E-AEASUREMENT GP DiS-SQCIATIQN PRESSURES OF HYDROUS MiNERALs USENG THERMISTORS Thesis §or flu Dogma of DH. D. MICHIGAN STATE UNEVERSITY COOper Harry Wayman 1959 This is to certify that the thesis entitled Measurement of Dissociation Pressures of Hydrous Minerals Using Thermistors presented by Cooper Harry Wayman has been accepted towards fulfillment of the requirements for __Eh.D_.__degree in_.G.erQ_l_g3L__0 s K “6% gm woman/tea Major professor y- , - ,. .. \ ‘p Q 5 k ~‘r 6’ Date Q5 A C ' '2‘ ‘r f 0-169 W (F DISSCDIATION PRESSURES CF HIDROUS MINERALS USING THEMSTORS By COOPER HAIRY W AN A$TRLCT Submitted to the School for.Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of mm 0? PIEIDSO'HII Department of Geologr 1959 Approved by: fl Egfiww 60°?“ *" "89““ {leaves}. A high temperature cell has been designed for the measurement of dissociation pressures in hydrous minerals by a newlyr developed method of thermistors. The vapor pressure over Gypsum was determined with an accuracy of 7-17 per cent as compared to a manometer method. With the present experimental set-up, the thermistor method will not detect vapor pressures with any degree of confidence in substances that must be heated above 100°C. A critical review of published thermodynamic data for Gibbsite and Boehmite was made. The dissociation pressure over Gibbsite measured experimentally does not agree with theoretically calculated curves as a result of complex surface reactions that occur during dehydration. The application of certain concepts in physical chemistry and elementary thermodynamics to account for equilibrium assemblages of minerals in nature is discussed. rigxted comb? Wayman r Harry Coope 1961 MEASUREMENT W DISSCL'IA'I'ION PRESSURE OF HYDROUS MINERALS USING mmsrons m COOPEHARRYW‘MAN AWE Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of ”TOR (F PHIIDSOPHI Department of Geology 1959 13b}: of C aliens. Acknowledgments List of Tables List of Figures I. II. III. V. VI. VII . VIII . Introduction Historical Background Preparation of Materials and Mineralogy A. Gibbsite B. Boehnite Co Gypsum Thermochemical Considerations A. Thermodynamic Equilibrium Constant and the Phase Rule B. Method I. Calculation of Equilibrium Constant from Free Energy Values 0. Method II. Calculation of Equilibrium Constant from Calorimetric and Spectroscopic Data Description and Design of Experimental Apparatus A. High Temperature Cell B. Themistor Characteristics 0. The Rhoatstone Bridge Circuit Experimental Method and Results A. Basis for Determining Vapor Pressure B. Delvdratien ef Gypsum C. Dehydration of Gibbsite Microscopic and X-ray Diffraction Examination of Detwdraticn Products A. Microscopic Examination B. X-ray Diffraction Examination C. Discussion of Results Discussion A. Importance of Dissociation Pressure Measurements B. Surface Reactions on Solids C. Effoot of Total Pressure on Dehydration D. Relationship Between Natural Mineral Phases, Thermodynamics, and Kinetics 8335 21 91 91 9h 97 98 99 1101 Table of Contents (can't) 11:. Conclusions X. Suggestions for Future Research Appendix I. Brief Description of B.E.T. Method Appendix II. Description of Sedimentation Method Appendix III. Calculation of Standard Deviation Appendix IV. Method of Least Squares Appendix V. Derivation of the Clausius-CIapeyron equation for a Solid-Solid-Gas reaction Bibliograplw Biographical Sketch Ms” 108 110 113 119 121 127 Acknowledggnents I wish to thank Dr. Harold B. Stonehouse, Department of Geology, Michigan State University,for his kind help and constructive criticism throughout the entire investigation. I an very grateful to Dr. James Sternbezg for suggesting the possible use of thermistors for measuring vapor pressure and Dr. James Dye for contributing a great deal to xv understanding of thermodynamics and critically reviewing section IV on Themcchemical Considerations, both of the Department of Chemistry, Michigan State University. I an especially indebted to Dr. Gordon J .F. MacDonald, Institute of Geophysics, U.C.L.A., for originally suggesting the problem of measuring dissociation pressures of Ivdrcu minerals with their possible implications to weathering processes in nature. I also would like to acknowledge Dr. Robert Carrels, Harvard University, for stimulating my interest in calculating equilibrium constants from free energy values. To Dr. William Nickerson, Department of Mechanical Engineering, Massachusetts Institute of Technology, I am grateful for calibrating the thermocouples used in this work. It is also proper to thank those who have contributed equipment and samples used in this investigation. I wish also to extend thanks to my father in-law, George Treier, Sayreville, New Jersey, for doing an excellent job in reproducing the photographs shown in this thesis. Last, but not least, I want to give untold thanks to av wife, Ruth, for her moral support in addition to doing all the typing and helping to proof read the manuscript. List of Tables Tablo P e III.l. Sise fraction analysis of gibbsite I2 IV.1. List of thermodynamic values used in calculations 21; IV.2. List of constants usod for heat capacity calculations 26 IV .3. Enthalpy calculations for reaction gibbsite - boehnite or water vapor as a function of temperature 27 Iv.h. Calculated equilibrium constant(Methcd I) for gibbsite - boehmite + water vapor using Kusnetzov‘s thermodynamic values 28 Iv.S. Calculated equilibrium constant (Method I) using Deltombe and Pourbaix values 29 IV.6. Calculated equilibrium constant(Methcd I) using Bureau of Standards values 29 IV'.7 . Shomate and Cook heat capacity values for gibb- site and boehmite 31 IV.8. Shomate and Cook entropy data for gibbs its and boehmite . 32 IV.9. Difference in heat capacity of ibbsite and boehmite calculated between 200 to aoo’x 32 IV.10. Comparison of equilibrium constants calculated by Methods I and II using Kuznetzov's data 38 IV.11. Comparison of equilibrium constant calculated by Methods I and II using Bureau of Standards data no v.1. Cos-Mao data on thermal conductivity of gases 58 V1.1. hperimental results on calibration of cell without water vapor 72 V1.2. Reproducibility of thermistor resistance at different pressures 7h V1.3. kperimental results of temperature-log resis- tance for water vapor in calibrating cell. 7h V1.11. Experimental results of temperature-log resis- tance for Gypsum 77 Table v1.5 V1.6. V1.7. V1.8. V1.9. V1.10. VII .1. VIII .1. List of Tables (con't.) Comparison of Kelley and Usyman vapor pressures over Gypsum Experimental results of temperature-log resis- tance without water vapor in calibrating cell Experimental vapor pressure of water for 70.78% mixture of sulfuric acid-water Experimental results of temperature-log resis- tance for mixture sulfuric acid-water Experimental results of temperature-log resis- tance for gibbsite Comparison of Woyman and Funaki-Uchimura vapor pressures for gibbsite Dehydrated phases found by x-ray diffraction Distribution of ivdrcus aluminum oxides in "bauxite" deposits 8h 8h 85 89 9h 102 Figure IV.l. IV.2. v.1. V.2. v.3. V.h. v.5. v.6. V1.7. v.8. v09. V1.1. V1.2. V1.3. v1.h. v1.5. V1.6. VII.1. List “F3215. The deviation of water vapor from an ideal gas Calculations compared for dissociation pressure of gibb- site by Methods I and II(Kusnetzov data)‘ Calculations compared for dissociation pressure of gibb- site by Methods I and 11(Bureau of Standards data) Schematic diagram of the high temperature cell Photograph of the high temperature cell Photograph of hood used to help control temperature Comparison of temperatures measured by inside and outside thermocouples Graph showing temperature variation in sample cell Variation of thermistor resistance as a function of temperature using 1.5 volt battery Approach to steady state equilibrimn for thermistors Schematic diagram of uheatstone bridge circuit Photograph of laboratory apparatus Experimental curves for determining vapor pressure of Gypsum by thermistors Approach to equilibrium from low temperature and high tonperature s idos Comparison of Kelley and Harman vapor pressures over Gypsum Experimental curves for determining vapor pressure of gibbsite Approach to equilibrium from high and low temperature sides for gibbsite plus ton day tost Comparison of Waymn and Funaki-Uchimura vapor pressures for gibbsite X-ray diffraction patterns for dehydrated gibbsite 1. I. Introduction In the past many geological problems have been investigated from a qualitative, or at best, a semi-quantitative point of view because some important thermodynamic values were lacking to permit quantitative considerations, but the interesting problems of weathering which occur at surface temperature and pressure can be considered on a quantitative basis. Schnalz (1959) has recently published significant data on the Fe203-HZO system for the stability relationship of Goethite and Hematite under conditions of weathering. Other imortant weathering reactions that occur result in the formation of hydrous oxides of aluminum in "bauxite" deposits, hydrous borates in arid climates, and the hydrous copper carbonates and other onsalts found in mining areas . In I'bamcite" deposits, Gibbsite Al(ai)3, Boehmite A10(OH), and Diaspore AlO(OH) have been identified. On the basis of free energ relationships, Gibbsite should be the stable phase. The partial pressure of water at which Gibbsite dissociates into Boehnito plus water vapor can be determined from the simple reaction: 11(m)3: AlO(OH) o 1120“,). The equilibrium constant at surface temperature and pressure involves only the partial pressure of water or K - P320. In desert areas an interesting set of borates such as Inyoite (“236011 .13H20), Meyer- hofferite(Ca236On.7H20), Colemanite (Ca2360n5H20) are found. The partial pressure of water as a function of temperature again would determine which of these twdrate-pairs could co-exist. In the case of rydrous copper carbonates both Malachite and Azurite are found intimately associated. It is difficult to determine whether Azurite alters to Malachite or vic e-versa. No free energy .values are available at the H.oo o.mo 0.8 o.~o 0.8 0 93 0.5 o.wo o.~o 008 0.00 flab «floor tom 05.05.53 Nada 9o mono Hosea H: 0.6030. Zomob Mina—Cg. 20‘08 IRE GEE. Coco. Awwwwv. s arouaow wuoeoneuoo on moecwoaon.£o¢on son w¢0’ab .- Q. 3.. 2.3... go $.6ng NU” NoHINNOO $1“... u nonsense u H u Hoe-P as. m3 B—u WW! ml? r_uu 5—1;. mm bow eon—voodoo? Asa v as a function of temperature. Figure No. I.1 The deviation of water vapor from an ideal gas 3. present time for either of these species although Carrels (1957) has suggested a method for calculating the free energy of Malachite. This reaction can be written as 2003(003)Z(GH)2* H20 ~——>' BCU2003(OH)2+ 002(v) (VI (Asurite) (Malachite) If the reaction goes as written the equilibrium constant would be K - :20? . If Malachite alters to Asurite, then the equilibrium constant 0 . 2 is K e P1420 . It would thus be necessary to investigate these ratios 1532’ to determine the direction of the reaction. On the basis of the equilibrium reaction, Malachite probably forms from Azurite under conditions of high relative humidities since P002 is approximately con- stant in the atmosphere. It appears that some of the important weather- ing reactions involve some good, basic chemistry. Any of the above problems studied experimentally from the view- point of vapor pressure measurements would reveal two things: (1) the partial pressure of gas or the partial pressure ratio of two gases as a function of temperature, at which the two solid phases can remain in equilibrium and (2) the heat of reaction (enthalpy) which can be calculated through the use of the Clausius-C lapeyron equation. It is tacitly assumed in the above that water vapor can be treated as an ideal gas for reactions at surface temperature and pressure; the validity of this statement can be demonstrated by plotting the ratio of g against temperature (figure I.l) which shows little deviation from unity at temperatures up to 14.13% (1hO°C). A good sumary of the various methods of measuring vapor pressures is given in Daniels, Mathews and Williams (19149). The most common types h. listed are the dynamic method, static method, gas-saturation method (transpiration method), and the isopiestic method. Each of these methods has definite limitations with perhaps the isOpiestic being the best. For example, the entire apparatus must be thermostated to permit vapor pressure measurements greater than those at the saturation pressure of water vapor at room temperature. If the unit were not thermostated, then water vapor would condense along the walls of the tubing and at joints whereby the only vapor pressure measured would be that at the point of lowest temperature in the system and not necessarily that over the sample. Other disadvantages are the elaborate glass blowing which is amenable to occasional leaks and requires a vacuum pump of high capacity due to the large volume of the system to be evacuated. Recently much attention has been given to vapor pressure measure- ments from the adsorption of a gas on a solid by the use of the McBain balance. In this method a'solid adsorbant is attached to a sensitive quarts Spring. Knowing the adsorption isotherm of a specific adsorbant for various gases permits the determination of the vapor pressure tar change in weight of the adsorbant in term of units of spring deflection. The obvious disadvantages of this method are that the sensitive quarts spring is affected by small changes in temperature and that a series of selective adsorbants would be required to measure the presence of more than one gas. in excellent method for measuring the concentrations, and there- fore determining pressures,of multiple gases is infra-red spectroscopy. This method has the nearly unique property of being selective to any gas providing its spectrum is determined. In this method it is necessary to use a heated, calibrated sample cell with a heated attached absorption 5. cell to prevent condensation of vapor along the walls of the tubing and cell windows. The cell should be constructed of high quality pyrex glass and calcium fluoride windows must be used on the absorption tube to eliminate erosion from water vapor which would occur if sodium chloride windows were used. The entire spectrometer must be flushed with dry nitrogen to remove water vapor from all sources other than the sample apparatus during any run. The vapor pressure over distilled water and mixtures of distilled water and sulfuric acid can be used as standards for water vapor. The recent work of Tosh, Field, Benson and Haynes (1959) has established a possible standard for both water vapor and carbon dioxide by measuring the partial vapor pressures of these gases over solutions of potassium carbonate. Thus with this method one simply would compare the unknown vapor pressures to those obtained from standards in terms of percent transmission. Percent transmission can be expressed in terms of IO, Ilooand IT where IO - the amount of stray energy reaching the detector when the beam is cut out, I100 :- the 100% transmission - 0% absorption, IT . quantity or point determined at the minimum: of the absorbed band . $T - IT ' IO 1: 100 I100"Io The writer investigated this method up to approximately 250mm. Hg. vapor pressure of water; pressures beyond this range could not be attained because of poor cell design . However, further exploration by this method should be undertaken since both water vapor and carbon dioxide are of geological interest and their presence can be simultaneously measured using this tecl'mique. It was suggested that the measurement of dissociation pressures by thermistors might be fruitful and so this was investigated. The 6. dissociation pressure of water over Gypsum was measured and the accuracy compared to a manometer technique of Kelley, Southard, and Anderson (19141). An attempt was also made to measure the dissociation pressure of Gibbsite and thereby determine the free energy of formation. This thesis is intended to have a three-fold purpose: (1) To develop a new method for measuring vapor pressures (2) To design a heated cell that can be used for making vapor pressure measurements on m'drous minerals (3) (a) To use some of the fundamental concepts of physical chemistry and elementary thermodynamics to calculate theoretical curves for dissociation pressures of hydrate-pairs and (b) To correlate the results of experiment and theory and their comparison with equilibrium processes in nature. 7. II. Histgrical Backgtrpundw Much work has been done in the past on the dehydration of Gibbsite, but unfortunately at high temperatures. The emphasis was placed on the dehydration as applied to industrial preparations of alumina with little attention given to its geological possibilities. Hackspill and Stempfel (1929) found that Gibbsite could be irreversibly dehydrated at 220°C. They suggest that dehydration does not take place by progressive loss of water, but this is incorrect. Achenbach (1931) indicates that synthetic Gibbsite begins to lose water at 170°C and passes into orthorhombic boehmite at approximately 200°C. Schwiersch (1933) states that Gibbsite starts to lose water at 150°C and converts into boeluuite. Borisevich (l9h8) has investigated the tensimetric dehydration of gibbsite and found three stages of water loss. Up to 175°C, i mole of water is released with a structural change to boehmite. At 200% an additional 1% moles of water is lost and a monomdrate is formed. The last stage of dehydration ends at hoo‘b. It is further pointed out that, within a rather narrow interval of temperature, two different reactions occur in the transition of the gibbsite lattice to that of boehmite which explains the complicated curves observed by some authors for thermal effects in Manic experiments. Ginsberg and Kbster (1952) investigatod gibbsite 1V heating under pressure in the presence of alkali and indicate that gibbsite is completely con- verted to boehmite with yields of over 90% when heated at 180°C for two hours at alkali concentrations as low as 0.6g .Na20/liter. These authors conclude that, if traces of Na20 enter the gibbsite lattice, less stable compounds form, which are easily converted to boehmite. Tertian and Papee (1953) reveal that the slow heating of gibbsite under reduced pressure yields two phases, a smaller fraction of boehmite and a larger 8. one of poorly crystalline alumina. The results of these workers are in disagreement with most of the previous work. Tertian, Papee and Charrier (1951;) studied the dehydration both in air and vacuo. In vacuo between 170° and 250°C, boehmite is the only well crystallised phase formed amounting to only about 25% of the sample. At hOOOC the demrdration product, boehmite, decomposes to gamma alumina. In air between 200° and hoo°c gibbsite completely converts to boehmite. Trambouse, The, Perrin and Mathieu (195M investigated gibbsite by D.T.A., thermogravimetry and B.E.T. measurements and found that between 25 and 570°C gibbsite loses 2.9h moles of water. The surface area increases to a maximm of 235 sq. m./g. at 380°C when H20. A1203- 0.55. Alexanian (1955) used X—rsy diffraction, dehydration and D.T.A. and found that gibbsite converts to boehmite at 220°C, while bayerite decomposes into gamna alumina up to 220°C. Courtial, Trambouze and Prettre (1956) suggest that the boehmite content of a gibbsite sample delwdrated rapidly at high temperatures is always much less than the boehmite content of a sample dehydrated to the same degree but more slowly and at lower temperatures. This work was done in air at tanperatures that ranged from BIN-378°C with a maximum of 30% gibbsite found as a partial dehydration product. Since it was shown previously that gibbsite loses nearly two-thirds of its water at slightly over 200°C, this work is questionable. Theoretically, in an open system at temperatures greater than 200°C and given sufficient time, gibbsite should convert completely to boehmite. Ginsberg, Huttig and Stnmk-Lichtenberg (1957) have found that the phases present after derwdration depend upon the starting material. Teclmically prepared gibbsite with a grain size of 9.1. microns demorate. at 105°C to gibbsite with a small amount of boehmite. At 200°C both gibbsite and boehmite are present in large quantities. Gibbsite prepared from KOH with a grain size of 6.7 microns does not derrate to boehmite at 10590. At ZmOC' the same material contains abundant gibbsite and boehmite after dehydration. Sato (1959) studied the dehydration of various preparations of gibbsite by thermo- balance, D.T.A., and x-ray diffraction. It was determined that gibbsite has a lower decomposition temperature if bayerite is present as an impurity from preparation. Fine-grained gibbsite (88% less than 5 microns) does not give an endothermic peak at 220-23000 whereas coarse-grained gibbsite (17% less than 5 microns) shows a reaction at this temperature. This’work would suggest that the stability of gibbsite is greater for fine-grained material. The del'wdration mechanism given by Sato is Gibbsite I ———) alumina \ some.” Gibbsite II --—> /\ alumina Day and Hill (1953) conclude that boehmite formed from the delvdration of gibbsite and bayerite is produced by secondary reactions between the original detvdration products, which are virtually anlwdrous aluminas, and the water vapor released during dehydration. Their proposed mechanism of dehydration is Gibbsite Rehydration ~—-) Bayerite i be low 11400 Dehydration Dehydration above 150° above ~1h5 ° Jr X- A1203 ___, Boehmite PCEZ- 3‘00“ 11592:: 3’ «A1203 ‘Rebydration DeBoer, Steggerda and Zwietering (1951:) have also studied the dehydra- tion of gibbsite and indicate that the products formed depend on the method of preparation. Gibbsite (I) formed when 130g. Al(CH)3 and 10. 180g. NaCH in 1:1 H20 were exposed to air for three months at room temperature and dehydrated to x alumina. Gibbsite (II) precipitates from a Na aluminate solution when carbon dioxide is bubbled through at 80°-90°c. Gibbsite (II) dehydrates to a mixture of -alumina and boehmite. In another portion of their work, these investigators found that normal water pressure and saturation water pressure give different reaction products on dehydration. The mechanism listed is V Gibbs ite Normal 493;; Pressure X ~al . a Gibbsite SatVQ‘Eflnérsssw Boehnite 2 All the above data, although somewhat controversial, suggest that (G1). radicals in gibbsite are broken to form water, which is progressively lost after perhaps 150% with boehmite forming most likely as a surface reaction. The obvious weakness of delydration studies is that no information is given with respect to temperature-pressure relationships. In addition to demdration studies, some work has appeared recently on the relydration of dehydrated gibbsite and a few accounts of the kinetics of these reactions. Imelik (1951) studied the rel'vdration 0f alumina that was a detwdrated Al(OH)3 gel (boehmite structure). The :01 was heated from too-900°C. After delvdration this product was ex- POBed to air saturated with water at 37°C (vapor pressure of Wm. Hg). After one week the sample ignited at 100° showed evidence of rehydration ‘50 boehmite and gibbsite from I-ray studies. This information might “(zest that gibbsite originally dehydrated to alumina would form bDel’mlz'tte if left in contact with water vapor in a closed system. mind and Goton (1951;) investigated the dissociation of gibbsite thermOgravimetrically. The dissociation covered a temperature range of 11. 206-21300 at pressures of 10'3‘, n.5, and 15mm. Hg. The dissociation was zero-order with activation energies of 31 kcal. at ID'Bmm. Hg 56 kcal. at b.5mm. Hg 63 kcal. at 15mm. Hg This data is interesting since it indicates that the reaction is independent of pressure. In general it obeys the Langmuir adsorption isotherm for strongly adsorbed, single reactants. This type of reaction can be expressed by the zero-order reaction as dx . k 7 ix - differential of products ‘dt dt - differential of time k n reaction constant which says that the reaction rate is constant and independent of pressure or in terms of the integrated form of the rate equation‘xdkt. A possible physical interpretation of this study is, that regardless of how small the pressure of water vapor over gibbsite, the gas is so strongly adsorbed at the surface and probably exerts a breaking effect or impedes the migration outward of(OHfgroups from within the crystal. Another important factor is suggested in that pressure influences the activation energy. Therefore, progressive increase of vapor pressure requires more energy for dehydration after‘water has been released from the crystal structure. The activation energy and heat of reaction would accordingly not be constant as pressure changed in the thermal system in the temperature range 206-2h3qC. It would be of interest to compare this observation to similar reactions under natural conditions. Eyraud, Goton and Prettre (195h) have found that gibbsite dehydrates in two steps. After making corrections for adsorption and diffusion interferences, the reaction is zero-order with an apparent activation energy of 31 kcal. between the temperature range 180°-2h5qc. .Above 2h5q8, the reaction becomes slightly positive as pressure increases with an increase in activation energy to 56-63 kcal. This result is explained in terms of the chemical adsorption of water on the surface of the solid without any transformation. Thibon and Calvet (1951;) have studied the retur- dration products of gibbsite which was dehydrated under vacuum at a temperature of hOOOO. The reactions were given in terms of temperature- time curves of exothermic peaks which most likely suggest a recrystalliza- tion. The rehydration reaction apparently depends on temperature. A very strong exothermic reaction takes place after one hour at all temperatures. A second exothermic peak occurs in 3 hours at 35°, a very weak peak in 1]; hours at 25° and no second peak after 2!; hours at 10°. The I-rayed products were identified as amorphous material at 10° and a mixture of bayerite and anhydrous alumina at 25° and 35°. Atbest, one finds that dehydrated gibbsite can rehydrate to boehmite, amorphous material or alumina. It appears that the activation energy for gibbsite at temperatures below 21.6% is about 31 kcal. and the reaction rate is of zero-order. Similar to the kinetic investigations, little work has been done on the thermodynamic properties of gibbsite. The first thermo- dynamic approach to this problem was done by Hattig and Wittgenstein (1928). The experimental method used was a manometer system whereby the volume and pressure of gas released could be measured. It was shown in this work that gibbsite loses about two-thirds of its water between 180° and 190°C and the remainder is lost continuously up to th°C. The following equation is reported for the reaction: (Gibbsite) A1203 .3azozs1203 .H20+«2E120(')-h3.1h kcal. or A1(OH)3+ 21.57 kcal.: noun) + 1120(7) 13. giving AHO = 21.57 kcal. for the second reaction. Fricke and Severin (1932) used a manometer method to study the dehydration pressures of gibbsite isobarically at 100nm. Hg and found the dissociation temperature to be 165°C. Their results indicate that two thirds of the water is lost between 115° and 175°C. The following heat effects were calculated: (Merits) Al(OH)3 :2 110(0H) . H20“) AHO - 16.2 kcal. (Gibbsite) Al(0H)3 g2 11 0(011). H2°(v) 4 14° - 18.15 kcal. Huttig and Kbebl (1933) investigated the isobaric decomposition of gibbsite and found that most of the water is released from 100° - 210°C and then more slowly up to [100° at which point the solid has a composition of 0.8 H20 . A1203. They discuss the reaction “solid: Xsolid «bias from classical thermodynamics ,but no quantities were calculated from their data. Kusnetzov (1950) has listed the properties for gibbsite and boehmite as follows: 4431*o 298.16% A F°298.l6°K Gibbsite -307.7 kcal. -27h.82 kcal. Boehmite -23h.9 kcal. -217.10 kcal. Using these data the heat effect for A1(OH)3 ‘2 A1 0(OH) :5 H20“) is 15.0 kcal. Funaki and Uchimura (1952) prepared pure bayerite and gibbsite and determined the dissociation pressure for a limited range of temperature by means of a spring manometer. The following thermodynamic relations were estimated from their results for the reactions : 1h. 13.12122 A1203e 3H20‘f7'A1203 £20 4' 2H20(v) A H° - 32.7 kcal. A r° - 32.7 x 103 - 68.5T 1°: KP - '7e18 x 103‘ + 1h.9 T G ibbs its 4 HO . 96e0 kcal. A F° - 96.0 x 103 -216r 10g . -21.0 x 103 . 117.11 KP r Latimer (1953) lists the following thermodynamic values for gibbsite and boehmite from the National Bureau of Standards as follows: o 4 "029m A F _298°x Gibbsite -613 .7 kcal. -h35 kcal. Boehmite -h71.0 kcal. -Sh7.9 kcal. From these values the heat effect of A1(0H)3 :3 Al 0(01) 4- H20“) is 13.55 kcal. Sabotier (1951;) measured the heat of reaction of gibbsite by UTA and gives a value of 276 ca1./g. which for the reaction Al(0H)3 :2 A1 0(0H) 0 H20”) can be recalculated as 21.5 kcal. Eyraud, Goton,and Prettre (1955) found that gibbsite delwdrates in 3 steps: (1) loss of 0.2 HZO/A1203 requiring 3.5 kcal./g. water (2) next step ends at a compn. of 0.5-0.6 H20/A1203and requires 1.1 kcal./g. and (3) last step consists of two rather ill-defined regions, one 15. requiring 1.0 -1.h kcal./g. and the other 1.8 -2.0 kcal./ g. A more intense study of step (1) showed that AH°298 is very close to that for the transformation into boehmite. Deltombe and Pourbaix (1956) determined electrochemically the standard free energies of formation of gibbsite and bayerite as -55’4.6 kcal./mole and -552.h7 kcal./mole respectively. To say the least, the literature review on the thermodynamics of gibbsite shows a high degree of incompatible results. These discrepancies have contributed to an interest in part of this thesis, in which the thermodynamic properties for the reaction 11(011)3 :1 11 0(cm) . 1120“) were re investigated . III. Preparation of Materials and Mineralggx A. Gibbsite The gibbsite used in this investigation was supplied by Kaiser Aluminum and Chenical Corporation, Baton Rouge, Louisiana. The material was prepared by the Bayer method. The chemical analysis supplied with the sample was Per cent (weight Loss on Ignition at 1000°c 311.70 5102 0.02 1"‘e203 0.01.3 Na20 0.37 Free water (adsorbed) 0.06 A1203. £3929 100.063 This analysis can be compared to the theoretical value of A1203.3H20 of 11.203- 66.61;: and 1120 - 33 .365. The size distribution of the grains was determined by dry screening a 25 gram sample on a Ro-Tap for 30 minutes. The results of this test are given in table III.l. Table IJI.l 143i}; Size (Microns) % of Total +100 +105 12.5 -1oo.270 53-105 73.7 -27o +325 hh—53 10.0 -325 -hh 3.8 10070 Table III.l indicates that approximately 75 per cent of this material ranges from 53-105 microns which is fairly coarse-grained. The surface area of the material as described in Table III.1 was lbhOcm.2/gm. as 1?. determined by the B.E.T. (Branauer, Emmett, and Teller) method. The details of this surface area adsorption method are given in Appendix I. Originally, it was intended to use samples with granularities of approximately 5 and 20 microns. Unfortunately, time did not permit any work on these size fractions. These fine size fractions were obtained by dry grinding the coarse ibbsite in a stainless steel ball mill for eight hours. The ball mill product was then sized by free-settling sedimentation techniques using Stokes' Law as the basis. Separations were made at 5 and 20 microns and the surface areas as determined by the ‘B.E.T. method were respectively 60,h00cm.2/gm. and 52,5000m.2/gm. The details of Stokes' Law calculation are given in Appendix II. Encamination of the unground material with the petrographic microscope revealed that gibbsite was the only phase present. Host of the fragments were coarse-grained, white aggregates. The indices of refraction obtained were 0( -= 1.558 1 0.002 (3 = 1.558 :- 0.002 Y = 1.579 g 0.002 and the optical sign was positive. Optical examination of the ground gibbsite showed that a dark, somewhat amorphous surface coating had formed as a result of grinding; this condition might be explained from the heat generated in the ball mill. The unground gibbsite was also studied by X-ray diffraction using CuKd radiation by recording the Zfivalues. Gibbsite was the only phase detected at the characteristic 19mlues of 18.1, 20.1, and 36.1. X-ray examination of the ground gibbs ite indicated that intense, but somewhat diffuse lines of gibbsite were present. The crystal structure of gibbsite was first determined by Megaw (19311) from Weissenberg photos and ionization spectrometer measurements. The crystallographic constants of monoclinic gibbsite were a - 8.6263 1 0.0007A° b - 5.0602 _+_ 0.00061° c - 9,699 _+_ 0.oolu° 6 - 85° 26' 1 5: Z - 8 052b ~P2,ln The structure is a layer lattice and is pseudohexagonal. Each layer consists of two planes of nearly close-packed oxygens, enclosing a plane of A] , which occupy 2 out of 3 possible hexagonal close- packed positions. Bayerite, the dimorph of gibbsite, is described by Montoro (19%) from Debye-Scherrer spectrograms. A sample with a composition of A1203 3.111820 had a hexagonal unit cell with parameters of a - 5.01A° c - L.76A° Z - 2 A specific gravity of 2.119 and molecular volume of 62.7 was calculated. No solid-solution is known to exist between arw phases of the mrdrates (hydroxides) of aluminum. Beneslavskii (1957) claims that solid solution does occur such as an Ill-containing goethite with the general formula k A1203 .mFe203.nHZO with m greater than n. It is pointed out that a mineral of the type A1203.2Fe203 .5H20 was isolated from insoluble residues from "bauxite" in the Enisei district. This 19. account is probably questionable, but no present work on phase equilibria is available to discredit it. B. Boehmite The synthetic Boehmite used as an x-ray standard was also supplied by Kaiser Aluminum and Chenical Corporation. The boehmite was prepared from the hydrothermal alteration of gibbsite. The chemical analysis given was Per cent Loss on Ignition at 100000 114.60 Free water 0.08 Na20 . 0.111 A1203 3229.9 1CD.O9 This analysis compared favorably to the theoretical amounts of water and alumina in boehmite which are respectively 15.02 per cent and 8h.98 per cent. Optical examination of this material revealed that the indices of refraction were 0‘ - 1.616 _+_ 0.003 6 - 1.655 1 0.002 Y - 1.663 _+_ 0.002 The lflvalues obtained by X-ray diffraction indicated that boehmite was the only phase present. The characteristic peaks using Cuxo‘ radiation appeared at 29values of 114.5, 28.2 and 38.2. Iberg (1956) has obtained the Infra-red absorption spectrum for boelmnite. Two 0H bands appear at wavelengths of 3.06 microns and 3.26 microns. It was considered unnecessary to identify boehmite with this new technique since positive results were obtained by other methods. 20. Ce Gig 231m The gypsum used was supplied by K.K.Kelley, Minerals Experiment Station, Berkeley, California. This material was originally obtained from the Perkins Deposit, Alaska and is identical to that utilized by Kelley in his vapor pressure experiments. It was essentially free from impurities. The gypsum was ground gently in an agate mortar and separated into a -100 mesh fraction by hand sieving. This size fraction was also used by Kelley. Optical and X-ray examination indicated that gypsum was the only phase present. 21. IV . Thermochemical Cons id erations A. Thermodynamic Equilibrium Constant and the Phase Rule In many types of experimental work, it is often possible to calculate theoretical'curves for an assumed reaction to see how well theory and experiment agree. This statement is based on the fact that previous experimental values have been determined which can be applied to empirical equations for some process or chemical reaction. The emphasis in this thesis has been to obtain additional data on the reaction Gibbsite 7;: Boehmite 4 water vapor or Al(0H)3 :2. Al 0(CH) 4» H20“) 6 (structural basis) or “203 332° :5: “203' H2O * 2320M (chemical Formula Basis) The equilibrium constant for the reaction on a structural basis can be written as K . ‘boehmite L 3water vapor ‘gibbsite where a - activity Since the activity of pure compounds can be considered unity at low temperatures, the expression reduces to K - The a 0 water vapor activity is defined as a - f where (a f - fugac ity é - fugacity is some standard state For geological purposes at surface temperature and pressure the stan- dard state can be chosen as one atmosphere pressure. Thus the activity to IQ is a - F/( = f . Figure 1.1 shows that for surface conditions water vapor may be treated as an ideal gas. Since the fugacity of an ideal gas can be approximated very well by its partial vapor pressure, the equilibrium constant becomes K - f - FHZO (partial pressure of water vapor) From the phase rule the number of degrees of freedom (F) equals C-Pez, where F - no. of degrees of freedom, P - no. of phases and C - no. of components. For the reaction under consideration three phases (gibbsite, boehmite, and water vapor) exist which can be described in terms of two components (water and aluminum). Hence F - 2.3.»2-1. The experimental pressure, temperature or composition can therefore be varied and the condition under which the three phases, gibbsite, boehmite and water vapor are in equilibrium is determined. Since the equilibrium constant for this reaction involves only the pressure of water, it is convenient to use a system to obtain the equilibrium pressure as a function of temperature at fixed composition. In order to find this equilibrium pressure, it is necessary to know the change in the equilibrium constant with temperature. The follow- ing derivation should suffice to show how the equilibrium constant varies with temperature; the change in free energy in a system undergoing a chemical reaction, when all reactants and products are in their stan- dard states is (l) A F0 2 411‘an where R =- gas const. T = absolute temp. K 8 equil. const. 4 F°= change in standard free energy 23. The interpretation of A F0 for a chemical reaction is A F0 - ¢(no spontaneous reaction) A F0 a 0(reaction is at equilibrium) 4 I"0 - -(reaction is spontaneous) If equation (1) is differentiated with respect to temperature at con- stant pressure we chtain {94F7fl2‘ ”Ry—{<9 but from the Gibbs-Helmholtz equation 0 (ELF = AF M-4H—-RTAK—4#o='fl1wK-§1 97" P 7- “ T *RkK Hence equating the expressions gives mm A” 0 a“ KLK (-—-—-—- -KA~K‘%_€.:-KT{-z—7r-)/‘ 0" 7:)! 372. which in integral femur is a 7. " .. 411' All 1,61 44am [7; 7;, ’0‘: fl j,”— _,+_ if A H0 is independent of temperature thus A K1]: 2' AT“ ETTJTZ - ATH [M T 7": K1 2 A”, __ (’1.- T; {2} K, 2.303 R T, T2. Equation (2) simply states that, if the equilibrium constant is known definitely at some temperature, in addition to knowing A H° as a function of temperature or if it is constant over the temperature range of interest, then the equilibrium constant at any other temperature can be determined. 211. B. Method I. Calculation of Equilibrium Constant From Free Enem Values The data used for method I are listed in Table IV .1. Table IV.1 Substance __ - AF°(298°K) -g0g29801q Source Gibbsite A1(CH)3 2714.82kcal./mole 307.7kcal./mole Kuznetzov(l950) Boehmite Al 0(CH) 217.10kca1./mole 23h.9kcal./mole Kumetzov(l9§0) Water Vapor 5h.635kca1./mole 57.798kca1./mole Kelley (19149) Gibbsite(A120331-I20)5h7.9kca1./m01e 613.7kca1./mole Bureau of Standards (1952) Boehmite(A12C§H20) h35.0kca1./n61e h71.0kcal.mole Bureau of Standards (1952) Gibbsite(A1203.3H20) 55h.60kca1./noie - Deltombe & Pourbaix (1956) Using the data of Kuznetzov (1950) we can calculate the equili- brium constant at 25°C from the relation AF° s-R'rinx a -1.987 cal./mole-deg. (at 1 atm. pressure) T -298° K or converting to logarithms to the base ten -- a r° - 2.303 .1.987 .298 log K (kcal.)- A F0 I 1.3614 log K Thus for Al(OH)3 ‘3 A1 0(CH) 4» water vapor 4 F° - AFO (Products) - 4 Po (Reactants) - 2714.82 - 271.735 - 3.085 kcal./mole —- .4 F0 - RT log K = 1.361; log K 25. “'3 0085 1.36h log K - log K --2.26l73 K 8 10.00000-10 -2.26l73 W315 K(25°C) - 0.00514735 - 5.147 x 10'"3 atmospheres = b.16m. Hg ‘ . Next 4 Ho, the standard heat of reaction, must be calculated before equation (2) can be used. We first evaluate the heat of reaction at 2500 using Kuznetzov's data from the relation 4 110(2593) - A H°(Boehmite) e A H°(water vapor)- 4 Ho (Gibbsite) " (-23h.9-57.793) + 307.7 - -292.698 + 307.7 - 15 kcal./mole We next assume that 4 H0 as a function of temperature is not constant. Thus we calculate A Ho at different temperatures. It is thus necessary to investigate this change by A no - 4 11° (Products) - 4 H°(Reactants) ( QAH_°_’ - (iflo producti) -.(3LQAH° Reactants ) if P 3T 1" 1T [/7 The two terns on the right-hand side of the equation are simply the heat capacity terms Cp (products) and GP (reactants). Hence (gig/4)? 2 c,(/'¢a.{ar7;/—c,/I?:A Vacuum ‘ N (:1 100m. _1L Vertical Sample Cell Figure No. 7.1 Schematic diagram of high temerature cell for vapor pressure measurements. 113. V. Description and Desigl of Biggerimental Apparatus A. High Temperature Cell When the research was in its preliminary stages, it was originally planned to use both infra-red spectroscopy and thermistors for determining vapor pressure. Hence, a cell was designed that had a sample tube which was connected to an absorption tube by pyrex glass. Although infra-red spectroscopy was investigated in a preliminary manner only, this design was well suited for vapor pressure measurements by thermistors. A schematic diagram of this cell is shown in Figure 17.1; all parts of the heated cell were constructed of high quality pyrex glass tubing. Both portions of the cell are drawn vertically for convenience, but the vapor cell is mounted perpendicular to the sample cell and attached to it by a 2 cm. diameter pyrex tube, 2 cm. in length. The apparatus could be evacuated through the ball and socket joint (N via the stop-cock (B). The sample tube could be loaded or the cell cleaned through the ground glass joint (C). Calcium fluoride windows" were attached to the ends of the vapor cell by clear glyptal. Each window was ground perfectly flat and polished. The windows were I; centimeters in diameter and 0.3 centimeters in thick- uses. It is vitally necessary that the ends of the vapor cell have flat surfaces before the glyptal is applied. After the windows have been cemented by glvptal the apparatus is placed under an infra-red lamp for at least 20 hours. Lord, McDonald and Miller (1952) have indicated «These windows were purchased from the Frank Cooke Corporation, North Brookfield, Mass. at a price of 826 each. The delivery date after ordering was four weeks. a. m m m w .u n r w. n m a m n 1:5. that clear glyptal resin holds well up to 250°C providing heating and cooling are not too rapid to crack the seals. Calcium fluoride win- dows are extremely useful in this type of work since they are not eroded by water vapor which might be conducive to leaks and in addition their transparent character allows observation of any water vapor which may have condensed on the cell walls or windows during the preliminary calibration work. The three different parts of the cell were heated independently; this was necessary since the sample cell was heated to temperatures beyond which thermistors would have disintegrated. The sample cell was unintained at a temperature above or below that of the vapor cell depending on the test measurement. The temperature was varied by three Wariacs" which were connected to three "801a“ oorrstant voltage sources. The vapor cell was heated by a chromel 'A' heating wire (leads Sand 6, figure 7.1) that had a total resistance of 110 ohms. The sample cell was heated by a chromel 'A' heating wire (leads 3 and h) that had a total resistance of 150 ohms and the vacuum attachment piece (leads 1 and 2) heated by a wire with 125 ohms resistance. The wire was separated from contact with the glass tubing by small strips of asbestos paper. Radiation was kept to a minimum by placing several wrappings of asbestos paper over this wire. Power was supplied by the line voltage which was fed to the "301a" constant voltage sources. Although the sample tube (was not operated above 180°C, it could easily be used to temperatures up to 250°-300°C. A photograph of the high temperature cell is shown in Figure v.2. Temperature was measured by copper constantin thermocouples that were calibrated in the Heat Measurements Laboratory of the MIT Mechanical Figure la. v.3. We hood :fi‘flfiififfii’fitm. ’ i. Engineering‘Department. Two thermocouples were attached externally at positions 7 and 8 of Figure v.1 on the sample cell. Thermocouples were attached externally to the vapor'cell at position 9 (Figure v.1) and another was sealed in hermetically by glyptal along with a thermis- tor at position 11 on the vapor cell (Figure 7.1). The E.M.F. of the thermocouples was measured by a Leeds and Northrup‘Model 8662 Potentio- meter. The 3.14.17. (m.v.) could be read to the nearest 0.01 m.v. and estimated to the nearest 0.001.m.v. Hence the temperature could be calculated from standard tables to the nearest 0.01 degrees Centigrade. This type of potentiometer had a room.temperature compensating dial which could be used for the cold junction. Unfortunately, the ambient change was as great as 293 depending on conditions,and this compensator could not be used. The cold junction was accordingly placed in a mixture of crooked ice and distilled water in equilibrium at 0‘0. To calculate the temperature the potentiometer is read (E observed) and the correction term (-A E) determined from the calibration chart. By adding - A s to E (observed), the standard EJ‘IJ“. is obtained. The standard E.M.F. can be used to determine the temperature by reference to standard tables. With these particular thermocouples A B was negative or E(Standard) - E (Observed) - A E. All measurements were made in a constant temperature room, the temperature of which fluctuated between 1.5 and 2.0’c. In order to reduce the change in ambient temperature to practical limits, an aluminum hood lined with glass wool as insulation was placed over the apparatus, controlling the temperature to a maxinmm.variation of 20.6 degrees with 30.380 being about the average. A photograph of the hood is shown in Figure v.3. The control of temperature depended on how well the airconditioner was functioning, the diurnal variation and other technical factors. hB. 5‘ <0 G 5‘ u osemwno eroHSOoosvHa ‘ ‘ 0 ‘§ H ‘ ______ L‘ “ ‘ b Humano.nronsooocmwm acne we: 20. H O u M as; was ze. n 50 db So do Pd Gd aoawonoafid A03 outside thermocouples. Figure No. v,h Temperature correction chart for inside and 1:9. 0 903805: We. .. mods coho on ape—Eh no: 0 652.3305: o». 3.530 on. creeps 3:. D 8388305: 5. «on. on. no.5? ooHH __ _ _ _ _ rr_u p a __ 40 mo we H00 HHO HNO 50 tab ”5.0 H00 ”50 “50 ”50 N8 83602956 A 03 Figure No. v.5 Graph of temperature variation from top to bottom of sample cell. 50. After calibration work it was decided to record only the temperature of the sample cell at position 7 (figure v.1) and use the other thermocouples merely for control work. Since the thermo- couple at position 7 (figure V.l) was mounted externally by a rigid packing of asbestos, it was necessary to run a calibration by inserting a themoc ouple inside the sell opposite the thermocouple tap and A compare the temperatures measumd. The results of this calibration are given in Figure V.h. It is obvious that corrections are necessary between temperatures determined on the inside sample by an external thermocouple, partly due to the weak heat conductivity through the thick glass which houses the external thermocouple. Another calibration was made to determine what thermal gradients might exist within the sample cell. This test consisted of inserting a thermocouple insido the ample cell at three positions, 9' from the bottom, at the mid- point and at the top. The results shown in Figure v.5 indicate that there is a general increase in tenperature from the bottom to the top of the sample ooll.. This fact is reasonable since there is an addi- tional sauce of heat at the top of the cell from the heated vacuum attachment piece over the sample ooll. No correction is necessary for the gradient, since all samples were within i“ of the thermocouple at position 7 (figure V.l). B. Thermistor Characteristics Thermistors can be defined as delicate electronic devises that have negative tauperature coefficients so that their resistance decreases with an increase in temperature. Thermistors have been used as detectors in gas chromatography as indicated by Davis and Howard (1958). Husgrave (1959) has also used thennistors for gas chromato- 51. graphic detectors. In Musgrave's work the thermistors were sealed in the test unit by "cold-curing" silicone rubber. Pairs of thermistors with 1000,2000 and 500,000 oluns resistance respectively, had comparatively little tendency to disintegrate when used for the detection and separa- tion of quinones, phenols and phenolic others at 180°-220°. Miller (1958) has shown that thermistors can be used in “Themistor Bridges" as very sensitive temperature detectors. Miller (1957) has published some data on considerations in testing thermistors. Some of the important points listed are the negative tenperature coefficient, the approach to equili- brium resistance with respect to time, and the power that thermistors can dissipate. These three points were investigated during the process of thesis research. The thermistors used in this work were purchased from Victory Engineering Corporation, Union, New Jersey. A matched pair of Catalog No. 1-59 thermistors with a resistance of 100,000 ohms each at 25°C was used. At 25°C, the Ro(resistanco at room tanperature) of the lower resistance unit is greater than 90% of the R0 of the other unit in terms of tolerance. The dissipation constant is 1.0 milliwatt/dog. c. The time constant is 25 seconds and the temperature coefficient-11.6% deg. c. All values quoted at 25°c. Miller (1957) lists the thermistor equation as RI - R? 86 %1.%2) where R1 - thermistor resistance at temperature T1 R2 - thermistor resistance at temperature T2 6 - Napierian base 2.713 9) . Material constant (°x) T1 - Reference temperature (0K) of thermistor 200,000 Resistance(0hms) 5 § 6,000 h.000 3,000 2,000 52. " UTostrIm#2 0 Test m #1 l l I l . 0 3L 50 75 100 125 f Temperature( 0c ) Figure R0.V.6 Variation of resistance of thermistors as a function of temperature using a 1.5 volt battery. ———- —_ e__1_ ._._.._ 53. T2 - Another thermistor temperature (OK) In this work the two thermistors were connected in series, one inside the vapor coll under vacuum and the other outside the vapor cell. The resistance of this series pair was measured by a Leeds and Northrup wheatstone Bridge. No. h760 with 1.5 volts put into the circuit. The temperature (°C) at the thermistor bead was measured and plotted against the resistance in ohms. The data are plotted in Figure v.6. This plot shows a reasonable linear logarithmic change in resistance with temperature or log R(T) - A-BT where log R (T) - resistance at temperature T A - intercept om ordinate - B - negative slope The approach to a steady state equilibrium for the thermistors was obtained by measuring the resistance over a time period for three different resistances. The results of this test are given in Figure v.7. At 8850 aims steady state is approached within one minute, but an ambient variation of z 15 ohm is present. At 10,180 ohm the aircond itioner cut on and reduced the resistance 50 ohms; after the air conditioner shut off the resistance increased back to about 10,190 ohms so the ambient variation is 50 ohms. At 18,500 ohms, the airconditioner was on for the entire 10 minutes. A steady state was obtained in about 7 minutes. Accordingly, using this information the current was turned on for each run an appropriate amount of time depending on the resistance before making a measurement. The other important point cmsidered in testing these thermistors was the amount of power that could be dissipated at the lowest possible Resistance (Ohms) 18700 18600 18500 181.00 18300 18200 18100 18000 17900 17800 10200 10190 10180 10170 10160 10150 101140 10130 8865 8860 8855 8850 88115 8810 8835 St. _ - Airconditioner on entire 10 minutes during measurement A-Aircondit ioner on B-Aircond itioner off Airconditioner off entire 10 minutes l l l l l I J l I 2 3 h § 6 7 8 9 10 Time (Minutes) Figure No. v.7 Approach to steady state equilibrium for thermistors. SS. resistance. w mounting the thermistors in series, a safety factor of two was gained in power dissipated. The mximum temperature for the vapor cell was 125°C. The dissipation constant was 1.0 milliwatts/deg.0 which for two thermistors is 2.0 nilliratts/degn. Since the temperature at the thermistor Junction ranged from 25°-125°c, A 'r was 100%. The total power that this series combination could dissipate is 2.0 milli- watts/dept: 1: 100°C - 200 milliwatts. 2 Power 8 (Voltage) - 200 m.w. - 0.2 watts. The battery finally selec- Resistance ted was 22.5 volts and the lowest resistance encountered was 8000 stuns. Hence 0.2 - 2 $385) - w - 0.063 watts Thus a 22.5 volt battery would only create 0.063 watts through the thermistors and a safe operatic; was permitted. However, if a £15 volt battery had been used 0.25 watts would have been created and the thermis- tors probably would have burned out. The importance of these tests on thermistors is thus demonstrated. In mounting the thermistors in series, opposite ends of the thermistor loads were Joined together with silver solder. One thermis- tor was maintained at a such lower temperature than the other by being mounted externally at position 10 on the vapor cell (figure v.1) After positioning the cold thermistor, asbestos was forced around it to make it firm and the end of the lip was sealed off with clear glyptal. The other thermistor was hermetically sealed inside the vapor cell with a thermcoupleat position 11 (figure v.1) by placing.a thick film of glyptal around it. The apparatus was then heated slowly to 50°C in a vacuum oven. After doing this several times the seal was firm and non- porous. A thick film of glyptal was next placed at the back of the y .. :r I f Illi‘: Elia .. 56. inside film and heated to 50°C. Asbestos was used to give finmess to the seal and more glyptal was applied at the end of slit ll for protection. c. The greatstMidflCimuit The principle involved in measuring the vapor pressure in terms of resistance drop of the thermistors necessitated the design of a "Weatstone bridge“ circuit. The simple principle for vapor pressure detection was that a calibration curve would be run in vacuum without water vapor at fixed temperatures on the vapor cell and varying tempera- tures on the sample cell. Then the resistance of the thermistors would be plotted as a functim of temperature of sample tube. This would be repeated with a liquid of known vapor pressure, such as water in the sample tubs. The change in resistance called A R resulting from the water vapor is a measure of the vapor pressure at the temperature on the sample tube. This uses the thermal conductivity properties of gases (water vapor). Thermal conductivity is a measure of quantity of heat conducted in unit time between two unit surfaces in the gas when they are unit distance apart and the temperature difference is 1‘0; this condition pertains to single gases, binary mixtures and ternary mixtures. In the determination, a fine wire, which is heated by a current, is surrounded by a gas that conducts heat from the wire to the walls of the chamber. A thermocouple in contact with the hot wire measures its temperature above that of the wall of the chamber, which difference is inversely proportional to the thermal conductivity of the gas for a given power input to the wire. In practice, two similar current—heated filaments in two similar cells with two similar inert resistances are used, the 57. four elements being connected to form a wheatstone bridge. If one cell contains air and the other cell contains a gas of different thermal conductivity, the two hot wires will not have the same resis- tance and the bridge will become unbalanced to an extent depending on the thermal conductivity of the gas relative to the standard or reference gas (Minter 1916) . Minter and Burdy (1951) have evaluated the effect of cell diameter by a so-called two bridge circuit. In their work a two bridge circuit was unployed. Bridge 1, in which cells have a diameter of 3/16~ is conventional, whereas bridge 2 is of unconventional design, having cells with a diameter of 3/h". 111 the filaments used in the bridges (1 and 2) are as nearly as possible alike, but the difference in cell d ismeter has an appreciable effect on the heat loss fran the filament when both types of cells contain air, so that when both bridges carry the some current, bridge 2 with large cells will have the higher redistance. The difference between the rate of loss of heat in the large cell and that in the snall cell becomes greater as the thermal conductivity of the gas decreases. This gaseous ”convection" increases with the molecular weight of the gas and cell diameter. From the foregoing, it would appear appropriate to use a cell with a large diameter for gases like water vapor with a medium thermal conductivity value. Minter (19147) has suggested that heat loss by natural convection is a function of gas pressure and that the magnitude of effects of pressure on convection depends uniquely on the nature of the gas. An equation proposed without experimental support indicates that the loss of heat by natural convection can be expressed by Ha<)(,071 58. where H I=heat loss P - absolute pressure X - convection factor depending on the gas The effect of pressure on convection is so negligibly small for turdrogen that therec an be no heat transfer by convection and I in the above eqnation would then be zero. For all other gases I has a posi- tive value which in general increases with the molecular weight of the gas. The relationship between convection and other plvsical properties of gases has not been investigated. A tentative approximate relationship between conductivity and convection in a gas might be writtenas xdh 513. X where K32 - absolute conductivity of hydrogen Kx - absolute conductivity of gas The relative deflections of various gases is given by Gow-Mac with their consuercial unit; their values are listed below in Table v.1. Table Vel Gas Relative Def lection Approx. Bridge Output in per 1% Gas in Air NV without Load ’ “9%;0 "0o '3 e§§ Argon -0.133 -3 .99 3.123110 “Del” ‘5 o70 Carbon Dioocide -o.11;3 -h.30 Carbon Monoxide -0.0lh -0.h2 Ethyl Alcohol -0.080 -2 .140 Ethyl ether o0.136 -3.90 Helium $0.610 +19.18 fwdrogen +1.0m *BOoOO Methyl alcohol -0.079 -2.36 Nitrogm -0.001 -0.03 m‘m *0.” 40.18 Water Vapor 40.068 +2 .01; It is shown that many important gases, chemically and geo- chexaically speaking, can be determined by thermal conductivity. 15.1.3.2]. :‘v 59. m consideration of many of the points listed above, it seemed reasonable to set up a bridge circuit and evaluate the effects of water vapor in conducting heat away from a thermistor, consequently lowering the temperature and increasing the resistance. It is also possible that the change in resistance of the thermistors can be attri- buted to a competitive heat effect. The amount of heat reaching the thermistor (detector) is proportional to that not absorbed by the water vapor. It is obvious in this type of approach that two measure- ments must be made to detect an absolute difference in vapor pressure. This condition is disadvantageous as compared to conventional thermal conductivity methods, but the apparatus is much less cumbersome. The real advantage of measuring vapor pressure by thermistors is that the absolute pressure can be detected whereas in the normal thermal con- ductivity method only relative changes in per cent of gases can be obtained by comparison with those of the reference gas. In the preliminary design of the Wheatstone bridge, first 1.5 volts were used as the EMF source and then 6.0 volts. Both of these sources were insufficient to heat the thermistors hot enough to enable the pressure of water to conduct heat away. Hence, no pressure effect was noted on the resistance measured in vacuum or under pressure of water vapor. The next step was the use of a 22.5 volt source of E.M.F. This change in source permitted the determination of the effect of pressure on resistance change and was used throughout the course of the investigation. A schematic diagram of the wheatstone bridge (D.C.) circuit is shown in Figure v.8. A photograph of the laboratory appara- tus which includes the D.C. bridge circuit and high temperature cell is Shown in Figure v.9o 60. X( Thermis tors ) :4 Figure No. v.8 Schematic diagram of (D.C.) wheatstone bridge circuit. 62. In Figure v.8, the letters have the following significance P - 100 K resistance box (variable resistor) M - 100 K resistance box - 9990 ohms N - 10 K resistance box - 9990 ohms X - 'Ihermistor resistance 4e' internal battery resistance 4’ . galvanometer resistance - 51 ohms E - source of E.M.F. - 22.5 volts A - shunt resistance - 9000 ohms The condition of balance for this bridge, that is, when no current goes through the galvanometer or there is zero deflection, is given by the voltage splitting rule as u (E) . x (E) m x‘TF‘ NX t N? - M + MX HP - MX (at balance) Hence, by reading the three resistances N, P, and M, the unknown thermistor resistance (X) can be determined by *2 I- I (ohms) Two important points about balanced wheatstone bridges are (l) The balance condition is independent of the battery source and (2) The galvanometer and battery can be interchanged without affecting balance. After taking some preliminary readings, it was found that the galvanometer was too sensitive. Hence, it was necessary to desensitize or protect the galvanometer from the high incoming current by a shunt resistance (A ). There are several methods of protecting galvanometers, 63. but the one selected was that of a "simple" shunt as suggested in Frank (1959). The galvanometer used was a weston Model 1.240 that had an interb nal resistance of 51 ohms and required an external resistance of 190 ohms for critical damping. Thus the shunt designed served a two-fold purpose of desensitizing the galvanometer in addition to providing the critical external damping resistance of 190 ohms. The "simple" shunt consists of a resistance across the terminals of the galvanometer. In diagrammatical form it has the appearance I I... I - incoming current R. - shunt resistance 0 - galvanometer Rm - galv. resistance Im - galv. current The decrease in current, I“, delivered to the galvanometer can be determined from the current splitting rule: “ I " R“ x a“ I - FI m Run. where F is the current desensitizing factor Experimentally it was found that 9000 ohms was convenient to use as the shunt resistance. 6h 0 Comparing the F factors by using Rs - l and Rs - 9000 011113: _ 1x51 . 1 . . 1m .1731. I 5/521 0.981 (Rs 1) Im - 9000 x 51 I - {1590001- 50.711 (R8 - 9000) m 9651?" Thus the 9000 ohm shunt protects the galvanometer 59:1}. - 51.71; times greater than a one ohm resistor would. .98 Another important feature was bridge sensitivity which can be demonstrated by using a slightly unbalanced wheatstone bridge and inter- changing the resistances in the battery and galvanometer branches. The two set-ups (A and B) used were as follows: The most sensitive bridge circuit will be the one which has the g' The unbalance is made by letting I - 8080 ohms as compared to 8000 ohns for P. A constant of 2 ohns was largest galvanometer current, I used for comparative purposes for the internal battery resistance. In calculating 1‘ it is best to use Thevenin equivalent circuits instead of mesh equations. The circuit can be set up w letting everything below the ‘Y —y on both diagrams equal the Thevenin internal circuit. Hence the R1 (Thevenin internal resistance) can be calculated In letting the battery resistance go to infinity or 65. . . .. 91*?) (Nd) . (9000+8000) (9000+8080) Case (A). R1 lid-PwNox 18000 + 16,080 - W - 8520 ohms ’ Case (B): R1 . P:X (M'N . (mi-8080)“(9m009m0) 1* 31.080 289 MO 000 311080; ' 81‘” °m3 Next the Thevenin open circuit voltage (30) is calculated. For Case (A): - 43 2.4. P P1 22.3w: x N I . Ri - 8&93 ohms I ' nggL“ " 22' - .0026a 8h?3+2 :- v .22.h9x9ooo a 202,th , 11.2” A 18625 18000 VB . 32.1.1.9 BE 8080 . 181719 . 11.3m 16080 16080 E°(A) - vB- vA - 0.05v. 66. Case (B) for E 3 o I ¥_ L_ T + 22.5'u-=-, p x I Hi - 8520 ohm I n_..._.22°5 - 2235 - 0.0026. 8520+2 8522 = Terminal Voltage ET - 22.5 -2x.0026 - 22.1w C 17080 17080 22.16 x 9000 202 810 v a r V I n . 17(00 17000 11 91V 30 (B) - VD- Vc - 0.06v Thus using the Thevenin equivalent circuit for Case A: I ,1 {/49 4_ g 0.052;.- G 5‘ o 9 5.. z .05 . _ fl . ,3 mm. 5 8520 o 51 5 3 micr Case B: I: ~ I I ”'06 - 7.11 micreamps ‘ 833 + 51 fl 67. Therefore the ratio of sensitivities for this circuit is 123:1...- 1.23 or set-up B is 1.2 times more sensitive than A. Thus by £33111; the fixed resistances on the same arms of the bridge, Optimum sensitivity is achieved; this consideration was applied to the bridge designed. The results at experiments with this bridge are discussed in the follow- in; section. 68. VI. Emperimentalmflethod and Results A. Basis for DetermininLVapor Pressure The basis of the experimental method for measuring vapor pressure was to heat the vapor cell to a constant temperature and then vary the temperature on the sample cell. The thermistor resistance was d etermined, first in a vacuum, at various temperatures and the 10garithm of this quantity was plotted as a function of temperature of the sample coll. Next a liquid was introduced into the sample cell and the apparatus again evacuated. The liquid, whose vapor pressure is known as a function of temperature was heated and again the resistance of the thermistor determined. The heat conducted away from the thermistor will decrease its temperature or increase its resistance. A curve of the logarithm of the resistance against temperature is drawn and the increase in the log of the resistance at a specified temperature is a measure of the vapor pressure in term of the quantity leg A R where log 4 R - log R(Water vapor,T) - log R(Vacuum,'l') Thus by determining the log 4 R values the vapor pressure as a function of temperature can be plotted. A solid twdrate or Ivdroxide can be placed in the sample cell and heated under identical conditions. Again the log A R values are determined and compared to those of the standaid in term of a ratio method. If the vapor pressure over the dissociating hydrate is identical to that of the liquid as observed by the log A R values, then the liquid may be used as a calibration curve for the solid. Practically this is rarely the case, so that the ratio method must be used. Assuming that a log A R value of 3.5 ohms has been determined which corresponds to a vapor pressure over the liquid of 300mm. Hg and 69. a value of log A R for the solid at the same temperature is 3.3, the vapor pressure of the solid is l A R (Solid 1 Vapor Pressure(1iqu.1d) or. 1q ) or 3-3 x300 -09hx300 3‘3 ' II 282ml. Hg It can be readily seen that this approach is best when the vapor pressure of the liquid and that of the solid are not too dissimilar. B. Dehydration of ' Gypsum (CaSOL. 211201 Gypsum is an interesting substance to study for several reasons. The structure as determined by Wooster (1936) is of the layer Lattice type. Sheets of Caz. and 801‘2- ions are so arranged that each cation is surrounded by six 02' ions and by two water molecules. Each water molecule is linked to one Ca2+ ion, to one 02" ion in a neighboring sheet, and these last-mentioned bonds are the only ones holding the sheets together. The perfect cleavage arises from the rupture of these weak bonds,and this weakness is has further revealed by the much higher coefficient of thermal expansion noml to the sheets than in am other direction. Halce, this weak water bond should be easy to remove when gypsum is heated. The loosely bound structural water in gypsum is like may other mdrates of geological interest such as the twdrous borates. Gypsum is additionally interesting because its vapor pressure was measured by Kelley, Southard and Anderson (19M) using a manometer method. Thus, the accuracy of the thermistor method can be determined by direct comparison to manometer results. The measured vapor pressure of gypsum follows quite closely the vapor pressure of liquid water. Log ResistanceLOhms) 'm f 70. 14.00. FLow temperature approach (No water vapor) h 0 U High temperature approach ' ® Low temperature approach 8 High temperature approach Ito'- ® A Low temperature approach V High temperature approach (Vater vapor) (Gypsum) h.‘ Curve B V h.o :"5 ‘7 A: 3 3.. Curve A 3.9 O 3.93 3o U 3.9 3, l 1 1 J J J 90 ho 50 60 70 80 100 Temperature ( o(3 ) Figure No. V1.1 Monumental curves for determining vapor pressure of Gypsum by thermistors. . ‘—---l m “m —w: fir'é _ _ 71. Therefore, liquid water can be used as a calibration tool for the ratio method previously described. After evacuating the vapor cell for 1mm. Hg, it was heated to a constant temperature one hour to< l x 10- of 9h.25@6. Then the temperature of the sample cell was varied and the change in the resistance of the thermistors recorded. In general, thermal equilibrium was obtained within one hour, but additional film was allowed to check on the equilibrium value with respect to time before the sample temperature was again changed. In this particular test, the sample temperature was varied from 113.8900 to 100.60°C, and the corres- ponding resistances varied from 10,637 ohms to 82143 onus. Resistance observations were approached from both a high temperature and a low temperature side, with the former being lower than the latter. This difference is most likely explained by failure to dissipate heat fast enough under the aluminum hood to enable the same values to be obtained from both the high side and low side approached. The results are tabu- lated below in Table V1.1 which also shows a standard deviation of the resistance and temperature of each point and plotted (curve A) in Figure VI.l. In general, a low standard deviation in temperature coincides with a low standard deviation in resistance, but there are exceptions. The method 'used for calculating standard deviation is from Iouden (1955). 72's 33.31.3112}. gpsisAtanceLLohms) ‘13: Resistance Te_:_np_._o_0_ 10,637 _+_ 70 h.02680 1.3.89 3 0.13 10,162 1 108 11.01920 16.30 _+‘ 0.02 10,020 1 105 h.00087 51.20 2‘. 0.03 9822 g; 66 3.99220 58.141 3 0.19 9537 3. 91 3.97m 68.70 _+_ 0.38 9166 1 5h 3.96218 77.30 _+_ 0.08 8825 ; 6h 3.91671 8h.78 3 0.10 87M 5 51 3.9le6 88.25 3 0.02 8509 g 55 3.92988 9h.8h g 0.08 82143 g 39 3.91609 100.60 2. 0.25 a 835 3; 10.8 3.92038 88.12 _+_ 0.09 e 9076 ; 1.1 3.95789 72.1.2 :2 0.11 * 961:6 :_ 1:7 3.981435 50.95 _+_ 0.12 *10170 3, 25 h.m732 1111.29 5 0.07 {These points correspond to measurements made from the high temperature side while the others represent the low temperature side. The next test was to determine the effect that the vapor pressure of water would have on the thermistor resistance. The total volume of the high temperature cell was 931; cubic centimeters. Hence, using the ideal gas law, it was possible to calculate the minimum amount of water necessary to fill the cell at a given tanperature. From the ideal gas law PV - NRI‘ where P - pressure of gas in atmospheres - 760mm. Hg V I volume of cell - 93h m1.(neglecting the volume occupied by the liquid) 73. wt. of gas in grams MM. N a no. of moles of gas '- where wt. of gas - wt. of water in condensed state R a gas constant - 82.07 ml.-atm./mol°0 T - tauperature in 0K. As an example the amount of liquid water necessary to fill the cell at a pressure of one atmosphere when the temperature is 100.0 is 760‘ x 93b 82 07 x 373 - 93h . 0.01 . X 30612 3 ”'8 Thus, the minimum amount of liquid water required to fill the cell with one atmosphere pressure was 0.031 grams. In consideration of the evacuation of the cell, thirty milliliters of distilled water were actually used. After the distilled water was placed in the cell, the apparatus was evacuated for fifteen minutes and heated to 9h.18°C. The equilibrium was permitted to develop for two hours, when the temperature on the sample was 16.8000. Another evacuation was made and then the temperature of the sample increased. A constant reading in resistance after evacuation was considered to be the true equilibrium value and thus was approached from both the high temperature and low temperature side. (he of the major difficulties encountered experi- mentally was that the removal of the hot cell to the vacuum line caused the windows on the vapor cell to crack and also developed leaks in the form of cracks on the glyptal seals. This problem was solved before am of these tests by forcing a gentle stream of heated nitr0gen, passed through hot copper tubing, on the vapor cell and no additional leaks were observed. The ability to develop a tight vacuum and the constancy of resistance was considered evidence that no 103k! were in 7b. the system. The previous experience with a cracked cell window never permitted a tight vacuum to be developed. The precision or reproducibility of the method was tested by taking ten consecutive readings at two minute intervals at resistances of 11,575 ohms, 10,6117 ohm and 10,551; ohm where the respective vapor pressure of water was 78,5116, and 76071311. Hg. The reproducibility in terms of standard deviation is given below in Table V1.2. Table V1.2 Resistance (ems) Pressure(m. Hg) 1.1575 g 33 78 106117 3 13 5116 1011511 3 8 760 This data suggests that an increase in water pressure gives a better reproducible reading. During the actual conditions of the experiment, only two readings were taken at any one time. ‘ The results of the test on water vapor are listed in Table V1.3 and plotted as curve B in Figure V1.1. Table V1.3 0 Resistance Selma) 12‘ Resistance T . C 11,580 3 31 11.06371 $.80 :_ 0.11 10,880 3 87 1.03663 57.53 3, 0.27 10,555 3. 21 1.023115 71.05 _+_ 0.18 10,710 3 10 11.02979 76.75 1 0.16 10,638 3 10 11.02680 811.63 .1 0.16 10,617 1 13 17.02715 91.08 .t 0.17 10,116 _+_ 23 11.01892 99.91 _+_ 0.22 10,1511 1 8 1.01925 100.014 _+_ 0.09 5 10,630 1 17 14.02653 83. 7 z 0.06 * 10,8110 L". 27 15.03503 61.32 :- 0.15 75. «u- The last two points in Table V1.3 represent approach from the high temperature side while the others are from the low temperature side. An example of the calculation of the standard deviation is given in Appendix III which is the method given in Youden (1955). The point calculated in Appendix III is (57.53, 10,880) in Table v1.3. Since the experimental method gave points somewhat spread out on the curve, the human error in drawing a line then was removed by calculating the best fit of the line by the method of least squares. In addition, the least squares method gives the minimum deviation that any point will have from the calculated line. The detailed calculation of the method of least squares was taken from Thomas (1956). The calculation is shown in Appendix IV for Curve A, Figure V1.1. The equation of the line for curve A, Figure V1.1 is I -0.0017hx 4- h.09 and that of curve B is I - -0.0CD36X a 11.056. There is good agreement between the points determined from the high temperature side and those from low temperature side. The experimental measurement at 16.80% on curve B is not con- sistent with the line equation. This fact would suggest that the thermistors are not smsitive or give reproducible results to vapor pressures less than 100m. Hg or slightly higher since the measurement at 57.5300 compares well with the others and the vapor pressure is about 133nm H:- After the work on liquid water was completed, dehydration tests on gypsum were begun; 27.11 gms. of gypsum were placed in the cell and the system was evacuated for one hour. Then the vapor cell was heated to 91141900. It seemed of interest to see how effective the vacuum system was in removing water adsorbed on the walls of the apparatus and also on the surface of the solid during the initial evacuation. 76. Resistance(0hms) 5.08 H0000 :88 8:8 Homoo H0000 lid/In. mun: meanness mums possess: Hostages? 3.300 0 1w 3 0| ’ < boa was-acne mums >338: adios-«sue @9300 111111_ :2: woucfifisjwvs eESAmosHev _ lill v4 genre sides for Gvssum. Figure No. V1.2 Approach to equilibrium from high and low 77. Consequently three measurements were made at temperatures of 51.10%, 67.1700 and 711.2100 before the system was evacuated. Then the system was evacuated and the subsequent points were measured. The equilibrium was approached from both the high temperature side and the low temperature side at temperatures of 77°C and 86° . The two directional approach to equilibrium at 86°C is shown in Figure “.2. The high side approach at 86°C gives a higher pressure than the low side approach. This might suggest that equilibrium takes a much longer time to establish from a high temperature approach as a result of the inability of water vapor to be readsorbed on the surface or to diffuse back into the broken down structure of the solid. The same effect was noted at 77°C for the high side approach. The results of the measurements on msum are listed in Table IV .11 and plotted as curve C, Figure V1.1. Table 71.1. Resistance (Ohmsl LyiResistance mi 10553 3 52 h.02335 51.13 3 0.18 1009b 3; 51 11.00105 67 .17 3 0.141 10061 3 89 11.00270 711.21 3 0.35 10605 3 1211 1.02550 77.81 3 0.21 _ 10361 3 11h 11.015110 86.70 3 0.23 11050 3 61: 17.01336 77.50 3 0.18 10501; 3 26 11.02110 91.10 3 0.33 108511 3 18 11.03558 98.5h 3 0.17 10851; 3 1h 31.03558 86.93 3; 0.08 Pressure water vapor(mm. Hg.) 78. 800— 700.— 500— 1100— 300— 200— 150... 100 GYPSUM DEHYDRA'I'ION PRODUCTS .9. MTER VAPOR Figure N0.VI .3 Comparison of the dissociation pressure of Gypsum as determined by themistorsWayman) to those found by a manometer method(Kelley) I l 7O 1 augment?" 96 10° 79. The equation of the line for curve C, Figure V1.1 by the least squares method is Y - 0.0002561 + 11.002. It appears that the original vacuum on the samle does not remove all the water vapor along the walls of the apparatus and that adsorbed on the surface of the solid. This is demonstrated by the fact that the pressures at 67.17°c and 7h.21°C are mach higher than those compared to Kelley's measurements. Also part of this error at 67.1700 may be attributed to poor temperature control (30.11106). One criticism of curves B and C, Figure V1.1 is the difference in slope. Curve B (liquid water) is negative and curve C (gypsum) is positive. The difference might be explained by the fact that the vapor pressure of gypsum increases much faster than water, partly from the error introduced by using the method of least squares, and somewhat due to the overall error in the method itself of measuring the vapor pressure. ‘ In order to calculate the vapor pressure of gypsum, it is necessary to use the ratio method described in V1.1. In using this method, we find that the vapor pressure of gypsum is W). x V .P. (liq.Water) V.P. (Gypsum) - 10, A a (liquid water) Hence, using the curves B and C, we calculate the pressure at 70° by Lo R G . .052 u 5 2 151‘; x v,p,(w) .663. x 235 19W. HE Thus the vapor pressure as determined by the thermistors method is 191mm. Hg at 70°C. Using the same method the vapor pressures are cal- culated at other temperatures. The values for the vapor pressure of water were taken from the International Critical Tables (1928). The vapor pressures are compared to those of Kelley, Southard and Anderson (19171) in Table 71.5 and plotted as the pressure against temperature (°c) in Figure 171.3. Table v1.5 Temperature °_C V.P. rSlKellgéz V.P. éwamn) Error 70 e H: e H‘ * 7 80 295m. Hg 331M. H: 910.88 90 1470mm. Hg 531m. Hg +ll.h9 96 6110mm. Hg 686m. Hg + 6.71 100 715m. 3‘ 810nm. H‘ *8002 The per cent error was based on comparing the measurement by thermistors to that of Kelley by a manometer. Thus at 70°C the error is %E X 100 ' 17.53% It is shown in Table V1.5 that the accuracy of the thermistor method for measuring vapor pressure in substances that contain (1120) structural water increases as the vapor pressure curves of liquid water and the unknown become more alike. Thus the overall accuracy for vapor pressures in the range 300-760mm. Hg. ranges from 7-10 per cent. The overall mechanism of this new method might be viewed as a tool by which the gas conducts heat away from the thermistor Just as a gas conducts heat away from a wire in the thermal conductivity method for a gas. The equation to represent best the mechanism is Pressure of water Vapor - log A R - log R (water)-log R(vac.) where log A R - log change in resistance log R (water) - log resistance due to water vapor leg R (vac.) - log resistance measured under vacuum Log Resistance(0hms) 81. h.26 : b.2h h.22 h.20 h.18 h.16 11.11; b.12 h.10 h.08 11.06 11.01; h.02 h.oo 3.98 3.96 - 309,4 — 3.92 0 Low temperature side approach Dngh temperature s1de approach oLow temperature side approach flHigh temperature side approach (No water vapor) (Gibbs ite ) AMixture of sulfuric acid and water = I 1 I l 1 l 1 1 1 I ill 1 Cl ho 50 6o 70 80 Temperature(°c) 90 100 110 120 130 1110 150 160 170 Figure No. V1.11 kperimental curves for determining vapor pressure of Gibbsite by thermistors. 82. C. Dehydration of Gibbsite [A1(OH)3] #‘3 As previously indicated gibbsite is interesting geologically because it is the main constituent of "bauxite" deposits. It also is one of the important minerals which contains (E type water and should therefore be called a hydroxide as compared to the true hydrates with H20 structural water. In addition, the thermodynamic properties of gibbsite are still not accurately known on the basis of detwdration studies. All of the above factors make gibbsite an interesting mineral to investigate. The work on gibbsite was begun with the same pattern as used for gypsum. However, from the previously published data of Funaki and Uchimflra (1952) it was reasoned that the vapor pressure of gibbsite should be nil below 100°C. This permitted the heating of the vapor cell to a much lower temperature before starting measurements since water vapor would not condense on the cell walls. In addition, these tests had to be run at a lower temperature on the vapor cell, otherwise the high heat convected from the sample cell to the vapor cell would have burned out the thermistors. The first test was run with no water vapor in the cell. After evacuating, the vapor cell was heated to 82.1500 and later the temperature on the sample cell was varied. The resistance was then measured as a function of temperature. The results of this test are given in Table V1.6, and plotted as Curve A in terms of log resistance against tanperature in °C in Figure V1.11. The equation of the line (by method of least squares) is Y - -0.0021l9X * 11.357. 83. Table VI_._§ Resistance (ohms) Msistanoe 13:93.31; 17912 _+_ 118 11.25318 110.110 3 0.07 16610 3 305 11.22128 52.1.1 3 0.38 111651 3 21. 11.16588 77.01 3 0.08 13795 3 280 11.13975 91.51 3 0.80 11678 3 59 11.06732 116.811 3 0.15 10850 3 28 11.035113 132.22 3 0.06 91.73 3 119 3.976119 15h.69 3 0.31 8555 3 115 3.93222 170.85 3 0.13 «81:75 3 109 3.92811; 166.51 3 0.110 *The last point in Table V1.6 was the only one approached from the high temperature side. Finding a good standard for this part of the work was a problem. A liquid whose concentration would not change with respect to time was the appropriate thing to use since equilibrium is much faster with liquids than solids. The liquid chosen was a 70.78% by volume mixture of distilled water and sulfuric ac id. Burt (1901;) measured the vapor pressure of water of this 70.78% solution It a dynamical method. It is realised that the concentration of this solution probably changed during Burt's work as a result of evacuation and consequently errors are involved by this method, but it was the only reasonable standard available . Thomas and Ramsay (1923) have shown that sulfuric acid has no appreciable dissociation below 200°C so no effect of 803 need be considered. The results of Burt's measurements are given in Table V1.7. 8h. gable VI o7 '3ng Vapor Pressure H20 (70.78% 323011 -H20)m.11g 120 1170.11 125 171.3 130 ‘ 205.2 135 2176.3 1110 291.2 1145 355.1; 150 1126.9 155 501.5 160 589.0 166.h7 710.05 It will be shown later that the vapor pressures of water over gibbsite as measured by Funaki and Uchimira (1952) have an approximate relationship to these values. Accordingly the sulfuric acid-distilled water mixture (30 milliliters) was placed in the cell and evacuated for ten minutes. Then the vapor cell was heated to 81.9000 and measurements commenced. Only one evacuation (at 21.16.31.100) was made after the test was begun to prevent a change in the concentration of the mixture on which the vapor pressure is based. The results of this test are given in Table V1.8 and plotted in Figure V1.11 as curve B and curve C which had to be resolved into two parts. Table 171.383 Resistance (ohms) 10 Resistance Temp.°C W W“ 39767: 0.09 17886 3 169 11.25251; 51.15 3 0.21 15722 3 117 11.19659 79.66 3 0.33 111981 3 h8 11.17555 89.146 3 0.16 12836 3 118 11.108143 116.311 3 0.115 1095h 3 1h? h.03968 135 .92 3 0.32 9768 3 119 3.98981 156.99 3 0.15 9016 + 50 3.956111 163.65 + 0.10 8868 ‘e‘ 62 3.98783 168.73 '3 0.18 85. The eQuations of lines for Curve B and Curve 0, Figure V1.11 are respectively 1 - -0.001751 + 11.335 and I - -0.002961 + 11.11116. An analysis of Curve 0 strongly suggests that this method of measuring vapor pressures is invalid at higher temperatures. It appears that the effect of temperature becomes very important at approximately 100°C and destroys the effect of pressure. The most reasonable explanation for this fact probably is that the heat is so great in the vicinity of the thermistor that pressure has little or no effect on the resistance. The same result has been observed for gibbsite. After the/unfortunate results with the sulfuric acid-water mixture, gibbsite was investigated. Thirty grams of gibbsite that had a surface area of 111110cm2/gn. was placed in the cell. After evacuating for one hour, the vapor cell was heated to 82.38°C and the measurements were begun. The results of the measurements on gibbsite are given in Table V1.9 and the points are plotted in Figure V1.11 along curve A and curve C. Table my Resistance (Ohms) _1_9_g_Resistanc_e__ mfg 18163 3 79 11.25920 110.11 3 0.13 15055 3 150 11.17770 68.33 3 0.60 13296 3 13 11.12371 911.17 3 0.10 10525 3 69 11.02225 1311.20 3 0.16 9625 3 38 3.983110 157.77 3 0.16 * 10380 3 15 11.01620 1311.113 3 0.09 8992 3 118 3.95386 167.211 3 0.211 * ”9699 3 30 3.98673 158.36 3 0.33 9293 3 110 3.96816 161.69 3 0.30 ... mop». men». ”5.3 1. 1. .11 1 1. .- m :0 G11- INouum 0.11-01 nu .9110111 1111111 1 H382, \\11G m . 00 0. .2. Oil... be: «assessed? sumo summonniufiqbueov D1 1 1 menu «aspen-85.0 «was sppwoooiummbmoov mo? m m (m We a hem W NM D D D D 1 1D woo 64 mos»- em DI. Ewtueo ._e____________ _ __ owesssmwmfinrfluouuumusfi H a dam engageswev o H .o. u r m a a a s S 5 3838.3 86. for gibbsite along the high and low temperature sides. Figure V1.5 Approach to equilibrium at approximately 158°C 87. *The equilibrium was approached from both a low pressure side and a high pressure side at temperatures of 158° C and 131100. To insure that equilibrium was established within 118 hours, a test was run for ten days at 161.91%. The results of the approach to equilibrium from two directions and the test run for ten days are given in Figure V1.5. Only the resistance against time is plotted since the pressures could not be determined. The positive result from the gibbsite test is that no water is lost before 135°C. The experimental points measured above 150°C appear to follow the curve C quite well. However, as will be shown, no confidence can be placed on the measurements in this range. Since the uperimental measurements on gibbsite coincided with those for liquid water-sulfuric acid solutions, it was assumed that these points represented the vapor pressure of the acid solution mixture at that temperature. The three points on the curve C that correspond to gibbsite are at temperatures of 157.7700, 161.6900 and 167.21106 with respective vapor pressures of 530, 615, and 775mm. Hg. The proof that the method is negative at high temperatures is assured when the heat of reaction was calculated by the Clausius-Clapeyron equation. A derivation of this equation for the hydrate (or hydroxide) reaction is given in Appendix V. The calculation of the heat of reaction for Gibbsite . Boehmite + water vapor was based on the data given in Table V1.10. Log pressure water(m. Hg.) 2.9 2.8 2.7 2.5 2.3 2.1 1.9 1.7 1.5 1.3 1.1 1.0 88. .10 I— \‘ — \‘ A. P I. — O Wayman A Funaki and Uchimura _ "' 1 2 I I I l 2.2 2.3 2.11 2.5 2.6 9?: ('70::103 Figure V1.6 Plot used to calculate the heat of reaction of del‘ydrated gibbsite from the Clausius- Clapeyren equation. 89. Table V1.10 T°c To}; % x 103(0K) P(mm.Fg) 10g P 157:7? 'HEUi77 "“1?1fl?“"‘ "530'“' 'E77EE' 161.69 1.31.6 2230 615 2.788 ("m1 167.211 1.110.211 2.27 775 2.889 1110 1113 2.1.2 211 1.380 was :8 812-31 his UChimflra) 170 hh3 2.26 760 2:880 The measurements of Funaki and Uchimira (1952) are also given in Table V1.10. The above data are plotted in Figure V1.6 in terms of log P(mn.Hg) against 7::- (OK) at 103. The heat of reaction was calculated for four curves, in one for Wayman's measurements (curve 11) and three for Funaki and Uchilnura's work (curves 1, 2 and 3). The calculation of the heat of reaction for (curve 11) is as follows: .411 - slo 2 .303R pe a 2.889 '2012h 2o2 '2e32 " .léé '3 o3 'o05 AH . 3e3 x 11.57 - 15.08 kcale/Mla Althomh this value agrees quite well with the work of Kuznetzov (1950) it disagrees with the dehydration work of Funaki and Uchimllra and no confidence can be attached to it since there is no way to check the accuracy and it may be merely fortuitous based on the assumption that the gibbsite vapor pressures agree with those of sulfuric acid-water at the corresponding temperature. The heat of reaction was also calcu- lated for the curves of the Japanese workers. The results for curves 1, 2, and 3 are respectively 63.80 kcal., 21.89 kcal., and 112.87 kcal. It appeared reasonable that one could get three possible A H values 90. from their results. It may be that their first two points at 111000 and 151100 are accurate since this A H value is reasonable. At higher temperatures their values are most likely in error. The temperature in their work could only be controlled to 31°C. It is quite reasonable to suspect that small errors in temperature measurement would lead to large errors in vapor pressure determinations. A critical analysis of both methods (Wayman) and (Uchimura and Funaki) would thus suggest that our knowledge of the thermodynamic constants for del'wdrated gibbsite are questionable and the system should still be studied. It is clear, however, at this point that the properties of gibbsite determined through heat of solution measurements and those from dehydration studies are at variance. The reason for this observa- tion is discussed in a later section. 91. VII. Microscopic” X-raz Diffraction Wtig of Dehydration Products In order to Justify the assumption that gibbsite delvdrates to boehmite plus water vapor, the dehydrated products were examined by the petrcgraphic microscope and x-ray diffraction techniques. It is believed that this is the first time that vapor pressure studies have been correlated with microscopic and X-ray examination. Fricke and Severin (1932) masured the isobaric dehydration of gibbsite at a pressure of 100m. Hg and identified the product as boehmite but did this only at one temperature and no microscopic identification. For this examination samples of gibbsite were detwdrated under identical conditions to those used in the vapor pressure measurements. Twenty milligram samples were dehydrated for 1.8 hours at 150% and 166°C. In addition twenty milligram samples were dehydrated .m air at 200°c and 225°C in a laboratory oven. a. Microscopic insemination The original gibbsite, before delwdration, was transparent, white and occurred in aggregate-like fragments. The samples detwdrated at 150°C and 166°C were somewhat amorphous-like and pitted on the surface. Elmixntion of the same samples with a magnification of 500x indicated that the sample at 166°c was highly fractured while the aggregates of the one at 150°C were somewhat intact. The samples dehydrated in air at 200°c and 225°C appeared morphous-Like and the surface was so obliterated that no significant detail was distinguished. B. X-ray Diffraction Wtion Samples were prepared for I-rav investigation by hand crushing in a cast iron mortar. Approximately one milligram of the crushed sample (-200 mesh) was then mixed with Duco cement and rolled between 920 -- "- 93'. two glass slides in the form of a small rod 0.5mm. in diameter and 1 cm. in length. The formed rods were glued to a pedestal in a Debye-Scherrer camera and X-rayed by (3qu radiation using a. nickel filter. Standard X-ray patterns were prepared from synthetic gibbs ite (same as used in the dehydration studies) and synthetic boehmite. The lines used to identiiy gibbsite correspond to d spacings (11°) of h.82, b.33. 2.hh, and 2.37. Those used for boehmite identification had d values (l°) of 6.15, 3.15, 2.33 and 1.85. The gibbsite samples I-rayed from the delwdration at 150°C and 166°C for five hours revealed that gibbsite was the only phase present. After extending the x-rav test to ten hours, the 166°c sample showed faint boehmite lines while the 150°C sample was unchanged. This data supports well the original premise tint gibbsite - boehmite or water vapor. In addition, the structure of gibbsite is not altered up to 150°C. The sample dehydrated at 200°c in air gave a good indication of boehmite; the sample heated to 225°C was completely converted to boehmite. These latter two tests might suggest that the amount of gibbs ite converted to boehmite is dependent on temperature and it would seem probably that delvdration time is also an important factor,but this was not investigated. The importance of using the X-ray technique and petrographic microscope is demonstrated. Both of these tools have their peculiar limitations but used together they complement one another. The results of the X-ray work appear in Figure VII.1 and are listed below in Table VII .1. 9h. Table mo]. X-ray Smle 3311230 Phases Identified (A) Synthetic gibbsite -- Gibbsite (B) Gibbsite Derwdrated (in vacuum) at 150 c 150° Gibbsite (C) Gibbsite Dehydrated (in o vacuum) at 166°C 166 c ibbs ite, boehmite (D) Gibbsi e Dehydrated in air at 200 200° Gibbsite, boehmite (8) Synthetic boehmite —- Boehmite (F) Gibbsi Delvdrated in air at 225 225° Boehmite c. Liscussion of Results Achmbach (1931), Schwiersch (1933). Borisevich (19h8), lleaanian (1955) and Courtial, Tranbouze, and Prettre (1956) have found that boehmite is the only well crystallised phase resulting from the delv- dration of gibbsite up to 225%. The detailed work in vacuo of Tertian, Papee, and Charrier (1951;) indicates that boehmite is the only phase formed. The results of this study are in accord with those enumerated above , but apparently no one has been concerned with the amorphous- like surface which was previously described. A good petrographic microscope and electron microscope study of these surfaces might be rewarding. Cmtrary to this theory of boehmite formtien only as a delvdration product, Tertian and Papee (1953) suggest that gibbsite dehydrates into boehmite plus a poorly crystalline variety of alunina. In the present work, no lines of any form of alumina were detected on the Lrsy film. However, the work of Tertian and Papee is interesting and the amolphous-like phase observed microscopically could very well be their poorly ciystalline alumina, but the amount insufficient to be detected by X-rays. The microscope might well throw some light «1 the theoly that gibbsite first delvdrates to alumina plus water vapor and 95. later the water vapor relwdrates the surface to form boehmite. With regard to the mechanism of dehydration Garner (1955) has perhaps the most extended treatment. It is pointed out that during dehydration of a lwdrate crystal in hard vacuum, water molecules or OH groups evaporate from the surface giving a delwdrated ionic network which is only stable to some extent in the case of some zeolites. In most other hydrate systems, the structure is unstable and undergoes rearrangement to give a phase which possesses no clearly defined struc- ture. This partly amorphous phase may consist of extremely small crystallites which are so separated in space that they cannot readily grow to larger units. The transformation is accompanied by only small changes in bulk volume and the absence of visible cracks. a further rearrangenent then occurs in this disorganized material giving crystalline nuclei of a new phase, which process is accelerated in the presence of water vapor. The process of clystallization is accommied by consider- able shrinkage of the products, allowing cracks to form usually at right angles to the interface. This excellent description has been observed on marry of the hydrate equilibris that Garner has investigated. It will be recalled that Tertian and Papee (1953) suggested that gibb- site delwdrates into boehmite plus a poorly clystalline variety of alumina. Also the microscopic examination in the present study indicated a somewhat amorphous surface product. The dehydration mechanism of Gamer appears to have some of the characteristics of gibbsite dehydra- tion built into it . Garner further indicates that two factors determine the rate of detydration namely (1) the rate of loss of water from the interface between the l'ydrate and its products and (2) the rate of diffusion of 96. water molecules through the solid. In addition to these two factors, it seems that another point to consider is the not rate of loss of water, 1.0. outward diffusion minus inward diffusion rates. As a result of the small temperature coefficient of diffusion, the impedance to release of water vapor is less at lower temperatures than higher temperatures. This point is danonstrated quite nicely with gibbsite since Courtial, Trambouae and Prettre (1956) found that the boehmite content of a gibbsite sample dehydrated rapidly at high temperatures is much less than the boehmite content of a sample dehydrated to the same degree but more slowly and at lower tenperatures. The impedance offered to the escape of water from within the crystal depends apparent- 1y somewhat on the micro-structure of the surface layer and its thick- mess. The impedance is greatest when the layer is amorphous or micro- crystalline and less so when the interface layer is coarsely crystalline and full of cracks. These few notes on the mechanism reassure us that the delvdra- tion of hydrous substances is complex. A future investigation on reac- tion rates accompanied by detailed emination of the surfaces could lead to one valuable information with respect to the mechanism of gibbsite delwdration. To form a molecule of water either from a surface evaporation or removal of GI" groups from the crystal lattice, the recombination reaction probably involves a!" . oa- - 320(3) «5 0" Other possible methods of forming the water molecule are (l) L—OA‘H: in which the H-0 bond breaks to reunite 11.3.6 .. H’: with the on bond severed from a or ~~- “ 97. I (2) 1.1.0111 inwhich the}! and 0 atoms are severed + o ,'. H from bonds and recombine to form water. 0 It certainly past be recognised that Inch more energy is necessary to eliminate twdroxyl-type water (Brucite and Gibbsite) than the H20 me water (Gypsum and hydrous berates) . VIII. Discussion A. Mortar!” of Dissociation Pressure Measureuents Much of the work on thermodynamic systems in the past has been done by heat of solution measurements, from concentration cells and by other means. Many natural geologic and mineralogic changes take place under atmospheric conditions and from relatively simple experi- ments it is possible to calculate the three important quantities, heat of reaction (A 11°), change in standard free enorzy (A F’), and the entropy change (A S.) from studies of vapor pressure measurements over lydrate and hydroxide dissociations. The heat of reaction can be de- termined through the use of the Clausius-c lapeyrm equation. The change in free energy can be determined from the relationship A r' - -R'l‘anp - -h.57'r 10¢ PHZO The change in entropy is given byAS' - 4H0 " AF. and the equilibrium vapor pressure can be represented by 12g P- - $35!; 7:; o constant. Hence some very important thermodynamic constants can be determined from these detydration studies providing the gas can be represented under ideal conditions. The most direct application for this information is at surface tenperature and pressure where the processes of weatherim and sedimentation occur. 98. B. gurface Reactions on Solids One of the imortant contributions from this study has been the recognition of the difference in heat effects for the system gibbsite - boel'mite 4v water vapor when determined from heat of solution measure- ments as opposed to dehydration investigations. This effect has not been enphasised before for this particular system. The best A 11' value determined thus far for this reaction by heat of solution investigations have been that of Kuznetzov (1950) which is 15.0 kcal./ mole. The most reliable values of All from dehydration work are those of Sabotier (19510 and Funaki and Uchimura (1952) and are respec- tively 21.5 kcal./mole and 21.89 kcal./mole for a limited range. The difference in the values is probably a surface effect. In heat of solution measurements, the solid usually is completely dissolved and a true equilibrium is measured. With delvdration work, there is apparently an interplay at the surface between the originally formed dehydrated product and water vapor and the subsequent reactions that follow. It is also important to note that the effect of pressure on the system is contributory to the ease of escape of water molecules from within the crystal. Consequently, the reaction investigated by delv- dration is complex and a true equilibrium between the crystal and the environment is never attained; that is, the vapor pressure which is measured may represent an equilibrium between the original crystal, the complex surface products, and the vapor itself. These complexities could account for the difference in heat effects as determined by two different methods. Giaque (191:9) has considered the same problem for the Brucite - Periclase o H20“) reaction. One of the important points raised by Giaque is how often have experimenters recorded equilibrium 99. data which did not correspond to the more-crystalline properties of the phases present. Giaque has calculated the free energy difference between Mgo (crystals) - MgO (fine powder) as 800 cal/mole. It is concluded from his work that the dehydration of crystalline brucite should produce particles of MgO which become detached before they reach macroscopic dimensions, and it is believed that this is a fairly connonplace occurrence in other cases. It is thus easy to appreciate why the higher free energies of substances in a finely divided form give lower decomposition pressures than do macroscopic phases. For this particular system &(OH)2 - MgO 0 H20”) the true dissociation pressure, as determined from the third law of thermodynamics, is 130% higher than the measured values of Giaque on this system which had a reproducibility .of 0.1%. This mechanism no doubt accounts for the higher vapor pressures from heat of solution measurements than for the low values obtained by dehydration studies. MacDonald (1955) has also calculated theoretical curves for the brucite-periclase reaction and interprets the differences in his curves in terms of the method of preparation of material. These observations on deludration certainly show the complexity of surface reactions and should suggest that much caution be taken when making interpretations from such results. 6. Effect of Total Pressure on Dehydration in important point to consider in applying results from dehydra- tion studies in vacuum to those at natural conditions (1 atmosphere pressure) is what effect does an inert gas at one atmosphere pressure have on the vapor pressure (ideal gas). This point can be examined 100. in terms of a problem given in Glasstone (1958). The problem cited is that the true vapor pressure of water is 23.76 mm. at 25°C. Cal- culate the vapor pressure when water vaporizes into a space already containing an insoluble gas at 1 atmosphere pressure, assuming ideal behavior. In a vacuum the vapor pressure of water is the total pressure whereas under a total pressure of 1 atmosphere at 25°C it is only a fraction of the total pressure. The effect of external (total) pree- sure on thevapor pressure of a liquid or solid can be calculated by the Poynting equation k? on"? but since the change in small .312, can be replaced by APP. where Ap is the change in vapor pressure p is the partial vapor pressure AP is the Total Pressure change V1 is the specific volume R - gas constant T - absolute temperature or A 2 . Vi AP 0 At 25 C we have £l§_ ' 0e018 x 1.0 2 .76 mm AP 0e018 X 23e76 . 0.01-75"“. 0 e082 1 298 101. Hence the vapor increases by only a small fraction since p - 23.79. Perhaps the same results can be used for solids but at tenperatures not higher than 50.0 without involving too much error. Thus the change in total pressure on a solid in the range of one atmosphere at low temperatures can be neglected as affecting the vapor pressure developed over the solid. In terms of kinetics, the effect of total pressure becomes important. Between the temperature range 206-2h3°c, wrote and Goton (1951;) have shown that small changes in pressure lead to large differences between activation energies. This observation might suggest that total pressure is quite important as to the extent at which the rate of equilibrium is attained. D. Relationship Betwoen Natural Mineral Phases , Thermodynamics and Kinetics In nature all three of the hydrous oxides of aluminum have been observed. The following Table VIIIJlists the various phases that have been identified with geographical location in a few of the representa- tive deposits around the world. 3, 13,0 o G II Gibbsite 102. TOblc VIII e 1 KEATICN UNITED STATES Ark—ansas Oregon Georgia No. Carolina So. Carolina Missouri CARRIBELN AREA EUROPE Jamaica, B.W.I. Jmh‘, 13.3.1. Grenada, B.U.I. Dominican Republic British Guiana Surinam Brazil Spain Spain Ireland Greece Poland Croatia-Bosnia Hungary Hungary fitment? Hunter! Russia Pcrtugsss Guiana Turkey India PACIFIC B - Boehmite Australia Hawaii REFEREl‘UE “your (1916) Allen (19%) Alexanderfiiendricks and Faust (19111) Alexander, Hendricks and Faust (191:1) Alexanderfliendricks and Faust (191:1) Wyn-r (1923) Hill (1955) Kass (1950) Harry-Rodrigues (1939) Goldich-Berg uist (19h?) Bishopp (1955) van Kersen (1956) de Ravel (1953) Hiralles (1952) Tullet (1951) files (1952) Vachtl (19562 1; ) Spngenberg l9 9 Miholis (1956) Gedeon (1956) Net-era (1951:) Kiss (1952) do Weisse (19148) Chirvinskii (191.0) do Weisse (1951;) Ekrem (1951s) Oda (1955) Root“ (191:5) Sherman (1957) D - Diaspore The first letter of each series represents the predominant form. 1.03. There is no doubt that gibbsite predominates in these weathering pro- files on a world-wide basis. Even when associated with boehmite or diaspore, it is dominant except in a few instances. This data suggests that gibbs its is the stable phase at surface temperature and pressure. The instances where gibbsite and boehmite occur together could represent a demdration equilibrium. It is interesting to note that in the areas with high relative humidity (0.8., Hawaii, Jamaica, Brazil, and British Guiana), gibbsite is most stable; high relative humidities would proba- bly be conducive to the rehydration of boehmite to gibbsite. In rain forest areas, the excellent cover of high trees prevents extreme heat from penetrating the soil and dehydration of gibbsite is probably eli- minated. In areas like Jamaica, however, boehmite has been identified and might be the result of intense heat from the sun permitting surface dehydration of the gibbsite. In order to establish whether gibbsite or boehmite is the stable phase in nature, it is necessary to consider the relative humidity and temperature. At first glance, it would appear that a three coordinate system is required, the coordinates being temperature, partial pressure of water vapor, and relative humidity. However, relative humidity is given as partial pressure water in air (T) partial pressure water at saturation(T) R.H.(T) - Since the saturation vapor pressure is fixed at a given temperature, it is necessary to know only the relative humidity and temperature from which the partial pressure of water in air can be calculated. It would be extremely interesting to gather data on relative humidity and temperature, both areally and on a world-wide basis. By statistically plotting the relative humidity (ordinate) against temperature (abscissa) 1011. and superimposing the curve for dissociating pressure of water vapor for gibbsite (ordinate) against temperature (abscissa) and noticing where these curves intersect, it would be possible to establish the conditions of stability of gibbsite and boehmite in terms of relative humidity and temperature. Schmalz (1959) has expressed an equilibrium for the reaction hematite + water - goethite in terms of a ratio‘77 which represents the relative humidity in a system calculated at ary temperature. He lists an expression for calculating In as follows: on inn - (r'-r).[4v' (dp/dt)'- Asp]. Acp'r 1n (mu/1‘) where the volume A V' - expansion due to water or water vapor, dp/dt - AS'/ A V' and where '1" h T. Thus a knowledge of all the above quantities would give a specific value for the relative humidity for a reaction in some definite system. Then it would be possible to construct a two-dimensional plot for a dehydration reaction in terms of relative humidity and temperature. Having this plot, only a knowledge of relative humidity and temperature would be necessary to predict whether gibbsite or boehmite would be stable. Even though we might be able to predict the stability of one phase or the other in weathering profiles, this information places no limit on the time factor since thermodynamics is independent of time. A thermodynamically stable situtation now exist in nature, but kinetically my be impossible. Thus if boehmite is found in an environment which is unstable to its existence, it may be rehydrating to gibbsite, but on a kinetic basis the reaction rates may be so complex and slow that it remains in nature in a metastable state. In the future a thorough study of both the kinetics and thermodynamics may shed light on this stability problem. There are many limitations in the use of quantitative chemistry for solving geological problems, but an understanding of the real mechanism that prevail in nature can only be understood in this manner. IDS. 11. Conclusions 1. A quantitative approach to contribute more data on the understanding of the problem of weathering in geology has been done. To correlate measurements of vapor pressure on dissociation reactions, relative humidity, and tenperature, at least a two - coordinate plot is necessary. Through the use of an equation by Schmals (1959), it is possible to calculate the relative humidity of a reaction as a function of temperature. Then a knowledge of relative humidity and temperature dictates the stability of mineral phases which can be applied to nature. Probably effects of rate studies might explain disequilibrium mineral assemblages observed in bauxite deposits. 20 ‘ hilh t’emperature cell has been designed for use in either infra-red spectroscopic studies or for measuring the vapor pressure of geologically important hydrous mineral: by thermistors. 3. A new method was developed for measuring dissociation pressures for substances that contain H20 type structural water. The accuracy of the method varies from 7-10 per cent for measuring vapor pressures in the range 300-?60nm. Hg. The technique appears to be unreliable for minerals that contain CH“ type of water since the temperature effect sensed by the thermistor exceeds that of pressure. 1;. Equilibrium constants for the reaction Gibbsite - Boehmite .. water vapor have been calculated by two methods. A method is suggested for evaluating the inconsistencies of thermodynamic constants by the use of these calculations. When discrepancies are found behreen the two methods, the thermodynamic values should be questioned. 5. The best values currently for the heat of reaction for gibbsite - boehmite 0 water vapor are AHo - 15.0 kcal./mole (Heat of Solution) AH - 21.5 kcal./mole (Dehydration studies) 6. The variance betwoen thermodynamic values by heat of solution measurements and dehydration studies can be explained on the basis of complex reactions that occur on the surface of delvdration. 7. The most reasonable products formed from the dehydration of gibbsite are boehmite and an amorphous, poorly crystallized phase. 107. X. metions for Future Research 1. The accuracy of the thermistor method for measuring vapor pressure 60111-1 50 imrovod by usins a system where the temperature 1. controlled to :_ 0.01°c. In order to stuew systems where the heat effects are high, a wheatstone bridge circuit of the Kelvin type should be investigated. An extremely sensitive galvanometer like the Leeds and Northrup Model 211,30 could be used. This galvanometer is lCDO times more sensitive than the ordinary Weston M0. 2. Theoretical curves for relative humidity as a function of temperature should be made with the use of Schmalz's (1959) equation. 3. A theoretical phase diagram for the system Al-Water would be interesting to calculate through the use of heat of solution and dehydration A H. values. 14. The effect of grain size on dehydration should be investi- gated at a single temperature in order to evaluate reaction rates and equilibrium dissociation pressures. 5. A comprehensive study of reaction rates on gibbsite might lead to results that account for more than one mineral phase as observed in nature. 6. The thermistor method should be used, after improvement, to investigate other substances like the hydrous borates. 7. The possibility of using thermistors to measure the partial vapor pressure of 002 and H20 simultaneously should be studied. If these results are positive, then complex equilibria investigations like the Asurite-Halachite reaction could be mdertaken. 108. Appendix I Brief Description of B.E.T. Method The B.E.T. method enables one to determine the volume of gas necessary to form an adsorbed monolayer on the substance whose surface area is in question. Usually krypton gas is used. Known amounts (volume) of krypton are added to a sample container and the amount not adsorbed on the surface of the sample is measured. The difference between the amount not adsorbed and the amount added is a measure of the amount adsorbed on the sample. This data, in addition to the pressure of the gas in the container and the vapor pressure of the gas at the experimental temperature, can be used in the B.E.T. equation which states that P g 1 + 0-1. P where rm vs“ v?“ “r; V I volume of gas adsorbed (STP) P - pressure in sample container when Vcc. are adsorbed Po - vapor pressure of the gas at the experimental temperature 'Vm - volume of gas required to form.a mononolecular layer C = a constant related to the heat of adsorption Hence a plot of as ordinate against P/Po gives terms 1 ‘7"? C-1 . The above relationship‘hy rearranging terms can be written Vmc as'Vm . 1 __ . If the weight of sample used is known slope + intercept along wdth Vfi, the surface area is s.a. . m x saw {193. = cw We Wto Of smplo P VTPo-P) ‘ ofthefomy=m+Bwherebisequalto - andmisequalto 109. The value of 5.2h3 x 10b is found by the following: (1) one cc. of gas at (STP) has 23 6.02 x 10 moleculeslmol. wt. _ 19 ‘724505'00. gas per mol: wt. 2‘688 x 10 ”01°CU183 (2) although Livingston (l9h9) has suggested a cross-sectional area for the‘krypton molecule as 18.5 sq. A., most people assume a value of 19.5 sq. A. Thus the area covered by 1 cc. of gas for Vm is £3638 x 1019 x 12.5A , 3.2h3 x.10h sq, cm. area 10 sq. A. sq. cm. emf,” Using the above reasoning, the surface area was calculated for the gibbsite samples as follows: (coarse gibbsite) (l) 5.61 gms. was placed in the sample container (2)'Vm was calculated as 0.169 Hence Gel-69 x So23h x ldi _ 8 1.th cm.2/sm. Ser 3 110. Appendix.II Qgscription: of Sedimentation Method The sedimentation container was made of glass and had the shape of a cylinder‘with.an inside diameter of 6" and a length of 20n,.Approxi- mately 1% of solids by weight was used in these experiments. For any predetermined grain size, 20 grams of gibbsite was placed into two liters of water to which 10cc. of a 10% solution of Calgon, as dispersant,was added. The mixture was then violently agitated with the use of a glass rod, first in a clockwise direction and then slowly in a counter-clockwise motion until the liquid was at rest. The stopwatch was then started and the experiment was run for a length of time necessary for a calculated particle size to settle a definite distance. After the particle has settled to the calculated distance, the portion above this liquid plane is siphoned off and the container is again refilled to volume. The same process is repeated until the liquid above the settling plane becomes clear which is the end point for particles finer than the calculated size to be present. The siphoned material is then allowed to dry slowly at 50°C. For all wet-sedimentation methods, the following conditions must be met: (1) Reynolds number is less than 0.6. (2) the solid is completely dispersed (3) the suspension is no greater than 1% solids by weight (n) theminimum diameter of the sedimentation tube is 10 cm. (S) experiments be run at constant temperature (6) no mechanical disturbance of the liquid (7) particles are larger than inhomogeneities in the liquid (greater than intermolecular distances in liquid) 111. According to Stokes' law, the terminal settling velocity of a single spherical particle falling at low velocity in a quiescent, homogeneous fluid of infinite extent is given by: 18u where v - terminal velocity in cm./sec. g = acceleration of gravity in centimeters per second per second {1 Pr (3 density of particle in gms./cc density of fluid in gms./cc. diameter of particle in cm. 11 viscosity of fluid in poises Calculation of the settling velocity of a 20 micron particle of gibbsite would be 980(2.h-l.0) (.002)2 " ’i‘BT.o'i)'-“' = °°°°5h88 - 0.031 cm. .18 v =- .031 cm./sec. x 60 sec./min. Va /soc . 1.86 cmo/min Thus a 20 micron particle would settle through 25 cm. in 25 cm. - 134:1 minutes 10% chmin. In the particular case at hand, the experiment would run for 13.111 minutes for settling a 20 micron particle through a distance of 25 cm. The liquid above the 25 cm. would then be siphoned off and theoretically should contain only particles less than 20 microns. It is realized that in practice only an approximation to Stokes' law calculations can be made which necessitates almost an infinite number of sedimentations to effect a pure separation. 112. A portion of the 20 micron sample is still available for future work should the occasion arise. 113. Append ix III Calculation of Standard DeViation Standard Dev. - (2 0.27'0. Leasurement (I) X-i S7081 *o28 57o81 *e28 S7o97 *ouh 57o22 -.31 57o5h *eOI 57o5h *oOI 57.21 -.32 S7o88 c.05 57.19 -.3h 570h6 ‘oo7 57,533 i - 2%- "if-T- ; ' 57o53 s.n. _ .6721 * For the resistance we have (Jr-x)2 ) % gx-izz .07 8h .078h .1936 00%1 .0001 .0001 .1021. .0025 .1156 .0049 .6721 i - average of measurements I w. single measurement :1 I no. of measurements ) ' 0o27 Thus in the table the temperature is recorded as 57.53 1 0.27. This simply means that the temperature determined for all these points can be expressed 68% of the time or one standard deviation as 57.5300 3. (See following page for table) 11h. x x-i (x-i 2 11010 +130 16900 10970 + 90 8100 10970 0 90 8100 10820 - 60 3600 10760 ~120 lthO 10730 -150 22500 10870 - 10 100 10810 - 60 3600 109110 + 60 3600 10920 4- 1:0 1600 108,800 65,600 2 - 10,880 3.1). - (giggly/3 87 The resistance is 10880 I 87 ohms 68% of the time. Thus by the method of standard deviation the points have been determined as 57.53 3 0.2790 10880 f. 87 ohms 115. Appendix,I!_ Method of Least Squares This method is an important application of minimizing a func- tion of two variables and is important to the fitting 0f'a.straight line to experimental points. The line is of the form y I mx o b (positive slope) y - -mx + b (negative slope) Let the observed experimental points be (X1,'Yl), (12, 12)......(Xn,1n). Corresponding to each of the observed values of X we consider two values of‘y, namely, the observed value ICES and the value predicted by the straight line “ICES ab. The difference is'YOES -(mXOESob) called a deviation. Each deviation measures the amount by which the predicted value of’y falls short of the observed value. The set of all deviations d1 - y1§(mx1+b),.......dn "Yn’(mxn*b) 'which gives the description of how well the line fits the observed data. The line is perfect, if and only if, all of these deviations are zero. In general, no straight line will give a perfect fit. The problem thus established is to find the line which best fits the data. This is the method of least squares. For a straight line which comes close to fitting all of the observed points, some of the deviations will be _ positive and some negative. Their squares, however, will all be positive and the expression f (m,b) - (Yl-mxl-b)2 + (22 4.22 -b)2+.....+(Yn-mxn-b)2 counts a positive deviation d and a negative deviation -d equally. This sum of squares of deviations depends upon the choice of m.and b. It is never negative and it can be zero only if m.and b have values which produce a perfectly fitting straight line. Thus the method of 116. least squares seeks to determine the line of best fit for which the sum of squares of the deviations f (m,b) - dlz + d22 " eeeeeedn is a minimm. Hence, it is necessary to solve for m and b where the 2 surface expression w - f(m,b) in mbw-space has a minimum. Thus we must solve simultaneously the equations 31»: 1 9L This is done by having 2 f (nub) ' 2(Yom-mxons '43) where YOBS9XOB are the observed or given coordinates of the points to be fitted to the line. The data for curve A, Figure V1.1 are tabulated as follows : «smofi . “33.8 + 29%? up . nfio.muoo.3 meommm . nsom.aoa .s w.mo:.~n . seem.~-~m.ma «swam . 39a: 5.2m. up + nfim.78.mn memo: . 93.0.62 3.0%.. we. . n3w.7~m.mn N583." .. 32848 H5.57 up .. «53.7%.2 «2&8 . £5th 5.37 up .. 33.7.3.3 mama? . £3.05 . 53.5? up + pumméummfin Name: .. 85m.m3 . 5&3: mp .. 8%.7em.m.n mamRm . gem," + £43: «a . nsmméuofima «ENS . €3.52 . Essa- Na . £35-85 «2.33 + 9.23.3.” + 5.82.. mp . 38.7.3.3 Naamem . eao:.~oa ._so.mos. up . pooo.w.oo.ea mammou + aeoe.om . au.sem . «a . ammo.oama.ea ”gamma . name.~m . ge.mmm . we . ammo.mnau.efl + Q i O + 117 . NA.>onv 9.23 33-80.; anamm. omlaom. m 9133. ~7an . m 9.83. waomm. m 91.50. 8H!©.R.M n.ssm.amumwm.m 3mm . SA a . m also 7 £33m. n arson.e~-mem.m page». mold R. m enema. mmumam. m 35338. s .128. 3430.4 9.2%. 3.68.: O swunousuan » leg 80.4 amm.m 5mm. m cum.m 0.35 mmm.m 3m. m mama mom. m «$3 «$3 000.: who... 30.... mmo m~.ss mm.om ~4.- «H.mm sm.am m~.®m 05.;m 8.2. 078 H:.mm ouAm en.mq mm.ms mmou 118. z (dev)2 - 220.66 -111.151.b + 1hb2-767S.3m + 1938.mmb+723611m2 3 f .. o - -7675.3 + 1938.1b + 11.1.728m {f - o - 411.151. + 28b + 1938.1 m 0 or we have the two equations 7675.3.- 1938.1 b + 11111728 111 (l) 111.15h - 28 b e 1938.1 m. (2) Multiplying (1) by +1 and (2) by ~69.217 we get 7675.3 -1938.1 b + 11.11728 m (1) - 7693.7 --1938.1 b -13h11.9 m (2) (1)9(2): - 18.1: s 0 +10579 m n _ 48.1. "1357? m - -o.0017h Then substituting 111 into (2) gives 111.15!. -= 28 b + 1938.1(-o.0017h) 28 b - 111.151. + 3.37 b - 11.09 y'- -0.0017hX + h.09 x I 16 W02 50 14.003 60 3.986 70 3.968 80 3.951 90 3.933 100 3.916 Thus the equation of the line for curve A, Figure V1.1 is Y - -0.0017h1 + h.09 and the plotted points are those given above for X and Y. 119. Appendix V Derivation of the Calusius-Chpeyron Equation for Calculating Heat of m For a system of the type (1) ABsolid —-7 Aselid '0 Bgas at a given PlTl A FR - O at equilibrium. Now if the system is changed so that (2) A8801“ -—-; A8011, + 8:” at P + d? and T . er .1 AI“ - 0 at equilibrium. We can write (3) d1?“3 - swat. . VABdP and (1‘) “MB' "Sios‘t ‘ vA-thP «1F - (3)-(h) - 43.3 swam + (vAB - 1+3”? - o d? (SAB .SIUB) dt ”AB 'iMB) d . SAB 'SA+B _ éé 3% iAB 41.13 AV From the relationship AF - AH ~TAS at equilibriumwhere A F - 0 A S . ATH— which gives d . AH TAV If the stated reaction takes place at temperatures where the change in volume of AB and A can be neglected, we can write V - VB = volume of the gas. If the gas behaves as an ideal substance at the temperature range of interest, VB - 31?— from the relationship PV 8 RI' which now yields 6 - P A H or se arating variables at 7552“ " gives £2 - m which is written P m2 in the form M - 4n 1 (5) dt "ET This is the fern of the Calusius-Clapeyron equation. Now the Clausius-Clapeyron equation can be applied to calculate A H for hydrate or hydroxide dissociation pressures. The equilibrium constant at moderate temperatures for these reactions involves only the . partial vapor pressure of water. The equilibrium constant can be written as H where P - partial pressure of water vapor KR - P M 3 no. of moles of water vapor Hence 6111?“ 4 H which becomes T RT dlnP . AH ‘3? mm This expression can be integrated by assuming A H constant and converting to logarithms to the base 10 to give log P - 52.9.1). 1- + constant 10 (2.30412) '1 If the logo? vs. T]: is plotted, the slope of the line is (-4 H/2.303MR). Hence A H can be calculated from the expression A H - -2.303MR (slope). 1. 2. 3. h. S. 6. 7. 9. 121. Bibnn Achenbach 11., "Thermal Decomposition of Synthetic Hydrargillite (Gibbsite ," Chem. Erde 6:307-56 (1931) Alexander, L.T., Hendricks,S.B., and Faust,G.T., "Occurrence of Gibbsite in Sane Soil Farming Materials," Soil Sci.Soc. Amer. Proc. 6252 (19h1). Alexanian, C., "Derivation of the Aluminas," Com ompt. rend. 2110: 1621-2 (1955)- Allen, V .T. "Formation of Bauxite from Basaltic Rocks of Oregon," §_______co. Geol. L3. 619 (191.8) Beneslavakii, 8.1., "New Al-containing Minerals of Bauxites," Doklady. 11.1.. Nank. sssn 113:1130-2 (1957). Bichowsky, F.R., and Rossini, F.D., Thermochemistry of Chemical Substanceg, Reinhold Publishing Co., 1936. 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Vachtl, J ., "The Greek Bauxites, the occurrence, Age and Mineral Composition," Vestnik ustrednika ustanes geol. 31:105 (1956). van Kersen, J.F., "Bauxite Deposits in Suriname and Demerara(B.G)," Leidsche Geol. Mededeel 21: 2117 (1956) (in English) Wooster, W.A., I"l'he Structure of CaSOh.21-120," Zeit. Krist. 931:375 wysor, D.C., "Diaspore Clay of Arkansas- Missouri," J. Amer. Corgi. Youden, R.S., Staiispigg for Chemists, 1955. 127. Biogaph ical Sketch Cooper Harry waymn was born at Trenton, New Jersey on January 29, 1927. He is the son of Cooper 0. and Helen U. Mayman, Trenton, New Jersey. He received his pre-college education in the public school system of Hamilton Township, Trenton, New Jersey. He entered the U.S. Navy on February 20, 1915 and was honorably discharged as a radarman third class on July 23, 19146. He has attended the following educational institutions: Trenton State Teachers College, Trenton, New Jersey 19117-1919 Rutgers University, New Brunswick, New Jersey 19149-1951 University of Pittsburgh, Pittsburgh, Pa. 1953-1951: Carnegie Institute of Technology, Pittsburgh, Pa. 1953-1951; Massachusetts Institute of Technology, Cambridge, Mass. 195h-l958 Michigan State University, E. Lansing, Michigan 1958-1959 He received a 8.8. in Geology from Rutgers University, 1951. an 14.3. in Geology from the University of Pittsburgh, 19511. and a Ph.D. in Geology with a minor in physical chemistry from Michigan State University in Septenber 1959. He is a nether of the following honorary societies: Signs IiOflT) Sigma Gamma Epsilon (Michigan State) and holds professional membership in the American Institute of Mining, Metallurgical, and Petroleun Ehgineers and the American Geophysical Union. His professional experience consists of the following: Geologist Anerican Agricultural Chen. Co. 1951-1952 Pierce, Florida Geologist Lone Star Steel Co. 1952-1953 Lone Star, Texas Research Technologist U.S.Steel Corporation 1953-1951: Pittsburgh, Pa. 128. (Professional experience con ' t) : Research Assistant Department of Metallurgy l95h-l956 MIT, Cambridge, Mass. Consultant U.S. Steel Corporation 1955 Pittsburgh, Pa. Casnltant Union Carbide Ore Co. 1956 New York , New York Cmsultant Kaiser Aluminum and Chem. Corp. 1957-1958 ‘ 08km, CIMe Teaching Assistant Department of Geolog 8r. Geophysics MIT, Cambridge, Mass. 1956-1957 Teaching Assistant Department of Geology 1958-1959 Michigan State University East Lansing, Michigan Senior Technologist Applied Research Lab. September 1959 U.S. Steel Corp. Monroeville, Pa. He is oo-author of a paper entitled "The Effect of Chenical Reagents on the Size, Shape and Terminal Velocity of Single Air Bubbles in Solution" with D.W. Fuerstenau, M333 agineering, June 1958. He married Ruth Treier on June 16, 1951, and they have two children, Carol Both (2% years) and Andrea Lee (8 months) of age. 1564 muflflfl R“ B" U” V" I" &“ u " "ruvsn 13178 I 171117 3 1711“!