Figure 3. (a) Interfacial energy and (b) Energy ΔG* versus super saturation ratio S of pure and KCl added KAP solution.
Figure 4. Powder X-ray diffraction of (a) pure KAP and (b) KCl (10 mol%) doped KAP crystal.
3.4. FTIR Spectra
Figure 5 shows the FTIR spectra of the pure and KCl (10 mol%) doped KAP crystal. The peak assignment is given in Table 2. The data indicate shifting of symmetrical C=O stretching of KAP to higher energy for KCl doping. This budge to higher energy indicates interaction of KAP with KCl  . The characteristic C-COO stretching and C=C-C at 1285.58 and 581.55 cm−1 are shifted to 1286.54 and 582.51 cm−1, indicating substitution. The asymmetric stretching vibration of the carboxylate ion is shifted to lower energy (1562.37 cm−1) compared with pure KAP (1572.01 cm−1).
3.5. Optical Studies
The UV-VIS transmittance spectra and reflectance curve (inset) of pure and KCl (10 mol%) doped KAP crystals are shown in Figure 6. A cut off wavelength is noticed near about 240 nm. There is no striking absorption in the entire region of the spectrum. The investigation of the optical absorption coefficient on the photon energy has
Table 1. Unit cell parameters of pure and KCl doped KAP crystals.
Table 2. Vibrational frequencies obtained for pure and doped KAP crystals through FTIR studies.
Figure 5. FTIR spectrum for (a) pure KAP and (b) KCl (10 mol%) doped KAP crystals.
Figure 6. UV-VIS spectra and reflectance curve (inset) of (a) Pure KAP and (b) KCl (10 mol%) doped KAP crystals.
become a fashionable way to interpret the band structure and nature of transition of electrons. The optical energy gap Eg can be expressed with respect to the incident pthoton energy hn by Equation (5)  ,
where a is the optical absorption coefficient, A is a constant, hν = photon energy, Eg = Energy gap, p is thought to as 2 or 1/2 for a indirect or direct allowed transitions, respectively. The plot of absorption coefficient a on photon energy hn is given in Figure 7. Direct and indirect band gap Egd and Egi are evaluated by the extrapolations of the linear part down to and respectively  . The values are tabulated in Table 3.
The rise of the band gap due to doping may be thought of as falling off irregularity and defects in the crystal which is in fact viewed as rise of an electric field by an electrically charged particles within the crystal  . The extinction coefficient (K) can be written as
where λ is the wavelength of the incident radiation.
Figure 7. (a) (αhν)1/2and (b) (αhν)2 as a function of photon energy for pure and KCl (10 mol%) doped KAP crystals.
Table 3. Optical parameters of pure and KCl (10 mol%) doped KAP crystals.
crystal structure. Atoms easily polarizable (i.e. electron are easily displaced) give rise to a high refractive index. The equations relating transmittance (T), reflectance (R) and refractive index (n) can be expressed with the following equations (considering T + R = 1)  .
The complex dielectric constant εc can be expressed with real (εr) and imaginary (εi) parts of dielectric constant as, where and. As K is very small, it can be considered  . The optical conductivity σop of the crystal is associated with the absorption coefficient as 
where c is the velocity of light and n is the refractive index. The electrical conductivity can be written as 
Non linear optical (NLO) property is expected for the crystal because Figure 8 reveals the lower value of complex dielectric constant along the transmission range which in turn indicates induced polarization. Lower electrical conductivity at higher photon energy (Figure 9(a)) specifies the dielectric nature of the material. On the other hand, the higher value of optical conductivity at higher photon energy (Figure 9(b)) brings to light superior conversion capability for second harmonics generation devices.
The electrical susceptibility (χc) can be assessed by the relation 
From Figure 10(a), it is clear that electrical susceptibility is larger than 1 and the material is polarizable if the light is made highly intense.
Figure 8. (a) Real part (er) and (b) Imaginary part (ei) of dielectric constant as a function of photon energy for pure and KCl (10 mol%) doped KAP crystals.
Figure 9. Relations of (a) Electrical conductivity (σe) and (b) Optical conductivity (σo) with photon energy for pure and KCl (10 mol%) doped KAP crystals.
Figure 10. (a) Electrical susceptibility and (b) Refractive index as a function of wavelength for pure and KCl (10 mol%) doped KAP crystals.
Wemple and Di Domenico made use of the single effective oscillator equation and investigated refractive index data lower to the interband absorption edge. The relation between the refractive index and photon energy can be expressed by the equation 
where Eso and Ed are the single oscillator and the dispersion energy, respectively. Figure 10(b) plots the change of the refractive index with wavelength. In Figure 11(a), the oscillator parameters are figured out from (n2 − 1)−1 versus (hν)2 plot by measuring the slope and intersection of the straight line with y-axis. The above-men- tioned model establishes a connection between the single oscillator parameters Eso and Ed and imaginary part εi of the complex dielectric constant. The M−1 and M−3 moments of the ε(E) optical spectrum can be formulated as the following expression
Figure 11. (a) 1/(n2 − 1) as a function of (hn)2and (b) 1/(n2-1) as a function of l−2 for pure and KCl (10 mol%) doped KAP crystals.
The zero-frequency refractive index n0 can be achieved by the expression
The zero-frequency dielectric constant is obtained by using the relation. The oscillator energy Eso represents mean gap energy and can be expressed in terms of the lowest direct band gap Egd by the equation Eso = 2Egd on experimental basis  . The oscillator strength Sso can be obtained from the refractive index n which is expressed by single Sellmeier oscillator equation as (in low energy range) 
where is the oscillator wavelength. From Equation (18) we can get the following equation 
where. The values of M−1, M−3, no, eo, Sso and λso evaluated from versus λ−2 plot can be seen in Figure 11(b) and are given in Table 3.
Pure and KCl doped KAP crystals were grown by adopting slow evaporation method. The solubility varied proportionately with temperature. Incorporation of KCl resulted in increase of the metastable zone width and interfacial energy with respect to undoped solution. The possible reason of this enhancement might be considered as opposition in chemical activity faced by the metal ions in the mother solution. XRD analysis indicated incorporation of foreign atoms into the KAP crystal matrix. The UV-VIS spectra analysis showed that the transmission capability got better as well as revealed the coexistence of indirect and direct transitions in KCl doped KAP crystals. Optical constants such as the dispersion energy, oscillator strength, oscillator energy and zero-frequ- ency refractive index were evaluated by making use of the Wemple-Di Domenico single-effective-oscillator model and observed to change considerably due to KCl doping.
Authors are grateful to Dr. Abdul Gafur and Dr. Dilip Kumar Saha for their kind permission to perform FTIR and XRD study.