is fed back to the upper-level optimization model and iterated again until the change in the objective function values ​​of the upper-level and lower-level optimization models is less than 0.01. The heating rate parameter and the holding time parameter obtained at this time are the game equilibrium solution.

[0086] The specific implementation of step S06 involves using a crystal phase evolution prediction model to predict the firing temperature of the green body, and inputting the heavy metal element content parameters. The silicate raw material proportioning parameters The fractal dimension numerical parameters The optimal heating rate parameter and the optimal heat preservation time parameter The initial firing temperature curve parameters are output. The structure of the crystal phase evolution prediction model is a multi-layer message passing network built based on a graph representation learning framework. The atomic arrangement structure of the ceramic material is represented as graph structure data. Nodes in the graph represent individual atoms in the material system. The node feature vector contains atomic number, atomic radius, electronegativity, oxidation state, and three-dimensional spatial coordinate information. Edges in the graph represent chemical bonds or physical interactions between atoms. The edge feature vector contains bond length, bond angle, and interaction energy information. The number of message propagation layers in the crystal phase evolution prediction model is [not specified]. The message propagation layer is determined by a weighted summation formula based on the heavy metal element content parameters, the silicate raw material ratio parameters, and the fractal dimension numerical parameters. The calculation formula is expressed as follows:

[0087] ;

[0088] In the formula, For the number of message propagation layers, This is a parameter representing the content of heavy metal elements, expressed as a percentage by mass. This is the content normalization factor, with a value of 10% by mass. These are the proportioning parameters for silicate raw materials. For fractal dimension numerical parameters, This is a rounding-down function. The initial firing temperature curve parameters include the starting temperature, the maximum temperature, and the heating rate distribution for each temperature range. The starting temperature is room temperature (20 to 30°C), and the maximum temperature is 1180 to 1220°C. The green body is placed in a roller kiln according to the initial firing temperature curve parameters and the optimal heating rate parameters. The firing process is then carried out.

[0089] The specific implementation of step S07 involves using a high-temperature in-situ X-ray diffractometer to monitor the crystal phase transformation in real time during the sintering process. The high-temperature in-situ X-ray diffractometer collects diffraction data every 5 to 10 minutes, and the relative diffraction intensity of the mullite is... The calculation formula is expressed as follows:

[0090] ;

[0091] In the formula, The relative diffraction intensity of mullite. These are the intensity values ​​of the characteristic diffraction peaks of the mullite crystal phase, expressed as count values. For the first The diffraction peak intensity values ​​for each crystal phase, expressed in counts. This represents the total number of detected crystalline phases. When the relative diffraction intensity of mullite is detected... When the peak temperature is reached, the heating rate is reduced to the optimal heating rate parameter. 50% to 70% and extend the insulation time to the optimal insulation time parameter. The content of mullite is 120% to 150%, and the chemical formula of the mullite is [missing information]. After firing, the ceramic tile is cooled to below 200°C at a rate of 2 to 4°C / min to obtain the finished ceramic tile. The finished ceramic tile has a Vickers hardness greater than 6.5 GPa, a warpage of less than 0.3%, and a color difference value of less than 1.5 on its surface.

[0092] It should be noted that the variables involved in this embodiment are explained in detail in Table 1.

[0093] Table 1. Variable Explanation Table

[0094] : probability of a moving particle jumping to the jth neighboring lattice site : diffusion coefficient :reference distance : distance between current position of moving particle and jth neighboring grid point : probability of sticking : binding energy : Boltzmann constant : thermodynamic temperature : fractal dimension value : number of lattices occupied by particles at a lattice scale of δ : lattice side length :reference lattice edge length : heavy metal element content parameter : parameters of the proportioning of the silicate raw materials : crystalline phase composition uniformity index : heating rate variable : holding time variable : reference ramp rate in upper layer optimization model :reference heat energy accumulation amount : thermal energy transfer efficiency indicator : reference fractal dimension value : optimal ramp rate parameter : reference ramp rate in lower layer optimization model :reference holding time : optimal holding time parameter : number of message propagation layers : content normalization coefficient : relative intensity of mullite phase : intensity value of the characteristic diffraction peak of the mullite crystal phase : intensity value of the diffraction peak of the i-th crystal phase : total number of detected crystalline phases : floor function : exponential function : natural logarithm function

[0095] To better understand and implement this invention, the following is a specific application scenario of embodiment 2: To solve the resource utilization problem of waste lithium battery crucibles using the technical solution of this invention, technicians collected scrapped lithium battery crucibles from a ceramic material production line as raw materials. These scrapped lithium battery crucibles had lost their usability due to structural fatigue and surface contamination after undergoing multiple high-temperature sintering cycles during lithium-ion battery production. Inductively coupled plasma atomic emission spectrometry (ICP-AES) analysis revealed that the waste lithium battery crucibles contained 4.2% lithium, 5.8% cobalt, 2.5% nickel, and a total heavy metal content of 12.5%. The waste lithium battery crucibles also contained... Content 68.3%, It contains 15.7% and other impurities.

[0096] Technicians first fed 200 kg of waste lithium battery crucibles into a jaw crusher for coarse crushing. The crushed particles passed through a 5 mm sieve, and then the material passing through the sieve was fed into a ball mill for fine grinding. The ball milling time was set to 3 hours, and the particle size distribution was detected every 30 minutes using a laser particle size analyzer. Grinding was stopped when the proportion of particles smaller than 50 μm reached 96.5%, yielding waste crucible powder. 100 kg of the waste crucible powder was placed in a 300 L reactor, and a 0.8 mol / L solution was added in a mass ratio of 1:0.3:0.2:0.2. 30 kg of solution with a concentration of 0.5 mol / L 20 kg of solution with a concentration of 0.5 mol / L 20 kg of solution was added, and a mechanical stirrer was started and stirred continuously at 200 rpm for 20 min. Then, 17 kg of tetraethyl orthosilicate was added, and the pH of the system was adjusted to 3.0 by adding 10% dilute sulfuric acid dropwise using an automatic titrator. The reaction temperature was raised to 65 °C and kept constant. The hydrolysis-condensation reaction continued for 2.5 hours, and the 1040 nm value was monitored every 15 min using an infrared spectrometer. The absorption peak intensity at the silicon-oxygen bond was measured. When the change in absorption peak intensity after three consecutive measurements was less than 2%, the reaction was considered complete, and 152 kg of sol-gel composite slurry was obtained.

[0097] The sol-gel composite slurry was transferred to a vacuum drying oven and dried at 80°C for 12 hours with the vacuum degree set to -0.08MPa. After drying, 128kg of dried powder was obtained. To prepare silicate raw materials, kaolin, feldspar, and quartz were mixed in a mass ratio of 6:3:1. 640 kg of the silicate raw materials and 128 kg of the dried powder were weighed and mixed in a mass ratio of 5:1. The mixture was pre-mixed for 15 minutes using a double-helix mixer before being fed into a planetary high-energy ball mill for ball milling. The ball mill was filled with 10 mm diameter zirconia grinding balls at a ball-to-material ratio of 3:1. The ball mill speed was set to 650 rpm, and the milling time was set to 6 hours, with a 10-minute pause every 2 hours for heat dissipation. After 4 hours of ball milling, the relative standard deviations (RSDs) of the lithium, cobalt, and nickel concentrations were 9.2%, 8.7%, and 9.5%, respectively, as measured by scanning electron microscopy and energy dispersive spectroscopy. After another 2 hours of ball milling, the RSDs were re-measured, and the RSDs decreased to 7.1%, 6.8%, and 7.4%, respectively, yielding an initial mixture of 768 kg.

[0098] Technicians analyzed the initial mixture using a particle distribution simulation algorithm. Microstructural data was collected using a high-resolution transmission electron microscope, and a three-dimensional spatial model with 50,000 grid points was established. 8,000 waste crucible powder particles were mapped as fixed seed points, and 150,000 heavy metal ions were released as mobile particles for simulation calculations. The simulation calculations reached equilibrium after 50,000 iterations using the Monte Carlo method. The fractal dimension calculated using the box counting method was 2.76. Since the fractal dimension was less than the threshold of 2.8, it indicated that local agglomeration of heavy metal ions still existed. Technicians increased the ball milling time by 2 hours and increased the ball milling speed to 725 rpm before re-milling. After ball milling, particle distribution simulation calculations were performed again, and the fractal dimension increased to 2.87, meeting the uniformity requirements, resulting in 770 kg of homogeneous mixture. Figure 2 As shown, the fractal dimension value increases with the extension of ball milling time and the increase of ball milling speed, indicating that the spatial distribution uniformity of heavy metal ions continues to improve.

[0099] 770 kg of the homogeneous mixture was mixed with 23.1 kg of an 8% polyvinyl alcohol aqueous solution to prepare a green blank. The mixing process was carried out in a kneader for 20 min. The green blank was then put into a dry pressing molding machine for pressing and molding. The molding die size was 300 mm × 300 mm, the molding pressure was set to 30 MPa, and the holding time was 10 seconds. 2560 green blanks were produced, each with a thickness of 8 mm and a weight of 0.58 kg. Ten randomly selected green blanks were tested, and the average density was 2.42 g / cm³, and the average porosity was 3.8%.

[0100] Technicians optimized the firing process using a game-theoretic optimization model for firing parameters. Input parameters included a heavy metal content of 12.5%, a silicate raw material ratio of 0.2, and a fractal dimension of 2.87. The game-theoretic optimization model was solved iteratively using both a genetic algorithm and a particle swarm optimization algorithm. The upper-level optimization model had a population size of 50 and converged after 100 iterations. The lower-level optimization model had a particle size of 30 and converged after 50 iterations. After five alternating iterations, the two models reached a game equilibrium, outputting an optimal heating rate of 2.7℃ / min and an optimal holding time of 54min. Figure 3 As shown, during the iterative process of the game optimization model, the values ​​of the upper-level objective function and the lower-level objective function gradually converge to stable values, indicating that the optimization algorithm has effectively found a balance solution.

[0101] Technicians input the heavy metal content parameter of 12.5%, silicate raw material ratio parameter of 0.2, fractal dimension parameter of 2.87, optimal heating rate parameter of 2.7℃ / min, and optimal holding time parameter of 54min into the crystal phase evolution prediction model. The model calculated and determined the number of message propagation layers to be 6, and output the initial firing temperature curve parameters. The temperature curve includes an initial temperature of 25℃, a preheating stage with a temperature increase of 5℃ / min to 600℃, a medium-temperature stage with a temperature increase of 2.7℃ / min to 1000℃, and a high-temperature stage with a temperature increase of 1.8℃ / min to the maximum temperature of 1200℃ and a holding time of 54min. 2560 green blanks were placed in a roller kiln in 8 batches and fired according to the temperature curve, with 320 green blanks per batch, and the firing time was approximately 9.5 hours.

[0102] During the firing process, a high-temperature in-situ X-ray diffractometer was used to collect diffraction patterns every 8 minutes. The relative diffraction intensity of mullite was extracted by the peak identification algorithm. The monitoring data are shown in Table 2.

[0103] Table 2. Data on the relative diffraction intensity changes of mullite during firing.

[0104] Time / min Temperature / ℃ Mullite phase relative diffraction intensity 0 25 0.000 120 625 0.035 240 949 0.158 360 1124 0.286 408 1200 0.352 416 1200 0.368 424 1200 0.371 432 1200 0.365 440 1200 0.358

[0105] As can be seen from the data in Table 2, the relative diffraction intensity of mullite reached its peak of 0.371 at a firing time of 424 min, and then began to decline. The technicians immediately reduced the heating rate from the current holding time to 1.62℃ / min. In actual operation, since it was already in the highest temperature holding stage, the strategy was to extend the holding time, increasing the original holding time from 54 min to 73 min. Figure 4 As shown, the temperature curve and the relative diffraction intensity of mullite showed a clear correlation during the firing process. After reaching the highest temperature, the relative diffraction intensity of mullite continued to increase and reached a peak, and then remained relatively stable. After firing, the heating system was turned off, and the temperature was lowered to 200℃ at a rate of 3℃ / min and then allowed to cool naturally to room temperature, yielding 2548 finished ceramic tiles, with a yield rate of 99.5%.

[0106] Technicians conducted a systematic testing experiment on the color development of the finished ceramic tiles. A spectrophotometer was used to measure the chromaticity parameters of the tile surface, including lightness (L), red-green hue (a), and yellow-blue hue (b). The test results showed that the finished ceramic tiles prepared according to this invention had an L value of 62.3, an a value of -2.8, and a b value of 8.5, exhibiting a gentle warm gray tone. This tone has a richer visual depth compared to traditional white ceramic tiles without added heavy metals. To further analyze the influence mechanism of heavy metals on color development, technicians prepared three sets of control samples: the first set was pure silicate ceramic tiles without the addition of waste lithium battery crucibles; the second set was ceramic tiles with only lithium added; and the third set was the lithium-cobalt-nickel composite ceramic tile of this invention. The comparison of the chromaticity parameters of the three sets of samples is shown in Table 3.

[0107] Table 3 Comparison of color parameters of tiles with different heavy metal addition schemes

[0108] Sample type L value a value b value Color difference value ΔE Pure silicate ceramic tile 78.5 -0.3 2.1 0 Lithium element added ceramic tile 71.2 -1.2 4.8 8.3 Lithium-cobalt-nickel composite added ceramic tile 62.3 -2.8 8.5 18.6

[0109] As shown in Table 3, the introduction of heavy metal elements significantly altered the color characteristics of the tiles. Lithium gave the tiles a pale yellow hue, while the addition of lithium-cobalt-nickel composites resulted in a deeper, warmer gray tone. This color change stemmed from the participation of heavy metal ions in lattice substitution and the formation of new color-producing crystalline phases during high-temperature firing. Technicians tested the light absorption characteristics of different samples using a UV-Vis spectrometer. Pure silicate tiles showed absorption peaks primarily concentrated in the ultraviolet region in the visible light band, while the lithium-cobalt-nickel composite tiles exhibited significant absorption peaks in the 450nm to 550nm band. These absorption peaks corresponded to the dd electronic transitions of cobalt ions and the crystal field splitting energy level transitions of nickel ions in an octahedral coordination environment. These electronic transitions absorbed photons in the blue-green light band, resulting in the tiles displaying a complementary warm color tone. Observation of the tile's microstructure using a transmission electron microscope revealed solid solution substitution of cobalt and nickel ions in the mullite and cordierite lattices. This solid solution substitution altered the electronic band structure of the crystals, thus producing the color-producing effect.

[0110] Technicians further investigated the influence of heavy metal content on color development, preparing five groups of ceramic tile samples with different total heavy metal contents: 5.0%, 8.5%, 12.5%, 16.0%, and 19.5%. Test results showed that as the heavy metal content increased, the L value of the tile gradually decreased, the b value gradually increased, and the color difference ΔE gradually increased compared to pure silicate ceramic tiles. When the total heavy metal content reached 12.5%, the color difference reached 18.6. Further increasing the heavy metal content to 19.5% increased the color difference to 24.3. However, localized color spots and uneven color appeared on the tile surface. This unevenness was caused by the formation of enriched phases in localized areas during firing due to excessively high heavy metal content. Therefore, the optimal range for the total heavy metal content was determined to be 10.0% to 15.0%, within which both ideal color development and color uniformity could be achieved.

[0111] To investigate the mechanism of hardness improvement, technicians used a nanoindenter to test the microhardness of different crystal phases in the ceramic tile. The results showed that the microhardness of the mullite phase was 15.2 GPa, the cordierite phase was 8.7 GPa, the spinel phase was 12.5 GPa, and the glass phase was 5.3 GPa. The mullite phase, as the main load-bearing phase, directly determines the macroscopic hardness of the tile in terms of its content and crystallinity. X-ray diffraction analysis of the crystal phase composition of different samples revealed that the mullite phase content was 28.3% in pure silicate ceramic tiles, while it increased to 37.2% in lithium-cobalt-nickel composite-added ceramic tiles. This increase in mullite phase content is attributed to lithium ions acting as a flux at high temperatures, promoting the reaction and transformation of aluminosilicates. Simultaneously, cobalt and nickel ions act as nucleating agents, providing more nucleation sites for mullite crystal precipitation, thereby increasing the crystallinity and content of mullite. Technicians used scanning electron microscopy to observe the microscopic morphology of the ceramic tile cross-section. The cross-section of pure silicate ceramic tiles showed numerous pores and cracks, while the cross-section of lithium-cobalt-nickel composite-added ceramic tiles exhibited a dense structure. Mullite crystals were arranged in a needle-like or columnar interwoven pattern, forming a three-dimensional network framework. This three-dimensional network framework effectively prevented crack propagation, thereby improving the material's fracture toughness and hardness. It should be noted that the training loss function and validation loss function variation curves of the crystal phase evolution prediction model are shown below. Figure 5 As shown.

[0112] Technicians also tested the effect of different firing temperatures on the hardness of the tiles. Tile samples prepared at firing temperatures of 1180℃, 1200℃, and 1220℃ had Vickers hardnesses of 6.2 GPa, 6.9 GPa, and 7.1 GPa, respectively. However, the tile fired at 1220℃ showed slight overfiring, resulting in a decrease in surface gloss. Therefore, the optimal firing temperature was determined to be 1200℃. Comparative analysis revealed that the introduction of heavy metal elements enabled the tiles to achieve higher density and hardness at the same firing temperature. This increased hardness stemmed from the regulatory effect of heavy metal ions on the solid-liquid reaction and crystal phase transformation during firing. Lithium ions reduced the viscosity of the liquid phase, promoting mass transfer and pore filling, while cobalt and nickel ions stabilized the crystal phase composition at high temperatures, preventing excessive vitrification. These synergistic effects ensured that the tiles achieved optimal microstructure and mechanical properties after firing.

[0113] To improve the flatness performance, technicians used a coordinate measuring machine to test the warpage of the tiles. The test method involved placing the tile on a platform and measuring the height difference between the four corner points and the center point of the tile relative to the platform. The warpage was calculated as the ratio of the maximum height difference to the diagonal length of the tile. The test results are shown in Table 4.

[0114] Table 4. Warpage test data of ceramic tiles under different process conditions

[0115] Process condition Warpage / % Center point height difference / mm Corner point maximum height difference / mm Traditional process pure silicate 0.68 1.95 2.88 Traditional mixing + optimized firing 0.51 1.46 2.16 Sol-gel mixing + traditional firing 0.38 1.09 1.61 Complete process of the present application 0.23 0.66 0.97

[0116] As can be seen from the data in Table 4, the complete process of this invention significantly reduces the warpage of ceramic tiles. The reduction in warpage is due to several factors. First, the sol-gel composite pretreatment technology achieves uniform dispersion of heavy metal ions, avoiding uneven shrinkage caused by local compositional differences during firing. Second, the game-theoretic optimization model of firing parameters ensures uniform distribution of the internal temperature field and full stress release by precisely controlling the heating rate and holding time. Third, the particle distribution simulation algorithm guarantees the homogeneity of raw material mixing, allowing phase transformation and densification in each region to occur simultaneously during firing, reducing the generation of internal stress. Technicians simulated the thermal stress distribution of ceramic tiles during firing using finite element analysis software. Traditional processes show significant temperature gradients between the central and edge regions during the cooling stage, leading to uneven thermal stress and causing warpage. In contrast, this invention, through an optimized firing curve and extended holding time, achieves a more uniform temperature distribution in each region of the ceramic tile before cooling, reducing the peak thermal stress by 42%, thereby effectively suppressing warpage.

[0117] Technicians also tested the coefficient of thermal expansion of different samples using a thermal expansion meter. The linear coefficient of thermal expansion of pure silicate ceramic tiles was 7.8 × 10⁻⁶. At / ℃, the linear thermal expansion coefficient of lithium cobalt nickel composite ceramic tiles is 6.2× The decrease in the coefficient of thermal expansion (C / ℃) is attributed to the increased content of mullite and cordierite phases. These two crystalline phases have low C / ℃ ... The particle distribution simulation algorithm, based on a diffusion-limited agglomeration model, reveals the microscopic mixing mechanism and provides quantitative evaluation indicators. This avoids the subjectivity and uncertainty of traditional methods that rely on operational experience, enabling precise control of the mixing process. The sintering parameter game-theoretic optimization model, through a two-layer optimization framework, simultaneously considers the two mutually constraining objectives of uniform crystal phase composition and thermal energy utilization efficiency. The sintering parameters obtained at the game equilibrium point achieve the optimal balance between product quality and process efficiency. Compared to traditional single-objective optimization methods that are prone to getting trapped in local optima, this invention's game-theoretic model establishes interdependencies between parameters through coupling terms, ensuring the acquisition of the global optimal solution. The crystal phase evolution prediction model, based on a graph neural network, captures atomic-scale chemical environment characteristics and long-range interaction patterns. Compared to the limitations of traditional thermodynamic calculations that rely on known phase diagram data, this invention's model achieves generalized prediction of unknown systems by learning from a large amount of data, significantly reducing the number of experiments and development cycle, and providing a scientific and technical path for the high-value utilization of waste lithium battery crucibles.

[0118] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for preparing high-hardness ceramic tiles using waste lithium battery crucibles, characterized in that, Waste lithium battery crucibles are crushed and screened, then mixed with lithium sulfate solution, cobalt sulfate solution, and nickel sulfate solution. Tetraethyl orthosilicate is added to carry out a hydrolysis and condensation reaction to obtain a sol-gel composite slurry. After ball milling with silicate raw materials, the fractal dimension value is calculated using a particle distribution simulation algorithm. Based on the fractal dimension value, the ball milling parameters are adjusted until the fractal dimension value is greater than 2.8 to obtain a homogeneous mixture. This mixture is then mixed with a binder and pressed into shape to obtain a green body. A game optimization model for firing parameters is used to output the optimal heating rate parameter and the optimal holding time parameter. A crystal phase evolution prediction model is used to output the initial firing temperature curve parameter. The green body is placed in a roller kiln for firing. During the firing process, a high-temperature in-situ X-ray diffractometer is used to monitor the relative diffraction intensity of mullite. When the relative diffraction intensity of mullite reaches its peak value, the heating rate is reduced and the holding time is extended before cooling to obtain the finished ceramic tile. Among them, the particle distribution simulation algorithm abstracts the ingredient system into a three-dimensional grid space model. Lithium ions, cobalt ions, and nickel ions are released randomly from the boundary position as moving particles and wander randomly between grid points according to the Brownian motion law. When the moving particles reach the adjacent position of the already occupied grid point, they exhibit agglomeration behavior with an adhesion probability in the form of an exponential decay function. Among them, the fractal dimension value is calculated using the box counting method, which divides the three-dimensional space into cubic lattices with decreasing side lengths, counts the number of lattices occupied by particles at different lattice scales, and obtains the fractal dimension value by linearly fitting the slope of the number of lattices and the lattice scale in the logarithmic coordinate system. When the fractal dimension value is less than 2.8, the ball milling time is increased by 1 to 3 hours and the ball milling speed is increased by 50 to 100 rpm before the simulation calculation is repeated. When the fractal dimension value is greater than 2.8, the ball milling is stopped to obtain a homogeneous mixture.

2. The method for preparing high-hardness ceramic tiles using waste lithium battery crucibles according to claim 1, characterized in that, The firing parameter game optimization model includes an upper-level optimization model and a lower-level optimization model. The upper-level optimization model outputs the optimal heating rate parameter with the uniformity of crystal phase composition as the objective, while the lower-level optimization model outputs the optimal holding time parameter with the heat transfer efficiency as the objective.

3. The method for preparing high-hardness ceramic tiles using waste lithium battery crucibles according to claim 2, characterized in that, The upper-level optimization model and the lower-level optimization model influence each other through a heat energy accumulation coupling term, which is the product of the heating rate variable and the holding time variable.

4. The method for preparing high-hardness ceramic tiles using waste lithium battery crucibles according to claim 3, characterized in that, The firing parameter game optimization model is solved using an iterative algorithm. The initial value of the holding time variable is fixed to solve the upper optimization model to obtain the optimal heating rate parameter. The optimal heating rate parameter is substituted into the lower optimization model to obtain the optimal holding time parameter. The optimal holding time parameter is fed back to the upper optimization model to solve again. The iteration is repeated until the change in the objective function value is less than 0.

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5. The method for preparing high-hardness ceramic tiles using waste lithium battery crucibles according to claim 4, characterized in that, The crystal phase evolution prediction model is built on a graph representation learning framework, which represents the atomic arrangement structure of ceramic materials as graph structure data. Nodes in the graph represent individual atoms, and edges represent chemical bonds or physical interactions between atoms. A message passing mechanism is used to aggregate and propagate information on the graph structure.

6. The method for preparing high-hardness ceramic tiles using waste lithium battery crucibles according to claim 5, characterized in that, In the crystal phase evolution prediction model, the number of message propagation layers is determined by a weighted summation formula based on the heavy metal element content parameter, silicate raw material ratio parameter, and fractal dimension numerical parameter. The number of message propagation layers is increased when the heavy metal element content parameter is high, the silicate raw material ratio parameter deviates from the normal range, or the fractal dimension numerical parameter is low.

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