Cement and Concrete Research 79 (2016) 344–352
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In situ synchrotron powder diffraction study of the setting reaction kinetics of magnesium-potassium phosphate cements Alberto Viani a,⁎, Marta Peréz-Estébanez a, Simone Pollastri b, Alessandro Francesco Gualtieri b a b
Institute of Theoretical and Applied Mechanics ASCR, Centre of Excellence Telč, Batelovská 485, CZ- 58856 Telč, Czech Republic Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Sant’Eufemia 19, I-41121 Modena, Italy
a r t i c l e
i n f o
Article history: Received 20 April 2015 Accepted 16 October 2015 Available online 14 November 2015 Keywords: Kinetics (A). Reaction (A) X-Ray Diffraction (B) MgO (D) Chemically Bonded Ceramics (D)
a b s t r a c t This work reports a kinetic study of the formation of magnesium-potassium phosphate cements accomplished using in-situ synchrotron powder diffraction. The reaction: MgO + KH2PO4 + 5H2O → MgKPO4 · 6H2O was followed in situ in the attempt of contributing to explain the overall mechanism and assess the inﬂuence of periclase (MgO) grain size and calcination temperature (1400-1600 °C) on the reaction kinetics. Numerical kinetic parameters for the setting reaction have been provided for the ﬁrst time. The best ﬁt to the kinetic data was obtained using a weighted nonlinear model ﬁtting method with two kinetic equations, representing two consecutive, partially overlapping processes. MgO decomposition could be described by a ﬁrst order (F1) model followed by a Jander diffusion (D3) controlled model. Crystallization of the product of reaction was modelled using an Avrami model (An) followed by a ﬁrst order (F1) chemical reaction. A reaction mechanism accounting for such results has been proposed. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Magnesium-potassium phosphate cements (MPCs) are chemicallybonded ceramics (CBCs) [1,2]. Because of their peculiar properties, like high early age and long term strengths, good water resistance, high adhesive properties and afﬁnity for cellulose materials [3,4], they have been considered attractive for many applications [5–14]. Like other CBCs, they harden at room temperature as a consequence of the acidbase aqueous reaction between magnesium oxide and acid potassium phosphate. When MgO (periclase) reacts with potassium di-hydrogen phosphate (KDP): KH2PO4, formation of the isomorphous potassium equivalent of mineral struvite (MKP) occurs, according to the reaction: MgO + KH2PO4 + 5H2O → MgKPO4 · 6H2O. The reaction is rapid and exothermic, and its mechanism has been investigated by several authors [4,15–17]. When MgO powder is gently stirred in phosphate solution, a three-step mechanism for MKP formation was devised . This involves: (i) formation of aquosols composed by water molecules complexing dissolved cations; (ii) formation of a gel by reaction of the sol with phosphates in water; (iii) crystallization of a thickened gel into a ceramic around the unreacted core of MgO grains. This gel converts into a saturated phosphate solution with undissolved oxide particles representing nuclei for crystallization. The rate of MgO dissolution is considered the main factor controlling the degree of crystallinity of the ﬁnal ceramic. The pH of the solution is critical in favouring or
⁎ Corresponding author. Tel.: +420 567 225 322. E-mail address: [email protected]
http://dx.doi.org/10.1016/j.cemconres.2015.10.007 0008-8846/© 2015 Elsevier Ltd. All rights reserved.
inhibiting precipitation. Following another view , MKP sets through the onset of an insoluble barrier coating, consisting of polyphosphate units cross-linked with Mg2 + ions. This gel then slowly crystallizes into an interlocking microstructure of MKP. A solution mediated process, in which dissolved phosphate and a part of MgO are involved, has been also inferred [4,19]. Crystallization starts at nucleation points by gathering ions in solution. This hypothesis was later excluded on the basis of considerations about the mechanism of MgO dissociation in water, supposed to occur via the formation of Mg(H2O)2+ 6 complexes . Some of them replace water molecules at the magnesia surface, hindering further wetting of MgO grains. Together with PO34 ions in solution, they supply the structural units required for crystallization of MKP. The reaction is thus controlled by the reactivity of MgO powder, the amount of Mg(H2O)26 + complexes formed at the grain surface (preventing water molecules from further wetting magnesia), and the relative amount of each reactant. The reaction stops when the magnesia grains are entirely covered by hydrates and can no longer dissolve. When MgO grains (1-2 mm in size) are immersed in monopotassium phosphate solution MKP was observed to form preferentially as elongated crystals lying parallel to the grain surface . They accumulate quickly, bonding grains together. Kinetic studies are scarce and none of them provided quantitative data for this reaction. Isothermal calorimetric experiments , conducted with water to solid weight ratios (w/s) ranging between 2.5 and 10, showed a ﬁrst endothermic peak followed by two exothermic ones. Dissolution of KDP in water was believed to produce the ﬁrst peak, while the following exothermic events were ascribed to MgO dissociation and MKP formation, respectively. All these events largely overlap in time, and the superimposition
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of the calorimetric signals prevented for an accurate quantiﬁcation of each contribution. For practical applications the range of w/s is usually comprised between 0.2 and 0.4. Evidence was also found of the presence of an amorphous or poorly crystalline phase with a lower degree of hydration in mortars prepared with low water content (b8 wt%) , and in ammonium phosphate cements [20,22]. The quantiﬁcation of amorphous content in MPCs at different times after hydration, allowed us to prove that consumption of MgO occurred faster than formation of crystalline MKP [23,24]. Over long times, amorphous content decreases, whereas MKP increases , suggesting that the amorphous phase might be a precursor of MKP. At the current state of knowledge, the nature of this amorphous phase remains unexplained. One of the major factors affecting reaction kinetics was recognized to be the calcination temperature of magnesite (MgCO3), the primary source of magnesium oxide. As conﬁrmed by the literature on MgO dissolution in various acidic environments , it has proven to be critical in determining the reactivity of MgO formed [2,20,24,26,27]. At temperatures above 1300 °C, less reactive well crystallized MgO crystals of higher mean grain size and without amorphous coatings are formed . In this work the MPC setting reaction was followed by means of insitu synchrotron powder diffraction in the attempt of providing insights into the overall mechanism of this reaction and the inﬂuence of the reactivity of MgO on the reaction kinetics. As recently pointed out , these aspects are of crucial importance for a better understanding of the development of the microstructure in view of designing products for applications. 2. Experimental 2.1. Materials The raw materials employed in this study were pharmaceutical grade MgCO3 (42 wt% MgO) and reagent grade KDP (assay 99.8%) (Lach-ner s.r.o). MgO was obtained from magnesium carbonate by calcination for 40 min in laboratory furnace at 1400 °C, 1500 °C, 1525 °C, and 1600 °C. Two additional samples for each annealing temperature were obtained by milling MgO in agate shatterbox for 1 min and 5 min, respectively, for a total of 12 MgO samples. MPCs with KDP/MgO molar ratio of 1 were obtained by mixing 675.3 mg of KDP with 200 mg of MgO by hand in agate mortar. The powder was then added 262.6 mg distilled water to attain the w/s of 0.3, and mixed by hand for 1 min. MPC samples were then loaded in a syringe from the back side to be injected into capillaries 0.7 mm in diameter, open on both sides. Capillaries were then immediately sealed and mounted on a goniometric head for synchrotron data collection. 2.2. Analytical Methods Data were collected with the MYTHEN solid-state silicon microstrip detector implemented at the beamline MS X04SA, Paul Scherrer Institut, Swiss Light Source (SLS), Villigen (Swiss), employing a wavelength of 0.775 Å, and at the beamline BM01b, European Synchrotron Radiation Facility (ESRF), Grenoble (France), employing a wavelength of 0.505 Å with the Dexela CMOS-2D detector (PerkinElmer). Isothermal runs at room temperature (20 °C) were conducted on spinning capillaries following the reaction for variable times (from few up to 13 hours). Samples will be labelled with their activation temperature followed by milling time (in min). Setting was followed in situ employing the following 7 samples: 1400_0, 1400_1, 1500_0, 1500_1, 1500_5, 1525_5, 1600_5. Scanning electron microscope (SEM) observations have been conducted on samples of MgO and hardened MPC. Instrument (Model Quanta 450 FEG, FEI) was equipped with an energy dispersive X-rays ﬂuorescence spectrometer (EDS) (Model Apollo X, EDAX). A tiny amount of sample was loaded on an aluminum stub and coated with a gold 10 nm thick ﬁlm. Observations were performed using secondary electrons.
BET speciﬁc surface area measurements have been accomplished on MgO (Model ASAP 2020, Micromeritics). Grain size distribution of MgO was determined on samples dispersed in isopropyl alcohol with a laser granulometer (Model LD 1090, CILAS). 2.3. Kinetic Analysis Kinetic analysis was conducted using a combination of different approaches suitable for isothermal data. After inspection of the in situ synchrotron XRPD patterns, the decomposition of the reactant MgO and crystallization of MKP were independently analysed, using the integrated area of the (002) diffraction peak (corresponding to a d-spacing of 2.10 Å) for MgO, and the (021) diffraction peak (corresponding to a dspacing of 4.10 Å) for MKP, as a direct evidence of these processes. Their values are proportional to the weight fractions of the corresponding phases. Integrated areas of Bragg reﬂection peaks were normalized to phase fraction (α) and plotted as α vs. time curves. Integration was accomplished with the software PeakFit employing 2 pseudoVoigt functions and a ﬂat background for each diffraction peak. For many datasets, both processes showed in the second part an asymptotic behaviour. It must be noted however, that, as explained later in Section 5, only a fraction of the amount of MgO expected to react (according to the stoichiometry of the reactants) was consumed during the experiments, indicating that this ﬁnal stage is extremely sluggish and likely extends in time beyond the end of the experiment. In this description, the choice was made to adopt for both processes the same approach in the deﬁnition of the point corresponding to complete conversion, that is, α = 1 was assumed as the asymptotic value obtained from the ﬁt of the curve with an exponential function rising to a maximum for MKP crystallization, and from the ﬁt of the curve with an exponential decay function (y = y0 + A1*exp(-x/t1) + A2*exp(-x/t2)) for MgO decomposition. In the latter case, as the reaction was not followed from time t = 0, the integrated area of XRPD peaks corresponding to α = 0 was extrapolated from the ﬁt of the curve to time t = 0 using the same function, whereas in the case of MKP crystallization, the value of α = 0 is automatically set, as no MKP peaks in the XRPD pattern are initially observed. The study of each α-time plots was preliminarily attempted using the classical linear-model ﬁtting method for heterogeneous solid-state reactions described by the general expression of the Avrami or Johnson-Mehl-Avrami–Erofe’ev-Kolmogorov - JMAEK equation . n α ¼ 1− exp ð−kt Þ
The logarithmic transform of this equation is used to build a graph of ln[–ln(1 – α)] vs. ln(t) in which isothermal experimental data are made linear in the so-called ln–ln plot, where the reaction order (n) is calculated from the slope of the regression line and the rate coefﬁcient k is calculated from the intercept. To get an idea about the reaction model and assess if the reaction is single-step or multi-step, plots of d α/dt vs. α were drawn and compared to master plots . Because the dependency upon temperature was not investigated, isoconversional methods such as the Friedman model [31,32] were not applied. Initially we tried to ﬁt the data with a single nucleation and growth model (diffusion models and reaction-order models which belong to the class of deceleratory reactions) without success. Fitting was attempted with the major kinetic equation relative to deceleratory reactions  D1, D3, F0/R1, F1, F2, and F3 (see below) but resulted unsuccessful. Plots testifying the poor quality of the ﬁts are available as supplementary material Fig. S1. According to the indications of multi-step reactions, we decided to ﬁt the data with a more complex combined model. Each α-time plot was ﬁtted using the nonlinear regression approach in the so-called nonlinear model ﬁtting method . In principle, if the reaction is single step, data should be ﬁtted with one of the kinetic models developed for solid state reactions. The most important kinetic models used in solid state reactions in integral form
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are: power laws kt = α1/3 (P3), kt = α1/2 (P2); diffusion kt = α2 (D1), kt = (1-(1-α)1/3)2 (D3), kt = 1-(2/3)α-(1-α)2/3 (D4); Avrami-Erofeev (Sestak-Bergreen) [-ln(1-α)]1/n (An); contracting area kt = 1-(1-α)1/2 (R2) and contracting volume kt = 1-(1-α)1/3 (R3); zero-order kt = α (F0/R1) and ﬁrst-order –ln(1-α) (F1) . The model known as the boundary nucleation and growth (BNG), successfully used to interpret the hydration kinetics of cement and tricalcium silicate, the main mineral phase in cement, was also applied . The BNG model is related to the widely used Avrami nucleation and growth model. Whereas the Avrami model assumes that nuclei form randomly throughout the volume of the sample, the BNG model assumes that nuclei only form on boundary surfaces that are randomly distributed in the sample volume [33,34]. In the case of multi-step reactions, when more processes are overlapping in time, the extraction of kinetic parameters of each individual process has been shown possible through a ﬁt of the overall data with a combination of the models described above [35,36]. The combination of two kinetic steps was not ﬁtted as simple sum but as a weighted sum of two kinetic equations, following the model proposed by Perejón et al. in which a multi-step reaction composed of two distinct, partially overlapping processes, is disentangled into two weighted terms, with l1 and l2 being the contribution fraction of the ﬁrst and second process to the overall reaction. It is evident that l1 and l2 must respect the following relationships: l1 + l2 = 1 and l1α1 + l2α2 = α. An example of weighted kinetic equation P2 and F1 would be: h i 2 n α ¼ l1 ðkt Þ þ ð1‐l1 Þ 1‐expð‐kt Þ
Eq. (4) is clearly only approximated if the weight of the two processes is changing in time. In this case, a mathematical expression including l1 function of time [l1(t)] would be needed. To our knowledge, such mathematical tool has not yet been proposed. It should be noted, however, that, although l1 reﬂects the mean weight of the two equations (mechanisms) used to ﬁt the kinetic curve, if one mechanism is prevailing in the ﬁrst part of the curve, it will be the corresponding equation to mostly ﬁt this region, whereas the second mechanism will mostly ﬁt the second part. The data analysis was performed with different programs: LAB Fit , OriginPro 9.1.0 (Origin Lab) and SigmaPlot for Windows version 12.0 (Systat Software, Inc). 3. Results Table 1 reports BET speciﬁc surface area and relevant grain size distribution parameters for the investigated samples. The speciﬁc surface area of the MgO powder decreases when increasing the calcination temperature, and increases only slightly with the milling time. Fig. 1a,b,c,d depict SEM micrographs of MgO samples 1400_0, 1500_0 and 1600_0 and 1600_5, respectively. The effect of temperature is apparent in both the increase in mean grain size and degree of sintering. An abrupt change in particle shape was observed above 1500 °C, with a net reduction in the number of steps and irregularities at the grain surface. The general reduction in grain size produced by milling was frequently accompanied by a bimodal distribution. Samples annealed at Table 1 BET surface area and d10, d50 and d90 values obtained from laser granulometry of MgO samples discussed in the text. 1400_0 1400_1 1500_0 1500_1 1500_5 1525_5 1600_0 1600_5 SBET (m2/g) d10 (μm) d50 (μm) d90 (μm)
2.3_ 7.3_ 16.1_
0.6 4.9 18.5
1.4 5.8 13.8
0.8 3.0 11.3
0.4 2.1 9.3
0.6 1.7 5.2
1.3 6.1 37.0
0.2 2.2 5.5
1400 °C were only slightly affected by milling because of their lower degree of sintering and very small initial mean particle size (see Fig.1a). Fig. 2 reports an example of 3-dimensional plot (2θ-Intensity-time) relative to the decomposition of MgO and growth of MKP phases in the sample 1500_0. It’s clear form the picture that only a fraction of the available MgO was consumed in this time interval. The intensity of the MgO peaks decreases very quickly in the ﬁrst hour and remains roughly constant for the rest of the experiment. The ﬁrst peak, at 2θ ~ 10.5° is the most intense peak (111) of the MKP phase which forms after ca. 1 h from the beginning of the experiment. Peaks of KDP are visible in the ﬁrst diffraction patterns and disappear quickly because of the fast dissolution rate. α-time plots relative to the MgO decomposition are reported in Fig. 3a, whereas those relative to the MKP formation are reported in Fig. 3b. The shape of the curves indicates an overall decelerating character of the kinetic reaction characterized by an initial steep slope and a later smooth trend that might be compatible with a complex multistep reaction. In Fig. 4a an example of dα/dt vs. α plot relative to MgO decomposition for sample 1525_5 is reported. Fig. 4b reports an example of dα/dt vs. α plot relative to the MKP crystallization for the same sample (1525_5). The very fast ﬁrst part of MgO decomposition reaction, that, for some of the samples (see also Fig. 3), means all the way to the consumption of a large amount of MgO (up to α = 0.8), adversely affected the accuracy of the extrapolated value corresponding to α = 0, thus limiting the accuracy of the kinetic analysis of this reaction. However, plots for MKP are better deﬁned, and, as for the reported example, point to a two-step reaction with a ﬁrst part (up to ca. 0.5α) similar to the Avrami An master plot curves and a ﬁnal part (above ca. 0.5α) comparable to a ﬁrst order F1 or to a diffusion controlled D master plot curve. Similar results were obtained for almost all the samples. The analysis of the kinetic data was successfully accomplished using a nonlinear model ﬁtting method with a weighed combination of two kinetic equations, representing two consecutive, partially overlapping processes with two distinct values of rate constants k1 and k2, relative to the initial part of the curve and the sluggish ﬁnal part of the curve, respectively . All possible combinations were tested and the best ﬁt for the MgO decomposition was obtained by the combination of a ﬁrst order (F1) for the ﬁrst fast part of the curve and a Jander diffusion (D3) controlled model for the successive sluggish part. For MKP crystallization, the best ﬁt was obtained with the combination of an Avrami (An) model and ﬁrst order (F1) for the second part of the curve. An example of ﬁt for the MgO decomposition and MKP crystallization (sample 1500_1) is depicted in Fig. 5; all the other graphical results of the ﬁts obtained with the combined model for both MgO decomposition and MKP crystallization are available as supplementary material Fig. S2. The ﬁgure clearly shows that two distinct reaction progresses are observed for MgO decomposition and MKP crystallization (asymmetric kinetic curves). Table 2 summarizes all the calculated rate constants, n coefﬁcients of the Avrami model, weight coefﬁcients, and ﬁt statistics. The value of n for the Avrami section of the curves was in most cases calculated from the ﬁt. However, for samples 1500_5 and 1525_5, it was necessary to ﬁx it at the value of 2 to improve the stability of the ﬁtting procedure. 4. Discussion The study of the decomposition of MgO and crystallization kinetics of MKP using in situ synchrotron XRPD resulted very problematic. The major problems arose because of the quick setting behaviour of the pastes, which complicated the procedures for manual mixing and successive injection into the glass capillaries. This resulted in a non-perfect synchronisation of the beginning of the experiments. Furthermore, due to the extremely sluggish character of the second stage of the reaction, in some cases the amount of MgO consumed during the experiments was rather low. According
A. Viani et al. / Cement and Concrete Research 79 (2016) 344–352
Fig. 1. SEM micrographs of MgO prepared at (a) 1400 °C, (b) 1500 °C and (c) 1600 °C without milling and at (d) 1600 °C after 5 min of milling.
to the stoichiometry of the system, the reaction is expected to extend much further in time, but, as shown by the α-time plots, this occurs at a very low rate. It can be argued that also MKP crystallisation extends beyond the time scale of the experiment. Although in terms of mass balance our kinetic analysis accounts for a fraction of the entire process, in the remainder of the discussion it will be shown that the adopted approach didn’t prevent from a description of the mechanism driving this last sluggish stage. Mechanisms for the dissolution reaction of MgO and formation of MKP will be proposed making reference to previous results on the setting reaction of CBCs, Ca-P cements, and Portland cement. Our considerations will be supported by SEM observations and particle size analysis of powders, but should be regarded as tentative, considering that there are no models to date based on kinetic data, and the limits in the interpretation of phenomenological rate models in terms of reaction mechanisms. When the reaction sequence reported in Ding et al.  is considered, KDP releases various ions in solution , according to the:
The aqueous solution becomes acid, favouring the dissolution of the MgO particles. It is long known that the dissolution rate of MgO has an inverse exponential dependence upon pH of the solution . This may lead to the immediate release of Mg ions in solutions (as protonation was recognized to be the main process at very low pH ),
+ KH2PO4 → K+ + PO34 + 2H
Fig. 2. Example of 3-dimensional plot (2θ-Intensity-time) relative to the decomposition of MgO and growth of MKP phase in the sample 1500_0.
Fig. 3. α- time plots relative to (a) MgO decomposition; (b) MKP formation.
A. Viani et al. / Cement and Concrete Research 79 (2016) 344–352
Fig. 5. (1-α) vs. time plot of MgO decomposition and α vs. time plot of MKP crystallization for sample 1500_1.
Fig. 4. (a) dα/dt vs. α plot of MgO decomposition for sample 1525_5; (b) dα/dt vs. α plot of MKP crystallization for sample 1525_5.
however, the complete reaction, which obeys a ﬁrst order F1 equation, describes chemical dissolution of the MgO particles to form an alteration brucite-rich corona  as: MgO + H2O → MgOH+ + OH-
direction . As a matter of fact, MKP with an orthorhombic struvite structure, may display a needle-like acicular crystal habit, elongated along the a axis  (see inset in Fig. 6a). With the exception of 1400_1 data, at higher calcination temperatures/milling times ratios, the increase in the values of the Avrami coefﬁcient (2-3) points to the same rate limiting step, but a 2-3-dimensional crystal growth. This means that the crystal habit likely changes to a more isometric shape (see inset Fig. 6b). Remnants of these ﬁrst crystals might still be found in hardened MPC pastes, but, most probably, more apparent differences should have been preserved if these ﬁrst crystallization stages conditioned the development of the whole microstructure. Partial conﬁrmation to this hypothesis came from SEM observations. Fig. 6a,b depict the occurrence of elongated crystals in sample 1400_0 and tabular crystals in sample 1600_5. In the latter case, tabular MKP crystals grew bigger and were arranged in extended domains of roughly parallel platelets ﬁlling the entire volume. As the alteration layer around the former MgO particles thickens, the character of the reaction considerably changes and becomes much slower. For the MgO decomposition, the reaction becomes diffusion-controlled (D3, a model especially developed for spherical particles , such as cubic MgO) with the rate limiting step governed by the diffusion of water molecules through the layer to the surface of the MgO core to form further intermediate brucite-like reaction product. At this stage crystallization is considered to proceeds very slowly inward, to the core of the MgO particles but without substantial release of Mg2+ ions in solution. The proposed kinetic model
MgOH+ + 2H2O → Mg(OH)2 + H3O+ From the XRPD data we cannot prove the nature of this MgO alteration layer other than it is amorphous (or paracrystalline) and we will generally refer to it as brucite-like corona. As a matter of fact, the composition of this transient layer may be more complex and include other ions too. This reaction is known to be exothermic [39,40] as hydration of MgO to brucite is energetically favoured (-37 kJ/mol ). The literature already reports that the rate-controlling step of MgO dissolution is the surface chemical reaction . The brucite corona readily releases Mg2+ ions in solution : Mg(OH)2 → Mg2+ + 2OH2+
With the Mg ions available, the crystallization of MKP starts at the surface of the former MgO particles, or better at the surface of the altered corona layer according to the: + K+ + PO3Mg2+ + 6H2O → Mg(H2O)2+ 6 4 → MgKPO4⋅6H2O Initially, the Avrami-like reaction with n ≈ 1-2 is compatible with a phase boundary control with deceleratory nucleation and growth in one
Table 2 Kinetic parameters for MgO decomposition and MKP crystallization reactions calculated with the multistep ﬁtting. Data set
MgO decomposition 1400_0 0.33(2) 1400_1 0.875(4) 1500_0 0.77(1) 1500_1 0.81(2) 1500_5 0.81(2) 1525_5 0.920(5) 1600_5 0.86(2)
0.141(9) 0.291(3) 0.204(5) 0.072(6) 0.110(1) 0.0455(2) 0.145(3)
0.0016(1) 0.0013(1) 0.0020(2) 0.0024(2) 0.0039(3) 0.0002(1) 0.0011(2)
0.9971 0.9991 0.9970 0.9986 0.9984 0.9997 0.9950
4995 12934 4073 20606 304065 92863 4219
MKP crystallization 1400_0 0.39(1) 1500_0 0.89(8) 1400_1 0.36(1) 1500_1 0.90(9) 1500_5 0.66(1) 1525_5 0.91(8) 1600_5 1.00(1)
0.0345(4) 0.0047(1) 0.0590(9) 0.0059(2) 0.0064(1) 0.0060(1) 0.0012(1)
1.3(1) 2.0(1) 2.7(2) 1.7(2) 2 2 3.4(1)
0.0085(1) 0.0010(9) 0.0107(3) 0.0023(3) 0.0041(2) 0.0003(1) -
0.9997 0.9957 0.9980 0.9930 0.9990 0.9852 0.9969
838815 26627 20640 23555 65293 4688 58974
l1 is the weight coefﬁcient of the model 1 (F1 for MgO and An for MKP), R and F are the parameters of the ﬁt statistics. For MgO, k1 refers to the F1 model (1) and k2 to the D3 model (2). For MKP, k1 and n refer to the Avrami model (1) and k2 to the ﬁrst order F1 (2).
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Fig. 6. Micrographs showing habit of MKP crystals on MPC exposed sample surface: (a) elongated, in sample 1400_0; (b) tabular, in sample 1600_0. Insets depict corresponding simulation of crystal habit: (a) needle-like, elongated along the a axis; (b) tabular.
is in agreement with the one proposed to explain the mechanism of dissolution of MgO followed by brucite precipitation at high temperature. The hydration seems to be initially driven by the dissolution of MgO (chemical control) but, as the reaction progresses, both the surface and pores of the MgO particles are progressively covered by the brucite produced. As a result, the diffusion of water is hindered, reducing the overall reaction rate (diffusion controlled). When water molecules, K+ and PO34 ions are available, the amount of MgO dissolved before the diffusion controlled process prevails, will be function of the rate of release of Mg2+ ions in solution (reactivity of MgO) and surface area of MgO. It turned out that in most of the investigated samples this happened when only a fraction (ranging between 50 wt% and 80 wt%) of the MgO expected to react, was consumed. Total consumption will be likely attained at the low rate dictated by the diffusion controlled mechanism. It has to be noted, however, that, at the time scale of the experiments, a variable but large part of the curves are dominated by this mechanism. This means that, there are enough experimental data to characterise this last stage despite the assumptions made in building the α-time plots. The late formation of MKP is governed by a ﬁrst order (F1) chemical reaction as water is available at the interface of the intermediate brucite layer and both K+ and PO34 - readily migrate through the MKP layer. Such hypothesis may ﬁnd support in similar processes observed during formation of Ca-P cements. A mechanistic model for the kinetics of hydrolysis of tricalcium phosphate (TCP) to hydroxyapatite (HAp) suggests that hydrolysis is controlled by different rate-limiting mechanisms . Initially, the hydrolysis kinetics depend on the surface area of anhydrous TCP. Subsequently, they change to a dependence on the rate of HAp product formation controlled by a nucleation and growth mechanism. The model predicts that HAp nuclei form essentially at one time and growth occurs in two dimensions, leading to a platelet-like morphology. The rate of
Hap cement formation is strictly dependent upon solubility of the basic component. The ﬁrst precipitate can also be an amorphous or paracrystalline gel. Although the rate determining step in the second part of the setting reaction is usually considered diffusion, some experimental evidences suggest also that hydrolysis of the basic reactant, over which products form, is not limited by diffusion [44,45]. The layer is porous, made by acicular or elongated crystals leaving room for water to move inward. The main difference with our system is that, here, once water reaches the surface, ions are released directly into solution. Conversely, we suppose that a mass, containing products of alteration of MgO, is still covering the available grain surface and acts as a diffusion barrier for water to reach the unreacted MgO core. Thus, by analogy, also considering the shape of our crystals, we can infer that MKP is permeable to all ions in solutions and that the top of the alteration layer is accessible to K+ and PO34 - ions to form MKP. The formation of MKP during the hydration process of MgO also bears a close resemblance to the exothermic process of hydration of tricalcium silicate (C3S), the main constituent of Portland cements, to form calcium-silicate-hydrate (C-S-H) during the setting stage. The hydration product grows along the surface of the particles, eventually covering them, and also outward into the pore space between the particles, so that product regions from adjacent particles eventually coalesce, causing the paste to set. As detailed in Section 3, the BNG model in which nucleation of the hydration product occurs only on internal boundaries, corresponding to the C3S particle surfaces, has been developed  and proved to ﬁt calorimetric data better than the Avrami model. This is because the Avrami coefﬁcient n from the ﬁt is difﬁcult to be interpreted  and because the C3S hydration process, in which the hydration product grows outward from the C3S particle surfaces, violates the conditions under which the standard Avrami equation is derived (spatially random nucleation) . Our tests of the BNG model on MKP crystallization data were however unsatisfactory, resulting in worse ﬁts with respect to the Avrami An + F1 model. One of the reasons can be that the nucleation does not only occur at the boundary surface of the MgO particles, but even randomly in suspension, so that the kinetic process somehow obeys the Avrami postulate on random nucleation. Another reason may be that the BNG model is only approximate, because it assumes that the boundaries are static. In fact, dissolution causes the reacting boundaries to move, and the development of hydration products on either side of the original interface (i.e., away from and into the reacting grain) will be different . As a matter of fact, the values of the Avrami coefﬁcients 1-3 are close to those reported in the literature for the C3S hydration reaction (the majority falling between 2 and 3) . In general, it should be emphasized that both the Avrami model and the Thomas model relies on a ground theory that was developed for solid state reactions. It is then understandable that such empirical models do not perfectly reproduce this speciﬁc case of solution mediated reaction. On the other hand, our interpretation is at variance with previous models locating all or the main steps of the reaction in solution [4,7,19]. MKP rate constants plotted against annealing temperature (Fig. 7a, b) and milling time (Fig. 7c) (parameters frequently considered for applications), simply show to which extent they are affecting the reactivity of MgO in terms of amount and rate at which Mg2 + ions are made available to the reaction. MgO particles annealed at lower temperature show more steps and surface defects, acting in favour of its reactivity [26,41]. But annealing temperature brings in also changes in surface area and grain size distribution (see Table 1). This invariably results in a sum of contributions convoluted in the ﬁnal rate constants. Although a good correlation between BET surface area and milling time, and BET surface area and calcination temperature, was found for some datasets, our attempts to separate each single contribution and relate them to the rate constants through a model with a sound physical meaning, were unsuccessful, mainly because of the limited number of observables. Details of this approach and some results obtained are
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Fig. 7. (a) rate constant k1 vs. activation temperature for MKP; (b) rate constant k2 vs. activation temperature for MKP; (c) rate constants k1 and k2 vs. versus milling time for MKP in samples activated at 1500 °C; (d) rate constants k1 and k2 vs. speciﬁc surface area.
available as supplementary material Fig. S3. From these considerations it follows that the discussion of such aspect will be only on a qualitative standpoint. The shape and surface of MgO particles annealed at 1600 °C (Fig. 1c) differ markedly from those of MgO annealed at 1400 °C and 1500 °C (Fig. 1a and b, respectively). As mentioned above, this would suggest that surface energy should also differ. This is conﬁrmed by the lower value of dissolution rate constant of the sample annealed at 1600 °C, although, in the studied samples, the most striking changes occur between 1400 °C and 1500 °C. In Fig. 7d, rate constants for MKP crystallization reaction are plotted against BET surface area of MgO. Although k2 is slightly affected by changes in BET surface area (in accordance with the mechanism suggested for this second step), k1 shows a progressive increase with increasing surface area and decreasing calcination temperature/milling time. Remarkably, points corresponding to samples 1400_0 and 1400_1 fall well apart from the others. This can be explained by the concomitant effect of the intrinsic high reactivity of MgO and much higher surface area, dramatically increasing the amount of product of dissolution of MgO. As the ﬁrst step of the MKP crystallization reaction slows down, because of decreasing the overall reactivity of MgO (increasing annealing temperature and/or decreasing milling time), the role of the ﬁrst reaction mechanism (An) increases against the second one, and the point at which the second mechanism prevails over the ﬁrst, shifts towards longer times. Table 2 shows that the weight coefﬁcient l1 of the An model, increases with decreasing milling time and increasing annealing temperature, the extreme example being represented by sample 1600_5, which is actually described with the Avrami model alone. In fact, the samples obtained from MgO produced at 1400 °C (1400_0 and 1400_1) show higher values of k1 than the others and weight factors l1 lower than 0.5. The speciﬁc surface area of the former MgO powder might be the factor playing a major role in determining not only the kinetic parameters for the formation of MKP, but also the reaction mechanism. A similar tendency has been described for the hydrolysis reaction of TCP. Owing to the increase in speciﬁc surface area of the reactants, the chemical reaction takes place
at much higher rate at the initial stage . This fact was explained by the increase of the reactivity of the initial particles, which gives rise to a higher degree of supersaturation in solution favouring the nucleation step over the growth, ﬁnally affecting the resulting microstructure . In a parallel way, the results presented in this work may open the door to further studies on how different kinetic mechanisms affect the microstructure and the mechanical properties of MKP, in the view of tailoring the structure at the micro and nanoscale. Further investigations should be needed to shed light on other aspects as well. As mentioned above, a simple mass balance of the crystalline phases shows that an amorphous or poorly crystalline fraction is involved in the reaction. Main MKP crystallization occurs slowly and is delayed in time with respect to MgO dissolution (see Table 2, Fig. 2 and Fig. 5). Over long times, the conversion rate into crystalline MKP was considered to be dependent on the reactivity of MgO [23,24]. However, no direct information on the chemical nature of this amorphous fraction is available to date. In this respect, the present work is far from being conclusive. Further knowledge on this system might be gained by combining results from different techniques; to this aim, isothermal calorimetry, small-angle X-rays scattering and quasielastic neutron scattering experiments are underway. 5. Conclusions Magnesium-potassium phosphate cements reaction kinetic was investigated by means of in-situ synchrotron powder diffraction. MgO decomposition and MKP crystallization showed two distinct reaction progresses, with the intervention in both cases of more than one single process. Kinetic analysis was successfully accomplished with a weighted nonlinear model ﬁtting method with a weighed combination of two kinetic equations, representing two consecutive, partially overlapping processes each one characterized by its own rate constant. According to the proposed model, the ﬁrst reaction step is the dissolution of MgO in aqueous solution via chemical control contributing to the
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formation of an intermediate amorphous product. The progressive accumulation at the grain surface of a thickening layer hindered diffusion of water for the further decomposition of MgO, shifting the mechanism towards a diffusion control. On the other hand, the late formation of MKP is again a ﬁrst order (F1) chemical reaction as water is available at the interface of the intermediate layer and nutrients can readily migrate through the MKP layer thanks to its open structure. The observed dependence of MKP reaction rate constants upon BET surface area, annealing temperature and milling time of MgO were interpreted in the light of the proposed model. Critical issues, such as the nature of the intermediate (amorphous?) precursor of MKP and whether this transient phase is a gel from which MKP slowly crystallizes, or not, didn’t ﬁnd explanation in this paper and will be matter for future investigations. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.cemconres.2015.10.007. Acknowledgments This research was partially supported by the project No. LO1219 under the Ministry of Education, Youth and Sports National sustainability programme I of Czech Republic. For experiments performed on the beamline BM01b at ESRF (proposal MA-2021), we are grateful to Wouter van Beek providing assistance in using the beamline. For experiments conducted on the beamline MS X04SA at SLS (proposal 20130049), we are grateful to Nicola Casati providing assistance in using the beamline. Authors also want to thank Dita Machová at the Centre of Excellence Telč for BET surface area and grain size distribution measurements. References  D.M. Roy, New strong cement materials: chemically bonded ceramics, Science 235 (1987) 651–658, http://dx.doi.org/10.1126/science.235.4789.651.  A.S. Wagh, Chapter 9 - Magnesium Phosphate Ceramics, in: E. Hurst (Ed.), Chem. Bond. Phosphate Ceram. 21st Century Mater. with Divers. Appl, 10.1016/B978008044505-2/50013-2Elsevier 2004, pp. 97–111.  B.E.I. Abdelrazig, J.H. Sharp, B. El-Jazairi, The chemical composition of mortars made from magnesia-phosphate cement, Cem. Concr. Res. 18 (1988) 415–425, http://dx. doi.org/10.1016/0008-8846(88)90075-0.  B.E.I. Abdelrazig, J.H. Sharp, B. El-Jazairi, The microstructure and mechanical properties of mortars made from magnesia-phosphate cement, Cem. Concr. Res. 19 (1989) 247–258, http://dx.doi.org/10.1016/0008-8846(89)90089-6.  M. Costato, Acid-base cements, Their biomedical and industrial applications. , Cambridge University Press, 1995http://dx.doi.org/10.1007/BF02451742.  Z. Ding, Z. Li, Effect of aggregates and water contents on the properties of magnesium phospho-silicate cement, Cem. Concr. Compos. 27 (2005) 11–18, http://dx. doi.org/10.1016/j.cemconcomp.2004.03.003.  M.F. Ibrahim, H.A. Sibak, A. Abadir, Preparation and Characterization of Chemically Bonded Phosphate Ceramics (CBPC) for Encapsulation of Harmful Waste, J. Am. Sci. 7 (2011) 543–548.  G. Mestres, M.P. Ginebra, Novel magnesium phosphate cements with high early strength and antibacterial properties, Acta Biomater. 7 (2011) 1853–1861, http:// dx.doi.org/10.1016/j.actbio.2010.12.008.  D.V. Ribeiro, M.R. Morelli, Inﬂuence of the addition of grinding dust to a magnesium phosphate cement matrix, Constr. Build. Mater. 23 (2009) 3094–3102, http://dx.doi. org/10.1016/j.conbuildmat.2009.03.013.  S.S. Seehra, S. Gupta, S. Kumar, Rapid setting magnesium phosphate cement for quick repair of concrete pavements — characterisation and durability aspects, Cem. Concr. Res. 23 (1993) 254–266, http://dx.doi.org/10.1016/0008-8846(93)90090-V.  F. Wu, J. Wei, H. Guo, F. Chen, H. Hong, C. Liu, Self-setting bioactive calciummagnesium phosphate cement with high strength and degradability for bone regeneration, Acta Biomater. 4 (2008) 1873–1884, http://dx.doi.org/10.1016/j.actbio. 2008.06.020.  Q. Yang, B. Zhu, S. Zhang, X. Wu, Properties and applications of magnesia - phosphate cement mortar for rapid repair of concrete, Cem. Concr. Res. 30 (2000) 1–7, http://dx.doi.org/10.1016/S0008-8846(00)00419-1.  S.Y. Singh, D., Wagh, A. S., Perry, L., Jeong, Pumpabale/InjectablePhosphate Bonded Cements, US Patent 6,204,214, 2001.  A.S. Wagh, D. Singh, S.Y. Jeong, Method of waste stabilization via chemically bonded phosphate ceramics. U.S. Patent No 5,830,815, 1998.  E. Soudée, J. Péra, Mechanism of setting reaction in magnesia-phosphate cements, Cem. Concr. Res. 30 (2000) 315–321, http://dx.doi.org/10.1016/S0008-8846(99) 00254-9.
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