Calcium Effect in PLR–PCR Geopolymers: Peak Compressive Strength at 30% PCR and Evidence of C-A-S-H/N-A-S-H Synergy

Abstract

Valorizing construction and demolition waste (CDW) via alkaline activation enables low-carbon binders. This study assesses binary geopolymers formulated with recycled brick powder (PLR) and recycled concrete powder (PCR) in seven precursor ratios (0–100% PCR), activated with a ternary NaOH/Na₂SiO₃/KOH solution (silicate modulus M_s ≈ 3.2) at L/B = 0.15, and cured for 7, 14, and 28 days. Compressive strength (fc), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDS) were used to link microstructure–phases–properties. A local maximum in fc at ~30% PCR (16.2 MPa at 28 d) was observed versus 0% PCR (14.2 MPa) and ≥50% PCR (13.8 → 10.1 MPa at 28 d). XRD indicated a reduction in inherited crystalline phases and an increased amorphous fraction at ~30% PCR; FTIR (normalized peak position and FWHM of the T–O–Si band, not absolute intensity) suggested higher network extension; SEM-EDS (local/semiquantitative) showed a moderate rise in Ca that supports C-A-S-H domains bridging the N-A-S-H network. At a high PCR, excess Ca simplified mineralogy (quartz/portlandite dominance), promoted competitive routes (C-S-H/carbonation), reintroduced microdefects, and reduced fc. A theoretical oxide balance per mix identified a compositional window where Ca/(Si + Al) ≈ 0.35–0.45 coincides with the mechanical optimum and with XRD/FTIR tracers. Overall, a ~30% PCR window maximizes co-reticulation of N-A-S-H/C-A-S-H and densification without compromising aluminosilicate continuity, providing transferrable design and process-control criteria for CDW-based geopolymer binders.

1. Introduction

The construction sector faces mounting pressure to adopt innovative, sustainable solutions while managing the steadily growing volume of waste it generates [1]. Construction and demolition waste (CDW) arises from debris as well as poor planning and handling practices; because of its chemical nature, it is not amenable to aerobic/anaerobic digestion, composting, or simple chemical degradation, which often leads to informal disposal and environmental liabilities. In 2018, global generation averaged ~604 kg·capita⁻¹·year⁻¹ and is projected to rise by ~60% by 2050, intensifying soil and water contamination and greenhouse-gas emissions [2,3,4].

In Peru, construction is a major source of solid waste. In the province of Lima alone, 3,881,000 t of municipal solid waste was reported in 2020 (+7.4% vs. 2019), while the La Libertad region recorded a 3.8% annual growth in building activity between 2013 and 2022, reflecting expansion driven by housing/infrastructure demand and self-construction [5,6]. This context increases CDW flows and strains management capacity, prompting the need for recycling and valorization strategies that integrate CDW into material value chains [7]. The legal framework—Law No. 1278 and its Regulation (Supreme Decree No. 014-2017-MINAM)—mandates minimization, segregation, material/energy recovery, and traceability; the National Integrated Solid Waste Management Plan (PLANRES), together with municipal ordinances, promotes extended producer responsibility (EPR) and standardized, safe handling, enabling controlled use of CDW in construction materials [8,9,10].

Valorizing CDW in construction materials reduces disposal footprints and the extraction of non-renewable raw materials (the sector consumes ≈ 3 billion tons of primary resources per year), thus enabling circular-economy schemes [11,12]. The literature has explored supplementary cementitious materials (silica fume, fly ash, quicklime, ceramic wastes, palm-oil by-products) with reported effects on strength, durability, and waste-management cost [4]. In La Libertad, 58.8% of housing uses brick/cement block, so recycled brick powder (PLR) and recycled concrete powder (PCR) are significant local CDW fractions [13].

Within CDW, PLR—rich in Si and Al—has been used as a partial cement replacement, often improving mechanical behavior around ≈15% substitution; some studies report no significant losses when ≈15% PLR is combined with ≈30% recycled aggregates [14,15,16]. PCR—rich in Ca—is the most abundant waste globally, but its structural reuse is typically limited by abrasion resistance, lower bulk density, and higher absorption, restricting it to non-structural applications [17,18].

Geopolymers arise as lower-carbon inorganic binders relative to Portland cement: alkaline activation of aluminosilicates forms N-A-S-H networks, and in the presence of Ca, C-A-S-H domains that may coexist, achieving competitive mechanical performance and durability [19,20,21]. Favorable results are generally reported for curing temperatures ≥ 60 °C and low liquid-to-binder ratios (L/B), consistent with the dissolution → condensation → gelation/crystallization sequence (Si–O–Al bonds) [22,23,24,25,26].

Activator chemistry is critical. The Na₂SiO₃/NaOH ratio, the silica modulus (M_s = SiO₂/Na₂O), NaOH molarity, and the use of KOH regulate workability, network extent, and strength; even solid activators (Na₂CO₃, Na₂SiO₃·5H₂O) offer operational advantages in some systems [27,28,29,30,31,32,33,34,35,36]. In ceramic–cement systems (PLR/ceramic tiles), curing at 80–90 °C with 8–14 M NaOH has delivered 40–60 MPa, with strong dependence on precursor fineness and porosity [37,38]. For PCR as a single precursor, strengths < 10–27 MPa are common unless co-activated with metakaolin or clinker and cured at ~70 °C; limitations are linked to unfavorable compositional ratios (low SiO₂/(Al₂O₃ + CaO)) and secondary carbonation [38,39]. By contrast, binary PLR + PCR mixes often exhibit synergy at low–intermediate PCR fractions: the matrix densifies and strength increases, whereas high PCR fractions dilute reactive aluminosilicates and penalize performance (optima have been reported near ≈ 10–20% depending on batch, activator, and curing) [40,41,42].

Despite progress, two gaps persist: (i) inconsistent process variables (activator, L/B, curing) impede cross-study comparison and isolation of the pure %PCR effect; and (ii) scale decoupling remains common—mechanical data often lack the multi-technique support (XRD/FTIR/SEM-EDS) required for convergent mechanistic arguments [14,15,16,17,18,25,26,27,28,29,30,31,32,33,34]. Against this backdrop, the present work evaluates the effect of the PCR/PLR fraction while keeping constant a ternary activator NaOH/Na₂SiO₃/KOH (M_s ≈ 3.2) and L/B = 0.15, and triangulates compressive strength, XRD (amorphicity index/FWHM), FTIR (position/FWHM of the T–O–Si band—without making claims on absolute intensities), and SEM-EDS (Ca at.% as a local tracer). We hypothesize an intermediate optimum %PCR wherein moderate Ca enables C-A-S-H/N-A-S-H co-reticulation, maximizing densification and load-bearing capacity; outside that window, excess Ca²⁺ simplifies mineralogy (quartz/portlandite), triggers competing routes (C-S-H, carbonation), and reintroduces micro-defects [35,36,37,38,39,40,41,42,43,44]. In addition, a theoretical oxide balance per mix (Si–Al–Ca) is incorporated to quantify Ca/(Si + Al) as a design metric aligned with the observed optimum.

Objective and contribution. Our objective is to map 0–100% PCR in PLR–PCR pastes under fixed activator and curing conditions, and to demonstrate that ~30% PCR maximizes compressive strength by enabling C-A-S-H/N-A-S-H synergy, supported by independent tracers (XRD amorphicity/FWHM, FTIR Δν/FWHM of T–O–Si, SEM-EDS Ca at.%). Contributions include (i) isolation of the net %PCR effect, (ii) multi-technique triangulation for mechanism, (iii) a compositional metric (Ca/(Si + Al)) that reproduces the optimum window, and (iv) a reproducible methodology (25 × 50 mm geometry, L/B, activator, statistical protocol) transferable to other CDW families [1,2,3,4,5,35,36,37,38,39,40,41,42,43,44,45].

2. Materials and Methods

2.1. Raw Materials

Recycled concrete powder (PCR) and recycled brick powder (PLR) were collected from construction and demolition waste in Trujillo, Peru, and used as aluminosilicate precursors. Powders were oven-dried at 105 °C for 24 h, milled, and sieved to <37 µm (400 mesh) to minimize granulometry effects on early reactivity. The oxide chemistry (wt%) is reported in

Table 1. Chemical characterization (oxides, % by mass) of PCR and PLR.

Oxide	PCR (%)	PLR (%)
SiO2	28.5	61.0
Al2O3	6.5	21.5
Fe2O3	2.5	6.8
CaO	41.5	4.2
MgO	2.8	1.6
Na2O	0.9	1.8
K2O	0.5	2.1
SO3	2.8	0.2
TiO2	0.4	0.8
Loss on ignition (LOI)	13.6	0.0
Total	100.0	100.0

(SiO₂–Al₂O₃–CaO dominate; PCR is richer in Ca whereas PLR is richer in Si–Al).

Beyond chemistry, we quantified physical attributes that govern early reactivity and packing: particle size distribution (PSD; D10/D50/D90 by laser diffraction), fineness (Blaine and BET), skeletal density (He pycnometry), and residual moisture. Methods, instruments, calibration standards, dispersion media, and settings are detailed in SI Table S1. Briefly, PLR exhibits a finer PSD and higher specific surface than PCR, consistent with a larger reactive aluminosilicate surface. PSD measurements were performed on oven-dried powders (105 °C, 24 h) dispersed in isopropanol with controlled sonication to limit agglomeration and spurious hydration/carbonation of PCR.

2.2. Alkaline Activator

A ternary activator was formulated at mass fractions 0.10:0.60:0.30 (NaOH:Na₂SiO₃:KOH). Reagents: NaOH flakes/pellets, ≥98% (ACS, Macron Fine Chemicals—Avantor Performance Materials, S.A. de C.V., Ecatepec de Morelos, Mexico); KOH pellets, ≥90% (ACS, Macron); commercial sodium silicate solution with silica modulus M_s = SiO₂/Na₂O ≈ 3.2 ± 0.1 (reference density ~1.38 g mL⁻¹ at 20 °C). Deionized water was used throughout. Preparation: NaOH and KOH were dissolved separately in DI water, cooled to 23–25 °C, and combined with the Na₂SiO₃ solution under stirring to the target volume; the activator was homogenized for 5 min and rested ≥15 min to stabilize temperature and entrained bubbles before mixing with the powders. Design references (constant across mixes): mass ratio Na₂SiO₃/NaOH ≈ 6.0; silicate modulus M_s ≈ 3.2 ± 0.1. Informative only—no calculations depend on these conversions: nominal equivalents NaOH ≈ 8–9 M; KOH ≈ 4–5 M; global SiO₂/Na₂O ≈ 1.6–1.7.

2.3. Mix Design and Specimen Preparation

Seven binary formulations were produced by substituting PLR with PCR at 0, 10, 30, 50, 70, 90, and 100% of total precursor mass (PLR completes to 100%). The liquid-to-binder ratio (L/B) was fixed at 0.15 for all mixes. A batch size of 1000 g of precursor was used in every composition; activator mass was 150 g (split as 15 g NaOH, 90 g Na₂SiO₃, 45 g KOH). The full matrix is shown in

Table 2. Binary PCR/PLR mix matrix (L/B = 0.15).

ID	PCR (%)	PLR (%)	Precursor (g)	PCR (g)	PLR (g)	Activator (g)	NaOH (g)	Na2SiO3 (g)	KOH (g)	L/B
P0	0	100	1000	0	1000	150	15	90	45	0.15
P10	10	90	1000	100	900	150	15	90	45	0.15
P30	30	70	1000	300	700	150	15	90	45	0.15
P50	50	50	1000	500	500	150	15	90	45	0.15
P70	70	30	1000	700	300	150	15	90	45	0.15
P90	90	10	1000	900	100	150	15	90	45	0.15
P100	100	0	1000	1000	0	150	15	90	45	0.15

. Mixing and molding: Dry powders (PCR + PLR) were pre-blended for 2 min. The activator was added and mixed for 3 min at low–medium speed in a Hobart paste mixer ((Hobart Corporation, Troy, OH, USA). Pastes were cast in steel cylindrical molds 25 mm diameter × 50 mm height, by uniaxial compaction (~500 psi). Demolding occurred at 24 h. Curing: A pre-cure at 40 °C for 72 h was applied in a ventilated oven, followed by storage at laboratory conditions (23–25 °C, RH 50–60%) until test ages (7, 14, 28 d). The overall experimental workflow is summarized in Figure 1.

2.4. Compressive Strength Testing

Compressive strength (fc) was measured in a universal testing machine Tecnotest Modena F060/EV (Modena, Italia) with parallel platens and verified alignment. Displacement control was set to 1.0 mm min⁻¹. For each mix and age (7, 14, 28 d), n = 5 cylinders were tested. Results are reported as mean ± standard deviation (SD). The loading protocol and alignment criteria followed the principles of ASTM C109/C109M-24 (Standard Test Method for Compressive Strength of Hydraulic Cement Mortars; ASTM International: West Conshohocken, PA, USA), adapted to 25 × 50 mm cylinders.

2.5. X-Ray Diffraction (XRD)

Phase identification was performed on a Bruker D8 Advance powder diffractometer (Bruker AXS GmbH, Karlsruhe, Germany) (Cu Kα, λ = 1.5406 Å, 40 kV, 40 mA), θ–2θ geometry, 5–80° 2θ, step 0.020°, counting time 1.0 s/step, with sample spinning. Powders were finely ground and mounted on low-background silicon holders (Si-zero). A semi-quantitative Rietveld refinement was used to estimate the residual amorphous fraction.

Amorphicity index and peak metrics. To avoid statements based on absolute intensities, an amorphicity index was computed from the background-subtracted broad hump (≈18–38° 2θ) combined with FWHM metrics of the principal envelope; values were normalized within pattern. Quartz (≈26.7° 2θ) and portlandite (≈36.6° 2θ) peak intensities (I_Q, I_Pr) were tracked as qualitative markers only, not used for absolute-intensity comparisons.

2.6. Fourier Transform Infrared Spectroscopy (FTIR)

Spectra were acquired in ATR mode with a diamond crystal (Thermo Scientific Nicolet iS50—Shimadzu Corporation, Kyoto, Japan) over 4000–400 cm⁻¹, at 4 cm⁻¹ resolution, with 32 co-added scans per spectrum. A fresh background was recorded before each measurement and the ATR crystal was cleaned between samples. Prior to metric extraction, spectra were vector (unit-norm) normalized. Comparisons across mixtures are based on within-spectrum indicators and band-shape metrics of the T–O–Si envelope (≈1200–900 cm⁻¹): (i) the centroid ($\overline{\mathrm{\nu }}$) as an effective band position, and (ii) the full width at half maximum (FWHM) obtained by assisted local fitting (Gaussian–Lorentzian/Voigt) with second-derivative verification of band limits. Additionally—and always within the same spectrum—we computed area fractions of the T–O–Si envelope relative to the total 4000–400 cm⁻¹ area; no external reference band was used to claim between-sample intensity changes. Samples were dried at 60 °C for 24 h prior to analysis to limit physically adsorbed water.

2.7. Scanning Electron Microscopy and EDS (SEM–EDS)

Microstructure and local chemistry were examined with a Thermo Scientific Axia ChemiSEM (Thermo Fisher Scientific, Waltham, MA, USA) under high-vacuum, uncoated conditions (no conductive metallization). Secondary-electron (SE, 5 kV) imaging was used for topography and backscattered-electron (BSE, 15 kV) imaging for compositional contrast; working distance was 9–12 mm. Surfaces were freshly fractured from 28-day specimens and gently cleaned with dry air to remove loose particles. To mitigate charging, low beam current, frame averaging, and short dwell times were used. For each mixture, ≥5 representative fields (covering dense matrix and interparticle regions while avoiding large pores/edges) were imaged and analyzed at magnifications typically between 500× and 10,000×.

EDS was acquired at 15 kV (WD ≈ 10 mm) with real-time integration. Quantification followed the standard flow without standards (ZAF/φ(ρz)), with calibration/drift verified at the beginning and mid-run. Results are reported as atomic percentages. In this work, area-averaged Ca (at.%) (representative fields, masking open pores and unreacted inclusions) is used exclusively as a local tracer of matrix enrichment and not as an overall material composition. Mean ± SD is reported per mixture.

2.8. Statistical Treatment and QA/QC

Compressive strength: n = 5 specimens per mix and age (7, 14, 28 d).

FTIR: n = 3 independent spectra per mix. SEM-EDS: n ≥ 5 representative fields per mix. Assumption checks included normality (Shapiro–Wilk) and homoscedasticity (Levene or Brown–Forsythe). When applicable, one-way ANOVA was performed at α = 0.05, reporting effect size (η² or ε²). For correlation analyses (see Section 3.6), we used Pearson’s r (two-tailed; n = 6 mixes: 0, 10, 30, 50, 70, 100% PCR, i.e., the subset with comparable multi-technique coverage) with 95% confidence intervals obtained via Fisher-z. Competing linear vs. quadratic models were compared using R² and Akaike Information Criterion (AIC); sensitivity analyses were conducted by excluding points > 3 SD to probe robustness.

To ensure valid cross-mix comparisons, the XRD amorphicity index and FTIR network indicators were computed as within-pattern/spectrum normalized descriptors (position/width metrics and internal ratios), thus avoiding claims based on absolute ATR intensity. In SEM-EDS, area-averaged Ca (at.%) from representative fields is used strictly as a local tracer of Ca enrichment in the reacted matrix, and not as a bulk composition measurement. Instrument QA/QC: XRD was verified with NIST SRM 640d (Si); FTIR with a polystyrene film (band position/shape check); SEM-EDS included periodic energy calibration and drift checks; UTM platen parallelism/alignment was verified prior to testing.

3. Results

3.1. Compressive Strength

Figure 2 reports compressive strength (fc) at 7, 14, and 28 d for PLR–PCR pastes spanning 0–100% PCR. The response is non-linear: strength rises from 0 → 30% PCR and declines for ≥50% PCR. At 28 d, means were 14.2 MPa (0%), 15.6 MPa (10%), 16.2 MPa (30%, local maximum), 13.8 MPa (50%), 10.8 MPa (70%), and 10.1 MPa (100%). The 7/14 d data preserve the same ordering (see SI Table S2 for raw values, descriptive statistics, and ANOVA). Error bars (SD) reflect the typical dispersion of alkaline-activated pastes tested at L/B = 0.15 with constant activator chemistry.

3.2. XRD—Composition Effect at 28 d

Figure 3 compares 28 d XRD patterns for 0, 10, 30, and 100% PCR. 0% PCR (PLR only): broad crystalline set (kaolinite, quartz, albite, belite, calcite, octahedrite, gehlenite, anorthite), with quartz dominant near 26.7° 2θ. 10–30% PCR: portlandite emerges at ≈36.6° 2θ; several PLR-derived reflections (e.g., albite at 29.54° 2θ) diminish in relative prominence; the amorphous hump (≈18–38° 2θ) becomes more pronounced. 100% PCR: simplified pattern dominated by quartz/portlandite, indicating Ca-rich products and a limited aluminosilicate network [46,47,48,49,50,51,52]. An amorphicity index (background-subtracted area at 18–38° 2θ plus the FWHM of the main hump, normalized within pattern) increases from 0 → 30% PCR and decreases thereafter, mirroring fc.

3.3. XRD—Curing Age (7 vs. 28 d, 30% PCR)

Figure 4 (30% PCR) shows stable peak positions (quartz, albite, portlandite, belite, calcite) and a slight decrease in portlandite/belite intensities by 28 d, consistent with continued reaction and growth of the amorphous fraction. The amorphous-hump FWHM broadens modestly with age, indicating extended gel formation within the aluminosilicate framework.

3.4. SEM–EDS—Microstructure and Local Chemistry (28 d)

Figure 5 compares 28 d microstructures. 0% PCR: visible porosity and microcracks; unreacted particles. EDS is Si–Al-dominated (N-A-S-H matrix) with low Ca. 10% PCR: reduced microcracking and tighter packing; EDS shows a small Ca increase. 30% PCR: dense matrix with minimal defectology; EDS shows higher Ca (at.%) than at 0–10%, compatible with C-A-S-H domains coexisting with N-A-S-H. 100% PCR: heterogeneous texture with reintroduced pores/microcracks; elevated Ca and lower relative Al–Si signal, consistent with an interrupted aluminosilicate network. EDS is used semi-quantitatively as a local tracer of Ca enrichment (area-averaged fields), not as a bulk composition measurement [53,54,55,56].

3.5. FTIR—Network Signatures (28 d; 7–28 d at 30% PCR)

Overview at 28 days (0, 10, 30, 100% PCR). After within-spectrum normalization, the T–O–Si envelope (≈1200–900 cm⁻¹) exhibits a centroid downshift ($\Delta \overline{\mathrm{\nu }}$ to lower wavenumbers) and a slight FWHM broadening at 10–30% PCR relative to 0% PCR (Figure 6). These two features are consistent with a more extended and compositionally heterogeneous aluminosilicate network (greater prevalence of Si–O–(Si/Al) linkages). At 100% PCR, the T–O–Si envelope remains detectable but with comparatively narrower traits, while the carbonate region (≈1460–1380 cm⁻¹) becomes more prominent, in line with higher Ca availability and secondary carbonation.

Age evolution at 30% PCR (7 → 14 → 28 d). A progressive downshift of $\overline{\mathrm{\nu }}$ and a modest FWHM broadening are observed in the T–O–Si region under the applied curing schedule, supporting ongoing condensation and network maturation over time (Figure 7) [57].

Processing and comparison criteria. All between-mixture statements are drawn from band position (centroid, $\overline{\mathrm{\nu }}$), band width (FWHM), and within-spectrum ratios computed inside the 1200–900 cm⁻¹ window; no absolute ATR intensity comparisons across samples are used. Crosslinks with mechanical and microstructural indicators are discussed in Section 3.6. Overall, the FTIR trends at intermediate PCR fractions are coherent with the mechanical optimum near 30% PCR and with the N-A-S-H/C-A-S-H co-reticulation scenario inferred from XRD (amorphicity changes) and SEM-EDS (moderate Ca enrichment) [42,58,59,60,61,62,63,64,65,66,67]. All conclusions are supported by position ($\Delta \overline{\mathrm{\nu }}$), width (FWHM) and internal ratios of the spectrum at 1200–900 cm⁻¹, consistent with the methodological approach of Section 2.6.

3.6. Property–Structure Correlations (28 d)

To integrate mechanical response with intensity-independent structural descriptors, we correlated $f_c$ (28 d) against three metrics: (i) a pattern-internal XRD amorphicity index, (ii) a normalized FTIR T–O–Si indicator derived from band position (centroid, $\overline{\mathrm{\nu }}$) and width (FWHM) within 1200–900 cm⁻¹ after within-spectrum normalization, and (iii) area-averaged Ca (at.%) from SEM–EDS as a local tracer (not a bulk composition). Statistics used Pearson’s $r$ (two-tailed), $n=6$ mixes (0, 10, 30, 50, 70, 100% PCR), with 95% CIs by Fisher-$z$. Linear and quadratic models were compared via $R^2$/AIC, with sensitivity analyses excluding points $>3$ SD; assumptions and QA/QC follow Section 2.8.

• $f_c$ vs. XRD amorphicity index. $r=0.973$, $p\approx 0.0011$, 95% CI $[0.77,0.997]$; linear fit $R^2=0.946$; a quadratic term yields a marginal gain ($R^2\approx 0.97$).
• $f_c$ vs. FTIR (normalized T–O–Si indicator). $r\approx 0.93$, $p<0.01$; linear $R^2\approx 0.86–0.90$; the quadratic model adds only minor improvement.
• $f_c$ vs. Ca (at.%) by SEM–EDS (local). $r=-0.849$, $p=0.032$, 95% CI $\left[-0.983,-0.121\right]$. A quadratic model markedly improves the fit ($R^2\approx 0.93$), revealing an intermediate Ca optimum (consistent with $\sim 30\%$ PCR) and performance losses at the extremes (0% and 100% PCR).

Overall, strength increases with higher amorphicity (XRD) and with the T–O–Si evolution (FTIR)—both proxies of network extension/densification—while Ca (at.%) acts as a non-monotonic driver: moderate Ca promotes C-A-S-H/N-A-S-H co-reticulation and improved load-bearing connectivity; excess Ca simplifies mineralogy (quartz/portlandite), favors C–S–H/carbonation pathways, reintroduces microdefects, and reduces $f_c$. These convergent trends align with the mechanical optimum near 30% PCR and the microstructural model (Figure 8).

3.7. Theoretical Oxide Balance Per Mix (Si–Al–Ca)

Using Table 1 oxides and Table 2 proportions, a theoretical Si–Al–Ca balance was computed for each mix (normalized to Si + Al + Ca in the precursor mass; activator oxygen not counted).

Table 3. Theoretical Si–Al–Ca balance per mixture (moles per 100 g of precursor) and Ca/(Si + Al) ratio derived from the oxide composition of PCR/PLR (Table 1) and mixture matrices (Table 2).

ID	PCR (%)	PLR (%)	SiO2 Mix (wt%)	Al2O3 Mix (wt%)	CaO Mix (wt%)	n (Si) (mol)	n (Al) (mol)	n (Ca) (mol)	Ca/(Si + Al)
P0	0	100	61	21.5	4.2	1.015	0.422	0.075	0.052
P10	10	90	57.75	20	7.93	0.961	0.393	0.142	0.105
P30	30	70	51.25	17	15.39	0.853	0.333	0.275	0.232
P50	50	50	44.75	14	22.85	0.745	0.275	0.408	0.400
P70	70	30	38.25	11	30.31	0.637	0.216	0.541	0.634
P90	90	10	31.75	8	37.77	0.528	0.157	0.674	0.983
P100	100	0	28.5	6.5	41.5	0.474	0.128	0.74	1.230

reports Si, Al, Ca (relative fractions) and the derived Ca/(Si + Al) index. The 30% PCR mix falls within Ca/(Si + Al) ≈ 0.35–0.45, coincident with the maxima of fc, the XRD amorphicity index, and the FTIR T–O–Si indicator. For ≥ 50% PCR, Ca/(Si + Al) exceeds that interval, aligning with pattern simplification (quartz/portlandite) and reduced strength. This compositional metric therefore defines a design window consistent with the observed optimum.

3.8. Visual Synthesis of Tracers

Figure 8 displays a horizontal bar chart that integrates six indicators across three compositions of PCR (10%, 30%, 70%). The categories on the vertical axis are: N-A-S-H, C-A-S-H, Inherited phases (quartz/portlandite), C–S–H/carbonation, XRD—Relative amorphicity (18–38° 2θ hump/FWHM), and FTIR band (T–O–Si, position/FWHM normalized). For each category, three bars compare the 10% PCR (orange), 30% PCR (green) and 70% PCR (purple) states. Bar lengths are normalized (0–1) within each indicator (qualitative scaling), so they illustrate trends observed in Section 3.2, Section 3.3, Section 3.4 and Section 3.5 rather than absolute intensities. Consistent with the results, 30% PCR (green) shows higher relative amorphicity (XRD) and stronger T–O–Si evolution (FTIR, position/FWHM), together with balanced N-A-S-H/C-A-S-H, whereas 70% PCR (purple) shows higher C–S–H/carbonation and inherited phases, and 10% PCR (orange) retains dominant N-A-S-H with limited C-A-S-H. The mechanistic implications are discussed in Section 4.8.

4. Discussion

4.1. Dominant Mechanism and the ≈30% PCR Optimum

The compressive strength (fc)–composition curve exhibits a local maximum at ≈30% PCR and decreases for substitutions ≥ 50%. This response is explained by co-reticulation between N-A-S-H domains (sourced from the aluminosilicate stock of PLR) and C-A-S-H domains (nucleated by Ca from PCR). Within the intermediate window, Ca is sufficient to bridge and densify the N-A-S-H network; beyond that threshold, excess Ca²⁺ and dilution of reactive Si–Al species activate competing routes (C–S–H and/or secondary carbonation), disrupt network continuity, and reduce fc. This framework is consistent with prior reports on ceramic–cement systems derived from CDW and with Figure 8, which synthesizes the micro/mesostructural tracers by PCR level.

4.2. Diffractometric Evidence: Mineralogical Simplification and Relative Amorphicity

At 28 days, XRD shows that PLR (0% PCR) retains a broad crystalline palette; with 10–30% PCR, portlandite (~36.6° 2θ) appears and the relative prominence of PLR phases (e.g., albite ~29.54° 2θ) diminishes, suggesting consumption/dilution of crystalline aluminosilicates and growth of the amorphous fraction associated with reaction gels. At 100% PCR, the pattern simplifies (quartz/portlandite dominant), indicating Ca predominance and a smaller aluminosilicate contribution. To avoid inferences from absolute intensities, we use a relative amorphicity index (area of the 18–38° 2θ hump + FWHM, normalized within each pattern), which maximizes at 30% PCR, in line with the mechanical peak.

4.3. Spectroscopic Evidence (FTIR): Normalized Δ$\overline{\nu }$/FWHM Descriptors

After within-spectrum normalization, the T–O–Si envelope (≈1200–900 cm⁻¹) exhibits a centroid shift ($\Delta \overline{\mathrm{\nu }}$) to lower wavenumbers and a moderate FWHM broadening at 10–30% PCR relative to 0% PCR—features consistent with greater network extent/heterogeneity of the aluminosilicate gel. At 100% PCR, carbonate features (~1460–1380 cm⁻¹) become more evident, in line with secondary carbonation in Ca-rich matrices. The 7 → 14 → 28 d evolution at 30% PCR shows a progressive $\overline{\mathrm{\nu }}$ downshift and slight FWHM broadening under the applied curing schedule, supporting ongoing condensation. All comparisons rely on position/width metrics and within-spectrum ratios; no claims are made from absolute intensity (Figure 6 and Figure 7).

4.4. Microstructure (SEM–EDS): Intermediate Densification and High-PCR Heterogeneity

SEM (28 d) reveals a transition from a porous/microcracked matrix (0% PCR) to a compact microstructure (10–30% PCR) and, again, to heterogeneity with reintroduced defects (100% PCR). EDS is used locally (representative fields, at.%) as a tracer of Ca enrichment, not as a bulk composition measurement: the increase in Ca (0 → 30% PCR) supports C-A-S-H nucleation/bridging; at 100% PCR, higher Ca with a lower relative Al–Si share is consistent with reduced co-continuity and lower fc (Figure 5).

4.5. Quantitative Integration: fc–Tracer Correlations (28 d)

To provide intensity-independent evidence of network development, fc was correlated with (i) a normalized XRD amorphicity index, (ii) a normalized FTIR T–O–Si indicator derived from band position (centroid, $\overline{\mathrm{\nu }}$) and width (FWHM) within 1200–900 cm⁻¹, and (iii) Ca (at.%) from SEM–EDS (local tracer). Significant associations were obtained:

fc vs. XRD amorphicity: r ≈ 0.97, p ≈ 0.001; linear R² ≈ 0.95; quadratic adds marginal gain.

fc vs. FTIR (T–O–Si, normalized): r ≈ 0.90, p ≈ 0.015; linear R² ≈ 0.86–0.90.

fc vs. Ca (at.%): non-linear relation; a quadratic model (R² ≈ 0.93) reveals an intermediate Ca optimum (≈30% PCR) and performance losses at the extremes (0% and 100% PCR).

4.6. Theoretical Oxide Balance and the Ca/(Si + Al) Metric

The per-mix theoretical balance (Table 3) shows that Ca/(Si + Al) ≈ 0.35–0.45 coincides with (i) the mechanical optimum (~30% PCR), (ii) the relative maximum in XRD amorphicity, and (iii) the most favorable evolution of T–O–Si (FTIR). Outside this window, dilution of reactive aluminosilicates and stronger carbonation explain the drop in fc.

4.7. Kinetics and Curing

The 40 °C/72 h pre-curing accelerates dissolution–condensation and early gel formation; subsequent room-temperature curing enables network maturation/reorganization, as reflected by the 7 → 14 → 28 d increase in fc and by FTIR metrics ($\Delta \overline{\mathrm{\nu }}$/FWHM).

4.8. Design and Quality-Control Implications

The results delineate a design window centered at ≈30% PCR. For scale-up: (i) keep L/B = 0.15 and Ms ≈ 3.2; (ii) ensure fineness < 75 μm and control inherited phases in incoming lots; (iii) adopt fast tracers (normalized XRD amorphicity and FTIR T–O–Si descriptors) as process controls; and (iv) verify Ca (at.%) by EDS at reception to maintain the Ca/Si–Al balance that enables co-reticulation (see Figure 8).

4.9. Limitations and Future Work

Activator chemistry and L/B were fixed to isolate the %PCR effect; granulometry and mineralogy of the CDW sources were not varied. A more direct confirmation of co-reticulation would benefit from absolute quantification (e.g., KBr-FTIR with an internal standard, ²⁹Si/²⁷Al NMR, selective fractionation) and from mapping Ms/molarity, granulometry/mineralogy, and curing windows; future work should also address durability (sulfates, chlorides, wet–dry cycles).

5. Conclusions

Mechanical optimum at ≈30% PCR. With NaOH/Na₂SiO₃/KOH (Ms ≈ 3.2) and L/B = 0.15, PLR–PCR pastes reached fc(28 d) = 16.2 MPa at 30% PCR, higher than 0% PCR (14.2 MPa) and decreasing systematically for ≥50% (e.g., 13.8–10.1 MPa).

Mechanism (N-A-S-H/C-A-S-H co-reticulation). Ca from PCR nucleates C-A-S-H that bridges/densifies the N-A-S-H network, maximizing connectivity at intermediate fractions; excess Ca²⁺ dilutes reactive Si–Al, promotes C–S–H/carbonation, and penalizes fc (see Figure 8).

Multi-technique convergence.

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XRD (28 d): reduced prominence of PLR crystalline phases and a relative maximum in amorphicity (18–38° 2θ + FWHM, normalized) at 30% PCR.

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FTIR (28 d): $\Delta \overline{\mathrm{\nu }}$/FWHM (normalized) of T–O–Si indicate a more extended network at 30% PCR; carbonates are more evident at high PCR.

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SEM–EDS (28 d): densification at 10–30% PCR; heterogeneity/defect reintroduction at 100% PCR; Ca (at.%) used as a local tracer.

Quantitative associations (28 d). fc correlates positively with the XRD amorphicity index (r ≈ 0.97, p ≈ 0.001) and with the FTIR T–O–Si indicator (r ≈ 0.90, p ≈ 0.015); fc vs. Ca (at.%) follows a non-linear trend (best quadratic fit, R² ≈ 0.93) with an intermediate optimum.

Compositional metric. The per-mix theoretical balance places Ca/(Si + Al) ≈ 0.35–0.45 in the vicinity of the mechanical optimum and of the XRD/FTIR relative maxima; outside that window, the network simplifies and carbonation increases.

Formulation and control implications. For reproducibility and scale-up: preserve L/B and Ms, ensure fineness, and control inherited phases; use XRD amorphicity and FTIR T–O–Si as rapid tracers; verify Ca (at.%) by EDS at reception to maintain the Ca/Si–Al balance enabling co-reticulation.

Scope/limitations and future work. The %PCR effect was isolated by fixing activator and L/B; future research should map Ms/molarity, granulometry/mineralogy, and curing windows, and include durability. For direct confirmation of co-reticulation, consider KBr-FTIR with a reference band and ²⁹Si/²⁷Al NMR.