Accelerated thermal history analysis of light-burnt magnesium oxide by surface properties

Homogeneity is of utmost importance in some applications of light-burnt magnesia (LBM), such as shrinkage compensation of cement composites, because if it is not detected reliably before application, it causes unpre-dicted expansion and cracking. This paper presents an accelerated method for homogeneity and thermal history detection in LBM. The proposed method provides an equation for computing the weighted mesopore probability distribution of light-burnt magnesia (LBM). Then, it deconvolutes the distribution ’ s peaks by Lorentz peak functions to analyze homogeneity. The method ’ s performance is evaluated by examining LBM samples produced by calcining magnesite at four temperatures and walking through several scenarios, including the mixtures of these samples. The results confirmed that the method accurately detects inhomogeneity and gives calcination temperatures and percentages of fractions of magnesia mixtures. These findings make it possible to prevent unpredicted expansion in cement composites incorporating expansive magnesia and can be employed to detect inhomogeneities in other porous materials applications.

Light-burnt magnesia (LBM) is usually produced by calcining magnesite at temperatures lower than 1000 • C. It accounts for one-third of magnesia applications and has high chemical activity. LBM has two significant applications in construction industry: Firstly, it is used as an expansive agent to compensate shrinkage of concrete. Carefully calcined LBM acts as an expansive agent and produces expansion at a rate closely matching the long-term shrinkage of concrete to prevent concrete cracking [30]. Secondly, LBM is used as a primary ingredient to produce Sorel cements. More information on the application of LBM in concrete is provided in the recent reviews by Walling and Provis [31], Mo et al. [32] and Du [33]. It is now well established that variation in the thermal history of LBM, significantly affects the properties of the final application products [34]. Cao et al. specified the importance of information on the thermal history of LBM and introduced an LBM reactivity assessment technique based on reaction with an ethylic buffer solution [35]. They studied the hydration characteristics and expansive mechanism of LBM [36] and evaluated the hydration procedure of LBM on the expansive behavior of shrinkage-compensating mortar [37].
Much of the current literature on LBM pays particular attention to the assessment of the average reactivity of LBM. Mo et al. [38] studied calcination of magnesium oxides and reported the change in porosity and crystal structure of magnesia due to calcination temperature. Harper used iodine number to index reactivity as used by American magnesia industry [23]. Alegret et al. [39] proposed potentiometry to study reactivity of magnesia. Hirota et al. [40] characterized sintering of magnesia by crystallite size, particle size, and morphology. Kim et al. [41] studied the transformation of the crystal structure of MgCO 3 and Mg(OH) 2 to MgO during calcination. Zhu et al. [42] proposed a corrected MgO hydration convention method for reactivity assessment. Chau et al. [43] introduced an accelerated reactivity assessment method based on the time required for acid neutralization of magnesia.
Surprisingly, none of the current LBM reactivity analysis methods provides information on thermal history.
The current study aims at filling this research gap by studying surface properties and analyzing the highly porous structure of LBM formed during calcination. This highly porous structure is thanks to the pseudomorphous calcination of magnesite and is identifiable by gas physisorption techniques [44][45][46][47]. Here, the nonlocal density functional theory (NLDFT) is used to compute the mesopore size distribution of LBM. NLDFT allows a better explanation of the adsorption and phase transitions in small mesopores, compared to classical Kelvin equation-based methods [48,49]. The proposed method provides an equation that weights this NLDFT data to compute the weighted mesopore probability distribution and deconvolutes the peaks of the distribution by Lorentz peak functions.
Four LBM samples are produced by the calcination of magnesite at 600 • C, 700 • C, 800 • C, and 900 • C. First, their adsorption mechanisms are studied by analyzing physisorption isotherm, BET surface area, C parameter, and alpha-s method. The samples' pore size distributions are computed by using nonlocal density functional theory (NLDFT). Next, their weighted mesopore probability distributions are computed and curve-fitted by Lorentz peak functions. Then, the weighted mesopore probability distributions of several scenarios, including the mixtures of these LBM samples, are analyzed. Finally, the distributions are deconvoluted by Lorentz peak functions, and a set of criteria for assessing homogeneity and thermal history of light-burnt magnesia is presented. This study shows how to use surface properties to characterize the thermal history of light-burnt magnesia, which is suitable for application in the construction field to produce Sorel cements and expansive magnesia.

Materials
The current investigation involved producing light-burnt magnesia by thermal decomposition of magnesite at 600 • C, 700 • C, 800 • C, and 900 • C. The magnesite was obtained from the company Magnesia (Germany). The calcination was effected in a muffle furnace and the residence time was 24 h to ensure that the influence of residence time on the samples is negligible, and only calcination temperature controls the properties of samples. The calcination temperatures have been indicated in sample designations throughout this paper. For example, M600 refers to the sample calcined at 600 • C. Fig. 1 demonstrates the mineral crystalline phases of the samples, measured by X-ray Diffraction (XRD). The diffraction patterns were obtained using a Bruker ENDEAVOR diffractometer, equipped with a Co-radiation source, divergence slit (0.5 • ), soller slit (0.04 rad), and Lynxeye detector. The main crystalline phase of the samples is periclase. The main peak of periclase was utilized to compare the crystal grain sizes of the samples, using the Scherrer equation [50]. The average periclase crystallite size of M600 was 7.0 nm. The average periclase crystallite size of M700, M800, and M900 were 1.28 (9.0 nm), 1.68 (11.8 nm), and 1.93 (13.5 nm) times as big as those in M600, respectively. Fig. 2   samples, taken by an environmental scanning electron microscope (ESEM). Micrographs were recorded by both secondary and backscattering electron detectors (MIX mode) at 5 kV with a spot of 3.0. In addition, four mixtures of LBM were prepared to investigate the applicability of the studied methods in characterizing homogeneity. Table 1 shows the composition of these mixtures.

Adsorption mechanism
Before measuring physisorption isotherms, possible contaminants on the surface of the samples were removed by a combination of heat (120 • C) and flowing nitrogen gas for 4 h. When weighing the samples, a sample quantity that yields at least 10 m 2 was prepared for good precision. This amount ensured reasonable pressure difference thanks to sufficient gas adsorption by the adsorbent at each step [51].
After sample preparation, adsorption and desorption isotherms were measured at 77 K using a Micromeritics TriStar II analyzer. The adsorption isotherms were plotted using [48] V a m s = f with V a the amount of adsorbate, m s the mass of solid, p the actual adsorbing gas pressure, p 0 the saturation pressure of the adsorbing gas at T, and T the thermodynamic temperature [48]. Point B was shown on the measured physisorption isotherms as the point where the adsorption isotherms become linear [52]. In order to obtain the BET surface area, the linear transformed BET equation was used by the formula [48] with V a the amount of adsorbed gas at the equilibrium pressure p, V m the monolayer capacity, C a constant, and p and p 0 as used previously [48]. From Eq. (2), a plot of p V a (p 0 − p) versus p p 0 was made to obtain a straight line with intercept 1 VmC and slope C− 1 VmC to calculate the values of V m and C. The BET specific surface area then was calculated by [48] with σ the mean molecular cross-sectional area (0.163 nm 2 for nitrogen molecule), L the Avogadro constant (6.02214 × 10 23 mol − 1 ), m s the mass of adsorbing sample, V 0 the gas molar volume (22,414 cm 3 ), and V m as used previously.
To obtain the surface area by α s curve, the standard data of a

Table 1
The composition of LBM mixtures (in weight percent).
nonporous specimen were obtained from Bhambhani et al. [53]. Next, the α s of the reference data was obtained from [52] with V a ref the amount of adsorbate in the standard data, and V 0.4 ref the amount of adsorbate at the pre-selected relative pressure of 0.4 in the standard data.
Then, the α s curve of the sample was constructed by specifying at similar relative pressures the value of α s of the standard data and the value of V a of the sample. Finally, a plot of V a versus α s was made to yield the α s curve.
The surface area of samples was calculated from the α s curve by [52] a ∝s = s test s ref

Pore structure
A complete mesopore size distribution was computed by the nonlocal density functional theory (NLDFT) method. In the NLDFT method, the pore size distribution was obtained by [48] N exp the measured number of adsorbed molecules and N theo the kernel of theoretical isotherms in model pores [48]. The computation procedure for pore size distribution by the NLDFT method can be found in Rouquerol et al. [48]. The NLDFT computations were done with a kernel, based on nitrogen adsorption at 77 K on graphitic carbon having slit-shaped pores, using the Tristar 3020 analysis program.

Adsorption mechanism
The physisorption isotherms of the samples are displayed in Fig. 3. Each graph consists of adsorption and desorption isotherms. All the adsorption isotherms are initially concave, then become linear, and finally convex to the p p 0 axis. All the desorption isotherms do not retrace the adsorption isotherms and create hysteresis loops. The hysteresis loops occur thanks to the intrinsic difference between the curvature of the liquid surface of condensate, from which the desorption occurs, and nucleation on the solid pore walls, from which multilayer adsorption and condensation starts [51]. This curvature hampers evaporation from the liquid surface, and therefore, the desorption isotherm falls behind the adsorption isotherm and leads to a hysteresis loop [51].
According to IUPAC recommendations, the general form of physisorption isotherms classifies adsorbents into six types [54]. Based on the measured physisorption data, all the four magnesia preparations belong to a Type IV-a class. Type IV isotherms initiate similar to Type II isotherms but have a characteristic plateau at higher relative pressures. They are a characteristic of mesoporous materials [48]. BET surface area. The selected range of linearity of the BET plot was within the relative pressures of 0.05-0.2, according to Gregg and Sing [52]. All the preparations were well captured by the linear transformed BET model (R 2 > 0.99). As mentioned earlier, the y-intercept and the slope of the lines in Fig. 4 were used to calculate the monolayer capacity and C parameter from Eq. (2) and Eq. (3). Table 2 compares and contrasts the BET surface area (a BET ) and C parameter of the samples. The BET surface area decreases with increasing calcination temperature. The parameter C provides useful information about the shape of the isotherm in the BET range. If the parameter C is less than 2, the competition between the gas-solid affinity and gas-gas affinity makes the BET method inapplicable [54]. On the other hand, a parameter C higher than 150 indicates high energy sites on the surface of micropores [54]. The beginning of the linear section of the adsorption isotherm indicates the monolayer completion and is usually referred to as Point B [54]. A parameter C of at least 80 indicates a rather explicit Point B [48,54]. The C parameter of M900 is just over 150, but as shown in Fig. 5, the monolayer capacity and Point B were in substantial agreement. The parameter C of the samples remains in the range of 80-150, Point B is demonstrable as a single point, and the value of monolayer capacity (V m ) is validated.
The first half of the adsorption isotherms of Fig. 3 are illustrated in Fig. 5. High energy sites on the surface of the samples cause the initial steep rise in the isotherms. This steep rise diminishes as the high-energy sites are covered. As predicted from the value of parameter C, the monolayer capacities of the samples (V m ), represented by horizontal dashed lines, are in substantial agreement with point B of the samples. curves is an indication of a non-microporous sample. The upward deviation from the linear section in the curves is due to capillary condensation [48]. The calculated surface area of the samples (a αs ) was determined by incorporating the slopes of these linear sections into Eq. (5). The results of this calculation are listed in Table 3.
The α s curves give an independent evaluation of the total available surface area in a mesoporous material or the external area in a microporous material [48]. Table 3 compares the surface area (a αs ), calculated from the physisorption isotherms and α s plots, to the BET surface area.
The small difference between the values of a αs and a BET in the samples suggests that almost all the surface area in the samples is external and that the adsorption mechanism is mainly governed by mesopores.

Pore structure
As outlined earlier in the Introduction, the nonlocal density func-     tional theory (NLDFT) is implemented to compute the mesopore size distribution of LBM samples. The mesopore size distribution is [55] I (w i ) = δV i (7) with δV i the i-th mesopore volume increment, and I (w i ) the mesopore size distribution. As can be seen in Fig. 7, on the whole, all the samples are highly mesoporous. This is explained by the pseudomorphous calcination of magnesite, in which magnesia retains the external shape and volume of magnesite [56,57] and is consistent with the studied adsorption mechanisms in the previous section. It is also apparent that the distributions shift to the right at higher calcination temperatures, and their peaks become smaller. The change in the pore structure of the samples at higher calcination temperatures is due to shrinkage and sintering [56,57] and is in line with the previously discussed change in the physisorption isotherms and surface area. The cumulative mesopore size distribution of the samples is expressed by the sum of the mesopore volume increments in the form [55] with C(w i ) the cumulative mesopore size distribution and δV i as used previously. As illustrated by Fig. 8, the pore structure alteration caused by shrinkage and sintering causes the total mesopore volume to decrease at higher calcination temperatures. It is also evident that the median mesopore width of the distribution shifts to the right at higher calcination temperatures.
In order to use the shift of the distributions in Figs. 7 and 8 to characterize the homogeneity of the samples, inspecting the probability density functions (PDFs) is constructive. The mesopore probability distribution of the samples is [55] with V tot,m the total mesopore volume, δw i the i-th pore width increment, P(w i ) the mesopore probability distribution (probability density func-  tion), and δV i as used previously. The mesopore probability distribution of the samples is reported in Fig. 9. The shift in the distribution peaks at different calcination temperatures can be used to form a hypothesis that, similar to the phase quantification in X-ray powder diffraction, convolution-based profile fitting can be utilized to analyze the homogeneity of the samples. Unlike XRD profiles, there is only one peak in the mesopore probability distributions of the samples. Furthermore, the peaks shorten at higher calcination temperatures and make convolution-based profile fitting less accurate. To overcome this issue, the distributions need to be weighted with a weighting factor. This weighting factor should give higher weights to distributions of higher calcination temperatures. As distribution peaks of the higher calcination temperatures occur at wider pore widths, this study proposes to choose a factor of the pore width (ln 10 • w i ) as the weighting factor.
The weighted mesopore probability distribution is [55] L(w i ) = 2.3 P(w i ) • w i (10) or with L(w i ) the weighted mesopore probability distribution, w i , P (w) , V tot,m , and δV i as used previously. Since 2.3 δVi δwi • w i in Eq. (4.11) is replaceable with δVi δ log(wi) the proposed equation for weighted mesopore probability distribution, in simplified terms, is As illustrated by Fig. 10, the weighted mesopore probability distributions' peak heights are almost equal (about 4). This facilitates identifying hidden peaks by deconvolution in inhomogeneous samples. The dashed lines represent the best Lorentz fit to the data. The Lorentz peak function usually is written as with y 0 the offset from the y-axis, A the area of the function, W the full width at half maximum (FWHM), and x c the center of the function. All the distributions could be well captured by this function (adjusted R 2 greater than 0.99). The Lorentz peak functions' parameters, namely center, FWHM, and area, are compared and contrasted in Fig. 11. On the whole, all the parameters increase with the increase in the calcination temperature. For example, the centers of the functions in M600 and M700 are at 7.3 nm and 10.3 nm, respectively, and move to 13.7 nm and 15.4 nm in M800 and M900. The same trend holds true for the area of the functions at different temperatures, as well. Later in this study, the center of these Lorentz fits is used to indicate the calcination temperature of fractions in inhomogeneous samples, and the area of the Lorentz fits is employed to calculate the weight percentages of these fractions.
To verify the methodology, Fig. 12 shows the weighted mesopore probability distribution of the LBM mixtures. The percentage of LBM fractions has been indicated in the mixture designations. For example, M600 (50%)+M900 (50%) is a mixture consisting of 50% M600 and 50% M900. The dashed and dotted lines represent the best Lorentz fits to the data. The properties of each peak are calculated by deconvoluting the distribution by Lorentz peak functions and reiterating peak deconvolution using the Levenberg Marquardt algorithm. All the distributions were well captured by the cumulative fits (adjusted R 2 greater than 0.94).
The centers of the Lorentz fits of Fig. 12 are demonstrated in Fig. 13. The horizontal dashed lines represent the centers of the Lorentz peak functions used for deconvoluting the weighted mesopore probability distributions of unmixed magnesia preparations in Fig. 10. It is evident that the centers of cumulative Lorentz fits are almost identical to those of unmixed LBMs. For example, the centers of the Lorentz fits in both M600 (50%)+M900 (50%) and M600 (80%)+M900 (20%) compare well with the centers of unmixed M600 (7.3 nm) and M900 (15.4 nm). As another example, the centers of the Lorentz fits in both M600 (50%)+M800 (50%) and M600 (80%)+M800 (20%) compare well with the centers of unmixed M600 (7.3 nm) and M800 (13.7 nm), as well. These results provide evidence that deconvoluting the weighted mesopore probability distribution of light-burnt magnesia by Lorentz peak functions is an accelerated method to analyze homogeneity and thermal history.
The percentage of each fraction in LBM mixtures is with A cumulative fraction i the area of the i-th Lorentz fit in the cumulative fit (captured from Fig. 12) and A unmixed fraction i the area of the i-th Lorentz fit in its unmixed form (captured from Fig. 10). Table 4 lists the computed percentage of each fraction in LBM mixtures. It is evident that the predicted percentages are in excellent agreement with real values. In addition, these results confirm that the proposed method quantifies the homogeneity of LBM.
LBM mixtures containing M600 and M700 were not studied here since the inhomogeneity caused by a large temperature gap (say M600  and M900 or M600 and M800) is more critical than one caused by a slight temperature gap (say M600 and M700). When the temperature gap is short, the weighted mesopore probability distribution peaks are close. This may not affect the accuracy of the deconvolution method at high inhomogeneity dosages (say 50% M600 plus 50% M700). However, it may reduce its accuracy at low inhomogeneity concentrations (say 80% M600 plus 20% M700).
This study indicates the benefits of deconvoluting the weighted mesopore probability distribution by Lorentz peak functions to analyze the homogeneity of light-burnt magnesia. The proposed method is a cost-effective accelerated detection tool for detecting inhomogeneities in light-burnt magnesia. As the pseudomorphous structure of calcined magnesia provides the foundation of this method, the proposed method can be applied to a wide range of pseudomorphous materials to detect inhomogeneities.
However, some limitations are worth noting. This study only analyzed the light-burnt magnesia produced by calcining magnesite. The magnesia produced by calcining other magnesium compounds such as brucite has a different pore structure [41]. Furthermore, the presence of some gases, such as water vapor, may significantly influence the   structure of calcination products [47]. In addition, the presence of impurities in the parent solid may promote sintering [20]. Further research may include the influence of parent solid, impurities in the parent solid, and the calcination atmosphere to provide calibration curves for the method presented here.

Conclusions
In this study, a new technique for identifying and quantifying the homogeneity and heat treatment history of light-burnt magnesia (LBM) produced from the calcination of magnesite is reported. The method provides equations (i.e., Eqs. (12) and (14)) for computing the weighted mesopore probability distribution of LBM and analyzing the peaks present in the distribution to examine homogeneity. The properties of each peak are calculated by deconvoluting the distribution by Lorentz peak functions and reiterating peak deconvolution using the Levenberg Marquardt algorithm. Based on the results obtained, the following conclusions can be drawn.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.