J. Semicond. > 2017, Volume 38 > Issue 7 > 071001, doi: 10.1088/1674-4926/38/7/071001

INVITED PAPERS

Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water

Binbin Jie1, and Chihtang Sah1, 2,

+ Author Affiliations

 Corresponding author: Binbin Jie,Email: bb_jie@msn.com; Chihtang Sah,Email: tom_sah@msn.com

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Abstract: We report physics based confirmation (1% RMS deviation), by existing experimental data, of proton-prohol (proton-hole) ion product (pH) and mobilities in pure liquid water (0-100℃, 1-atm pressure) anticipated from our melted-ice Hexagonal-Close-Packed (H2O)4 Lattice Model. Five phonons are identified. (1) A propagating protonic phonon (520.9 meV from lone-pair-blue-shifted stretching mode of isolated water molecule) absorbed to generate a proton-prohol pair or detrap a tightly-bound proton. (2) Two (173.4 and 196.6 meV) bending-breathing protonic-proholic or protonic phonons absorbed during de-trapping-limited proton or proton-prohol mobilities. (3) Two propagating oxygenic-wateric Debye-Dispersive phonons (30.3 and 27.5 meV) absorbed during scattering-limited proton or proton-prohol mobilities.

Key words: solid, soft and liquid material physics, pure water, point-mass positive proton and negative prohol, pH, proton-ion product and mobilities, phonon scattering and detrapping-trapping of propagating-localized protons and prohols



[1]
William Shockley (Bell Telephone Laboratories, Shockley Semiconductor Laboratory of Beckmann Instrument Company, Shockley Transistor Corporation, Stanford University), Electrons and Holes in Semiconductors, 558pp, 1950, Van Nortrand, New York. Chapter 16 Statistical Mechanics for Semiconductors and Chapter 17 Theory of Transition Probabilities for Holes and Electrons give the historical first and still the best tutorial description and mathematical analysis of these two, the most important subjects on the mathematical modeling of the properties of a material in the solid phase of the three phases, solid, liquid and gas, in a container-volume containing many electrons, atoms and molecules, at thermodynamic equilibrium and at small deviation from thermodynamic equilibrium. It takes several careful readings to get the key notions on the underlying physics-based assumptions and approximations to appreciate what the author was and is trying to convey to the student of this subject.
[2]
Chih-Tang Sah and William Shockley, "Electron-hole Recombination Statistics in Semiconductors Through Flaws with Many Charge Conditions", Physical Review, Vol. 109, pp. 1103-1115, 15 February 1958.
[3]
Chih-Tang Sah, Fundamentals of Solid State Electronics, 1010pp. 1991. World Scientific, Singapore. Section 360, Generation, Recombination, Trapping and Tunneling, and its subsection on p. 270-290.
[4]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry-Electrical Conduction in Pure Water, " Journal of Semiconductors, Vol. 34(12), pp. 121001-1-8, December, 2013.
[5]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water, " Journal of Semiconductors, Vol. 35(02), pp. 021001-1-19, February, 2014.
[6]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry Ⅲ. Electrical Conductance of Pure and Impure Water, " Journal of Semiconductors, Vol. 35(04), pp. 041001-1-20, April, 2014.
[7]
Binbin Jie and Chihtang Sah, "Ion Product of Pure Water Characterized by Physics-Based Water Model, "Chinese Journal of Chemical Physics, Accepted on September 21, 2015 and published Online on December 21, 2015, Vol. 29, No. 2, pp. 167-170, April 27, 2016.
[8]
Sah Chihtang and Jie Binbin, "Semiconductor View of Liquid Chemistry, " 20130913@1400-1600, Sah Pentung (薩本棟) 111th Anniversary Memorial Symposium, Friday, September the 13th, 2013, Annual National Fall Meeting of the Chinese Physical Society, 20130911-0922, Xiamen University, Xiamen, Fujian, China.
[9]
Jie Binbin and Sah Chihtang, "Solid-State Physics View of Liquid-State Chemistry-Electrical Properties of Pure and Impure Water" (Keynote), 20140508@1040-1125, 2014 International Symposium on Next-Generation Electronics (ISNE2014), May 8-10, 2014, Chang Gung University, Taoyuan, Taiwan, China.
[10]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry" (Invited), 20140616@0830-0900; "Water Physics-Condensed State Physics View of Liquid State Chemistry" (Tutorial), 20140616@1530-1630, 2014 Workshop on Compact Modeling (WCM), NanoTech, TechConnet World Innovation Conference & Expo, June 15-18, 2014, Washington DC, USA.
[11]
Jie Binbin and Sah Chihtang, "Experimental Verification of a Water Physics and Model in Pure Water at Thermodynamic Equilibrium and Non-Equilibrium" (Invited), 20160524@0830-0900, 2016 Workshop on Compact Modeling (WCM), NanoTech, TechConnet World Innovation Conference & Expo, May 22-25, 2016, Washington DC, USA.
[12]
Binbin Jie and Chihtang Sah, "Electrical Conduction in Pure Water, Trapping and Scattering of Positive Protons and Negative Proton Holes, " D26. 00012, 20150302@1642-1654, 2015 March Meeting of the American Physical Society, March 2-6, 2015, San Antonio, Texas, USA.
[13]
Binbin Jie and Chihtang Sah, "Electrical Mobility of Protons and proton-holes in Pure Water Characterized by Physics-Based Water Model, " K47. 00005, 20160316@0848-0900, 2016 March Meeting of the American Physical Society, March 14-18, 2016, Baltimore, Maryland, USA.
[14]
Binbin Jie and Chihtang Sah, "Proton Transports in Pure Liquid Water Characterized by Melted Ice Lattice Model, " E3. 00004, 20170314@0836-0848, 2017 March Meeting of the American Physical Society, March 13-17, 2017, New Orleans, Louisiana, USA.
[15]
Sah Chihtang and Jie Binbin, " Water Physics-Condensed State Physics View of Liquid State Chemistry, " (Invited) 20140609@1400-1600, Research Seminar, June 09, 2014, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
[16]
Sah Chihtang and Jie Binbin, "Semiconductor Physics and Model of Liquid Water-Ion Product and Ion Mobilities in Pure Water, " (Invited) 20160602@0830-0900, Reports for Academicians, June 2, 2016, General Assembly of Academicians, Beijing, China. "Semiconductor Physics and Model of Liquid Water 1. Ion Product and Ion Mobilities in Pure Water 2. Theory and Experimental Confirmations, " (Invited) 20160603@0930-1130, Research Seminar, June 3, 2016, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China.
[17]
Sah Chihtang and Jie Binbin, "Water Physics and Model-Fundamentals, " and Jie Binbin and Sah Chihtang, "Water Physics and Model-Experimental Verifications-Pure Liquid Water", (Tutorials) 20160806@0830-1100, Soft Matter Physics Summer School, of the 10th Annual Summer School on Theoretical Physics of the Natural Science Foundation of China, August 01-13, 2016, Xiamen University, Xiamen, China.
[18]
Peter Atkins (Lincoln College, U. Oxford, UK) and Julio de Paula (Lewis and Clark College, Portland, Oregon, USA), Atkins' Physical Chemistry, 972pp, 9th Edition, 2010, Oxford University Press.
[19]
David Eisenberg (UCLA) and Walter Kauzmann (Princeton U. ), The Structure and Properties of Water, 296pp, 1969, Oxford University Press. Published 2005 in the Oxford Classics Text in Physical Sciences, reprinted, 2011.
[20]
Victor F. Petrenko (Dartmouth College, New Hampshire, USA. ) and Robert W. Whitworth (U. Birmingham, UK. ), Physics of Ice, 374pp, 1999, Reprinted 2003, Oxford University Press.
[21]
Charles Kittel (UC Berkeley, 19160718-), Introduction to Solid State Physics, Editions: 1st 396pp 1953 (2nd-Printing April 1954), 2nd 617pp 1956, 3rd 648pp 1966 (2nd Corrected Printing November 1967), 4th 766pp 1971, 5th 599pp Taiwan-Edition 1976 (8th-Printing August-1984); in the next three latest editions: -First 3 chapters on classical Newtonian Mechanics harmonic oscillators and next 2 chapters on Schrodinger Wave and Dirac Quantum Mechanical harmonic and anharmonic oscillators and phonons of an array of host atoms and molecules located on a space lattice: 6th 646pp 1986, 7th 673pp 1996, and 8th 680pp, 2005. The 9th Edition overdue for decade release, might be due on the 101th birthday, 20170718.
[22]
Neil W. Ashcroft (Cornell U. ) and N. David Mermin (Cornell U. ), Solid State Physics, 826pp, 1976, Holt, Rinehart and Winston, New York. First and only Edition, 5th Printing, 1977. (a) Lattice atomic or nucleus vibration frequency versus wave number or normal mode characteristics for one-dimensional (1-D) monatomic Bravais Lattice on p. 430. (b) 1-D lattice with a basis illustrated by a two atoms per primitive unit cell with two different force constants on p. 433. (c) 3-D monatomic Bravais lattice on p. 437. (d) Dynamical matrix defined on p. 439. (e) Normal modes of a 3-D lattice with a basis on p. 442. (f) Connection with elasticity, on p. 443. (g) Quantization of the lattice vibration modes into phonons in Chapter 23, starting on p. 451. (h) Graphical illustration of the differences among the dispersionless and dispersive Debye and Einstein models of the phonon dispersion characteristics shown by Fig. 23. 4 on p. 462. (ⅰ) Density of normal modes, on p. 464, and van Hove singularities on density of electron states (same as phononic modes) on p. 145. (j) Jahn-Teller effect on p. 659. (k) Anharmonic effects in Chapter 25 starting on p. 487.
[23]
Frank S. Crawford, Jr. (UC Berkeley), Waves - Berkeley Physics Course - Volume 3, 600pp, 1965, 1966, 1968, McGraw-Hill, New York. Preface (One of 5 volumes for a 2-year elementary college physics course for undergraduate students majoring in sciences and engineering). Free internet download.
[24]
J. D. Bernal and R. H. Fowler, "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and hydroxyl ions, " J. Chem. Phys. , Vol. 1(8), pp. 515-548, August, 1933.
[25]
Linus Pauling, "The Structure and Entropy of Ice and Other Crystals with Some Randomness of Atomic Arrangement, " J. Amer. Chem. Soc. , Vol. 57(12), pp. 2680-2684, December 1935.
[26]
W. F. Giauque and H. L. Hohnston, "Symmetrical and Antisymmetrical Hydrogen and the Third Law of Thermodynamics. Thermal Equilibrium and the Triple Point Pressure", J. Amer. Chem. Soc. , Vol. 50, pp. 3221-3228, 1928; J. O. Clayton and W. F. Giauque, "The Heat Capacity and Entropy of Carbon Monoxide. Heat of Vaporation. Vapor Pressures of Solid and Liquid. Free Energy to 5000°K. From Spectroscopic Data, " J. Amer. Chem. Soc. , Vol. 54, pp. 2610-2626, 1932; W. W. Blue and W. F. Giauque, "The Heat Capacity and Vapor Pressure of Solid and Liquid Nitrous Oxide. The Entropy from its Band Spectrum, " J. Amer. Chem. Soc. , Vol. 57, pp. 991-997, 1935. Quoted by Pauling in Ref. [25].
[27]
George Malenkove (AN Frumkin Inst. Phys. Chemistry and Electrochemistry, Moscow), "Liquid water and ices: understanding the structure and physical properties, " J. Phys. Condens. Matter 21, 283191, 35pp, 2009. This is the only article at this time (20170531-20170630) which describes the key issues of the short range but sufficient long range order of the structural properties of liquid water, but from the structural viewpoint and its solid-phase transformations-transitions, giving comparison with the electronic Si and Ge, however, the author was hanged up on the proton bond, not visualizing proton as the mobile particle in the protonic liquid water Lattice (same as the electron as the mobile particle in the electronic Si and Ge) with the sufficiently long-range short-range order, as indicated by the fluidic softness. See Sections 2. 1 Proton order on page 4 and Section 2. 2 Structure of crystalline ice modifications and its Subsections 2. 2. 1 Simple frameworks on page 5-6 for the rare cubic and abundoned hexagonal form of type I ice, Icand Ih respectively. We only appreciated the descriptions of this author in this 2009 review, after our second reading of this article 36 months later during our last polishing of our present report on May 31, 2017. Our protonic water model was evolved before our second reading of this article by Malenkove[26], which further clarified the differences between our proton transport model and the hydroxyl ion (hydroxide and hydronium) transport model reviewed by Malenkove[27]. Our protonic potential energy band-landscape model of liquid water with the melted (hence 'soft', flexible and fluidic) hexagonal close packed Ice Lattice, contains twice as many proton traps as there are protons, as proposed in 1933 by Bernal and Fowler[24] and proven by Linus Pauling's 1936 residual entropy theory[25] on the low temperature specific measurements during 1928 to 1936 by Giauque and his graduate students[26]. Our two proton transport models discovered by us and reported in the present article, hidden in the 50-more years of ion product and mobilities data of pure liquid water, are (ⅰ) proton-prohol two-band potential energy band or landscape model and (ⅱ) three proton trapping at two proton traps in the proton potential energy band or landscape model, both visualized and accurately scaled by the simple Newtonian Mechanics of vibrating string and mass, taught in undergraduate freshmen-sophomore physics[23].
[28]
John L. Finney (University College London), "Bernal and the structure of water, " J. Physics, Conference Series 57, pp. 40-52, 2007. This article reviewed the latest successes, as of 2007 or 10 years ago, of the crystalline lattice model of liquid water, proposed by Bernal in 1933[24] but abandoned by him in the 1960's as "a delusive approach, postulating a greater degree of order in the liquid than actually exists there" after he, Bernal, developed a very successful "random packing" model of simple fluids. See also John L. Finney (University College London), "What's so special about water?", Phil. Trans. R. Soc. B, 359, pp. 1145-1165, 2004. This article gives an accurate authoritative summary of the most important properties of the water molecule in liquid water. Zero point vibrational frequency of 4634 cm-1 (574. 58 meV) from Eisenberg & Kauzmann, 1969. [19] The three normal modes of vibration of isolated water molecule from Benedict et al. (1956) for ν1= 3657 cm-1= 453 meV symmetrical stretching, ν3 = 3756 cm-1 466 meV antisymmetrical stretching, and ν2= 1595 cm-1=198 meV bending or breathing. But the author fell to the Hydrogen bonding picture just like all the rest. See Section 3. Interactions between water molecules starting with the statement, Water molecules interact with each other through hydrogen bonding, with the interaction energy of 20 kJ/mole = 5 kcal/mole = 207 meV = 10 (8) times larger than the thermal fluctuation at room temperature =kBTRoomTemperature= 25 meV. Furthermore, he insisted, just like the rest of them, that liquid water is not a crystal, from failing to recognize the flexibility long range order can and does exist in crystalline liquid with the softness that conforms to the shape and size of the harder container of the liquid. This article gives marvelous pictures, the best we have seen, of the various kinds of molecular clusters of solid waters and their liquid phases.
[29]
Herbert S. Harned and Benton B. Owen (Cornell University), The Physical Chemistry of Electrolytic Solutions, First Edition 345pp, 1943. Second Edition, 645pp, 1950. Third Edition, 803pp, 1958. First Printing 1958, Second Printing, 1963 and Third Printing, 1964. Monograph Series No. 137. American Chemical Society. Reinhold Publishing Corporation, New York. Chapman and Hall, Ltd. London.
[30]
N. F. Mott (Cavendish Professor of Physics in the University of Cambridge) and E. A. Davis (Royal Society Mr. and Mrs. John Jaffe Donation Research Fellow, Cavendish Laboratory), Electronic Processes in Non-Crystalline Materials, 437pp, Clarendon Press, Oxford, 1971. Section 2. 9. 1 Conduction due to electrons with energies near the Fermi energy, pp. 39-42. N. F. Mott (Emeritus, Late Cavendish Professor of Physics, University of Cambridge), Metal-Insulator Transitions, 1st Edition, 278pp, 1974. Taylor & Francis Ltd, London, Barnes & Noble Books, New York. Section 1. 7 Disordered systems: Localization and the Anderson Transition, pp. 30-40. 2nd Edition, 286pp, 1990.
Fig. 1.  Diagram illustration and thinking aid for modeling the pure Water Material, by a LATTICE in the Physical Space or Direct Lattice Space ( $x,y,z$ ) for Type I water's hexagonal crystalline Solid Phase, designated as the Solid-Ice, and its quiet or pre-fluidity Liquid Phase, designed as the Melted-Ice.Fig. 1(a) The Lattice-Point position picture of the constituent particles of the water material: Oxygen nuclei (diameter scaled to the spacing between the adjacent lattice points), and Protons and Electrons (diameters significantly enlarged for legibility; the oxygen binding electron-pair bonds are thick diameter bars for the 2-electron pair bonds). Two dimensional view on an a-b plane perpendicular to the $c$ -axis along the $y$ -axis, at $z_{\mathrm{1 }}(x_{\mathrm{r}}$ , $y_{\mathrm{r}}$ , $z=z_{\mathrm{1}})$ where $r$ is the number label of the $j$ th oxygen nuclei $r=j_{\mathrm{oxyen}}$ , $k$ th proton $r=k_{\mathrm{proton}}$ , and $l$ -th electron $r=l_{\mathrm{electron}}$ , all projected along the $c$ -axis of the hexagonal close packed (HCP) primitive unit cell, onto the flat paper page of the journal article. The upper part of (b) is the same as (a) with the proton transport arrows added and the involved phonon energies labeled in meV (milli-electron-Volt) and cm $^{\mathrm{-1}}$ (reciprocal wavelength in centimeter, using 1 meV = 8.06554 cm $^{\mathrm{-1}})$ . The lower part of (b) is the static or frozen Potential Energy Landscape (PEL) picture in Physical Space or Direct Lattice Space, ( $x,y,z,t$ ), where $t=t_{\mathrm{1}}$ is a "sufficient" time with an interval of a quiet state, or a snap shot to represent a monitor time dependent Kinetic Energy Landscape (KEL). It is an 1-dimensional view, PEL $(x,y,z)$ = PEL $_{\mathrm{1}}(x,y=y_{\mathrm{1}}$ , $z=z_{\mathrm{1}})$ . From Fig. 4(c) of Ref. [4]. Presented at 2016 Summer School of Xiamen University[17] and at 3 invited seminars of the 2014[15] and 2016[16] CAS Assembly of Academicians in Beijing.

DownLoad: Full-Size Img PowerPoint
Fig. 2.  The Arrhenius Least Squares Fit (LSF) with $n=0$, and the Physics Based Fit (PBF or PBFit) with $n=+3/2$ of the charge carrier (proton-prohol) concentration product in liquid water and solid silicon. The energies at the ice point $T=0$ ℃ is the tangent or slope. The energies in the liquid range 0 ℃ $<$ $T\leqslant 100$ ℃ are the values needed to give the measured $n_{\mathrm{i}}=(e^{\mathrm{-}}e^{\mathrm{+}})^{\mathrm{1/2}}$ and $(p^{\mathrm{+}}p^{\mathrm{-}})^{\mathrm{1/2}}$ .

DownLoad: Full-Size Img PowerPoint
Fig. 3.  The Arrhenius Least Squares Fit (LSF) with $n=0$ and the Physics Based Fit (FBF or PBFit) with $n = -3/2$ of the detrapping limited mobility of the two charge carriers, Protons and Prohols (Proton-holes) in liquid water limited by the absorption of a protonic or proholic phonon localized at the occupied proton and prohol trap site.

DownLoad: Full-Size Img PowerPoint
Fig. 4.  The correlations showing better than 0.390% RMS deviation, among the energies or vibration frequencies, of the five phonons that limit the rate of the proton-prohol generation-recombination-trapping transport kinetics, from our PBFits (Physics Based Fits), from the optical properties of isolated water molecules in the vapor phase measured by others, and from those predicted by the simple 1-D spring-mass linear chain model, $\omega_{{m}}/\omega =(K_{{m}}/M_{{m}})^{{1/2 }}$ where m is the total mass number of the mobile protons on the four neutral ( $m=8$ ) or charged ( $m=8+1=9$ and $m=8-1=7$ ) water molecules and also of the immobile protons in the nuclei of the four water oxygen nuclei in the 4-water molecule hexagonal close packed primitive unit cell of our Melted-Ice Liquid Water model, which also differentiates from the 2-water molecule cubic primitive unit cell which appears in about 20% volume at lower-temperature ( $< -140$ ℃) type $I_{\mathrm{C }}$ ice.

DownLoad: Full-Size Img PowerPoint
Fig. 5.  Comparison of three models of positive point-mass proton transport in pure liquid water, all limited by variable-frequency (time-dependent polarization -Doppler effect) single-phonon emission. The first five rows of each table involve one propagating or localized phonon during the proton's trapping, generation-recombination and scattering transitions. (ⅰ) Two single protonic phonons. (ⅱ) One protonic and one proholic phonon. (ⅲ) Three single protonic phonons. All three models are also limited by the elastic and inelastic propagating water phonon, longitudinal and transverse(weak-shear), Debye dispersive formula we used from all four water molecules in the primitive unit cell, $m=72$ , $\omega_{\mathrm{72}}$ , during Step B in Fig. 1(b), with long scattering-free-path during positive point-mass proton drift and diffusion. In our discussions, this is sometimes jargonized as oxygen phonon to avoid confusion with the general material name, water, although there are very few, 1 part in 10 $^{\mathrm{8}}$ ( $C_{\mathrm{H_2O}}/p^{\mathrm{+ }}$ $C_{\mathrm{H_2O}}$ /p $^{\mathrm{-}}$ 10 $^{\mathrm{22}}$ /10 $^{\mathrm{14}})$ , localized resonant or gap mode oxygen phonons.

DownLoad: Full-Size Img PowerPoint
[1]
William Shockley (Bell Telephone Laboratories, Shockley Semiconductor Laboratory of Beckmann Instrument Company, Shockley Transistor Corporation, Stanford University), Electrons and Holes in Semiconductors, 558pp, 1950, Van Nortrand, New York. Chapter 16 Statistical Mechanics for Semiconductors and Chapter 17 Theory of Transition Probabilities for Holes and Electrons give the historical first and still the best tutorial description and mathematical analysis of these two, the most important subjects on the mathematical modeling of the properties of a material in the solid phase of the three phases, solid, liquid and gas, in a container-volume containing many electrons, atoms and molecules, at thermodynamic equilibrium and at small deviation from thermodynamic equilibrium. It takes several careful readings to get the key notions on the underlying physics-based assumptions and approximations to appreciate what the author was and is trying to convey to the student of this subject.
[2]
Chih-Tang Sah and William Shockley, "Electron-hole Recombination Statistics in Semiconductors Through Flaws with Many Charge Conditions", Physical Review, Vol. 109, pp. 1103-1115, 15 February 1958.
[3]
Chih-Tang Sah, Fundamentals of Solid State Electronics, 1010pp. 1991. World Scientific, Singapore. Section 360, Generation, Recombination, Trapping and Tunneling, and its subsection on p. 270-290.
[4]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry-Electrical Conduction in Pure Water, " Journal of Semiconductors, Vol. 34(12), pp. 121001-1-8, December, 2013.
[5]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water, " Journal of Semiconductors, Vol. 35(02), pp. 021001-1-19, February, 2014.
[6]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry Ⅲ. Electrical Conductance of Pure and Impure Water, " Journal of Semiconductors, Vol. 35(04), pp. 041001-1-20, April, 2014.
[7]
Binbin Jie and Chihtang Sah, "Ion Product of Pure Water Characterized by Physics-Based Water Model, "Chinese Journal of Chemical Physics, Accepted on September 21, 2015 and published Online on December 21, 2015, Vol. 29, No. 2, pp. 167-170, April 27, 2016.
[8]
Sah Chihtang and Jie Binbin, "Semiconductor View of Liquid Chemistry, " 20130913@1400-1600, Sah Pentung (薩本棟) 111th Anniversary Memorial Symposium, Friday, September the 13th, 2013, Annual National Fall Meeting of the Chinese Physical Society, 20130911-0922, Xiamen University, Xiamen, Fujian, China.
[9]
Jie Binbin and Sah Chihtang, "Solid-State Physics View of Liquid-State Chemistry-Electrical Properties of Pure and Impure Water" (Keynote), 20140508@1040-1125, 2014 International Symposium on Next-Generation Electronics (ISNE2014), May 8-10, 2014, Chang Gung University, Taoyuan, Taiwan, China.
[10]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry" (Invited), 20140616@0830-0900; "Water Physics-Condensed State Physics View of Liquid State Chemistry" (Tutorial), 20140616@1530-1630, 2014 Workshop on Compact Modeling (WCM), NanoTech, TechConnet World Innovation Conference & Expo, June 15-18, 2014, Washington DC, USA.
[11]
Jie Binbin and Sah Chihtang, "Experimental Verification of a Water Physics and Model in Pure Water at Thermodynamic Equilibrium and Non-Equilibrium" (Invited), 20160524@0830-0900, 2016 Workshop on Compact Modeling (WCM), NanoTech, TechConnet World Innovation Conference & Expo, May 22-25, 2016, Washington DC, USA.
[12]
Binbin Jie and Chihtang Sah, "Electrical Conduction in Pure Water, Trapping and Scattering of Positive Protons and Negative Proton Holes, " D26. 00012, 20150302@1642-1654, 2015 March Meeting of the American Physical Society, March 2-6, 2015, San Antonio, Texas, USA.
[13]
Binbin Jie and Chihtang Sah, "Electrical Mobility of Protons and proton-holes in Pure Water Characterized by Physics-Based Water Model, " K47. 00005, 20160316@0848-0900, 2016 March Meeting of the American Physical Society, March 14-18, 2016, Baltimore, Maryland, USA.
[14]
Binbin Jie and Chihtang Sah, "Proton Transports in Pure Liquid Water Characterized by Melted Ice Lattice Model, " E3. 00004, 20170314@0836-0848, 2017 March Meeting of the American Physical Society, March 13-17, 2017, New Orleans, Louisiana, USA.
[15]
Sah Chihtang and Jie Binbin, " Water Physics-Condensed State Physics View of Liquid State Chemistry, " (Invited) 20140609@1400-1600, Research Seminar, June 09, 2014, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
[16]
Sah Chihtang and Jie Binbin, "Semiconductor Physics and Model of Liquid Water-Ion Product and Ion Mobilities in Pure Water, " (Invited) 20160602@0830-0900, Reports for Academicians, June 2, 2016, General Assembly of Academicians, Beijing, China. "Semiconductor Physics and Model of Liquid Water 1. Ion Product and Ion Mobilities in Pure Water 2. Theory and Experimental Confirmations, " (Invited) 20160603@0930-1130, Research Seminar, June 3, 2016, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China.
[17]
Sah Chihtang and Jie Binbin, "Water Physics and Model-Fundamentals, " and Jie Binbin and Sah Chihtang, "Water Physics and Model-Experimental Verifications-Pure Liquid Water", (Tutorials) 20160806@0830-1100, Soft Matter Physics Summer School, of the 10th Annual Summer School on Theoretical Physics of the Natural Science Foundation of China, August 01-13, 2016, Xiamen University, Xiamen, China.
[18]
Peter Atkins (Lincoln College, U. Oxford, UK) and Julio de Paula (Lewis and Clark College, Portland, Oregon, USA), Atkins' Physical Chemistry, 972pp, 9th Edition, 2010, Oxford University Press.
[19]
David Eisenberg (UCLA) and Walter Kauzmann (Princeton U. ), The Structure and Properties of Water, 296pp, 1969, Oxford University Press. Published 2005 in the Oxford Classics Text in Physical Sciences, reprinted, 2011.
[20]
Victor F. Petrenko (Dartmouth College, New Hampshire, USA. ) and Robert W. Whitworth (U. Birmingham, UK. ), Physics of Ice, 374pp, 1999, Reprinted 2003, Oxford University Press.
[21]
Charles Kittel (UC Berkeley, 19160718-), Introduction to Solid State Physics, Editions: 1st 396pp 1953 (2nd-Printing April 1954), 2nd 617pp 1956, 3rd 648pp 1966 (2nd Corrected Printing November 1967), 4th 766pp 1971, 5th 599pp Taiwan-Edition 1976 (8th-Printing August-1984); in the next three latest editions: -First 3 chapters on classical Newtonian Mechanics harmonic oscillators and next 2 chapters on Schrodinger Wave and Dirac Quantum Mechanical harmonic and anharmonic oscillators and phonons of an array of host atoms and molecules located on a space lattice: 6th 646pp 1986, 7th 673pp 1996, and 8th 680pp, 2005. The 9th Edition overdue for decade release, might be due on the 101th birthday, 20170718.
[22]
Neil W. Ashcroft (Cornell U. ) and N. David Mermin (Cornell U. ), Solid State Physics, 826pp, 1976, Holt, Rinehart and Winston, New York. First and only Edition, 5th Printing, 1977. (a) Lattice atomic or nucleus vibration frequency versus wave number or normal mode characteristics for one-dimensional (1-D) monatomic Bravais Lattice on p. 430. (b) 1-D lattice with a basis illustrated by a two atoms per primitive unit cell with two different force constants on p. 433. (c) 3-D monatomic Bravais lattice on p. 437. (d) Dynamical matrix defined on p. 439. (e) Normal modes of a 3-D lattice with a basis on p. 442. (f) Connection with elasticity, on p. 443. (g) Quantization of the lattice vibration modes into phonons in Chapter 23, starting on p. 451. (h) Graphical illustration of the differences among the dispersionless and dispersive Debye and Einstein models of the phonon dispersion characteristics shown by Fig. 23. 4 on p. 462. (ⅰ) Density of normal modes, on p. 464, and van Hove singularities on density of electron states (same as phononic modes) on p. 145. (j) Jahn-Teller effect on p. 659. (k) Anharmonic effects in Chapter 25 starting on p. 487.
[23]
Frank S. Crawford, Jr. (UC Berkeley), Waves - Berkeley Physics Course - Volume 3, 600pp, 1965, 1966, 1968, McGraw-Hill, New York. Preface (One of 5 volumes for a 2-year elementary college physics course for undergraduate students majoring in sciences and engineering). Free internet download.
[24]
J. D. Bernal and R. H. Fowler, "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and hydroxyl ions, " J. Chem. Phys. , Vol. 1(8), pp. 515-548, August, 1933.
[25]
Linus Pauling, "The Structure and Entropy of Ice and Other Crystals with Some Randomness of Atomic Arrangement, " J. Amer. Chem. Soc. , Vol. 57(12), pp. 2680-2684, December 1935.
[26]
W. F. Giauque and H. L. Hohnston, "Symmetrical and Antisymmetrical Hydrogen and the Third Law of Thermodynamics. Thermal Equilibrium and the Triple Point Pressure", J. Amer. Chem. Soc. , Vol. 50, pp. 3221-3228, 1928; J. O. Clayton and W. F. Giauque, "The Heat Capacity and Entropy of Carbon Monoxide. Heat of Vaporation. Vapor Pressures of Solid and Liquid. Free Energy to 5000°K. From Spectroscopic Data, " J. Amer. Chem. Soc. , Vol. 54, pp. 2610-2626, 1932; W. W. Blue and W. F. Giauque, "The Heat Capacity and Vapor Pressure of Solid and Liquid Nitrous Oxide. The Entropy from its Band Spectrum, " J. Amer. Chem. Soc. , Vol. 57, pp. 991-997, 1935. Quoted by Pauling in Ref. [25].
[27]
George Malenkove (AN Frumkin Inst. Phys. Chemistry and Electrochemistry, Moscow), "Liquid water and ices: understanding the structure and physical properties, " J. Phys. Condens. Matter 21, 283191, 35pp, 2009. This is the only article at this time (20170531-20170630) which describes the key issues of the short range but sufficient long range order of the structural properties of liquid water, but from the structural viewpoint and its solid-phase transformations-transitions, giving comparison with the electronic Si and Ge, however, the author was hanged up on the proton bond, not visualizing proton as the mobile particle in the protonic liquid water Lattice (same as the electron as the mobile particle in the electronic Si and Ge) with the sufficiently long-range short-range order, as indicated by the fluidic softness. See Sections 2. 1 Proton order on page 4 and Section 2. 2 Structure of crystalline ice modifications and its Subsections 2. 2. 1 Simple frameworks on page 5-6 for the rare cubic and abundoned hexagonal form of type I ice, Icand Ih respectively. We only appreciated the descriptions of this author in this 2009 review, after our second reading of this article 36 months later during our last polishing of our present report on May 31, 2017. Our protonic water model was evolved before our second reading of this article by Malenkove[26], which further clarified the differences between our proton transport model and the hydroxyl ion (hydroxide and hydronium) transport model reviewed by Malenkove[27]. Our protonic potential energy band-landscape model of liquid water with the melted (hence 'soft', flexible and fluidic) hexagonal close packed Ice Lattice, contains twice as many proton traps as there are protons, as proposed in 1933 by Bernal and Fowler[24] and proven by Linus Pauling's 1936 residual entropy theory[25] on the low temperature specific measurements during 1928 to 1936 by Giauque and his graduate students[26]. Our two proton transport models discovered by us and reported in the present article, hidden in the 50-more years of ion product and mobilities data of pure liquid water, are (ⅰ) proton-prohol two-band potential energy band or landscape model and (ⅱ) three proton trapping at two proton traps in the proton potential energy band or landscape model, both visualized and accurately scaled by the simple Newtonian Mechanics of vibrating string and mass, taught in undergraduate freshmen-sophomore physics[23].
[28]
John L. Finney (University College London), "Bernal and the structure of water, " J. Physics, Conference Series 57, pp. 40-52, 2007. This article reviewed the latest successes, as of 2007 or 10 years ago, of the crystalline lattice model of liquid water, proposed by Bernal in 1933[24] but abandoned by him in the 1960's as "a delusive approach, postulating a greater degree of order in the liquid than actually exists there" after he, Bernal, developed a very successful "random packing" model of simple fluids. See also John L. Finney (University College London), "What's so special about water?", Phil. Trans. R. Soc. B, 359, pp. 1145-1165, 2004. This article gives an accurate authoritative summary of the most important properties of the water molecule in liquid water. Zero point vibrational frequency of 4634 cm-1 (574. 58 meV) from Eisenberg & Kauzmann, 1969. [19] The three normal modes of vibration of isolated water molecule from Benedict et al. (1956) for ν1= 3657 cm-1= 453 meV symmetrical stretching, ν3 = 3756 cm-1 466 meV antisymmetrical stretching, and ν2= 1595 cm-1=198 meV bending or breathing. But the author fell to the Hydrogen bonding picture just like all the rest. See Section 3. Interactions between water molecules starting with the statement, Water molecules interact with each other through hydrogen bonding, with the interaction energy of 20 kJ/mole = 5 kcal/mole = 207 meV = 10 (8) times larger than the thermal fluctuation at room temperature =kBTRoomTemperature= 25 meV. Furthermore, he insisted, just like the rest of them, that liquid water is not a crystal, from failing to recognize the flexibility long range order can and does exist in crystalline liquid with the softness that conforms to the shape and size of the harder container of the liquid. This article gives marvelous pictures, the best we have seen, of the various kinds of molecular clusters of solid waters and their liquid phases.
[29]
Herbert S. Harned and Benton B. Owen (Cornell University), The Physical Chemistry of Electrolytic Solutions, First Edition 345pp, 1943. Second Edition, 645pp, 1950. Third Edition, 803pp, 1958. First Printing 1958, Second Printing, 1963 and Third Printing, 1964. Monograph Series No. 137. American Chemical Society. Reinhold Publishing Corporation, New York. Chapman and Hall, Ltd. London.
[30]
N. F. Mott (Cavendish Professor of Physics in the University of Cambridge) and E. A. Davis (Royal Society Mr. and Mrs. John Jaffe Donation Research Fellow, Cavendish Laboratory), Electronic Processes in Non-Crystalline Materials, 437pp, Clarendon Press, Oxford, 1971. Section 2. 9. 1 Conduction due to electrons with energies near the Fermi energy, pp. 39-42. N. F. Mott (Emeritus, Late Cavendish Professor of Physics, University of Cambridge), Metal-Insulator Transitions, 1st Edition, 278pp, 1974. Taylor & Francis Ltd, London, Barnes & Noble Books, New York. Section 1. 7 Disordered systems: Localization and the Anderson Transition, pp. 30-40. 2nd Edition, 286pp, 1990.

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    Received: 02 June 2017 Revised: 05 June 2017 Online: Published: 01 July 2017

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      Article Navigation >  Journal of Semiconductors  > 2017  >  38(7): 071001
      Binbin Jie, Chihtang Sah. Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water[J]. Journal of Semiconductors, 2017, 38(7): 071001. doi: 10.1088/1674-4926/38/7/071001 B B Jie, C T Sah. Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water. J. Semicond., 2017, 38(7): 071001. doi:  10.1088/1674-4926/38/7/071001.Export: BibTex EndNote
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      Binbin Jie, Chihtang Sah. Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water[J]. Journal of Semiconductors, 2017, 38(7): 071001. doi: 10.1088/1674-4926/38/7/071001

      B B Jie, C T Sah. Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water. J. Semicond., 2017, 38(7): 071001. doi:  10.1088/1674-4926/38/7/071001.
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      Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water

      doi: 10.1088/1674-4926/38/7/071001
      • 1.

        Department of Physics, Xiamen University, Xiamen 361005, China

      • 2.

        Chinese Academy of Sciences, Beijing 100864, China

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      • Corresponding author: Binbin Jie,Email: bb_jie@msn.com; Chihtang Sah,Email: tom_sah@msn.com
      • Received Date: 2017-06-02
      • Revised Date: 2017-06-05
      • Published Date: 2017-07-01

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