REVIEW OF FUNDAMENTAL DEVELOPMENTS IN
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DifferentiaI Thermal Analysis C. B. MURPHY General Engineering laborafoiy, General Elecfric Co., Schenectady,
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has been made in this review to cover the significant developments in differential thermal analysis, from its advent to about October 1, 1957. This survey does not include an exhaustive coverage of the literature with respect to materials. A critical study of the method has been made by Norton (83). Two bibliographies have also appeared on this subject. An excellent review was written by Grim (38). More recently, an extensive review has been given by Lehmann, Das, and Paetsch (64). Because of the increased activity of chemists in this technical area, i t was considered appropriate to review some of the problems involved in the application of this technique, to indicate recent attempts to improve and standardize it, and to illustrate the widespread application of this procedure. N EFFORT
EARLY HISTORICAL DEVELOPMENT
Differential thermal analysis is a technique developed by ceramists and mineralogists for studying the phenomena occurring when materials are heated. Le Chatelier (23, 24) was the first to use the thermal transformations occurring in matter as an analytical procedure. Other investigators (5, 70, 99, 1.25, 136) took up t,his technique.
The usual practice involved charging a material into a platinum crucible and following the response of a single, centrally embedded thermocouple on heating. This technique advanced to where a single recording gave results from two galvanometers, one for the material and the other for a reference substance (99). Austen ('7) devised the differential thermocouple circuit from which the process derives its name. In this case, the differential thermocouple was used to measure the difference in temperature between the sample and ambient furnace conditions. Burgess (20) elaborated on the principles of this circuit and suggested practical working thermocouple systems. Fenner (30) used the differential thermocouple to study silicate minerals, the first application outside metallurgy. Differential thermal analysis, as we know i t today, was first applied by Houldsmorth and Cobb (49). I n their study of clays, the temperature of a reference material, rather than the furnace, was used for comparison. THERMOCOUPLES
Many varieties of thermocouples have been used in differential thermal analyses. In general, they fall into two
N. Y.
classifications, base metal and noble metal. Copper-constantan, (61, 89), Chromel-Alumel ( l l ) ,and nickel-nickel chromium (48) are some of the base metal types that have been used The platinum-platinum rhodium system is a very commonly used noble metal thermoelement, Gold palladium-platinum rhodium has been used (61). Iron-constantan (19.2) and ChromelAlumel (32) tliermopiles offer greatest advantage where the thermal effects must be amplified. The choice of thermocouples for differential thermal analysis apparatus is governed by the temperature limitations to be imposed, the thermal response desired from the thermocouple, and the chemical reactivity of the materials to b3 investigated. I n general, the noble metal thermocouples are operable a t higher temperatures and are less sensitive to chemical attack. A tungsten - molybdenum thermocouple has been reported (19) for use up to 2200" C. Thermocouples for high temperature application have recently been reviewed by Wisely (1%). The base metal thtirmocouples have to be applied with more caution because of their reactivity. However, they will give a much greater differential electromotive force response to thermal excitation than the noble metal type, VOL. 30, N O 4, APRIL 1958
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and are less expensive. This latter permits more frequent replacement, and reduces the possibility of spurious effects produced by contaminated thermocouples. Base metal thermocouples also have lower thermal working limits. Opposing physical and electrical factors are encountered in thermocouple circuits. A large thermocouple bead requires more heat to raise the temperature of its mass. However, a large bead is much more efficient in maintaining the electromotive force to give a significant differential thermal analysis peak. Moreover, these two factors make it essential that both beads in the differential thermocouple circuit be identical in size, to reduce the tendency for base line drift. Wire size must also be considered. Large wires have high thermal conductivity and low electrical resistance. It is obvious that there must be a compromise in these two properties. Boersma has calculated (14) that the heat leakage through thermocouple wires can reduce a peak area to less than 50% of its theoretical value. This would indicate the desirability of having fine thermocouple wires. These would offer high electrical resistance to the small current generated in the thermocouple circuit and mould require frequent replacement, because they could not withstand many exposures to high temperatures. The platinum-platinum-10% rhodium thermocouple is the most midely used noble metal thermocouple and is so well characterized that it is used to define the International temperature scale from 630' to 1063' C. The platinum-6% rhodium-platinum-3OOJo rhodium thermocouple, introduced recently in the field of high temperature measurements, appears to have a number of advantages over the platinumplatinum-lOyo rhodium type. The alloy has greater mechanical strength than the pure metal, and can be used to higher temperatures. The thermal response, somewhat lower a t low temperatures, is equal to that of the platinum-platinuni-lO~o rhodium thermocouple a t high temperatures. A study has been made of the effects of mire and bead size in the platinumplatinum-lO% rhodium system (46). With illite under identical conditions, a bead 1.43 mm. in diameter gave the more significant thermograms, compared with beads 0.80 and 0.90 mm. in diameter. A comparison of mire size effects with beads 1.43 mm. in diameter showed that 2s-mm. mire gave more significant thermographic effects than 22-mm. wire. Similar experiments were conducted with kaolin. The thermocouple circuits have been employed (Figure 1). I n A temperature measurement is controlIed by a separate thermocouple. In B, the tempera868
ANALYTICAL CHEMISTRY
ture measuremer 1 is made with a part of the differential circuit. Both methods give timilar results. However, from a m iintenance standpoint, i more easily repaired the A circuit E than B. By ming a platinum foil sample holder, it has been demonstrated by West (128) bhat the temperaturemeasuring couple can be completely encapsulated by the foil and used continually. This same technique, applied to the reference material, introduces a degree of constancy in all thermograms. 1 II this way, calcination of the refererice material is repeated with every run.
B
A Figure 1.
Thermocouple circuits
The centering of thermocouples is also important A thermocouple is subjected to er.cessive thermal transmission from the sampler holder if not centered. This results in a gradually increasing therinal difference between the t v o thermol:ouples, and a base line drift in the theiinogram. Smyth (111) has discussed the problem of temperature distribution during an endothermic reaction, and h w shown that a marked variation in peak shape will result from noncentered thermocouples. His calculations show hhat if the differential temperature is ])lotted against the temperature of the center of the reference specimen, neither the point of departure from the base liite nor the peak temperature corresponds to the inversion temperature. Smyth's work indicates that if the differenhl temperature is recorded as a function of the surface temperature of the, sample.or the temperature of the center of the sample, the point of del~arturein the former or the peak tempei,ature in the latter will give the temperature of t,he inversion. I
SAN )'LE HOLDERS
Sample ho1dci.s may be classified in several ways. The simplest is based on thermocou ;)le insertion. Side-inserted thermocouples have been employed by Par:k and Warner (86), McConnell and Ihrley (67),and Berkelhamer (13). Sjvtems with top-mounted thermocouples have been used by West (128), Vold (I,@), and Gordon
and Campbell (56). Thermocouples inserted through the bottom of the block have been used by Stone (112), Parodi (86), and Carthem and Cole (28). Top - mounted thermocouple systems have found special application in the study of waxes, greases, and liquidforming systems. The thermal behavior of substances into the liquid state can be followed in other types of systems by using an inert material as an adsorbent (78). This prevents the material from running out of the sample holder. Multiple sample holders have been used by IZulp and Kerr (65),McConnell and Earley (67), and ICauffman and Dilling (68). The variation in sample holders has ranged from inexpensive and simple to complex and costly. Insley and Emell (60) used a divided platinum cylinder. A simple refractory block was used by Houldsworth and Cobb (49). Refractory blocks with replaceable refractory cups (40) and platinum cylinders (46) have also been employed. Nickel blocks have been used by Grim and Romland (59),Norton (85),and many others. The most simple holder developed consists of holes drilled into sections of insulating brick (31). Platinum foil has been wrapped about thermocouple beading to form the sample holder by West and Sutton (129) and Icissinger (69). Pask and Warner (86) have used blocks made of nickel, graphite, and platinum. Platinum microcrucibles (4.2) in some cases have been incorporated as part of the thermocouple system (110). An aluminum sample holder has been developed for moderately high temperature application in the field of soaps and greases (27). Normal procedure in differential thermal analysis has been to arrange the thermocouple circuit so that junctions are embedded in the sample and reference material. I n a new type of sample holder developed by Boersma (14) the thermocouple junctions are inserted in insulated nickel block sections without physical contact between the thermocouple junction and the materials. This system is claimed to alleviate the dependency of the peaks on sample packing and thermal conductivity of the sample. Another obvious advantage is that thermocouples do not have to be replaced because of contamination by reactants. Most equipment in use today has metal blocks of nickel, Inconel, or stainless steel. A ceramic block, because of its low thermal conductivity, would give more intense thermographic peaks. A smaller temperature differential would exist between the programing thermocouple and the furnace in a metal holder because of the high thermal conductivity of the metal block. This would
result in better control of the furnace with a metal block. The comparative performance of nickel and porous alumina sample holders of identical dimensions was investigated by MTebb (127), studying the thermal decomposition of calcium hydroxide and calcium carbonate. Lower decomposition temperatures were observed with the ceramic holder. When vitreous silica inserts were used with the porous black, this effect disappeared. It was reasoned that permitting the escape of gaseous decomposition products led to a more rapid completion of reaction. The nickel block also gave a smaller peak area, showing less sensitivity than the porous alumina. The temperature difference between the furnace atmosphere and the center of the inert reference material was smaller in the nickel holder than the porous material. Similar experiments conducted by Mackenzie (68) on the exothermic peak for kaolinite confirm these results. Maclienzie has also shown that the nickel sample holder, without a cover, approaches the same maximum temperature value obtained with the porous holder. But, again, the peak area was smaller than that obtained with the latter material. It was also shown that low porosity alumina compares favorably with the nickel as a sample block material. Using the same mass of kaolin, the nickel sample block and the platinum foil type holder have been compared by Patterson (87). The larger peaks with the platinum foil sample holder are attributed to the heat capacity differences in the two sample holders used. The platinum foil type holder has a tendency to show marked drift in the base line, because the specific heats of the sample and reference material become significant. More attention to this variation might develop a comparative method for the determination of specific heats. However, using this type of holder, and replacing the platinum {oil after each run, have the distinct advantage of preventing contamination in subsequent experiments. Scrap platinum can be salvaged to reduce operational costs. Until recently, sample holders have been constructed to conform with the dimensions of available furnaces. Geometric design was applied to the bulk material that could be accommodated. 'The design of the sample holder involves several factors. Most important is that the material of construction should not react with the substances investigated or the furnace atmosphere to be used. The sample cell should be small to minimize the thermal gradient through the material, yet sufficiently large to give maximum differential thermal effects. These and other fac-
tors have been considered a t some length. One of the first investigators to determine the relationship of the physical dimensions of the sample holder and the resulting thermograms was Hauser (46). Using platinum foil sample holders, I/g, 3/16, and l/4 inch in diameter and a/., inch long, he obtained best results with the 3 / ~ ~ - i nholder. ~h It gave peaks more intense than the smaller unit, and more distinct than the larger cell. A more complete investigation was published (86) on the construction of nickel blocks, and confirmed with platinum and graphite sample holders. Using cell diameters of 3/*, and inch, much larger peaks n-ere obtained with the larger cells, but much of the detail was lost. Excessively large peaks conipletely obliterated small thermal reactions. The maximum number of reactions was shown by the smallest holder. Pask and Warner (86) also found that the variation of the ratio of the bulk volume of the sample holder to the volume of the sample holes, for values of 2.7, 5.8, and 10.6 produced only minor effects in the thermograms of ball clay. These numbers apply with a small total mass of sample block. Mackenzie and Farquharson (69), reporting on the results obtained with standard clay samples from 32 laboratories, have concluded that ceramic sample holders give higher peak temperatures than metal types up to 650" C. Comparable results are obtained to 750" C. Above this last temperature reproducibility appears t o be better with the metal sample holder. A recent report by Walton (126) illustrates the use of pressed pellets of clay into which the thermocouples are inserted. No sample holder is used. Morita (71, 7.2) has used 150-mg. samples between 200-mg. portions of calcined alumina compressed a t 200 pounds per square inch to ensure a compacted mass for examination. RATE OF HEATING
Rates of heating have been employed from 0.5" (27) to 100" C. per minute (9). Because a rate of heating is employed, the temperatures recorded for various phenomena are not those of thermodynamic conditions. A time lag occurs. The slower the rate of heating, the smaller the variation. However, with a slow rate of heating, the temperature differential between the roference material and the substance examined will become less. This will result in rounded peaks that tend to be more insignificant as the heating rate is lowered. With a rapid rate of heating, peaks become intense and considerable detail is lost. Larger deviations from thermodynamic temperatures will also result (79).
Most published differential thermal analysis results have been made a t heating rates of from 8" to 15" C. per minute. Recommendations made a t the Internstional Geological Congress in London, in 1948, called for a heating rate for the s:tmple of 10" C. per minute, with a max.mum variation of 1' C. per minute (69). The development of modern apparatus has tended toward controls permitting varis#bilityin the heating rate (89, 119, 132). Such apparatus has been applied to the determination of reaction kinctics (69). EFFECr OF PARTICLE SIZE
The effect of particle size on the nature of the thermogram has been considered by several investigators. Norton (83) has pointed out that finer particles give up their heat more rapidly and have a distinct effect on the thermogram. It has been said (41) that the temperature a t which reaciiions begin and end thermographically will be lowered witli increasing fineness of the material studied. Recent results published by Berg (10) show increased peak area as well as peak intensity with increased finencss of the clay particles examined. The areas of OS-g~am samples of various particle size fractions of kaolinite were measured by Carthew @I); variation of area with particle size was found. It is unfortunate that the bulk of this work ha!; been conducted with clays. These fire such complex chemical structures 1,hat there is no assurance that various fractions have the same composition. Further efforts in this direction should be conducted on materials of unquestioned structure and purity. I n a simple cubic crystal, the unit cell rupture involves the breaking of three bonds per atom. I n gross crystals, six bonds are ruptured per atom. From a theoretical point of view, it would appear that difierences in energy would result with increasing fineness. However, particles sizes employed to date have by no means approached this limit. Also, with fine samples, the packing of the sample should be greater. This would lead to art increased thermal conductivity in the denser material. A quicker thermo Eouple response would result, lowering the temperature a t which reaction occurs, as reported by Grimshaw, Heaton, and Roberts (41). ATMOSFHERE CONTROL
The original differential thermal analysis systems p.rovided for the programed heating of samples in the air present in the furnace atmosphere. This technique resulted in thermograms that were difficult to interpret because thermal [effectswere not always VOL. 30, NO. 4, APRIL 1958
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separable from oxidative effects. The desire to separate these two effects first led to the development of equipment operable under vacuum. Such apparatus has been described by Whitehead and Breger (131), West ( I d s ) , Stone (112), Haul and Heystek (CZ), and others. I n vacuum techniques, endothermic reactions resulting from phase transitions would show little or no variation because of the lack of pressure dependency of such reactions. However, endothermic reactions originating from the volatilization of decomposition products-Le., release of gases such as carbon dioxide, mater, sulfur dioxide, etc.-would show peaks a t lower temperatures under vacuum. This would result from the lowered partial pressure of these materials in vacuum systems. Oxidation reactions would not be likely to occur, and peaks for such phenomena would disappear from thermograms obtained using vacuum. A greater understanding of the thermal properties of materials could be obtained by studying the effects of various atmospheres on resulting thermograms. Equipment to serve such a purpose mas developed by Rowland and Lewis (100). Greater significance could be attached to results obtained over a wide variation of pressures. Stone (111) has developed equipment capable of operation from vacuum up to 6-atm. pressure, and uses either a single gas or a mixture of two gases under dynamic conditions. This shows promise as being the most versatile type of equipment devised to date. FURNACES
For the most part, furnace construction has consisted of a ceramic tube wound with a resistance wire element. The tube has been mounted vertically and horizontally; no particular advantage has been found in either method. Nichrome, Ilanthal, and platinum wire have been used most frequently as resistance heating elements. Globars have also been used. More recent furnace construction has incorporated design tending to reduce induced e.m.f. in the thermocouples. Stone's (11g) equipment has six symmetrically located, electrically balanced coils as the heating element; this eliminates induced effects in thermocouples. A sufficiently large uniform zone of heating should exist, so that the sample block and thermocouple system can be accommodated at the same temperature. This ensures that the differential temperatures observed are a function of materials examined rather than furnace construction. Brewer and Zavitsanos (18) developed an inductive heated differential ther870 *
ANALYTICAL CHEMISTRY
mal analysis appxatus and applied it to a study of tlLc germanium-germanium dioxide system. The sample was held in silica sanple holders inserted in a molybdenum block. Temperatures were measured w'ih platinum-platinum rhodium thermocouples. The results agreed satisfacto1,ily with those from conventional diff xential thermal analysis equipment. This same equipment was applic tl to the silicon-silica system (17). 11, was suggested that this technique, using pyrometric temperature determinations, should permit differential ther iial analysis to temperatures of 3000" C. MULTIPURI'OSE EQUIPMENT
Many investig;ntors have used other techniques to obtain information to complement differential thermal analysis results. ?ypical examples are resistance analysis used by Reisman, Triebmasser an 1 Holtzberg (96), zdiffraction appliyd by Stone and Weiss (115), and thertnogravimetric analysis utilized by Johnson (52). The desire to obtain supplementary information led Powell (94) to the deveIopment of equipment givin i; simultaneous thermogravimetric and differential thermal analysis curves from one sample. AF I'LICATIONS
Phase Equilibria. Differential thermal analysis iegisters the thermal transformationri occurring in matter, and, therefore, can be applied to the detection of phases formed when materials are heated. The hydrates of many comr ounds, including those of nickel nitrate (61), chromium orthophosphate (Ilti), cupric chloride (66), magnesium sulfate (55), and chromic chloride (84), liave been studied. A study of the sy!,Lem of magnesium oxidemagnesium chloride-water (26, 29) has shown four hydrated oxychlorides. Ilatz and IZedcIsdy (67) have used the method to shohv the existence of a new hydrate of aluminum arsenate. Phase equilibria in €,teases has been studied by a number of investigators (27, IW.%'-lZ4). Pe*loff (90) has used the method to distinguish between two forms of aniydrous gallium orthophosphate. Heats of Reaction. The relationship of the pe2k area in a thermogram to the heat ci' reaction has been discussed by 33orchardt and Daniels (16), Ramachandran and Bhattacharyya (95), and many others. Borchardt and D sniels have determined the heat of d ?composition of benzenediazonium diloride to be -37.0 kcal. per mob: and the heat of reaction of ethyliodide with N,N-dimethylaniline to bi? -20.4 kcal. per mole. The application of differential thermal analysis as a microcalorimeter has been
demonstrated by Wittels (I%$), Allison (4), Sabntier (101), and Talibudeen (118). Sabatier (101) has given heats of dissociation in calories per gram: gypsum 153, zinc carbonate 114, magnesium carbonate 302, and calcium carbonate 404. Stone (lis), using the dynamic gas method of differential thermal analysis (111),determined the heat of dissociation of magnesite to be 10.1 kcal. per mole. The thermograms showed increasing decomposition temperature with increasing carbon dioxide pressure. When log p is plotted against 1/T, the Clausius-Clapeyron equation, the slope of the plot, -A€I/R, can be used to determine the heat of reaction. Borchardt (16) has recently considered the kinetic effects in this method of determining heats of reaction, and has concluded that i t is probably a valid procedure. A practical application of this aspect of differential thermal analysis has been made with coal. Payne (88) has determined the AH values of semibituminous coals by differential thermal analysis, and has found that they compare favorably with values obtained by peroxide bomb technique. Glass (33) has been able to correlate the differential thermal analysis curves of coking coals with standard rank classification. Clegg (15) has presented an extensive report on experimental factors that modify thermograms of bituminous coal. QUANTITATIVE ANALYSIS
Quantitative differential thermal analysis has been reported by a number of investigators. The relationship of the peak area to the heat of reaction has been shown by Kracek and associates (34, 62), Alexander, Hendricks, and Nelson ( Z ) , Schafer and Russell (IO$, Berg (8),and many others. Recently, de Jong (53) published a detailed verification of the usage of peak area for quantitative measurements from an instrumental aspect. Apart from this, the thermograms of a material are often affected by the impurities present. Variations in dolonite thermograms have been determined as a function of contaminants ($6, 106). Impurities have marked effects on the thermograms of kaoIin (75), calcium carbonate (117), ammonium nitrate ( I ) , and mullite (78). Lehmann and Fischer (65) have pointed out that the determination of quartz in clays may have interference from dehydration unless the sample is rapidly heated. Berkelhamer (12) has determined quartz in calcium and Schedling (104) reported that quartz can be determined in dusts a t concentrations of approximately 1%. Carthew (21) recently studied the 600" endothermic peak of
kaolinite. He found that an empirical relationship between the slope ratio of the peak and the ratio of area to width of the peak a t half amplitude gives a quantitative measurement of kaolinite, independent of particle size distribution and degree of crystallinity. Heystek (47) has applied differential thermal analysis to the qualitative determination of gangue minerals in chrome ores. Under favorable conditions, the thermograms can lead t o quantitative data. Recent trends in clay analysis involve complex formation with organic niolecules. Sand and Bates (102) have used ethylene glycol to form a complex with endellite in the presence of halloysite and kaolinite. The endothermic peak of the endellite complex allowed quantitative determination of this component to within 3y0 of the weighed amount. Konta (60) has used this technique for montmorillonite identification. Allaway (3) has investigated the differential thermal analysis of piperidine-clay complexes.
(122-126) was one of the first in this field. Pirisi and Mattu (93) have applied this technique to a number of organic compounds, including benzoic acid and sodium benzoate, 0-, m-,and p-aminobenzoic acids (92) and succinic acid, ammonium succinate, succinamide, and succinimide (91). Morita and Rice (74) first applied this method to polymeric materials, investigating the thermal phenomena associated with polg(viny1 chloride) and vinyl chloridevinyl acetate copolymers. Subsequent investigations by Alorita have demonstrated the applicability of this technique to the study of polyglucosans (73) and starch and related polysaccharides (72). IClurphy and coworkers (77) have recently applied differential thermal analysis to the study of cure in a series of Vibrin 135 resins prepared with different heat treatments. This technique has differentiated betveen two fundamentally different curing exotherms. Different polymerization catalysts produced markedly different effects in the final polymer.
SOLID STATE REACTIONS
The number of solid state reactions studied by this technique has been very extensive. Haul and Schumann (48) investigated the reaction between manganese dioxide and iron pyrites. Although manganous sulfate was formed, incompleteness of reaction eliminated consideration as a commercial process. Differential thermal analysis has also been used to study the formation of zinc-chromium spinel (80). Greenberg ( S 7 ) , Kalousek, Logiudice, and Dodson ( 5 4 ) , and Kewman (M)have applied the method to studies of reactions in the calcium hydroxide-silica-water system. The reaction of iron, alumina, and sodium hydroxide has been investigated by Smothers and Chiang (108). The reaction of alkali monohydrogen sulfate with monohydrogen phosphate was shown ( 6 ) to produce sodium sulfate and dihydrogen phosphate. Differential thermal analysis has been applied to solid state reactions occurring in phosphor formation (81, 98). Crandall and West (28) have used differential thermal analysis to study the oxidation of cobalt by alumina. The oxidation of uranium dioxide by air has been shown by Johnson (62). Differential thermal analysis has also been applied to the decomposition of heteropoly acids of molybdenum and tungsten (130). ORGANIC APPLICATIONS
I n general, application of differential thermal analysis to organic materials has not progressed very rapidly. The study of greases by Vold and associates
CATALYST STUDIES
Stone and Rase (114) have shown that differential thermal analysis can be used to measure the act,ivity of silica-alumina cracking catalysts. Fischer catalysts have been studied by Trambouze (120). I n this work, it has been shown by differential thermal analysis patterns of variously prepared nickel precipitates that a close relationship exists between the conditions of precipitation and catalytic activity. Hauser and le Beau (44) have used differential thermal analysis to assist in studies of reactivity of alumina and silica gels. Murphy (76) has used a differential thermal system to study the recombination coefficient of oxygen atoms on various surfaces. The system used incorporated differential thermocouples in the apparatus developed by Linnett and Marsden (66). KINETICS
To extend the usefulness of differential thermal analysis, many investigators (79, 106, 107) have attempted to obtain kinetic data. Borchardt and Daniels (16) have applied the method and obtained kinetic data for the decomposition of benzenediazonium chloride and the reaction of ethyl iodide with N,hTdimethylaniline. Data obtained were in good agreement with those reported using other techniques. Kissinger (69) recently has derived an expression relating peak temperature a t different heating rates to kinetic quantities. Borchardt (16) has applied kinetics t o magnesium carbonate decomposition.
LIl'ERATURE CITED
Alekseenko, L. A,, Boldyrev, V. V., Zhur, Priklad. Khim. 29, 529 (1956). Alexandw, L. T., Hendricks, S. B., Nelson, R. A., Soil Sci. 48, 273 (1939). Allaway, W, H., Soil Sci. SOC. Amer., Proc. 13, 183 (1948). Allison, E. B., Silicates Ind. 19, 363 (1954). Ashley, 1%.E., J . Ind. Eng. Chem. 3, 91 * ( l E l l l ) . Audrleth, L. F., XIills, J. R., Netherton, L. E., J . Phys. Chem. 482 (1'354). Austen, R., Fifth Rept. Alloys (7) Research Comni., Proc. Inst. Mech. Eng. 1899, 35. Berg, L. G., Compt. rend. acad. sci. U.R.S.S. 49,648 (1945). Berg. L. G., Rassonskays, I. S., Dolilaily Acad. Nauk S.S.S.R. 73, 113 (1950). Berg, P. W., Ber. deut. Keranz. Ges. 313, 231 (1953). Berkelhz.mer, L. H., U. S. Bur. Mines, Rept. Invest. 3762 (1944). Ibid., 37153.
Berkelhz,mer, L. H., U. S. Bur. Mines, Tech. Paper 664 (1954). Boersma, S. L., J . Am. Ceram. SOC.33, 281 (1955). Borcharclt, H. J., J . Phys. Chem. 61, 827 (1957). Borchardt, H. J., Daniels, F., J . A m . Chem. SOC.79, 41 (1957). Brewer, L., Greene, F. T., J. Phys. Chem. Solids 2, 286 (1957). Brewer, L., Zavitsanos, P., Ibid., 2,284 (1957). Budnikov, P. P., TresvyatskiI, S. G., 13gneupory 20,166 (1955). Burgess, G. K., U. S. Bur. Standards, 13ull. 5 , 199 (1908-9). Carthew, A. R., Am. Mineralogisl 40, 107 (1955). Carthew, A. R., Cole, W. F., Austrcilian J . Instr. Technol. 9, 23 (1053). Chatelier, H. le, Bull. SOC. franG. minertrl. 10, 204 (1887). Chatelier, H. le, 2. physik. Chem. 1 , 396 (1887). Clegg, K. E., Ill. State Geol. Survey',Rept. Invest. 190 (1955). Cole, JV* F., Demediuk, T., Australian J . Chem. 8 , 234 (1955). Cox, D. B., RfcGlynn, J. F., ANAL. CHEW 29, 960 (1957). Crandall, W. B., West R. R., J . Am. Ceram. SOC.35, 66 (1956). Demediuk, T., Cole, W.F., Hueber, H. V., Australian J . Chem. 8, 215 (1955). Fenner, C. N., Am. J . Sci. 36, 331 (1913;. Gale, R., Rabitin, J., unpublished resultri. Gamel, C. M., Smothers, W. J., Anal. Chim. Acta 6,442 (1952). Glass, H. D., Fuel 34,253 (1955). Goranson, R. W., Kracek, F. C., J . P h p . Chem. 36, 913 (1932). Gordon, S., Campbell, C., ANAL. CHEW27, 1102 (1955). Graf, D. L., Ill. State Geol. Survey, Rept. Invest. 161 (1952). Greenberg, S. A., J . Phys. Chem. 61, 373 (1957). Grim, IL. E., Ann. N . Y . Acad. Sci. 5.1, 1031 (1951). Grim, 13. E., Rowland, R. A., J . A m . Ceram. SOC.27. 65 (1944). (40) Grimshaw, R. W., T;ans.* Brh. Ceram. Sac. 44,72 (1945). (41) Grimshaw, R. W., Heaton, E., VOL. 30, NO. 4, APRIL 1958
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Roberts, A. L., Ibid., 44, 87 (1945).
(42) Haul, R. A. W.,Heystck, H., Am. Mineralogist 37, 166 (1952). (43) Haul, R. A. W.,Schumann, H. J., J . S. African Chenz. Inst. 8 , 80 (1955). (44) Hauser, E. A., le Beau, D. S., J . Phys. Chenz. 56, 136 (1952). (45) Hauser, R. E., thesis, N. Y. State College of Ceramics, Alfred University, Alfred, N. Y., 1953. Herold, P. G., Plange, T. J., J . Am. Ceram. SOC.31, 20 (1948). Heystek, H., Bull. Am. Ceranz. SOC.35, 133 (1952). Hiller, J. E., Probsthain, IC., Erzmetall 7, 257 (1956). Houldsm-orth, H. S., Cobb, J. W., Trans. Brit. Ceram. SOC. 22, 111 (1922-33). Insley, H., Endl, R. H. J . Research Natl. Bur. Standards 14, 615 (1935). Jaffray, J., Rodier, N., J . recherches centre natl. recherche sci. Lab. Belleme (Paris) No. 31, 282 (1955). Johnson, J. R.. J . Metals 8 . 660
I
Proc. Intern. Symposium Reactivity of Solids, Gothenburg, 1952,
(55) (56)
(94)
(95)
(97)
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ANALYTICAL CHEMISTRY
Schedling, J. A., Chim & ind. (Paris) 69, 1066 (1953). Schwob, Y., Contpt. rend. 224, 47 (1947). Segawa, I
