## 1 Introduction
### Factors Affecting Bond Vibrations  
The molecules could vibrate whenever there is an energy level difference [44]. Change in molecular energy (\(\Delta E\)) shown in Equation (4) is defined as the product of [PERSON]'s constant (h = 6.63 \(\times 10^{-34}\) m\({}^{2}\frac{\text{kg}}{8}\)) and frequency of the normal mode (f = velocity(c)/ wavelength (\(\lambda\))):  
\[\Delta\text{E}=\text{hv} \tag{4}\]Many factors affect the position or characteristics of the absorption band, which include the strength or stiffness of the bond between two adjacent atoms (k), which invariably depends on the valency of atoms and increases across the period, the square root of atomic weight (u), and the coordination number of cations (CN) [1,44]. Further, the lighter the masses of the atoms and the stiffer the bonds, the higher the frequency of the vibrations (wavenumbers) of the molecules attached to the bond (Equations (2)) [45]. According to [PERSON] et al. [15], from [PERSON]'s law, the frequency of the absorption band (v) can be given in terms of the reduced mass (u) and unique chemical bond constant (k), as shown in Equation (5). \[\
u=\frac{1}{2\pi}\sqrt{\frac{k}{u}} \tag{5}\]  
With wavenumber, \(\overline{\
u}=\
u\) /speed of light (c), and Avogadro number (N), Equations (6) and (7) become:  
\[\overline{\
u}=\frac{1}{2\pi c}\sqrt{\frac{k}{\left(\frac{u}{N}\right)}} \tag{6}\]  
For \(h_{c}=3\times 10^{10}\frac{cm}{s}\) and [PERSON]'s number, N = \(6.02\times 10^{23}\):  
\[\overline{\
u}=4.12\sqrt{\frac{k}{u}} \tag{7}\]  
where \(u=\frac{m_{1}m_{2}}{m_{1}+m_{2}}\) is the reduced mass (g/mol) of the two vibrating atoms of masses, \(m_{1}\) and \(m_{2}\), N is Avogadro's number, c is the speed of light, and k (dyne/cm) is the unique chemical bond force constant which increases with the number of \(\pi\) bond within the molecules such that triple, double, and single bonds have the values of 1,500,000, 1,000,00, and 500,000 dyne/cm, respectively. 2 Historical Background of the Utilization of FTIR for Bond Characterization in Cementitious Binders  
Ordinary Portland cement, alkaline-activated slag (AAS), and geopolymer- or alkaline-activation of aluminosilicate materials, such as class F flyash, metakaolin, and others, may be used as cementitious binders for civil engineering applications [25,46,47]. Material science was one of the earliest applications of FTIR technology. Researchers in structural materials, civil engineering, and cement chemistry have been attempting to comprehend the skeletal framework of this binder, which is primarily composed of inorganic silica and alumina, for qualitative evaluation. On this note, [PERSON] et al. [48] were one of the first researchers to use FTIR to characterize inorganic minerals with wavelengths ranging from 2 to 16 microns. They reported the possible application of the method to soil and ceramics before [49] and used it to study silicate structures. [PERSON] [22] used IR spectroscopy to investigate inorganic extenders and pigment in the mid-IR region of 200-1500 cm\({}^{-1}\) in 1966 in an effort to comprehend their properties. To aid in the interpretation of spectra, [PERSON] [50] created an atlas of inorganic, organometallic, bioinorganic, and coordination compounds. As early as 1978, the technique was also utilized in various areas of material science, most notably in the characterization of clay minerals, such as illite and montmorillonite [44]. In addition, they distinguished kaolinite (doublet peak), halloysite (singlet peak), and nontronite (singlet peak) (no peak). The shifting in the spectral band distinguished montmorillonite, illite, and muscovite, which had the highest K\({}_{2}\)O, based on their respective wavelengths of 9.35, 9.7, and 9.6 microns. The application of FTIR directly to the analysis of cementitious binders began in the early 1970s. Based on this premise, [PERSON] used infrared (IR) and Raman techniques to identify the phases of OPC binders in 1974 [51,52], and Laser-Raman techniques were used to identify these phases in 1976 [24].