arulchemist

2008-03-21T22:19:00.000-07:00

nicholas rajesh
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Mar 21 (18 hours ago)
NUCLEARGRAVITATION
FIELD THEORY
Chapter IX:Comparison of the Nuclear Gravitational Field to theGravitational Field of the Sunand the Gravitational Field of a Neutron Star
The one characteristic that physicists observe regarding the "Strong Nuclear Force" is that it appears to be a very "short ranged" force. To the best of my knowledge, no empirical equation has ever been established for mathematically describing the characteristics of the "Strong Nuclear Force." The Physics Community has assumed that the "Strong Nuclear Force" is inversely proportional to the radial distance from the nucleus to at least the seventh power. The following equation is a representation of that assumed relationship where "F" represents the "Strong Nuclear Force," "K" represents a constant of proportionality, and "r" represents the distance between the center of gravity of the nucleus of interest and a proton or neutron at a specific point in space outside the nucleus.

The field of the "Strong Nuclear Force" appears to drop off almost immediately outside the nucleus of the atom. The "Strong Nuclear Force" holding the nucleus together has always been assumed to be a short ranged "super-force" much stronger force than the Electrostatic Force of Repulsion of the protons. Physicists and engineers are still trying to develop a reactor design to sustain a controlled Nuclear Fusion Reaction where the usable energy for work coming out of the reactor is greater than the energy required to initiate and maintain the fusion reaction. Initiating and maintaining a sustained, controlled, fusion reaction requires extreme temperatures (millions of degrees Kelvin) and pressures (millions of pounds per square inch). The extreme temperatures ensure the Deuterium and Tritium nuclei have sufficient kinetic energy to overcome the Electrostatic Repulsion Force of the protons in the Deuterium and Tritium nuclei. The extreme pressures ensure a high enough density of the nuclei to raise the probability of particle interaction. A stable "plasma" with the required temperature and pressure to sustain a fusion reaction is extremely difficult to maintain. The plasma must be "pinched" within a magnetic field of a reactor to provide the required temperature and pressure to support fusion. Figure 9-1 and Figure 9-2 demonstrate how the Tokamak Fusion Reactor establishes the "pinched" plasma to support fusion.

Figure 9-1:Cutaway Diagram of the Tokamak Fusion Reactor at Princeton UniversityIndicating Location of the Plasma in the Magnetic Field

Figure 9-2:Internal View of the Tokamak Fusion Reactorat Princeton University
What is a Tokamak?
The most successful and promising fusion confinement device is known as a Tokamak. The word Tokamak is actually an acronym derived from the Russian words toroid-kamera-magnit-katushka, meaning "the toroidal chamber and magnetic coil." This donut-shaped configuration is principally characterized by a large current, up to several million amperes, which flows through the plasma. The plasma is heated to temperatures more than a hundred million degrees centigrade (much hotter than the core of the sun) by high-energy particle beams or radio-frequency waves.
Reference: http://ippex.pppl.gov/fusion/fusion4.htm
Maintaining a stable "pinched" plasma in a magnetic field is very difficult at best. If a solid vessel is used to maintain the plasma and the plasma comes into contact with the vessel wall, then the plasma will immediately transfer heat to the vessel and cool off to below the required fusion temperatures. Likewise, the chance of the solid vessel vaporizing when coming into physical contact with the plasma is extremely high.

NOTE:
There are four states of matter: solid, liquid, gas, and plasma. Examples of the first three states of matter are water in the form of ice, a solid, water in the form of a liquid as is found in a lake or swimming pool during the Summer, and steam (gas or vapor) as what emanates from a teapot on a stove. The fourth state, the plasma state, can only exist at a extremely high temperatures where the kinetic energy of the subatomic particles, the nuclei and their electrons, is such that the electrons are no longer bound to their respective nuclei.
If the Nuclear Gravitation Field Theory is to demonstrate that the "Strong Nuclear Force" is the same force as that of Gravity, a reasonable explanation must be provided to explain why the "Strong Nuclear Force" does not follow Newton's Law of Gravity and provide an expected field strength reduction proportional to the square of the distance from the center of the nucleus. Recall Newton's Law of Gravity states:
As mentioned earlier, the field intensity of the "Strong Nuclear Force" drops off much more rapidly than predicted by Newton's Law of Gravity leading one to believe the Nuclear Gravitation Field cannot be the same as the "Strong Nuclear Force." The field intensity of the "Strong Nuclear Force" appears to drop off proportional to the inverse of the distance from the nucleus to the seventh power or greater. If the "Strong Nuclear Force" and the Nuclear Gravitation Field are the same, then the "Strong Nuclear Force" should drop off proportional to the inverse of the distance squared from the nucleus as predicted by Newton's Law of Gravity. However, what if the Nuclear Gravitation Field intensity, in close proximity to the nucleus, is on the same order of intensity of the gravitational field of a star? If that is the case, then the General Relativistic effects of strong gravitational fields may be affecting the Nuclear Gravitation Field as a function of distance from the nucleus. The intent of the methodology of the following evaluation is to determine whether or not the Nuclear Gravitation Field in the vicinity of the nucleus has the intensity to result in measurable "
Space-Time Compression."
Evaluate the "Pure Classical Physics" approach to calculating the Nuclear Gravitation Field at the surface of the nucleus of the atom using Newton's Law of Gravity.
Compare the "Pure Classical Physics" calculated Nuclear Gravitation Field intensity assuming fields of force, energy, and matter are continuous functions versus the estimated Nuclear Gravitation Field intensity using the principles of Quantum Mechanics assuming fields of force, energy, and matter are discrete functions.
In order to determine whether or not the Nuclear Gravitation Field at the surface of the nucleus has an intensity great enough to result in observable General Relativistic effects, one must compare the Nuclear Gravitation Field at the surface of the nucleus to the gravitational field in the vicinity of the Sun's surface and in the vicinity of the surface of a Neutron Star. Gravitational fields in the vicinity of stars are more than intense enough for significant General Relativistic effects to be observed. The Neutron Star was selected as one of the cases to study because the density of the nucleus, which is made up of protons and neutrons, is very close to the density of a Neutron Star. A Neutron Star typically contains the mass approximately that of our Sun, however, the matter is concentrated into a spherical volume with a diameter of about 10 miles or 16 kilometers. The radius of a Neutron star is about 5 miles or 8 kilometers. Figure 9-3 illustrates the relative size of the Earth to the size of a White Dwarf star and a Neutron star.

Figure 9-3:Comparative Sizes of the Earth,a Typical White Dwarf Star,and a Typical Neutron Star
Reference: "The Life and Death of Stars," by Donald A. Cooke, Page 131, Figure 8.12
This calculation will assume one solar mass for both the mass of the Sun and the Neutron Star. In this analysis, no General Relativistic effects will be considered in the calculations because the calculations are too cumbersome and not required to obtain the "ballpark values" needed to determine gravitational field intensities. Qualitative analyses are sufficient to satisfy the purposes for this evaluation. If the intensity of the Nuclear Gravitation Field at the surface of the nucleus is approximately equal to or greater than the gravitational field at the surface of our Sun, then it can be reasonably assumed that General Relativistic effects are present in the vicinity of the nucleus and must be considered when evaluating the "Strong Nuclear Force." Recall Newton's Law of Gravity and Newton's Second Law of Motion states:
Therefore:

The rearranging of Newton's Law of Gravity and Newton's Second Law of Motion can be used to determine the gravitational acceleration at any given distance from a gravitational source such as a planet or star. The acceleration of gravity is analogous to the gravitational field established by the mass of that planet or star.
First, the gravitational field at the Sun's surface will be determined. The Sun's mass, MSun, is 1.99×1030 kg. The Sun's diameter is 864,000 miles, therefore, the Sun's radius, RSun, is equal to 432,000 miles. In MKS units, the Sun's radius, RSun, is equal to 6.96×105 km equal to 6.96×108 meters. The Universal Gravitation Constant, "G," is equal to 6.67×10-11Newton-meters2/kg2. The gravitational field of the Sun's surface, which is represented by the gravitational acceleration at the Sun's surface, is calculated below:
aSun = 2.74×102 Newtons/kg = 2.74×102 meters/second2
Earth's gravitational field at sea level, which is represented by Earth's gravitational acceleration at sea level is about 9.87 meters/second2. The "g-force" at the Sun's surface can be determined by normalizing the Sun's gravitational field relative to Earth's gravitational field at sea level. Earth's gravitational field at sea level is assumed to be 1g. The ratio of the acceleration of gravity on the Sun's surface to the acceleration of gravity on the Earth's surface represents the g-force on the Sun's surface. The g-force on the Sun's surface is calculated as follows:

The Sun's gravitational field is strong enough to affect planet Mercury's orbit such that it deviates from the classical Newton's Law of Gravity and Kepler's Laws of Orbital Motion (see "Tests of Einstein's General Theory of Relativity," in Chapter V). Mercury orbits the Sun at an average distance of 36,000,000 miles from the Sun's surface. It was also previously presented that the Sun's gravitational field is strong enough to bend light. During a "Total Solar Eclipse," the background stars in the vicinity of the Sun will appear to be displaced because of the Sun's gravity bending their light. This bending of light is occurring in a gravitational field equal to or less than 27.8 g. Any gravitational field intensity equal to or greater than the Sun's gravitational field will require consideration of the effects of General Relativity.
Next, the gravitational field at the surface of a Neutron Starwill be analyzed. The Neutron Star is assumed to contain the same mass as the Sun, therefore, the mass of the Neutron Star, "MNeutron Star," is equal to 1.99×1030 kg. As presented previously, the Neutron Star's radius, which will be defined as "RNeutron Star," is about 5 miles equal to about 8 km or 8×103 meters. The gravitational field of a Neutron Star, which is represented by the gravitational acceleration at the star's surface, is calculated below:

aNeutron Star = 2.07×1012N-kg-1 = 2.07×1012 meters/second2
To determine the "g-force" at the Neutron Star's surface, the gravitational field of the Neutron Star must be normalized relative to Earth's gravitational field in the same manner used to calculate the g-force at the Sun's surface. Earth's gravitational field is 1g. The ratio of the acceleration of gravity on the Neutron Star's surface to the acceleration of gravity on the Earth's surface represents the g-force on the Neutron Star's surface. The g-force on the Neutron Star's surface is calculated as follows:
It has been previously demonstrated that the Sun's gravitational field of 27.8g can warp or bend Space-Time (see "Tests of Einstein's General Theory of Relativity," in Chapter V). The gravitational field of a Neutron Star, at 2.10×1010g, has an intensity of nearly a billion times greater than the Sun's gravitational field. The Neutron Star's gravitational field will result in substantial "Space-Time Compression." The mass of the Black Hole is about three times the Sun's mass and its mass is concentrated at a pinhead size singularity. The gravitational field and the warping of Space-Time associated with a Black Hole very well may approach infinity.
The next step is to calculate the gravitational field at the surface of a Uranium-238 nucleus, the most naturally occurring isotope of Uranium. This calculation will use Newton's Law of Gravity assuming purely Classical Physics so the Nuclear Gravitation Field for the Uranium-238 nucleus is assumed to be a continuous function. Hence, Quantum Mechanics will not be initially considered. Uranium, or Element Number 92, is the highest number element naturally occurring on Earth. The atomic mass of the Uranium nucleus is
238.050785 Atomic Mass Units (AMU) which is equal to 3.953×10-25 kg. The Uranium nucleus contains 92 protons and 146 neutrons for a total of 238 nucleons. The classical diameter of a neutron or proton is 1.0×10-15 meter. It is desired to determine the approximate diameter of the Uranium-238 nucleus. Protons and neutrons are assumed to be spherical in shape. However, because they are spheres, they do not pack together without having spatial gaps between them. Therefore, the actual space, both usable and unusable, in the nucleus that each proton and neutron takes up is assumed to be the smallest cube that either the sphere of a proton or neutron would fit into. If the diameter of a proton or neutron is 1.0×10-15 meter, then the smallest cube that can hold that proton or neutron will dimensionally have length, width, and height of 1.0×10-15 meter. The volume of such a cube would be equal the length of the side of the cube to the third power. The volume of the cube is equal to 1.0×10-45 meter3. Assuming all the protons and neutrons in a Uranium-238 nucleus were cubes, the number of cubes in the nucleus would be 238 and the volume of the cubes would be 2.38×10-43 meter3. To determine the approximate diameter of the sphere of the Uranium-238 nucleus, it must be assumed that all 238 cubes must fit inside the volume of the sphere of the nucleus. First, one must find the radius and diameter of a sphere that has a volume of 2.38×10-43 meter3. The equation for the volume of a sphere is provided below:
Where "V" represents the volume of the sphere and "R" represents the radius of the sphere. The next step is to assume the volume of the sphere is that of the volume of a Uranium-238 (
92U238) nucleus, "VU-238," calculated to be 2.38×10-43 meter3, above, and solve for the radius, "RU-238," of the 92U238 nucleus:
The diameter of the nucleus is twice the radius, hence, the diameter = 7.689×10-15 meter. The diameter of a single nucleon is about 1.0×10-15 meter. In order to have "whole nucleons" lined up across the diameter of the 92U238 nucleus, the calculated diameter will be rounded up to 8.00×10-15 meter. The rounded nuclear diameter is conservative because the density of the 92U238 nucleus used in the calculation is smaller than the actual density. This will also ensure that all the protons and neutrons that make up the 92U238 nucleus exist within the imaginary sphere of interest assumed to be the 92U238 nucleus. The original assumption of the sphere radius did not prevent partial cubes from being placed in different locations within the 92U238 nuclear sphere to allow 238 cubes to fit within the 92U238 nuclear sphere. It is not reasonable to assume protons and neutrons be cut up into fractions in order to fit within the total sphere of the 92U238 nucleus. A diameter of 8.0×10-15 meter for the 92U238 nucleus is a reasonable value to ensure whole cubes fit within the nuclear sphere. The radius of the 92U238 nucleus is half the diameter of the 92U238 nucleus or 4.0×10-15 meter. Now that the dimensions of the 92U238
nucleus are known, the gravitational field at the surface of the 92U238 nucleus can be determined. As noted previously, acceleration of gravity represents the gravitational field intensity. The mass of the 92U238 nucleus, "MU-238," was determined to be 3.953×10-25 kg and the radius of the 92U238 nucleus, "RU-238," was determined to be 4.0×10-15 meter. Using Newton's Law of Gravity, the acceleration, or gravity field, at the surface of the 92U238 nucleus is calculated below:

aU-238 = 1.648×10-6 Newtons/kg = 1.648×10-6 meter/second2
To determine the "g-force" at the surface of the 92U238 nucleus, the gravitational field of the 92U238 nucleus must be normalized relative to Earth's gravitational field in the same manner used to calculate the g-force at the Sun's surface. Earth's gravitational field is 1g. The ratio of the acceleration of gravity on the surface of the 92U238 nucleus to the acceleration of gravity on the Earth's surface represents the g-force on the surface of the 92U238 nucleus. The g-force on the surface of the 92U238 nucleus is calculated as follows:

Using the "Classical Newtonian Physics" analysis for this calculation, it appears that the acceleration of gravity in the vicinity of the 92U238 nucleus is very insignificant and feeble. This analysis assumes the purely Classical Physics approach in the calculation, disregarding any Quantum Mechanical effects. Therefore, the calculated Nuclear Gravitation Field is assumed to be a continuous function at the surface of the 92U238 nucleus. Assuming Classical Physics, only, the gravitational field of the 92U238 nucleus is too feeble to have any measurable amount of "Space-Time Compression" occur. The rapid "drop off" of the "Strong Nuclear Force" as it propagates outward from the nucleus would indicate that the "Strong Nuclear Force" is not a gravitational field if the "Classical Newtonian Physics" analysis is accepted as the final evaluation. Without "Space-Time Compression" taking place, the "Strong Nuclear Force" and Gravity could only be the same if the intensity of the "Strong Nuclear Force" drops off proportionally to the inverse of the square of the distance from the center of the nucleus as observed.
What if the effects of Quantum Mechanics are considered? The protons and neutrons exist in discrete energy levels within the nucleus just as the electrons "orbit" about the nucleus within discrete energy levels. The electron energy levels were determined by solving the Schrodinger Wave Equation used in Quantum Mechanics for the Nuclear Electric Field. If Classical Electrostatics and Classical Physics are applied to the electron orbits about the nucleus, then the electrons should spiral into the nucleus and neutralize the protons by changing them to neutrons and the atom would not continue to exist as observed. Quantum Mechanics must also be applied to the analyses when analyzing the forces in the atomic or nuclear realm. The discrete energy levels of the protons and neutrons in the nucleus can be determined by using the Schrodinger Wave Equation for the Nuclear Gravitation Field. The probability of absorption of a proton or neutron by a nucleus is related to the kinetic energy of the proton or neutron. Protons or neutrons must have discrete energies in order to be absorbed by the nucleus. Since the energy levels within the nucleus are known to be discrete energy levels, then it would be reasonable to assume that the fields associated with those energy levels would also be discrete rather than continuous. If the "Strong Nuclear Force" and Gravity are the same force, then the Nuclear Gravitation Field must be made up by quantized, or discrete, fields to be consistent with the discrete energy levels that exist for the protons and neutrons in the nucleus. If Gravity is quantized, then the intensity of the Nuclear Gravitation Field in the vicinity of the nucleus may very well be equal to or greater than the gravitational field intensity of the Sun at its surface.

Index and Direct Links to Other Chapters of Nuclear Gravitation Field Theoryand Nuclear Gravitation Field Theory Home Page/Table of Contents:
Nuclear Gravitation Field Theory
Purpose for Evaluation of the Strong Nuclear Force and the Force of Gravity
Executive Summary
The Classical Physics Evaluation of Electrostatics and Gravity
The Electrostatic Repulsion Force
Newton's Law of Gravity - The Attractive Force of Masses
Comparison of Electrostatic Repulsion and Gravitational Attraction
Nuclear Gravitation Field Theory: Major Stumbling Blocks to Overcome

New Theory Results Must Equal Old Theory Results When and Where Applicable
Newton's Law of Gravity as It Applies to Large Masses and Nuclear Gravitation Field Theory
Kepler's Laws, Gravity, and Nuclear Gravitation Field Theory
Structure of the Nucleus of the Atom
The Schrodinger Wave Equation and Quantum Mechanics - The Particle and Wave Characteristics of Matter
Nuclear Gravitation Field Theory Versus Accepted Strong Nuclear Force Overcoming Electrostatic Repulsion
Comparison of the Nuclear Gravitation Field to the Gravitational Field of the Sun and the Gravitational Field of a Neutron Star
Quantum Mechanics, General Relativity, and the Nuclear Gravitation Field Theory
Properties of the Strong Nuclear Force, Nuclear Properties of Bismuth, and the Nuclear Gravitation Field Theory

Conclusion
Appendix A: References
Appendix B: Background of the Author
Index and Direct Hyperlinks to the Other Web Pages on this Website:
Gravity Warp Drive Home Page
Nuclear Gravitation Field Theory (Specific Chapter Links are Provided on this Web Page)
Purchase e-Books
History of My Research and Development of the Nuclear Gravitation Field Theory
"The Zeta Reticuli Incident" by Terence Dickinson
Supporting Information for the Nuclear Gravitation Field Theory

Government Scientist Goes Public
"Sport Model" Flying Disc Operational Specifications
Design and Operation of the "Sport Model" Flying Disc Anti-Matter Reactor
Element 115
Bob Lazar's Gravity Generator
United States Patent Number 3,626,605: "Method and Apparatus for Generating a Secondary Gravitational Force Field"
United States Patent Number 3,626,606: "Method and Apparatus for Generating a Dynamic Force Field"
V. V. Roschin and S. M. Godin: "Verification of the Searl Effect"
The Physics of Star Trek and Subspace Communication: Science Fiction or Science Fact?
Constellation: Reticulum

Reticulan Extraterrestrial Biological Entity
Zeta 2 Reticuli: Home System of the Greys?
UFO Encounter and Time Backs Up
UFO Testimonies by Astronauts and Cosmonauts and UFO Comments by Presidents and Top U.S. Government Officials
Pushing the Limits of the Periodic Table
General Relativity
Rethinking Relativity
The Speed of Gravity - What the Experiments Say
Negative Gravity
The Bermuda Triangle: Space-Time Warps

The Wright Brothers
Website Endorsements and Favorite Quotes
Sponsors of This Website
Romans Road to Eternal Life In Jesus Christ

2007-08-18T06:35:00.000-07:00

Cryst. Res. Technol. 34 1999 4 519–525
The crystals of KNbO3 have been grown by the micro-pulling-down method. Colorless, transparent, and crack-free crystals were produced from the melts containing excess of K2O as a flux. Growth of relatively large size (up to 2 mm in diameter and up to 30 mm in length) single crystals was found is possible using the crucibles with corresponding nozzle size (up to 2.0 mm in outer diameter). Second harmonic generation was observed in the crystals irradiated by fundamental beam with wavelength about 860 nm.
Keywords: potassium, niobate, fibers, flux, growth, pulling-down
1. Introduction
Potassium niobate (KNbO3 or KN) is a well known ferroelectric material for electro-optic, nonlinear optic, and photorefractive applications (FUKUDA; FLÜCKIGER). It is efficient material for doubling the frequency of near-infrared (Ga, Al)As diode lasers used for recording and reading data from optical compact discs. The information density of optical systems arranged with KN crystal is expected to be four times greater than those of nonarranged ones. However, it is difficult to grow these crystals because KNbO3 melts incongruently at temperature above 1000°C (IMAI; IRLE; REISMAN; ROTH). Therefore the crystals have to be grown from a K2O rich, non-stoichiometric melts. Moreover KNbO3 is known to exist in three phases. High temperature phase crystallizes in the cubic perovskite structure. Within the temperature range 225-435°C KNbO3 has tetragonal structure. At room temperature it is isostructural with the distorted perovskite form of BaTiO3 and has an orthorhombic structure with two formula units per unit cell. Therefore it is also difficult to obtain high quality crystals because of structural reordering that occurs during the crystal cooling. The flux growth technique is widely used to grow KNbO3 crystals from the melts containing K2O excess (FUKUDA; FLÜCKIGER). However reproducibility of growth results is difficult to control because of non-stoichiometry of the starting mixtures and easy volatilization of K2O from the melt and crystal surface (FLÜCKIGER; IMAI). It was reported also (IMAI), that single crystal fibers of K(Ta,Nb)O3 solid solutions were grown by the laser heated pedestal growth method (LHPM). The source rods were enriched with K2O to prevent formation of K4Nb6O17 phase which is stable in the KNbO3 stoichiometric melt without excess of K2O (IRLE; REISMAN; ROTH). The temperature gradient in this method is steep enough to prevent constitutional supercooling and therefore to avoid spontaneous nucleation on the liquid-solid interface. In the case of K(Ta,Nb)O3

V.I. CHANI*, K. SHIMAMURA, T. FUKUDA
*
Center for Interdisciplinary Research, Tohoku University, Sendai, 980-8578, Japan
Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan
Flux Growth of KNbO3 Crystals by Pulling-Down
Method
520 V. I. CHANI et al.: Flux Growth of KNbO3 Fiber Crystals
mixed crystals (IMAI) the addition of a gas blower to the apparatus was necessary to increase
and to control the gradient in the vicinity of the molten zone.
Micro-pulling-down (m-PD) technique (YOON) is reported in the present paper to be a
versatile method of preparation of high quality KNbO3 fiber crystals starting from the melts
of non-stoichiometric composition. We discuss the experimental procedure and the growth
parameters which allow us to produce relatively large KNbO3 crystals.
2. Growth procedure
The starting materials with various compositions were made using K2CO3 (Rare Metallic
Co.) and Nb2O5 (High Purity Chem. Lab.), both of 99.99% purity. Desired quantities of
compounds were carefully weighed and mixed by grinding in ethanol with an agate mortar
and pestle, and dried at 100°C during 5-10 hr. Special attention was paid to prepare waterfree
K2CO3. Therefore preliminary annealing of starting K2CO3 at temperature 350-400°C
during 5-10 hr was necessary. The compositions of the melts used in our experiments are
summarized in Table 1.
No. K2O Nb2O5 Nozzle Seed Pulling
rate
Length
12-2 40 60 1.2x1.0 Pt wire 0.35 35
1-2 50 50 1.2x1.1 Pt wire 0.11 32
4-2 50 50 1.2x1.0 Pt wire 0.10 8
3-3 52 48 1.2x1.0 Pt wire 0.08 10
7-1 54 46 1.2x1.0 Pt tube 0.30 50
7-2 54 46 1.4x1.3 No. 7-1 0.15 34
6-1 55 45 1.2x1.0 Pt wire 0.13 25
8-1 56 44 1.2x1.0 Pt wire 0.09 22
8-2 56 44 1.2x1.0 Pt tube 0.20 45
8-3 56 44 1.4x1.3 Pt tube 0.12 30
8-4 56 44 1.4x1.3 KTN
(flux)
0.13 37
15-1 57 43 1.7x1.6 Pt tube 0.10 30
15-3 57 43 2.0x1.9 Pt tube 0.10 19
11-1 58 42 1.2x1.0 Pt wire 0.11 13
11-2 58 42 1.2x1.0 Pt tube 0.16 27
11-4 58 42 1.2x1.0 Pt tube 0.30 70
11-5 58 42 2.0x1.9 Pt tube 0.10 20
13-1 62 38 1.2x1.0 Pt tube 0.15 18
Table 1.:Crystal growth conditions: melts composition (mol.%) outer and inner diameters of the
crucible nozzle (mm), seed material, pulling rate (mm/min), and crystal length (mm)
Schematic diagram of the m-PD system and the details of the experimental technique are
described in the above-mentioned paper (YOON). The crystals were grown under air
atmosphere. The melt was contained in a crucible, which was made of Pt plate of 0.1 mm
thickness and Pt pipe of 1.0-2.0 mm in outer diameter and a wall thickness of 0.05-0.01 mm,
as it is shown in Fig. 1. We will call the modified arrangement (large nozzle diameter) as
pulling-down (PD) technique to separate it from the conventional (m-PD) system.
In the main two variations of the seeding technique were used in the experiments
described here; solidification of the melt was started on Pt wire of 0.5 mm in diameter or Pt
pipe of 0.4 mm in outer diameter and a wall thickens of 0.05 mm. Using of KNbO3 single
Cryst. Res. Technol. 34 (1999) 4 521
crystal seed was also possible, but it was difficult because of cracking which occurred
during heating or seeding. Extremely high temperature gradient under the crucible nozzle
and phase transitions mentioned above are considered to be main causes of the cracking.
K(Nb,Ta)O3 seed crystals grown by conventional flux technique were used also to prevent
these disadvantages. The crystal grown on K(Nb,Ta)O3 seed (sample No. 8-4 of Tables 1
and 2) was crack-free.
Fig. 1. Schematic diagram of seeding procedure
using Pt pipe as a seed.
In case of seeding on Pt wire one crystallographic direction of high growth rate was
developed by pulling down rate of 0.50-1.00 mm/min and necking procedure. Further
orienting of the crystal was made during the growth process by manipulations of micro X-Y
stage. It was possible due to faceting of the crystals observed in situ by optical microscope.
No. W (mg) D (mm) Color Crystal Remain Melt Cracks
12-2 150 1.0 colorless K4Nb6O17 K4Nb6O17 Yes
1-2 - 1.0 colorless K4Nb6O17 K4Nb6O17 -
4-2 - 1.1 blue KNbO3 - -
3-3 39 1.1 colorless KNbO3 K4Nb6O17 Yes
7-1 206 1.1 colorless KNbO3 - Yes
7-2 171 1.3 dark blue KNbO3 - Yes
6-1 94 1.1 colorless KNbO3 K4Nb6O17 No
8-1 77 1.1 light blue KNbO3 K4Nb6O17 No
8-2 207 1.1 colorless KNbO3 - No
8-3 177 1.3 colorless KNbO3 - No
8-4 236 1.4 light blue KNbO3 - No
15-1 246 1.8 colorless KNbO3 K4Nb6O17 No
15-3 239 2.1 light blue KNbO3 K4Nb6O17 No
11-1 52 1.2 light blue KNbO3 K4Nb6O17 Yes
11-2 93 1.1 colorless KNbO3 KNbO3 No
11-4 255 1.1 light blue KNbO3 - No
11-5 231 2.1 colorless KNbO3 - No
13-1 57 1.0 blue KNbO3 KNbO3 Yes
Table 2. : Crystal growth results: weight (W), diameter (D), color and phase of the crystals grown and remain
melts
Best results were achieved in the runs where Pt tube was used as a seed similar to that of
described earlier (KIMURA) for the crystal growth by Czochralski method. Schematic
522 V. I. CHANI et al.: Flux Growth of KNbO3 Fiber Crystals
illustration of the seeding technique used is illustrated by Fig. 1. As a first step the tube was
inserted into the crucible nozzle and kept there about 1 min. At that time overheating of the
crucible was necessary to prevent solidification of the melt inside the nozzle because of high
thermoconductivity of platinum. Thereafter pulling down was started with a rate close to
that of used for crystal growth as it is given in Table 1.
All growth processes were stopped after observation of any kind of crystal imperfection.
After that the crystals were disconnected from the molten zone and pulled down with the
rate corresponding to cooling rate of about 30°C/min. Thereafter the crystals were removed
from the seed holder. As a second stage of each experiment the remain melt was removed
from the crucible using the same seeding material with a pulling rate of about 0.50 mm/min.
Deposition of small drops of a flux (K2O) was sometimes observed on the surface of the
crystals. Therefore the crystals were washed in warm water.
3. Growth results and discussion.
Fig. 2 shows the as grown KNbO3 crystals. The fibers grown had a habit corresponding to
published data (FUKUDA). The crystals showed simple crystallographic {100} faces because
of presence of flux. In the main the rod-like crystals had four-fold symmetry corresponding
to [100] orientation of pseudo-cubic high temperature phase (ZENG). Similar to the crystals
grown by top-seeded solution growth, the ones reported here had very flat cubic faces
because the progressive nucleation on cubic planes is quite difficult (HULLIGER).
Fig. 2. View of KNbO3 crystals (sample No. 11-2
above and sample No. 15-1 below) grown by PD
technique (scale in mm).
The crystals were blue and colorless depending on melt composition and pulling rate. In
general optimization of crystal growth conditions was necessary for all of the melts reported
here, because at least light blue coloration following from presence of some amount of
oxygen vacancies (FUKUDA; IMAI) was observed in all crystals grown at relatively high
pulling rate. Almost all crystals were transparent, as shown in Fig. 2. The typical size of
crystals was about 1-2 mm in cross-section depending on diameter of the nozzle and few
centimeters in length. In the main about 70-80 vol.% of the melt was crystallized into
KNbO3 single crystals. Maximum yield achieved (crystal/melt volume ratio) was about 90
Cryst. Res. Technol. 34 (1999) 4 523
vol.% for the melts containing insignificant excess of K2O.
It was also possible to grow the KNbO3 single crystals with an extremely high pulling rate of
about 1-2 mm/min. In such a case the crystals also were single phase and had typical fourfold
symmetry. However these crystals were dark blue in color.
Phase homogeneity of the crystals grown and the melts remain after growths were
studied by X-ray powder diffraction analysis. In the main the crystals grown were KNbO3
single phase (JSPDS data card No. 32-822) as it is given in Table 2. The remain melts were
found crystallized as either KNbO3 or K4Nb6O17 depending on composition of starting
mixture.
In the melts corresponding to the vicinity of stoichiometric composition of KNbO3
crystallization of the second phase was often observed. It was assumed that the phase is
K4Nb6O17. However the phase identification was difficult because X-ray diffraction data for
K4Nb6O17 compound found in JSPDS data cards are very different (cards No. 14-287, 21-
1295, 31-1063, and 31-1064). Therefore it was necessary to prepare this material by
ourselves. The K4Nb6O17 compound was produced by solid state reaction technique.
Moreover the K4Nb6O17 single crystals were grown by the PD method from stoichiometric
melt of the above composition using the procedure similar to that of described above. The
K4Nb6O17 crystals were transparent, colorless, and were well developed in shape. X-ray
diffraction pictures of the poly- and single-crystalline samples were very similar. X-ray
diffraction data are given in Table 3. The results of Table 3 show relatively high correlation
with the data found in JSPDS data card No. 14-287.
2q dobs I/I0
9.15 9.66 100
13.95 6.35 20
16.58 5.35 16
19.63 4.52 13
21.20 4.19 13
23.00 3.87 16
27.58 3.23 46
29.90 2.99 33
31.55 2.84 77
35.95 2.50 17
38.10 2.36 15
40.28 2.24 21
45.30 2.00 16
46.20 1.96 26
51.20 1.78 15
58.60 1.58 16
Table 3: X-ray powder pattern of the single crystal grown
from K4Nb6O17 stoichiometric melt in the range of 2q = 6-60°
(sample No. 12-2 of Tables 1 and 2)
The KN crystals were cut and polished. Second harmonic generation (SHG) was observed in
the samples with fundamental laser beam irradiated along the growth axis (a-axis).
4. PD and related growth methods
Comparison of most common features of PD and related growth techniques is given in
Table 4. Two most important advantages of the m-PD technique modified by increasing of
524 V. I. CHANI et al.: Flux Growth of KNbO3 Fiber Crystals
the diameter of capillary channel (PD) are discussed below briefly.
Methods m-PD and LHPM* PD Flux Growth
Crystal Diameter ~ 0.5 mm ³ 2.0 mm ³ 10 mm
Segregation
Coefficients
K » 1 K» 1 K» 1
Flux Growth Difficult because
K » 1
Possible Possible
Growth Rate
(mm/min)
Very high (0.1-1.0) Very high (0.1-1.0) Very low (< 0.01)
Growth control Easy Easy Difficult
LHPM* - laser heating pedestal method
Table 4: Comparison of PD and related techniques
4.1. Flux growth
One of the most important result of this study seems to be related with presence of
considerable amount of flux in the starting melts. For example, recalculation of the melts
used for the growth of the crystals No. 11-5 and No. 13-1 (Table 1) results KNbO3 : K2O =
84 : 16 and KNbO3 : K2O = 76 : 24 molar ratios, respectively.
In the case of conventional m-PD growth reported earlier (YOON) the crucibles were
fabricated with a nozzle diameter less than 1 mm. In such a case the segregation phenomena
was not observed because of low mass transport inside the narrow capillary channel.
Therefore intensity of the cations exchange between the liquid and solid phases was very
low. Same phenomena is usually observed in the LHPM crystal growth (IMAI). In both these
methods the segregation coefficients reported were close to unity: K » 1. However, in the
modified PD arrangement reported here the diameter of capillary channel has been increased
considerably up to 2 mm that is close to size of the crucible (about 10 x 5 x 2 mm, as it is
shown in Fig. 1). This way, the rate of natural convection has been increased also, and the
segregation on the liquid/solid interface was observed become possible (K » 1). Thus the
modification discussed here results unusual possibility of flux growth with high pulling rate
(0.1-1.0 mm/min).
4.2. Growth of macro-crystals
Another important result is related with examination of macro-limitations of the m-PD
system. In all previous reports concerning oxide crystal growth by m-PD technique the
diameter (or cross-section) of the fibers reported did not exceed 1 mm. The maximal size of
the KNbO3 crystals grown in this study was greater than 2 mm. Therefore fields of
application of the PD technique and the crystals reported is assumed increase considerably.
5. Conclusions
KNbO3 single crystals were grown by the pulling-down technique. The crystals were SHG
active. It was found that combination of the conventional pulling-down system with the
crucible arranged with large capillary channel can be used to produce relatively large macrocrystals
with diameter greater than 2 mm by flux method.
Cryst. Res. Technol. 34 (1999) 4 525
Acknowledgments
We thank Dr. K. Imai (NGK Insulators, Ltd.) for preliminary results related with measurements of
SHG in the KN crystals reported.
References
FLÜCKIGER, U., AREND, H., J.: Cryst. Growth 43 (1978) 406
FUKUDA, T., UEMATSU, Y.: Jpn. J. Appl. Phys. 11 (1972) 163
HULLIGER, J., GUTMANN, R., WÜEST, H.: J. Cryst. Growth 128 (1993) 897
IMAI, T., YAGI, S., SUGIYAMA, Y., HATAKEYAMA, I.: J. Cryst. Growth 147 (1995) 350
IRLE, E., BLACHNIK, R., GATHER, B., Thermochim. Acta 179 (1991) 157
KIMURA, H., NUMAZAVA, T., SATO, M., J. Cryst. Growth 165 (1996) 408
REISMAN, A., HOLTZBERG, F., J. Am. Chem. Soc., 77 (1955) 2117
ROTH, R. S., Progr. Solid State Chem, 13 (1980) 159
YOON, D.H., YONENAGA, I., FUKUDA, T., OHNISHI, N., J. Cryst. Growth 142 (1994) 339
ZENG, H. C., J.Cryst.Growth 173 (1997) 446
(received October 7, 1998; accepted October 30, 1998)
Author's address:
Dr. V.I.CHANI
Center for Interdisciplinary Research
Tohoku University
Aramaki aza Aoba, Aoba-ku
Sendai, 980-8578
Japan
Fax: +81 (022) 215-2104
E-mail: chani@lexus.imr.tohoku.ac.jp