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23 2. KDP SINGLE CRYSTALS This chapter gives the literature survey of various studies made on KDP single crystals in the near past. 2.1 Importance Potassium dihydrogen phosphate (KH 2 PO 4 , KDP) is a representative of hydrogen bonded (hydrogen bond between the phosphate tetrahedral ion) materials which possesses important piezoelectric, ferroelectric, electro-optic and nonlinear optical properties. Ferroelectrics with hydrogen bonds, due to relatively high nonlinear efficiency and dielectric permittivity, huge piezoelectric effect and pyroelectric properties, the possibility of the spontaneous polarization re-orientation in a relatively small field are successfully implemented in a wide class of optoelectronic devices and sensor technology, nonlinear optical and information optical storage, etc. Due to their interesting electrical and optical properties, structural phase transition (at Curie temperature 123 K), and ease of crystallization, KDP and its isomorphs have been the subject of a wide variety of investigations for over 50 years. A crystallochemical analogue of KDP, NH 4 H 2 PO 4 (amonium dihydrogen phosphate, ADP) found fairly wide practical applications and was used as piezoelectric transducers in microphones, gramophones and other sound reproduction devices. The very first materials to be used and exploited for their nonlinear optical and electro-optical properties were KDP and ADP. KDP single crystals have high laser damage threshold,

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2. KDP SINGLE CRYSTALS

This chapter gives the literature survey of various studies made on KDP single

crystals in the near past.

2.1 Importance

Potassium dihydrogen phosphate (KH2PO4, KDP) is a representative of hydrogen

bonded (hydrogen bond between the phosphate tetrahedral ion) materials which possesses

important piezoelectric, ferroelectric, electro-optic and nonlinear optical properties.

Ferroelectrics with hydrogen bonds, due to relatively high nonlinear efficiency and

dielectric permittivity, huge piezoelectric effect and pyroelectric properties, the

possibility of the spontaneous polarization re-orientation in a relatively small field are

successfully implemented in a wide class of optoelectronic devices and sensor

technology, nonlinear optical and information optical storage, etc. Due to their interesting

electrical and optical properties, structural phase transition (at Curie temperature 123 K),

and ease of crystallization, KDP and its isomorphs have been the subject of a wide

variety of investigations for over 50 years.

A crystallochemical analogue of KDP, NH4H2PO4 (amonium dihydrogen

phosphate, ADP) found fairly wide practical applications and was used as piezoelectric

transducers in microphones, gramophones and other sound reproduction devices. The

very first materials to be used and exploited for their nonlinear optical and electro-optical

properties were KDP and ADP. KDP single crystals have high laser damage threshold,

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large nonlinear optical coefficients, good structural quality and mechanical properties and

they have several device applications. The electro-optic effect of KDP leads to the

application such as polarization filter, electronic light shutter, optical rectifier, electronic

light modulator, piezo optic resonator, transducer, etc [46, 47]. The electro-optic

deflection property of KDP crystals is also used in frequency reformation in neodymium

laser. A tunable ruby laser uses a KDP electro-optical filter of improved design and

construction as a tuning element. The piezo- electric property of KDP crystal makes it

useful for the construction of crystal filters and frequency stabilizers in electronic circuit.

KDP used as a tuning element in laser operation of electro-optic devices is based on the

Pockel‟s effect in which the change in dielectric constant is a linear function of the

applied field [48]. Frequency converters and Pockel‟s cell fabricated from KDP and

DKDP crystals are critical components in fusion class laser system. The acousto-optic

tunable filters have been developed using KDP [49 - 53]. For the inertial confinement

fusion (ICF) experiments, the performance of large aperture switches based on KDP has

been assessed for high power laser experiments [54]. KDP based world‟s largest laser to

generate UV beams has been demonstrated [55]. Using cascaded partially deuterated

KDP crystals the broad band frequency tripling was demonstrated by Wang et al [56].

Rapid growths of large size (40 - 55 cm) KDP crystals as well as rapid growth of KDP

crystals with additives [57] have facilitated to obtain perfect KDP crystals for device

application on large scale.

KDP is an efficient angle-tuned dielectric medium for optical harmonic

generation in and near the visible region [58]. This material offers high transmission

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throughout the visible spectrum and meets the requirements for an optical birefringence

large enough to bracket its refractive index for even the extreme wavelength over which

it is transparent. An additional advantage of KDP is its ability to withstand repeated

exposure to high power density laser radiation without inducing strains and subsequent

inhomogenities in the refractive index [59]. These characteristics make KDP a desirable

material for frequency doubling and mixing experiments with many solid state and dye

lasers with fundamental wavelengths between 1060 and 525 nm.

Huge interest to KDP crystals is caused by their unique physical properties and

high manufacturability. In particular, KDP crystals which possesses extremely high

optical and structural perfection makes it possible to produce elements for doubling and

tripling of laser radiation frequency, electro-optic switches and modulators with an

aperture of several tens and hundreds of square centimeters to be used, e.g. in laser fusion

facilities. These crystals are distinguished by high efficiency of non-linear conversion and

a wide optical transparency range which extends far (up to 1760 nm) to the short-

wavelength region of the spectrum [60].

2.2 Growth of Single Crystals

KDP and its analogous systems such as deuterated KDP (DKDP) and ADP

crystals are of the most widely studied crystals. These crystals have been studied for their

different applications, but also for their morphologies, habits, effect of various growth

parameters, effect of impurities, etc. One of the aims of the researchers all over the world

has been to grow high quality KDP crystals rapidly. For this purpose various authors

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have made various modifications in the growth techniques as well as designed the new

set ups. The high and stable supersaturation of the water-soluble crystal molecule has

been the key issue of realizing the rapid rate of the crystal growth. The crystallization

occurs not only on the crystal surface but also on invisible small crystal cores in the

solution, which causes an undesirable crystal growth in the crystallizer. In 1987, a

splicing technique was reported by Sui et al [61] to speed up the enlargement of the

cross- section of KDP crystals. An n2 (n = 1, 2, 3, 4…) array of (001) oriented seed

crystals were applied to grow KDP crystals up to 72 cm2 in cross-section. The authors

reported the results of a research program concerning the seed splicing technique to grow

large KDP crystal. In 1983 an attempt was made to grow 40 x 40 cm2 cross-section and

100 cm length KDP crystals by Newkirk et al [62]. New technical tasks like high-power

laser systems for nuclear fusion have demand for very large size crystals. Sasaki and

Yokotani [63] have described the growth of huge KDP crystals which have a 40 x 40 cm2

cross section for a frequency converter for high power laser system for nuclear fusion

experiment. They have adopted conventional temperature reduction method (TRM) and

three-vessal method using constant temperature and constant technique. KDP and DKDP

crystals have been grown with the sizes up to 57 x 57 cm2 in cross section and about 55

cm in height by Zaitseva et al [64]. It is also important to control habit during the growth

of KDP crystals to achieve the large size crystal with specific habit for desired

applications. Zaitseva et al [65] proposed certain measures for the habit control. The habit

of solution grown KDP single crystals, space group 42d is formed by a combination of

prismatic {100} and pyramidal {101} faces as shown in Figure 2.1.

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Figure 2.1: Morphology of KDP crystal [66]

Rapid growth of KDP crystals has been obtained by various workers. Linear high

speed growth of 80 mm/day was obtained by computer controlled mechanism by

Minagawa et al [67] and earlier than this a rapid growth of over 50 mm/day was reported

by Nakatsuka et al [68] for KDP crystals. Recently, a movie of KDP crystal growth

weighing 800 pounds is put on internet in Youtube [69], which uses six feet high tank

containing one ton supersaturated solution of KDP. By using the turntable tank to rotate

the crystal it was possible to grow the crystal in two months, otherwise, it would have

taken two years in the conventional technique.

Bespalov et al [70] developed high-rate technique for the growth of KDP crystals

from water solution. Crystals were grown at a rate of 0.5-1 mm/h as compared with a rate

of 0.5-1 mm/day using a conventional technique and measure up to 150x150x80 mm.

Loiacono [71] et al and Bordui et al [72] attained increase in the growth rate of KDP

crystals up to 5 mm per day due to stringent growth conditions by controlling mainly the

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supersaturation using the computer. Fujioka et al [73] developed a set up to grow medium

sized KDP crystal (64x63x43 mm) for one day with a technique achieving higher

supersaturation in the growth solution. Masahiro et al [74] demonstrated KDP single

crystals at the growth rate of 54 mm/day achieving optical quality crystals. Two

important parameters affecting the growth rate and quality of KDP crystals are the pH

and the supersaturation of the solution. Velikhov and Demiraskaya [75] studied the effect

of solution composition on the growth rate of the {100} faces of KDP. Bespalov et al

[76] concentrated their efforts on finding the effect of supersaturation on the growth rate

of the {100} face. Efremova et al [77] reported the macroscopically measured growth rate

of the {100} and {101} faces as a function of pH at a fixed supersaturation. He found that

growth rate of the {100} and {101} faces remain almost constant up to pH of 3.5 beyond

which the growth rate starts to decrease. Zaitseva et al [78] have grown high quality KDP

single crystals of 5-16 cm in size at the growth rate of 10-40 mm/day without

spontaneous nucleation. Kolybaeva et al [79] developed large KDP single crystals with

cross section up to 300x300 mm2 and transmission at the wavelength λ=200 nm of about

86 %.

Impurities are present in all crystallization processes. Usually impurities are

adventitious and undesirable but sometimes they are intentionally added and then they are

called additive. The effect of impurities on the growth rate and habit of crystal growing in

solution has been the subject of many experimental and theoretical studies over many

years. For obtaining large size KDP plate, increasing the growth rate of the crystal is a

vital factor. The use of special additives is an effective way to accelerate the growth rate.

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Usually, different organic/ inorganic compounds are used as additives in industrial

crystallization, and positive effect of some organic additives for the growth of large size

crystals is widely known. In the recent years, efforts have been taken to improve the

quality, growth rate and properties of KDP, by employing new growth techniques [80 –

85, 57]. Podder [86] reported the presence of KCl in the medium is found to suppress the

metal ion impurities to a large extent and increase the growth rate. The increase in the

quality of KDP crystal in the presence of KCl is due to the complexation of trace metal

ion impurities in the solution by Cl- ion. The adjustment effect of additive on the growth

process and properties of crystal has been applied in recent years [87 - 89]. Some papers

[90 - 95] report a contrary effect involving an increase in the growth rate of crystal faces

in the presence of low concentration of additives. Such a growth promoting effect of

additive is called the catalytic effect of additive [94, 95]. The effect is observed in the

presence of organic [88, 90, 92] as well as inorganic additives [82, 92]. Kouji Maeda [96]

reported the growth rate, morphology and impurity dye distribution of faces, {100} and

{101} in KDP crystal due to the addition of organic dyes (sunset yellow, brilliant blue

FCF and sky blue). The growth rate of KDP is reported to increase 6-8 times when grown

from ethylene diamine tetra acetic acid (EDTA) added solution as compared to pure

solution [97].

Several investigators [98 - 102] have used the gel growth technique for growing

perfect and transparent single crystals. Brezina and Havrankova [103] attempted to grow

KDP crystal from agar gel. Later, Joshi and Antony [104] reported the growth of

transparent crystals of KDP in silica gels up to 40x8x7mm3 in size. In a quest to grow the

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long crystals of KDP, the Sankarnarayana – Ramasamy (S-R) method has been employed

by Balamurugan and co-workers [105, 106]. A KDP crystal of 15 mm diameter and 65

mm length has been reported. Furthermore, the feasibility of melt growth methods for

KDP crystals was checked by Pastor and Pastor [107].

2.3 Phase Transition

The potassium dihydrogen phosphate (KDP) crystal exhibits interesting physical

properties such as ferrolectricity and ferroelasticity and it is well known to present a

series of phase transition [108]. In KDP crystals, a decrease in temperature is

accompanied by the ferroelectric phase transition due to proton ordering over the O-

H…O hydrogen bonds. t has been conclusively established that, in the vicinity of the

transition temperature (Tc ≈ 122 K), the protons in this crystal predominantly form

configuration in which two of them are located either at the top of each PO4 tetrahedron

or at its bottom. In this case, one of the occupied proton-lattice modes becomes unstable,

thus giving rise to spontaneous polarization (Ps) along the tetragonal axis c of the crystal.

The oxygen proton configurations formed upon phase transition correspond to the

antiferroelectric-type ordering of dipole moments in the ab plane perpendicular to the

polar axis. Therefore, the phase transition in potassium dihydrogen phosphate can be

considered ferroelectric and antiferroelectric simultaneously [109]. So KDP crystals

represent the most typical hydrogen bonded ferroelectric with the order-disorder phase

transition. KDP exhibit an electric dipole moment even in the absence of external electric

field. It undergoes a phase transition from polarized phase to unpolarised phase. The

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temperature at which the transition takes place is known as the Curie temperature (123

K). KDP has phase transition to ferroelectric from its paraelectric state at 123 K. KDP is

ferroelectric well below room temperature [109]. The low temperature ferroelectric phase

has an orthorhombic unit cell (space group is Fdd2) having the dimensions (at 115 K)

given as a=10.467, b=10.533 and c=6.926 Å [110]. At room temperature KDP is

paraelectric phase has a tetramolecular unit cell (space group is 42d) having the

dimensions given as a=b=7.448 and c=6.977Å [111].

The H- bonded system in KDP and its analogues like ADP and DKDP possessing

continuous three-dimensional H – bond network has been recently studied for proton

transfer along H bonds and to effective anti-coupling of proton that plays the key role on

the ferroelectric behaviour of crystals and discussed by the tunneling parameter (Ω) and

the Ising parameter (Jij ) by Dolin et al [112] and the same is represented in Figure 2.2.

Figure 2.2: H surroundings of PO4 tetrahedron in KDP crystal

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The molecular weight and density at room temperature are respectively 136.09

and 2.33 g/cc [113]. The true melting point of KDP is difficult to determine owing to the

evolution of water vapour and condensation of phosphate species. The reported value is

400 0C [113]. KDP is highly soluble in water and sparingly soluble in alcohol. Above

Curie temperature, Tc (123 K), in the parametric phase transition, the crystal structure of

KDP and deuterated KDP, DKDP (KD2PO4) have been studied by several groups using

X-ray and neutron diffraction [114 - 117]. Below Tc, in the ferroelectric phase, the

accurate crystal structure of DKDP has been reported by Nakano et al [118] using an X-

ray automatic diffractometer. The crystal structure of KDP has been reported by Frazer

and Pepinsky by an X-ray diffraction study in 1953 [115] and by Bacon and Pease by a

neutron diffraction study in 1955 [119] except for the anisotropic temperature factors of

K, P and O atoms. On the basis of the temperature dependence of dielectric constant and

infrared spectra, Ginberg et al [120] observed KDP as ferroelectric phase at 180 0C;

Rapoport [121] found paraelectric phase at 233 0C by differential thermal analysis.

The polymorphism of KDP was reported by Subramony et al [122]. The structural

ordering below Tc in KDP has been studied by using high resolution neutron diffraction

by Nelmes et al [123]. The nature of hydrogen bond and the electron density distribution

in tetragonal KDP at room temperature was obtained by Maximum Entropy Method

(MEM) using the synchrotron radiation X-ray powder diffraction data by Yamamura et al

[124]. Moreover, the synchrotron radiation X – ray multiple diffraction study of KDP

phase transition induced by electric field has been reported by Santosh et al [125]. Xu and

Xue [126] reported the molecular structure of KDP crystal from the chemical bond

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viewpoint. A quantitative study on the structure-property correlation of KDP has been

done on the basis of chemical bond method [127]. The crystallographic structure of KDP

is shown in Figure 2.3, in which important bonds are indicated by lines in Figure 2.4

which give the bond graph of molecules, which clearly shows how constituent atoms are

bonded (including the bonding among the inner and intermolecule).

Figure 2.3: Crystallographic structure of KDP: Hydrogen bonds are indicated

Figure 2.4: Bond graph of KDP molecules

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The hydrogen bonds (dashed lines in Figure: 2.4), which link the neighboring

H2PO4- groups, and the chemical bonds inside H2PO4

- groups (solid lines between P, O

and H atoms in Figure: 2.4), are remarkably similar in these two isomorphs, i.e., the bond

number, length and strength, as well as the bond direction are approximately same..

However, the bond strengths between the adjacent anions (H2PO4-) and cations (K

+) is

significantly different, while the bond number and bond direction are still analogous.

Though there are various kinds of chemical bonds existing in KDP crystals, only the

weaker chemical bonds formed in the crystallization process have a dominant influence

on the crystal growth. When growing crystals in aqueous solution, the constituent atoms

enter into the crystal in the form of fundamental growth units produced by the strong

chemical bonds within them; the bond strength and bond number inside the growth units

are almost invariable in the whole crystallization process. As a constituent part of growth

units, the bond strength inside the growth unit is often stronger but has little influence on

the crystal growth [126].

The effect of doping on crystal structure of KDP and the presence of KDP and

the presence of extra phase can be detected by powder XRD. Podder et al [128] have

investigated lattice distortion in urea and KCl doped KDP crystals, and found that the

structures of the doped crystals were slightly distorted compared to pure KDP crystal.

This might be attributed to strains on the lattice by the absorption of urea and KCl.

Pritula et al [129] studied the effect of urea doping concentration on unit cell parameters

of KDP by powder XRD. To determine the lattice parameters of KDP crystals more

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precisely, the parameter c depending on the concentration of urea in solution has been

measured by the Bond method. The lattice parameter c (Δc = 1.4 x 10-3

) essentially

increased with the addition of 0.2M/2.0M of urea to the solution. At urea concentration

exceeding 0.2M, the observed lattice parameter variation was insignificant. Kumaresan et

al [130] studied the powder XRD patterns of various organic dye (Amaranth, Rhodamine

B and Methyl Orange) doped KDP crystals. Dyes distorted the crystal structure of doped

KDP slightly. This might be due to the strain on the lattice by absorption or substitution

of dyes. Peaks observed in the doped KDP crystals were correlated well with those

observed in individual parent compound with slight shift in the Bragg angle.

Recently, several authors [131 - 135] have reported powder XRD studies of

amino acid doped KDP crystals. All the workers have reported the single phase nature

after doping and shift in the peak positions with change in unit cell parameters.

Gunasekaran and Ramkumar [136] obtained the unit cell parameters of α- histidine doped

KDP crystals and also found less value of axial ratios for doped crystals than the pure

KDP crystal. Kushwaha et al [137] have recently reported the powder XRD pattern of L-

threonine doped KDP crystals and observed a systematic variation in the intensity of

diffraction peaks with varying L-threonine concentration. They did not report any extra

peak due to doping of L-threonine. Also, recently Parikh et al [138] have reported that the

single phase nature of L-alanine doped KDP crystals. Also, L-histidine doped KDP

crystals [135] and L-arginine doped KDP crystals [139] were reported. They reported the

single phase nature and slight change in the unit cell parameters on doping.

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Several other authors studied thermogravimetry of pure KDP crystals [140, 141]

and various doped KDP crystals [54, 142-144]. It has been found that glycine doped KDP

crystal starts decomposing at 204.93 0C and KDP crystal at 207.91

0C [143]. This also

further supports that amino acid doping slightly increases thermal destability and reduces

the phase transition temperature. Moreover, thermal studies on amino acids (L-glutamic

acid, L-histidine and L-valine) doped KDP crystals are reported by Kumaresan [144]

using TGA and DTA. Suresh Kumar and Babu Rajendra [53] found that the doping of L-

arginine, L-histidine and glycine increase the thermal stability of KDP. Delci et al [145]

also reported the thermal stability of the doped crystal is improved than KDP due to the

presence of boron. Deve et al [146] reported the doping with L-threonine made the KDP

crystal comparatively more thermally unstable. Parikh et al [135] have also reported that

when the amount of doping increases the thermal stability decreases as well as the values

of thermodynamic and kinetic parameters decrease.

2.4 Electrical Properties

The dielectric constant is one of the basic electrical properties of solid, which are

correlated with electro-optic property of the crystals [147]. The measurement of dielectric

constant as a function of frequency and temperature is of interest both from theoretical

point of view and from the applied aspects. Essentially, dielectric constant εr is the

measure of how a material is polarized in an external electric field. The dielectric

parameters depend on the frequency of the AC voltage across the material. The electrical

properties of molecules are generally characterized by three quantities:

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(i) Polarizability due to electronic displacement within atoms or ions.

(ii) Polarizability due to atomic or ionic displacement within the molecules. (changes in

bond angles and inter-atomic distances)

(iii) A permanent dipole moment

Electrical conductivity of ionic crystals yields useful information regarding the

mobility and production of lattice defects in these materials. In potassium dihydrogen

phosphate (KDP) type of crystals, the possible type of point defects which help the

electrical conduction process are the ionization defects, viz (HPO4)- and H3PO4 is

produced as a result of proton jump from one phosphate group to another along the same

bond [148]. Electrical conductivity of the KDP group crystal is determined by the proton

transport within the frame work of hydrogen bond [149]. Two mechanisms can be

proposed, which are: (1) considering similarity to the conductivity mechanism in ice

having hydrogen bonds [139, 149-151] and (2) considering conductivity associated with

the incorporation into the crystal lattice of impurities having different valences and the

formation of corresponding defects in the ionic crystals [150]. It has been assumed that

the conductivity of ice is obtained by the simultaneous presence of positive and negative

ions and orientational defects – vacant hydrogen bonds (L-defects) and doubly occupied

hydrogen bonds (D-defects). Other possible defects are vacancies and defect associates

[149].

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The temperature dependence of conductivity has lead Meena and Mahadevan

[139] to consider that the conductivity of KDP crystals can be determined by both

thermally generated L-defects and the foreign impurities incorporated into the lattice and

generating the L-defects there. Lokshin [152] assumed that (HPO4)-2

ions are also

responsible for the formation of vacant hydrogen bonds (L-defects). Therefore, it is easy

to understand from this discussion that the proton transport depends on the generation of

L-defects. The increase of conductivity with increase in temperature for L-arginine doped

KDP and ADP crystals [139] can be due to the interstitials which are expected to be

occupied by L-arginine molecules in KDP. This induces bulk defect states due to

competition in getting the sites for the L-arginine molecules to occupy. The L-arginine

molecules can be added to some extent in addition to the replacement of ions in the KDP

and ADP lattices and creating additional hydrogen bonds. As the conduction in KDP and

ADP occurs through protons and mainly due to the anions (H2PO4)- ions and not due to

the cations (K+, NH4

+), the additional hydrogen bonds created may reduce the L-defects

and consequently obstruct the movement of protons. This is the possible explanation

given by Meena and Mahadevan [139] for the decrease in the conductivity value with

increase in impurity concentration. The addition of L-arginine leads to decrease electrical

parameters such as ζdc, ζac, εr and tanδ for both KDP and ADP crystals, which has lead

Meena and Mahadevan [139] to conclude that L-arginine addition makes possible for the

KDP and ADP crystals to become low εr value dielectrics.

Moreover, the dielectric study of amino acids (L-glutamic acid, L-histidine and L-

valine) doped KDP crystal was carried out by Kumaresan [144, 153]. The authors found

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that on doping of amino acids the value of dielectric constant of KDP crystals decreased

and also decreased with increase in the frequency of applied field. Moreover, Larginine,

L-histidine and glycine doped KDP crystals were grown by Kumar and Babu [154]. They

have studied the dielectric behaviour and found the dielectric constant and dielectric loss

less in doped crystals when compared to pure KDP crystals. The dielectric constant

values were obtained comparatively low for Li+ ion added KDP crystals than the pure

KDP crystals within the frequency range 8 to 12 GHz. This suggested that the Li+

ion

added KDP crystals were more suitable for high speed electro-optic modulation than pure

KDP crystals [155]. Similarly high frequency dielectric study of thiourea doped KDP

crystals was carried out in X-band region of micro-wave frequency by Hussaini et al

[156]. They also found that the dielectric constant of thiourea doped KDP was less than

the pure KDP crystals. Suresh Kumar et al [53] reported the lower value of dielectric

constant due to doping with L-arginine, L-histidine and glycine in KDP crystal.

Earlier reports on KDP crystals doped with oxalate and chloride impurities have

shown increase in conductivity, which has been explained as due to the replacement of

(H2PO4)- ions by (C2O4)

-2 and Cl

- ions [157,158]. It was found that the activation energy

of KDP crystal does not vary much on adding oxalate impurity of various concentrations

[159]. Udupa et al [160] have found for KDP crystals that the dielectric constant

decreases with the increase of temperature at all frequencies studied. The same authors

also have observed the appreciable increase in the value of dielectric constant after

impurity (MgO) addition and decrease in its value with increase in frequency. It has been

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observed that the KDP system has become complex after ion irradiation and it shows

irregular behaviour with regard to conductivity property.

O‟Keeffe and Perrino [161] had measured the electrical conductivity of pure and

found that there is knee point at 180 0C. The activation energies were 0.72 eV and 0.56

eV for the temperature above and below 180 0C respectively. Harris and Vella [149]

measured the DC conductivity, a knee was found in the thermal evalution of conductivity

at 100 0C with the slightly different activation energies of 0.99 and 0.53 eV. Sharon and

Kalia [162] measured the DC conductivity with activation energy of 0.76 eV without any

anomaly in the conductivity plot. The carrier of the electrical conduction in KDP-type

crystals has been proved to be proton by coulomeric determination [163,164].

Various parameters affect the dielectric properties of the materials. Doping of

various impurity ions changes the dielectric of KDP crystal. Ananda Kumari and

Chandramani [165] have studied dielectric properties of Au+

doped/undoped KDP

crystals containing KI/NaI with varying frequency at room temperature. They have found

that the dielectric constant decreases with increase in frequency of applied field. Parikh et

al [166] have grown L-alanine doped KDP crystals. It was found that the dielectric

constant and dielectric loss values of L-alanine doped KDP crystals were lower than that

of pure KDP crystals. Recently, Ambujam [167] studied the effect of cation doping

(Mg2+

, Cu2+

, Ni2+

and Ca2+

) in KDP crystals on their dielectric properties. The variation

of dielectric constant with frequency suggested that as the frequency increased the

dielectric constant decreased and at high frequency the leveling of the plot to the X-axis

was observed.

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41

Chen et al [168] studied the electrical conduction and dielectric relaxation of KDP

crystals. The author found that the conduction mechanism in KDP crystal is due to the

protonic hopping between hydrogen vacancies at temperatures below 179 0C. Sekar

Ramasubramanian and Mahadevan [169] found that the doping of KCl increases the

dielectric constant with the increase in supersaturation of the solution, from which the

KDP crystal is grown. Deepa et al [170] observed that the impurity (NaCl and NaBr)

reduced the conductivity of KDP crystal. The author found that the non-observance of

systematic variation of conductivity with impurity concentration and impurity addition

due to the complex situation created by the halide impurity ions in the electrical

conduction of KDP crystal. Priya et al [171] have grown pure and impurity (urea and

thiourea) added KDP single crystals and reported the electrical conductivity

measurements along a- and c- directions at various temperatures. Goma et al [172] have

studied the variation of dielectric parameters when urea is added in KDP single crystals.

It was determined that the inclusion of urea leads to the low value of dielectric

permittivity. Balamurugan and Ramasamy [173] found that the dielectric constant was

higher and dielectric loss was less in SR method-grown KDP crystal as against

conventional method grown KDP crystal. The large value of dielectric constant at low

frequency is due to the presence of space charge polarization [174].

2.5 Mechanical Properties

Hardness is one of the important mechanical properties of the materials. The

hardness of a material is defined as the resistance it offers to the motion of dislocations,

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42

deformation or damage under an applied stress [175]. The most common measurement of

hardness is the indentation type. In order to describe the ISE (Indentation Size Effect) and

RISE (Reverse Indentation Size Effect) behaviours of materials, several models for

relation between applied indentation test load and indentation diagonal length have been

reported in the literature [176]. The hardness test methods used to determine the hardness

consist of indenting a solid surface by a loaded indenter of a definite geometrical shape

and measuring the contact area between the indenter and the material. It is used to

determine the stress needed to produce plastic flow in the brittle material. The ratio of the

load and the contact area is the experimental definition of hardness.

The hardness is not a simple property but rather a complex of mechanical

properties and at the same time a measure of intrinsic bonding of the material [177].

There are clear connections between chemical bonding, hardness and dislocation mobility

[178]. Resistance to the movement of dislocations will determine the hardness of the

materials [179].

Potassium dihydrogen phosphate (KDP) is relatively soft and brittle as compared

to other optical materials, including glasses. Anbukumar et al [180] have measured

Vickers micro-hardness on {100} face of KDP within the load range from 5 to 50 g and

found the variation of hardness from 1.77 to 1.57 GPa. They have also observed that the

indentation increased with increase in applied load. Rao and Sirdeshmukh [181]

measured the Vickers hardness of KDP crystal and reported a Vicker hardness of 1.45

GPa at 200 g. Shaskol‟skaya et al [182] reported measurement of both hardness and

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43

cracking in the Vickers measurement of KDP and KD2xH2-2xPO4 (deuterated KDP, with

x=0 to 0.95). They used load of 50 to 200 g and reported a hardness reduction from 1.44

to 1.22 GPa as the extent of deuteration x increased from 0 to 0.95. They also measured

the length of crack due to Vickers intents. Marion [183] has reported measured values of

fracture toughness in KDP crystals. Marian apparently used the direct crack method and

reported fracture toughness Kc of 0.2 MPa.m1/2

, as well as 0.09 MPa.m1/2

along the

weakest direction (longest crack). Shanmugham et al [184] observed a value of 187.5

kgmm-2

for the Vickers hardness number of KDP crystal. Joshi and Antony [185] as well

as Joshi et al [186] have studied dependence of hardness on indentation load and

anisotropy of {100} and {011} faces of KDP crystals. They also indicated the presence of

crack patterns around the indentation mark; which were found to be dependent on the

indenter orientation [186].

Micro-hardness studies on {100} face of gel grown KDP and ADP crystals have

been reported by Sengupta and Sengupta [187]. They observed slip lines on the {100}

face of ADP crystal at corners of the impression mark. However, micro-cracks were

observed around the indentation on {100} face of KDP crystals from 10 g load, which

spread out as the load increased. The Vickers micro-hardness decreased as applied load

increased for both crystals and the work hardening coefficient was less than 2, which

indicated the soft material nature. Hardness value of solution grown KDP crystal are less

than that of gel grown KDP crystals [187]. This implies that solution grown crystals are

softer than gel grown crystals which apparently contain more defects. Recently,

Balamurugan and Ramasamy [173] have observed the hardness value for SR method

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44

grown crystal which is very much higher (≥ twice) than the hardness of the conventional

method grown crystal. Due to the application of mechanical stress by the indentor,

dislocations are generated locally at the region of indentation. Thus the major

contribution to hardness is attributed to the high stress required for homogeneous

nucleation of dislocation in the small dislocation-free region indented [188]. Larger

hardness value for SR method grown KDP crystals indicates greater stress required to

form dislocation thus confirming greater crystalline perfection.

Further, it has been observed that the hardness value of KDP crystals is greater

than that of ADP crystals [184,187]. This could be attributed to the difference in their

molecular structures. Crystallographically, both ADP and KDP are similar in H2PO4

network. In ADP crystals, N-H…O bond occurs between ammonium and phosphate

groups, whereas KDP structure is a polar structure consisting of K+ and H2PO4

- ions. The

ionic bonding between K+ and H2PO4

- ions is stronger than N-H…O bond existing in

ADP molecules. As a result, KDP shows increased hardness.

The variation of Vickers micro-hardness with load was studied for KDP crystals

grown with organic additives; it was found that the hardness value of KDP is increased

with organic additive via the order urea, thiourea and EDTA respectively [189]. Kannan

et al [50] have studied the influence of La3+

ions on the growth of KDP crystals. They

confirmed by using Vickers micro-hardness that the presence of La3+

ions in the

superfacial crystal growth layers produced weak lattice stress. Recently, Ramakrishna

Murthy and Venkateshwar Rao [190] have reported the study of He+ ion beam

modification of the {100} surfaces of KDP and ADP crystals relative to the as-grown to

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45

assess the nature and extent of radiation damage. Moreover, Balamurugan et al [191]

have studied the effect of KCl doping and measured the micro-hardness of KDP crystals.

Rajesh et al [189] have reported that the organic additives improved the

mechanical strength of KDP crystals. Dhanaraj et al [192] found that the hardness value

of potassium thiocyanate doped KDP crystal is lower than that of pure KDP crystal and it

decreases with the increase in dopant concentration. This may be the result of loosely

packed lattice with reduced bond energy due to the introduction of the additive into the

crystal. Here increase in additive (dopant) concentration into parent material leads to the

increase in interatomic distances which results in the diminishing of hardness value with

the additive concentration. Kumaresan et al [193] have reported that the hardness value of

copper thiourea complex doped KDP is less than the other semi-organic crystals.

Rahman and Podder [194] have observed that the hardness and work hardening

coefficient increases with the addition of EDTA in KDP crystal. Jagdish and Rajesh [195]

have grown L-proline doped KDP crystal with improved mechanical hardness. As L-

proline possesses ring structure, which is a stable molecular structure and hence good

mechanical hardness is observed in the doped crystals. Saravanan et al [196] have

reported that the L-arginine doping in KDP crystal improves the hardness. Delci et al

[145] have found that the microhardness value of the pure KDP crystal increases with

doping of boron. This is because of the incorporation of the boron ions into superficial

crystal lattice and removing defect centers which reduce the weak lattice stress on the

surface. Pritula et al [60] have reported room temperature Vickers micro-hardness studies

on {100} and {001} faces of KDP crystals grown from urea doped solutions. They found

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46

increase in hardness values for doped crystals compared to pure KDP crystals. Similarly,

Podder [86] earlier concluded in his study that Vicker microhardness exhibited higher

mechanical stability of urea doped crystals than KCl doped.

2.6 Optical Properties

Nonlinear optical (NLO) materials play a vital role in the fabrication of

optoelectronic devices. Recent interest is focused on the development of materials which

have suitable NLO properties for use as the active media in efficient second harmonic

generators, tunable parametric oscillators and broadband electro-optic modulators. In this

regard, a large number of compounds are needed to be screened for NLO applications.

Kurtz and Perry [197] proposed a powder SHG method for comprehensive analysis of the

second order nonlinearity. Employing this technique, Kurtz surveyed a very large number

of compounds. A good NLO crystal should also possess good transmission in ultraviolet

and visible region. It is also important to find the UV cut-off limit for particular crystal.

For this purpose UV-Vis spectroscopy is usually employed.

Traditionally, the materials used to measure second order nonlinear optical

behaviour are inorganic crystals such as lithium niobate (LiNbO3), potassium dihydrogen

phosphate (KDP), ammonium dihydrogen phosphate (ADP), potassium titanyl phosphate

(KTP). KDP is among the most widely used NLO material. It is characterized by good

UV transmission, high damage threshold but still their NLO coefficients are relatively

low. These crystals are distinguished by rather high efficiency of non-linear conversion

and wide optical transparency range which extends far to the short-wavelength region of

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47

the spectrum [198]. Various techniques have been employed to study the nonlinear

optical behaviour of KDP crystals. To improve the NLO property of KDP crystal,

researchers have attempted to modify KDP crystal by doping with different type of

impurities. Ganeev et al [199] studied the third order susceptibilities χ(3)

and the non-

linear refractive indices (n2) of KDP at wavelengths 1064 nm and 532 nm by Z-scan

technique. The measurements were carried out at different pulse energies, focusing

conditions and crystal lengths. It was shown by the authors that the increase of phase

matching angle leads to decreasing of χ(3)

of KDP crystals. Also, the self and gross-phase-

modulation coefficients in KDP crystals were measured by the Z-scan technique by

Zheng and Meyerhofer [200].

Guohui et al [57] have grown KCl and EDTA doped KDP crystals by rapid

growth technique. Higher NLO efficiency and laser damage threshold were observed

when the crystals were annealed. Podder [86] observed that the KCl doped KDP crystals

show better non-linear optical properties than the pure KDP crystals. Pure and L-Lysine

doped KDP crystals were grown by Kanagathara and Anbalagan [201]. It was found that

the transmittance percentage is increased for the doped KDP crystals. The effect of

doping of amino acids such as L-glutamic acid, L-valine, L-histidine [144], L-arginine,

L-histidine and glycine [154] in KDP crystals have been reported. Jagdish and Rajesh

[195] have studied the growth of L-proline doped KDP crystals. They found that the

optical transparency increases due to doping and transmittance percentage increases with

the increase in dopant concentration. High conjugation and delocalized π bonding orbitals

of L-proline are responsible for absorption in UV visible region. As the concentration of

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48

dopant increases, the zwitter ionic property decreases due to the interaction between

opposite charge ends of L-proline which reduces the delocalized π bonding orbitals. As a

result, the electron jump takes high energy and absorption occurs. Suresh Kumar and

Babu Rajendra [53] have reported that the amino acid doped crystal enhances

transparency and NLO efficiency of KDP crystals.

Lin et al [202] studied the mechanism of the optical behaviour of KDP crystals

theoretically by using the plane wave pseudo-potential total energy software package.

The origin of non-linear effects has been explained through the real space atom cutting

analysis of KDP. In another study, Xue and Zhang [203] have studied the hydrogen

bonds such as O-H---O, N-H---O in KDP and ADP. The second order NLO behaviour of

crystals studied and it is found that hydrogen bonds play very important roles in NLO

contributions to the total nonlinearity.

Mulley et al [134] have studied the growth of L-arginine and L-alanine doped

KDP crystals. Modifications in the lattice parameters and improvement in SHG

efficiency was observed. Parikh et al [166] have investigated the effect of L-alanine on

the growth of KDP crystals. They observed higher SHG efficiency and percentage optical

transmission in KDP crystal by doping with L-alanine, with a slight sacrifice in the UV

cut-off limit. Prasanyaa and Haris [204] have grown L-arginine trifluoroacetate (LATF)

doped KDP single crystals. The enhancement in the transmittance of grown KDP with the

addition of LATF at different ratios was determined by UV-visible spectral analysis.

Suresh Kumar and Babu Rajendra [53] have studied the effect of L-arginine, L-histidine

and glycine on the growth of KDP single crystals. Enhanced SHG efficiency was

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49

observed in the case of doped crystals. Pritula et al [129] have investigated the optical

properties of KDP crystals grown from urea doped solutions. It was found that the laser

damage threshold value increases by 25 % on doping. Kumaresan et al [205] have grown

metal ions and dyes doped KDP single crystals. It was observed that dye doping

improves the nonlinear optical properties of the grown crystals. Shirsat et al [54] have

studied the influence of lithium ions on the NLO properties of KDP single crystals.

Enhancement of SHG efficiency after the addition of lithium ions was observed. Delci et

al [145] have reported that the boron addition improves the optical transparency of KDP

crystals.

Rajesh et al [189] have investigated the transmission spectra of pure and organic

additives added KDP crystals. They found that the percentage of transmission has

increased in the order of KDP with urea, KDP with thiourea and KDP with EDTA system

respectively. They also observed that the cut off wavelength is almost the same for pure

and organic additive added KDP crystals. Mulley [206] have found that the transparency

and SHG efficiency of KDP crystal increase by doping with urea phosphate. The increase

in doping level improves the fine cut off at lower wavelength side but no change in the

cut off wavelength has been observed. Dhanaraj et al [85] have studied the potassium

acetate and potassium citrate doped KDP crystals. The optical transparency and SHG

efficiency of KDP crystal are increased by the addition of potassium acetate and

potassium citrate. They have also observed the cut off wavelength is the same for pure

and additive added KDP crystals. The addition of dopants in the optimum condition to

the solution is found to suppress the inclusion and improve the quality of crystals with

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50

higher transparency. Kumaresan [207] have investigated the irradiation effect on second

harmonic generation of dyes doped KDP crystals. It has been observed that the NLO

efficiency is increased in dyes doped KDP crystal after irradiation and cut off wave

length is same for pure and dyes doped KDP crystals. The π-conjugation electrons in

dyes after the irradiation alter the lattice orientation in the doped crystal and irradiation

effect diffuses the dyes uniformly in the crystal due to lattice disorder. Kumaresan et al

[193] have observed the transmission is higher for L-valine doped KDP crystals grown at

an optimized pH value of 4.2. They also reported that L-valine doped KDP crystals have

higher NLO efficiency. Akhtar and Podder [208] have reported the enhancement of

optical transmission of L-alanine doped KDP crystals. Dave et al [146] have reported, as

the doping of L-threone increases in KDP crystals, the percentage transmission increases

and the UV cut off frequency are not getting affected due to doping. They have also

found that the SHG efficiency increases due to the doping of L-threone in KDP crystals.

Dhanaraj et al [192] have grown potassium thiocynate added KDP crystals by seed

rotation technique. They observed that the measured SHG efficiency of KSCN added

KDP crystal was 1.31 times that of pure KDP crystal. Neutralization of OH group by

KSCN might be the cause for enhanced NLO property, as electron delocalization to be

much more enhanced than in pure KDP crystal. Saravanan et al [196] have observed a

lower cut off wavelength for L-arginine (235 nm) doped KDP crystal. They also found

the improved SHG efficiency of L-arginine doped KDP crystal. Justin Raj et al [209]

have grown potassium dihydroge phosphate from aqueous solution along {001} plane

with the aid of modified growth assembly of SR method. They have observed the

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51

improved transparency of SR method grown KDP crystals than that of conventional

solution grown KDP crystals. Robert et al [210] have also reported the high optical

transparecy of SR method grown KDP crystals.

2.7 Recent Trends in Crystal Growth

The nanocrystals (NCs) are supermolecules with nanometric size, arranged

periodically in three directions of space. The importance of the NCs is that when the

dimensions of crystallites approach the atomic scale, significant changes can occur in the

electronic and the optical properties compared to those of bulk materials [211]. There is a

little research on nanocrystals embedded in crystalline lattices. More recently, a strong

interest has been devoted to NCs of semiconductors embedded in wide gap matrix, such

as glass [212–214] and alkali halide matrices [215–217]. Harada et al [218] fabricated

ZnO NCs embedded in thin alkali halide crystals from their melts. In their PL

measurement, the bound exciton (BE) and free exciton (FE) appeared clearly. The BE

was located at 3.363 eV, the FE appeared at 3.373 eV and the 1 phonon and 2 phonon

replica were observed at 3.32 and 3.25 eV, respectively. However, the authors indicated

that the PL signals have never been detected for the ZnO NCs embedded in bulk alkali

halide matrices grown by usual Bridgeman technique.

Recently, Boudine and his co-workers [219-222] successfully embedded

nanocrystals into the crystalline matrix. Halimi et al [219] have investigated ZnO NCs

embedded in KBr single crystal fabricated by using the Czochralski method. The X-ray

diffraction analysis demonstrated that the KBr cell has not been deformed after the

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52

incorporation of ZnO NCs. The optical density measurements indicated a shift of the

absorption edge about 0.71 eV. Moreover, they showed that ZnO NCs present an

intermediate confinement. The study of PL at 1.6 K of ZnO NCs embedded in KBr single

crystal showed that the signals are dominated by the BE exciton lines. This work

indicates that Czochralski method allows the fabrication of semiconductor NCs

embedded in alkali halide matrices with a high crystalline quality. Boudine et al [220]

have elaborated CdS NCs embedded in an NaCl single crystal matrix, performed using

the Czochralski method. They observed that the incorporated CdS is in nanocrystalline

form, as indicated by the optical density spectrum, which exhibits a significant blue shift

of the energy band gap of the CdS NCs. Boudine et al [221] have also successfully grown

CdS nanocrystals (NCs) embedded in bulk KCl single crystal matrix performed using the

Czochralski method. They found the incorporation of CdS NCs with a cubic structure

inside the KCl matrix. The optical density measurements of the CdS NCs embedded in

KCl single crystal show a shift of the absorption edge towards higher energies. The

optical band-gap is estimated to be about 2.60 eV. The photoluminescence (PL) spectrum

of the CdS NCs embedded in KCl single crystal presents four emission bands in the range

of 2.20–2.56 eV. It is useful for NLO applications. Bensouici et al [222] report the

experimental results on the fabrication and optical characterization of Czochralski (Cz)

grown KBr single crystals doped with CdTe crystallites. Optical absorption results

confirm a partial chemical decomposition of CdTe showing two absorption bands at 250

and 585 nm, revealing, respectively, Cd and CdTe incorporation in the KBr lattice.

Photoluminescence spectra at room temperature after annealing show a luminescence

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band located at 640 nm due to size increasing of CdTe aggregates during temperature

treatment. Balasubramanian et al [223] found that the density and mechanical properties

of TGS crystals were improved by doping water soluble CdS nanoparticle dispersed in

water. They observed the absorption band in the range 490-520 nm in the UV-visible

transmission spectra which indicate the presence of impurity (water soluble CdS) in the

lattice of CdS added TGS crystals.

A promising trend in the development of up-to-date functional optical materials

based on dielectrics is incorporation of nanoparticles into the crystalline matrixes of

traditional nonlinear optical materials, for the improvement of the efficiency of their

nonlinear optical response. Very recently, Pritula and his co-workers [224-230] have

grown KDP crystals doped with TiO2 nanocrystals by the method of temperature

reduction from aqueous solution and studied the effect of titanium dioxide nanoparticles

on the functional properties of KDP single crystals. They found the possibility to grow

KDP single crystals containing incorporated anatase (TiO2) nanocrystals. The KDP single

crystalline matrix was chosen for the TiO2 incorporation under the assumption of:

(1) The possibility to input the anatase nanoparticles into mother liquor at the stage of the

crystal matrix growth;

(2) The possibility of strong coupling of protons, potassium and H2PO43-

ions with active

sites (in particular, with oxygen vacancies) on the surface of the nanoparticles both in the

growth solution and in the crystal matrix;

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(3) The possibility to control the hydrogen bonds system in the crystalline matrix by

means of photoinduced giant local fields at the TiO2 nanocrystal surface with resonance

excitation of their surface defect states due to the „„soft‟‟ hydrogen bonding structure of

the KDP crystal;

(4) The possibility of the creation and annihilation of pair defects in the KDP crystal due

to reduction–oxidation processes at the nanoparticles surface, i.e. the generation of

hydrogen vacancy and the creation of interstitial hydrogen atom (typical intrinsic

defects).

It has been found that the effect of giant nonlinear optical response of anatase

nanoparticles in KDP crystal matrix substantially depends on the character of

incorporation and distribution of these nanoparticles in the matrix and on the structure

perfection of the matrix itself [224]. They have observed the concentration of the

nanoparticles in the solution does not influence the growth rate of the doped crystals

when the growth is realized under the conditions of natural convection. It is established

that the nanoparticles with adsorbed phosphate-ions are incorporated predominantly into

the pyramidal growth sector of KDP crystals. The process of the growth of TiO2 doped

KDP crystals is that the nanoparticles are rejected by the crystallization front and then

“captured” by the boundaries between the growth layer packets. It was found that the

nanoparticles have no essential influence on the laser damage threshold of KDP with

10-5

wt% [226]. The investigation shows the incorporation of TiO2 nanoparticles slightly

changes the optical quality of KDP crystals and reported the high optical quality crystals

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with transmittance in the visible range ~90 %, scattering loss < 3 %, and the anomalous

biaxiality value 2V<20' [225]. The presence of TiO2 nanoparticles in the crystal matrix

results in the cubic nonlinear response enhancement and the sign inversion of the

nonlinear refraction index in the intensity range up to 20 MW/cm2 [227]. For the first

time they have obtained the frequency conversion efficiency enhancement in the “thick”

(10 mm) KDP:TiO2 in comparison with KDP crystal due to the internal self-focusing

effect that was observed as the jump beam spatial profile narrowing at moderate peak

intensities up to 100 MW/cm2 [229, 230].

For instance, an attempt [231] was made to design a composite optical material

possessing the properties of both active laser and nonlinear optical media, the

combination “KDP crystal-SiO2 particles” being used as a model system. The influence

of the size of paricles on the probability of their capture was studied, and the growing

crystal was shown to be able to capture effectively 1x10-2

-250 µm SiO2 particles. A study

was performed to prove the possibility of embedding II-VI compound CdTe nanoparticle

in KDP crystalline matrix. They found that CdTe inclusion has been obtained with an

average size of about 24 nm. They observed large blue shift of the band gap of CdTe NCs

from 1.56 eV (bulk) to 2.85 eV (CdTe~2 nm size) which reveals the intrinsic quantum

confinement effect of these nanocrystals [232]. Some of the recent research works done

in the field of nanocrystals embedded in crystalline matrix are listed in Table 2.1.

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Table 2.1: Recent research work in nanocrystals embedded in crystalline matrix

SI.

No

Title of the work Authors Journal name

1. Structural and optical

properties of CdTe

nanocrystals

embedded in KDP

dielectric crystal

A.Bensouici, J.L.Plaza,

O.Halimi, B.Boudine,

M.Sebais, E.Dieguez

J.Optoelectronics

and Advanced

Materials 10, 2008,

3051-3053.

2. Growth and

characterization of

KDP single crystals

doped with TiO2

nanocrystals

I.Pritula, V.Gayvoronsky,

M.Kopylovsky, M.Kolybaeva,

V.Puzikov. A.Kosinova,

V.Tkachenko, V.Tsurikov ,

T.Konstantiniva, V.Pogibko

Functional Materials

12, 2008, 420-428.

3. Solution growth of

KDP single crystals

doped with titanium

dioxide nanoparticles

I.Pritula, O.Bezkrovnaya,

M.Kolybaeva, A.Kosinova,

D.Sofronov, V.F.Tkachenko,

V.Tsurikov

Materials Chemistry

and Physics 129,

2011, 777-782.

4. Peculiarities of the

growth of KDP single

crystals with

incorporated

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V.G.Grachev, I.A.Vrable,

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