Determination and interpretation of firing temperature in ancient porcelain utilizing thermal expansion analysis

This study utilizes a multidisciplinary approach, combining simulation experiments, thermal expansion analysis, XRD, SEM, and physical property assessments to investigate the firing temperature in illitic-kaolinitic porcelain. Our findings indicate that the accuracy of the thermal expansion method depends on both the actual firing temperature and dwell time. When dwell time is uncertain, the method provides a range of possible actual firing temperatures, differing by approximately 100 °C. Remarkably, as the porcelain body nears full vitrification, the determined firing temperature tends to be notably higher. A critical analysis of previous research suggests potential overestimation of ancient kiln temperatures. Additionally, our study highlights the usefulness of bulk density, water absorption, porosity, and mullite content in determining dwell time. Overall, our research offers new insights into ancient porcelain firing processes


Introduction
The determination of firing temperatures in ancient ceramics serves as a critical avenue for understanding the technological advancements achieved in ceramic production during antiquity.Employing a plethora of scientific methodologies, including X-ray diffraction (XRD) [1], thermal expansion analysis, scanning electron microscopy [2], and infrared spectroscopy [3], researchers can unravel the intricacies of ceramic firing temperatures.Notably, while several techniques are adept at assessing the firing temperature of pottery, the thermal expansion method emerges as a preeminent choice for scrutinizing the firing temperature of porcelain.
The genesis of employing the thermal expansion method for ascertaining ceramic firing temperatures traces back to seminal works by Tite [4] and Robert [5].The thermal expansion method determines the firing temperature of ceramics by measuring their thermal expansion and shrinkage behavior during heating.This method is based on the following principle: when a ceramic sample is heated, its length changes, exhibiting thermal expansion or shrinkage.For fired ceramics, they undergo reversible thermal expansion before the heating temperature reaches the equivalent firing temperature of the initial firing.Beyond this temperature, the sample experiences irreversible shrinkage due to the onset of the sintering process.By measuring the temperature at which the ceramic sample stops expanding and begins to shrink, the equivalent firing temperature of the initial firing can be estimated.This temperature represents the degree of sintering achieved during the initial firing [6,7].
In practical measurements of the thermal expansion curves of ancient ceramics, it has been observed that some samples undergo rapid, irreversible expansion after experiencing reversible thermal expansion, without showing shrinkage.This is due to the bloating effect, often associated with phase transitions, bubble formation, and anomalous grain growth [4].At this point, the thermal expansion curve also reveals a temperature at which rapid expansion begins.Previous studies suggest that this temperature can also be used to estimate the equivalent firing temperature of the sample [8].
Predominantly composed of kaolin and illite minerals, ancient northern Chinese porcelain forms the focal point of numerous investigations utilising the thermal expansion method for firing temperature determination [8][9][10][11][12][13].Usually, the onset temperature of rapid expansion or shrinkage on the thermal expansion curve functions as the equivalent firing temperature of the porcelain [6].Existing scholarship suggests that ancient Chinese kilns in the northern regions achieved firing temperatures of 1300℃ or even 1400℃ during the Tang Dynasty.Nonetheless, delving deeper into the relationship between the onset temperature and the firing temperature warrants further inquiry.
While the concept of firing temperature is commonly used in ceramic archaeology to study ancient ceramic production techniques, ceramists recognize that firing temperature alone does not hold absolute physical significance.Most of the reactions occurring in porcelain bodies are kinetically controlled processes that do not reach thermodynamic equilibrium [14].Therefore, measuring temperature alone does not accurately reflect the heat work performed on the porcelain body.Extensive research has shown that the reactions during the ceramic firing process are influenced by a combination of particle size, time (heating rate and dwell time), temperature, and firing atmosphere [15].These factors can be understood through micro-mechanical mechanisms.
From a micro-mechanical perspective, the sintering and densification of ceramics primarily involve particle diffusion, liquid phase formation, pore shrinkage, and grain growth [16].The formation of the liquid phase, in particular, plays a crucial role in these processes.In ancient ceramic materials, some raw materials melt at lower temperatures, forming a liquid phase.This liquid phase reduces the system's viscosity, promoting particle rearrangement and closer packing.The dissolutionprecipitation mechanism is vital in liquid phase sintering.Substances in the liquid phase dissolve surface asperities of particles and then precipitate at contact points between particles, forming strong bonds.This process not only enhances particle bonding but also reduces porosity [15].Additionally, gases produced during sintering escape through the pores, further promoting densification.
At a macroscopic level, the sintering and densification of ceramics are influenced by four key factors: particle size, time, temperature, and firing atmosphere [16].Firstly, finer particles melt and diffuse more readily at high temperatures, forming a liquid phase.Thus, selecting and controlling particle size is essential for optimizing the formation and distribution of the liquid phase [15,17,18].Secondly, time and temperature are critical factors.An appropriate heating rate and dwell time, along with the correct sintering temperature, ensure that the liquid phase forms and diffuses adequately on particle surfaces, aiding particle rearrangement and densification.Lastly, the firing atmosphere significantly affects the formation and properties of the liquid phase.For instance, in a reducing atmosphere, Fe 2+ in the ceramics participates in the formation of eutectic phases or low-melting-point crystalline phases, resulting in a significant decrease in the sintering temperature of the ceramics [19].
Therefore, the firing temperature determined by thermal expansion methods is inevitably influenced by particle size, time, temperature, and firing atmosphere.Previous research has mainly focused on the effects of temperature and atmosphere on measurement results, with less attention given to the influences of particle size and time.Among these factors, dwell time assumes paramount significance in shaping firing outcomes and onset temperatures [14], yet the precise extent of its influence remains elusive owing to the absence of definitive investigations.
The dwell time profoundly impacts the physical attributes of ceramics [20].Extending the dwell time, while maintaining a consistent degree of sintering, can lower the firing temperature and consequently reduce firing costs [21][22][23].Unravelling the dwell time for ancient porcelain constitutes a pivotal facet in reconstructing bygone ceramic manufacturing techniques [24], yet scholarly investigations in this realm remain nascent.We posit that variations in firing temperatures and dwell times engender conspicuous discrepancies in the onset temperatures of thermal expansion curves and the physical characteristics of ceramics, thus facilitating inferences regarding the dwell time.This hypothesis undergoes rigorous validation in subsequent sections.
In this study, we controlled the factors of particle size and atmosphere to investigate the effects of varying temperature and dwell time on the results obtained using the thermal expansion method.We also discussed the potential impact of particle size on these measurements.Our research validates both the feasibility and limitations of using the thermal expansion method to determine the firing temperature of ancient porcelain through simulation experiments.Furthermore, we discuss strategies to enhance the interpretation of data obtained from this method.Finally, our findings highlight the significant potential of combining the thermal expansion method with assessments of porcelain's physical properties to accurately determine the dwell time in porcelain production.

Materials and methods
The chemical composition of the clay is presented in Table 1.Illite, kaolinite, quartz, and feldspar primarily constitute the clay used in this investigation, categorised as illitic-kaolinitic clay [25].(Mineral composition was semi-quantitatively determined from X-ray diffraction (XRD) patterns, depicted in Fig. S1.) We ground the clay raw material and mixed it with an appropriate amount of water to create a clay-based paste with a water content of approximately 30%.The paste was then manually shaped into uniformly-shaped ceramic samples and dried.This procedure ensured the consistency of particle size across different samples.We applied a layer of glaze to the surface.The glaze formula originates from an ancient Chinese celadon glaze.Subsequently, the samples underwent firing under varying processes.Prior to measuring the thermal expansion curves at different firing temperatures, samples were fired in an electric furnace following a specific firing protocol: heating to the maximum temperature over an 8-h period, dwelling at the maximum temperature for 5 h, followed by cooling within the furnace.The firing atmosphere maintained an oxidizing environment.The firing experiments were conducted at maximum temperatures of 1100, 1130, 1160, 1190, 1220, 1250, and 1280 °C, respectively.
The ensuing analyses employed the following methods: Thermal Expansion Analysis: The thermal expansion curves of the samples were measured using a horizontal differential thermal dilatometer (TA DIL 806).The sample dimensions for thermal expansion measurement were 10.0 mm × 5.0 mm × 5.0 mm.The heating rate of the instrument is 7 k/min.X-ray Diffraction (XRD): A TERRA-583 diffractometer (Olympus, Japan) was utilised under conditions of 45 kV voltage and 200 mA current.Prior to testing, the glaze was removed from the sample and the body was ground into a powder for analysis.Patterns were interpreted via database search using XPowder12 software (J Daniel Martín-Islán, Spain).Quantitative phase analysis was conducted using the Reference Intensity Ratio (RIR) method [26].All XRD patterns were initially subjected to background subtraction.We assumed that the sum of the mineral phase contents was 100%.The RIR values were provided by the built-in data of the software.By comparing the experimentally measured intensity ratios of each mineral phase to the standard RIR values, the relative content of each phase in the sample was calculated.
Scanning Electron Microscopy (SEM): The microstructure of the bodies was examined using a VEGA3 scanning electron microscope (TESCAN, Czech Republic) equipped with an Amptek Fast SDD X123 X-ray energy dispersive spectrometer (EDS).We cut each sample at the same location, embedded the samples in epoxy resin, and polished them after curing.The polished cross-sections of the samples were then observed.Prior to analysis, the samples were coated with a thin layer of gold to prevent charge aggregation.Backscattered electron images were captured at 20 kV voltage, while EDS analysis was conducted at 20 kV voltage.Quantification was facilitated using internal standards.

Thermal expansion curves at different firing temperatures
It is imperative to differentiate between three temperature parameters: the onset temperature ( T o ), the equivalent firing temperature ( T e ), and the actual firing temperature ( T a ).T a serves as a crucial parameter for reconstructing the firing process, representing the maximum temperature reached during firing.T o denotes the onset temperature of expansion or shrinkage acceleration on the thermal expansion curve [6], while T e signifies the constant temperature that would yield the same level of sintering (or T o ) achieved during the initial firing process [4].The determination of T e , derived from T o , is contin- gent upon T a and a (dwell time).Thus, elucidating the relationship among T o , T e , and T a is paramount.Prior to the thermal expansion analysis, simulated firing experiments were conducted as described in the Methods section.
We measured the thermal expansion curves of samples fired at various temperatures (Fig. 1, original figures can be found in the supplementary material: Original curves).It is noteworthy that, unlike single-step firing, the secondary firing induced by thermal expansion analysis modifies the reaction kinetics, consequently altering the temperature at which the liquid phase forms.The thermal expansion curves were depicted in Fig. 1a.At firing temperatures below 1160 °C, the samples underwent shrinkage followed by expansion; conversely, at higher firing temperatures, the samples solely exhibited expansion.There are various methods for determining the onset temperature [6,10].We drew tangents on the reversible and irreversible expansion curves of the thermal expansion graph and used the intersection point of these tangents to determine the onset temperature.If the irreversible expansion curve exhibits significant fluctuations, the onset temperature is directly determined based on the points of significant fluctuation.Previous research has established that when the firing temperature exceeds the vitrification threshold, the disparity between T o and T e remains relatively constant [4].Figure 1b demon- strated the relationship between T o and T e under the con- dition of a 5-h dwell time and firing temperatures outside the range of 1160-1220 °C: The error in the above equation was approximately 20 °C.However, within the temperature range of 1160-1220 °C, T o is more than 100 °C higher than T e (Fig. 1b), thus relying solely on the thermal expansion curve to determine the firing temperature at this point would result in an overestimated measurement.Previous studies have indicated that this phenomenon is related to bloating of the body [4], but the underlying causes require further investigation.Currently, we were unable to ascertain the range of T a as we must also consider the influence of dwell time ( a ) on T o .

Microstructural analysis of bodies
We conducted a microstructural analysis of the bodies to elucidate the limitations encountered by the thermal expansion method within the temperature range of 1160-1220 °C. Figure 2 illustrated the microstructure of bodies at various firing temperatures.Notably, at 1100 °C and 1130 °C, the body exhibited numerous tiny pores and a plethora of unmelted quartz particles.As the firing temperatures ascend between 1160 °C and 1220 °C, the abundance of tiny pores decreased, and the edges of quartz particles became more discernible, indicative of enhanced quartz particle melting.Furthermore, the emergence of numerous holes in the body became apparent as the firing temperature reaches 1280 °C.At elevated temperatures, the body's viscosity decreased significantly, while gases generated from mineral decomposition accumulated, resulting in the formation of numerous holes.
The bodies at all firing temperatures primarily consisted of quartz and mullite (Fig. 3a, original figures can be found in the supplementary material: XRD patterns).Notably, as the firing temperature surpassed 1130 °C, there was a substantial increase in mullite content and a decrease in quartz content within the body (Fig. 3b).In ceramic materials, mullite predominantly exists in two morphologies: cuboidal primary mullite (2:1 mullite) and elongated secondary mullite (3:2 mullite) [28].The formation process of mullite as the temperature increases can be outlined as follows: Between 900 °C and 1000 °C, metakaolin decomposes to form γ-alumina and amorphous silica, resulting in the formation of an Al-Si spinel phase.Around 1000-1200 °C, this Al-Si spinel gradually transforms into 2:1 mullite, releasing amorphous silica.Above 1200 °C, 2:1 mullite further converts into 3:2 mullite.This transformation involves the reabsorption of amorphous silica and the redistribution of aluminum and silicon ions, ultimately forming stable 3:2 mullite [14,29].Primary mullite can serve as a seed for the nucleation of secondary mullite [30].We subsequently discussed the implications of these findings on the limitations of the thermal expansion method.

The effect of dwell time on T o
Our results indicated a significant effect of dwell time ( a ) on T o .The samples were fired at 1100 °C with varying dwell times, and their thermal expansion curves were measured, as depicted in Fig. 4a.At a dwell time of 0, T o was recorded at 1080 °C, markedly lower than the other measured values.However, when the dwell time exceeded 1 h, T o essentially converged, stabilizing around 1180 °C.
Figure 4a also revealed that a single determined T o could correspond to multiple values of T e and a , a phe- nomenon previously overlooked in studies on porcelain firing temperature determination.Hence, we proceeded to establish the variation curve of T e with dwell time when T o was maintained at 1180 °C (with an error mar- gin within ± 10 °C).
The samples were heated to 900 °C over a period of 5 h, then subjected to a heating rate of 2 °C/min until reaching the maximum temperature, where they were held for varying dwell times before undergoing cooling Figure 4b demonstrated that T e stood at 1180 °C when T o was 1180 °C and the dwell time was zero.With increas- ing dwell time, T e gradually decreased, albeit not indefi- nitely.Beyond a dwell time of 2 h, T e remained relatively unchanged at approximately 1100 °C.Thus, the actual firing temperature ( T a ) was anticipated to fall within these two limit values, yielding the following relationship: In this study, when T o was 1180 °C, the actual fir- ing temperature of the samples was expected to fall T e (a = 0)≥ T a ≥ T e (a = 2) between 1100 °C and 1180 °C.This underscores how the results obtained from the thermal expansion method for determining porcelain firing temperature are influenced by both the actual firing temperature and dwell time.In the absence of a precise determination of the dwell time, the T a or T e measured by the thermal expansion method is likely to represent a range value, with the upper and lower limits differing by approximately 100 °C.This highlights the inadequacy of previous studies that directly used T o to represent T a or T e , potentially leading to an over- estimation of the true firing temperature of ancient porcelains.Furthermore, our findings suggest that the thermal expansion method serves as an effective Fig. 4 a Thermal expansion curves (first-order differential curves) of samples at T a =1100 °C with various dwell times listed on the left; b plot of T e versus dwell time at T o =1180 °C means of determining the lower limit of the actual firing temperature (Fig. 4b).

Possibility of dwell time determination
Given the significant impact of dwell time on the determination of firing temperature in ancient porcelains, estimating the dwell time of these artifacts becomes imperative.However, a notable dearth of relevant studies exists.We hypothesized that different firing processes might yield varying physical properties in porcelain, prompting us to ascertain the bulk density, water absorption, porosity, and mullite content of the samples in relation to dwell time.
The samples with T o of 1180 °C were categorised into three groups based on firing temperature and dwell time: Group A comprised samples from groups (1180 °C, 0 h) and (1160 °C, 0.25 h); Group B encompassed samples from groups (1140 °C, 0.5 h), (1120 °C, 1 h), and (1100 °C, 2 h); and Group C consisted of samples from groups (1100 °C, 3 h) and (1100 °C, 5 h).Group A exhibited the highest firing temperature and shortest dwell time, whereas Group C featured the lowest firing temperature and longest dwell time.The results of these samples were depicted in Fig. 5 (Refer to Tables S1 and S2 for specific data).
From Group A to Group C, the bulk density of the samples exhibited a decreasing trend followed by an increase (Fig. 5a).Conversely, water absorption (Fig. 5b) and porosity (Fig. 5c) demonstrated the opposite pattern.However, regardless of the attribute, Group B markedly differed from both Group A and Group C. Generally, the bulk density of the body exhibited a positive correlation with heat absorption, while water absorption exhibited a negative correlation with heat absorption until the ceramic body reached optimal conditions.Consequently, although the T o values of the three groups were consistent, the heat absorption of Group B was notably the lowest.Regarding mullite content (Fig. 5d), there was little disparity between Group A and Group B, whereas the content of Group C surpassed that of the other two groups.
Given that the data for Group A and Group C overlapped, we conducted a two-sample mean consistency test (refer to supplementary material Two Sample t-test).The calculated p-values were 0.02 (water absorption), 0.02 (porosity), and 0.03 (mullite content), all of which were below the significance level of 0.05.Consequently, a statistically significant difference was observed between Group A and Group C.
This result suggests the feasibility of determining the dwell time of ancient porcelains, as porcelain sherds with varying dwell times exhibited distinct physical properties for a given T o .This can be further articulated through the following relation: Here, P represents a physical property, such as bulk density or water absorption.If functions f 1 and f 2 are defined in a manner that prevents the two equations from being related by a simple transformation, then T a and a typically have unique solutions.Our results une- quivocally demonstrate this assertion.

Limitations of the thermal expansion method for the determination of porcelain firing temperature
Our investigation revealed that the thermal expansion method faced challenges in accurately determining the firing temperature of the samples when T e fell within the range of 1160-1220 °C, with correspondingly high T o measurements observed during this period.This phe- nomenon can be attributed to changes occurring in the ceramics' firing process.
Prior to achieving full vitrification, the ceramic body experiences a rise in both the liquid phase and bulk density, accompanied by a decrease in water absorption and porosity, resulting in shrinkage observed in the thermal expansion curve of the body.Upon complete vitrification, the porosity of the ceramic body increases, leading to bloating effects and subsequent expansion in the thermal expansion curve [27,31,32].The initial shrinkage of the body is attributed to the formation of the liquid phase, disappearance of the gaseous phase, and melting of quartz crystals [33].Conversely, body expansion is caused by the formation of the gaseous phase and mullite [34].The predominant gases in the body originate from the decomposition of minerals [35].When the firing temperature surpasses 1200 °C, the viscosity of the kaolin body diminishes significantly, facilitating the accumulation of gases to form larger pores, thereby inducing substantial body expansion [36].In fact, the bubbling of low-iron illite clay is commonly utilized in industrial applications to manufacture expanded clay balls for use in vehicle soundproofing panels.
Our findings indicate that samples fired within the range of 1160 °C-1220 °C exhibited the lowest porosity (Fig. 2), suggesting proximity to the complete vitrification temperature of this body.Additionally, at temperatures above this range, a significant number of pores formed within the body (Fig. 2f ).Moreover, the mullite content increased with temperature (Fig. 3).Therefore, within the range of 1160 °C-1220 °C, as the shrinkage force diminishes and the expansion force intensifies, the opposing effects of shrinkage and expansion result in an inability of the thermal expansion method to accurately measure T o , leading to elevated measured values.However, to truly understand the microstructure of porcelain, future studies involving transmission electron microscopy (TEM) images and diffraction patterns are essential.
The aforementioned temperature range (1160 °C-1220 °C) can be termed the failure range of the thermal expansion method.We further analyzed the practical factors that might affect the accuracy of the thermal expansion method.(1) Raw materials.Changes in clay raw materials can alter the temperature at which the liquid phase forms.For instance, if the raw material contains a high amount of potassium feldspar, according to the K 2 O-Al 2 O 3 -SiO 2 phase diagram, the lower liquid phase formation temperature in this system will reduce the complete vitrification temperature [14,37], thereby lowering both the upper and lower limits of the failure range.(2) Particle size.When the raw materials of the body are the same, the complete vitrification temperature of a body with smaller particles is lower than that of a body with larger particles [17], resulting in different failure ranges.Therefore, even if all other conditions are identical, there may still be significant discrepancies in the equivalent firing temperature measurements between the two.(3) Firing atmosphere.When the raw material contains a high amount of Fe 2 O 3 , the liquid phase formation temperature decreases in a reducing atmosphere.This alteration affects the failure range and may even change the difference between the onset temperature and the equivalent firing temperature ( T o − T e ), leading to inaccurate temperature measurements.
Our results suggest that the firing temperature of porcelain, as measured by the thermal expansion method, may significantly exceed the actual temperature when the firing temperature approaches the full vitrification temperature of the body.In practical applications, if a substantial contraction is observed in the thermal expansion curve, accurate determination of the firing temperature can be achieved.Conversely, if only expansion is noted in the thermal expansion curve, it is imperative to consider the potential for an excessively high measured value.

New interpretation of firing temperature data for ancient porcelain wares
The thermal expansion method is widely employed for determining the firing temperature of ancient porcelain.Before the Song Dynasty (960-1279 A.D.) in ancient China, many significant kilns in northern China utilized kaolin clay as the raw material for body making.Previous studies have indicated firing temperatures of these kaolin porcelains exceeding 1300 °C, with some even surpassing 1400 °C [9][10][11].However, most studies directly equate the onset temperature with the actual firing temperature when measuring porcelain firing temperature, often overlooking the influence of dwell time, potentially leading to an overestimation of the firing temperature.
In a study on white porcelain from the Xing kiln of the Tang Dynasty (618-907 A.D.) [11], researchers systematically measured the firing temperatures of coarse and fine white porcelain spanning the Middle and Late Tang Dynasty to the Five Dynasties period (907-960 A.D.).They discovered that the average firing temperature of coarse white porcelain during the Mid-Tang period ranged between 1260 and 1300 °C, whereas that of fine white porcelain was 1360 °C.In the Late Tang-Five Dynasties period, both coarse and fine white porcelain exhibited an average firing temperature of 1300 °C.Based on these findings, researchers speculated that coarse and fine white porcelain were fired together in the same kiln during the Late Tang-Five Dynasties period, whereas they were fired separately during the Mid-Tang period.The firing technology for fine white porcelain had evidently advanced to temperatures exceeding 1400 °C, indicating a high level of firing technology.However, it remains uncertain whether different kilns were utilized for firing, as both types of porcelain originated from the same archaeological context.Therefore, solely considering firing temperature makes it challenging to discern the techniques contributing to such significant differences in firing temperatures between the two types of porcelain.Hence, we propose a novel perspective for analyzing this issue based on dwell time.
As mentioned earlier, the onset temperature on the thermal expansion curve is influenced by both firing temperature and dwell time.With a constant firing temperature, the difference in onset temperature resulting from varying dwell times can reach up to 100 °C.The average firing temperature difference between coarse and fine white porcelain during the Mid-Tang period is 60 °C, which may suggest similar firing temperatures but differing dwell times.Fine white porcelain likely underwent a longer dwell time, leading to a higher onset temperature and improved physical properties.Additionally, variations in onset temperature between coarse and fine white porcelain may also stem from differences in clay raw material, necessitating further simulation experiments for validation.
Ancient literature also contains records of the porcelain firing process."Tao Shuo" ("陶说"), authored by Zhu Yan in the Qing Dynasty (1616-1911), documents that ancient Yue kiln porcelain was fired vigorously for 1 to 2 days and nights during the high-temperature stage."Tian Gong Kai Wu" ("天工开物"), written by Song Yingxing (1587-?), states that ancient porcelain required firing for 24 h.These records suggest prolonged firing periods in ancient kilns, implying that the onset temperature measured by the thermal expansion method may exceed the actual firing temperature.Furthermore, "Tian Gong Kai Wu" mentions the practice of kiln workers removing an artifact (known as "huo zhao ( 火照)") at high temperatures to assess heat sufficiency and decide whether to cease firing.This implies that, with a consistent kiln structure, ancient kiln workers likely regulated porcelain heat absorption by adjusting dwell time rather than raising the firing temperature by 100 °C during the high-temperature stage.By amalgamating ancient literature with our experimental data, we posit that the firing temperature of porcelain in ancient northern China may be lower than the onset temperatures determined by the thermal expansion method, although further data is required to substantiate this hypothesis.
Direct measurement of dwell time for ancient porcelain would enhance our understanding of the firing process and temperature.However, there is currently a gap in measuring dwell time.Our study demonstrates the significant potential of combining the thermal expansion method with physical property measurements in determining porcelain dwell time.The data clearly illustrates that, with identical onset temperatures, samples with varying dwell times absorb different amounts of heat, resulting in distinct physical properties.These disparities enable us to estimate porcelain dwell time effectively.However, it is important to recognize that the firing of porcelain is a complex process, with the dwell time being influenced by various factors such as the uniformity of heat conduction in the kiln and the size of the fired objects.Consequently, it is challenging to directly compare samples fired in modern electric kilns with those fired in ancient times.Nevertheless, our results demonstrate the potential for determining the dwell time.Additional simulation experiments are essential to verify the feasibility of this method for determining dwell time at various firing temperatures.

Conclusion
This paper has examined the feasibility and constraints of employing the thermal expansion method for determining the firing temperature of illitic-kaolinitic porcelain, shedding light on its limitations through simulation experiments.It elucidated the substantial impact of dwell time on the thermal expansion method's outcomes.In instances where the dwell time of ancient porcelain remained uncertain, only a range of actual firing temperatures could be inferred based on the onset temperature provided by the thermal expansion method, with an approximate deviation of 100℃ between the upper and lower limits of this range.Historically, many studies investigating the firing temperature of ancient porcelain neglected to consider the influence of dwell time, potentially resulting in inflated measured values relative to the actual firing temperature.Furthermore, this study underscored the potential significance of bulk density, water absorption, apparent porosity, and mullite content in elucidating the dwell time of porcelain.Future simulation experiments could delve deeper into the alterations in physical properties and mineral composition of porcelain crafted from diverse raw materials under varying firing conditions.This comprehensive exploration would facilitate a nuanced discussion on the feasibility of employing this method to determine the dwell time of ancient porcelain.However, it is important to acknowledge a limitation of this approach, namely, the possibility that the raw materials utilized in simulated samples may not precisely mirror those of ancient porcelain, thus warranting further examination of the applicability of simulation results to ancient materials.

Fig. 1
Fig. 1 Thermal expansion curves of samples at different firing temperatures: a thermal expansion curves; b first-order differential curves, with onset temperatures listed on the right side.Firing temperatures are indicated on the left side of each curve

Fig. 2
Fig. 2 Electron microscope images of samples at different firing temperatures.The labels indicate the firing temperature of the samples.The scale bar is placed in the lower right corner of each image

Fig. 3 a
Fig. 3 a XRD patterns of samples at varying firing temperatures, with the firing temperatures listed on the left; b semi-quantitative analysis of mineral content in samples at different firing temperatures

Fig. 5
Fig. 5 Statistical plots of parameters for three sample groups: (a) bulk density, (b) water absorption, (c) apparent porosity, (d) mullite content.The mean and standard deviation for each group were presented in the figures

Table 1
Chemical and mineralogical analyses of raw materials used in this work