On the Dissimilarities in Solid, ~r Solid, Phase Transformations Paul D. Garn The University of Akron, Akron, Ohio 44304 The behaviors of materials undergoing crystalline phase transitions have been assumed to be much simpler than they are in fact. Of twelve species selected for possible use as dynamic temperature standards, only three yielded near-“ideal” DTA curves. Supercooling, skewing, and superheating are among the effects observed by thermal methods.
LEN
TWO P E N
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THECOMPARISON of thermoanalytical data obtained in different laboratories has been difficult for a number of reasons, one of which is lack of a suitable temperature reference scale by which the recorded temperature could be corrected. This need for correction is brought about by differences in experimental apparatus but because these differences generally have good reason for being, the apparently simple solution of standardizing on a single type of apparatus is undesirable as well as being impracticable. Neither differential thermal analysis curves nor thermogravimetric analysis curves are normative for the substance examined. In this, both techniques differ from absorption spectrophotometry or X-ray diffraction. While the thermograms obtained on one instrument will ordinarily bear a close resemblance to thermograms obtained for the same material on another instrument, there are deviations large enough and common enough to cause great concern. Several authors have attempted to describe DTA peaks mathematically, although seldom completely. Smyth (I) had studied the temperature distribution within a specimen by using a mathematical model, assuming a moving interface between phases. Vold (2) set up a differential equation using constants containing parameters which are not constant. Sewell and Honeyborne (3) set up a model describing the behavior of a system undergoing a first-order decomposition or a reversible phase change but their treatment requires coexistence of reacted and unreacted materials for finite times, so the application to phase transformations is questionable. Deeg ( 4 ) treats the phase change in the “advancing front” method used also by Smyth, but notes that a self-contained analytical form is not possible. Kissinger (5)andWilburn,HesfordandFlower(6) choose to assume a priori that the differential thermal analysis dx
A ( l - X)” exp (- E/RT). dt Kissinger then defines a “shape index” by which an apparent order of reaction can be estimated, while Wilburn ef ai.,used the curve as a model in an electrical analog treatment of variables in heat flow. Their treatment has the interesting property of predicting an exothermic indication following an endothermic event for a particular class of sample holder. The equation does not describe the peak for materials cited in either work ( 5 , 6 ) and certainly does not describe Solid12 Solid2 transitions.
peak can be described by
- =
(1) H. T. Smyth, J . Amer. Ceram. Soc., 34, 221 (1951). (2) M. J. Vold, ANAL.CHEM.,21, 683 (1949). (3) E. C. Sewell and D. B. Honeyborne, in “The Differential Thermal Investigation of Clays,” R. C . Mackenzie, Ed. Mineral SOC., London, 1957. (4) E. Deeg, Ber. Deut. Keram. Ges., 33, 321 (1956). (5) H. E. Kissinger, ANAL.CHEM. 29, 1702 (1957). (6) F. W. Wilburn, J. R. Hesford, and J. R. Flower, ibid., 40, 777 (1968).
MILLIVOLT
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RECORDER
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1 1-mCLA.TN
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SUPPLY
SILICON
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CONTROLLED
RECTIFIER
Figure 1. Circuitry for differential thermal analysis of proposed temperature standards The small temperature span with precise zero offset permits a sensitive measurement of the several data points of Figure 2 Standard Test Materials. As the use of the technique of differential thermal analysis has progressed from qualitative identification to quite elaborate studies of reactions, the need to know the actual temperature of the sample more accurately has also grown. Many of the sample containments and measurement systems do not permit the direct recording of the temperature of the sample. Standardization on a particular type, or even a few types of sample vessel is not desirable because the several designs are characterized, generally, by special utility for particular types of measurement. The appropriate solution is the use of standard materials which undergo reproducible crystallographic phase transformations under the dynamic conditions of differential thermal analysis. These “dynamic conditions” comprise, in particular, a continual temperature increase or decrease, existence of a temperature gradient within the sample and variation in that temperature gradient, especially during the changes being studied (7). The need for standards of this type arises from attempts to correlate data from two or more laboratories. For illustration, consider two laboratories studying what is presumed to be the same compound but which yields different transition, fusion, or decomposition temperatures on the apparatus available at the two laboratories. Each laboratory could perform a differential thermal analysis on the nearest (in temperature) standard-if standards were available-and report both the observed temperature of the standard transition and of the (7) Paul D. Garn, “Thermoanalytical Methods of Investigation,” Academic Press, New York, 1965. VOL. 41, NO. 3, MARCH 1969
447
Table I.
Material Barium carbonate Potassium chromate Potassium nitrate Potassium perchlorate Potassium sulfate Silicon dioxide Silver sulfate
Average Temperatures of the Departure, Intersection, and Peak for the Tentative Standards at Two Heating and Cooling Rates Heating Cooling Heating rate Departure Intersection Peak Departure Intersection 2.8 "C/min 796.0 802.0 810.0 753.0 753.0 8.o 797.0 804.0 808.0 770.0 769.0 2.8 664.5 666.3 669.3 669.4 665.4 8.0 661.8 664.2 667.7 670.5 665.7 2.8 128.0 128.9 131.3 123.1 122.8 8.0 128.8 129.3 132.6 123.8 123.4 2.8 298.2 299.3 301.0 293.7 293.5 8.0 297.4 298.3 300.2 292.7 292.7 2.8 577.9 580.0 582.3 580.4 577.9 8.0 577.9 583.9 587.4 585.9 585.1 2.8 566.2 568.1 569.9 572.0 569.9 8.0 561.4 567.7 570.9 577.8 570.9 2.8 421.6 424.4 428.4 405.8 405.6 8.0 422.2 427.8 433.7 409.3 408.6
thermal event in the sample. The difference between these measurements will be the same if the materials studied by the two laboratories are the same compound. The problem of selecting materials for use as standards is prima facie very simple. The usual practice has been to name a few compounds with well known equilibrium transition or fusion temperatures. Only in the past few years ha5 a substantial effort been made to verify behaviors under the dynamic conditions of differential thermal analysis. Part of the reason for this gross oversight is the fact that some well known transitions behave almost ideally. Keith and Tuttle (8) had shown that the well known quartz transition occurred at virtually the same temperature on heating and cooling at 0.5 "C/min. This investigator, in testing the resolution of his first apparatus, ran a mixture of quartz and potassium sulfate (9) and found the transition temperatures for both materials t o be virtually the same for heating a n d cooling at a much higher rate (10 'Cjmin) than Keith and Tuttle had used. Because this investigator has studied decomposition reactions much more than transitions, the rarity of this behavior was not known t o him. By the time the monograph cited as Reference 7 was completed, this investigator had become aware that most Solidl 2 Solidz transitions were not simple. See, for example, the author's work on potassium perchlorate, cited therein. During the past three years, the Committee on Standardization of the International Conference on Thermal Analysis has been examining materials for potential utility as standards. The Committee reported on its work t o the Second International Conference (10) in August, 1968. The data reported herein were used in the computations for that report but they d o not appear uniquely nor are the conclusions derived therefrom a part of that report. These data are not at variance with the report but the conclusions are important supplemental information. A more complete report of this investigator's participation in that work may be found in his report t o the Air Force Material Laboratory (11). EXPERIMENTAL
Apparatus. GENERAL DESCRIPTION. The experimental apparatus comprises a differential thermal analysis apparatus
(8) M. L. Keith and 0. F. Tuttle, Artier. J. Sci., Bowen Vol., Pt. 1, 203 (1952). (9) P. D. Garn and S . S . Flaschen, ANAL.CHEM.,29, 271 (1957). (10) Thermal Analysis-Proceedings of the Second International Conference. Edited by R. F. Schwenker, Jr., and P. D. Garn. Academic Press, New York (in press). (11) P. D. Garn, Air Force Materials Laboratory Technical Report AFML-TR-68-139, Wright-Patterson Air Force Base, Ohio, Sept. 1968. 448
ANALYTICAL CHEMISTRY
Peak 750.0 775.0 664.3 665.1 122.2 123.1 293.8 292.4 578.3 584.3 569.0 569.2 413.6 414.3
assembled by this investigator. The display of temperature and temperature difference is made on a two-pen Speedomax G ( X I ,XZL'S. time) (12) strip chart recorder. The AT signal is amplified by a L & N 9835B stabilized microvolt amplifier. The programming is accomplished by use of a L & N motor driven cam programmer, modified to facilitate speed changing, a Speedomax H. C.A.T. recorder-controller, and a LABAC silicon controlled-rectifier power unit. The furnace assemblies used were the DTA 12 for the higher temperatures and DTA-LT for the lower temperatures. (13) The provisions for subambient temperatures on the latter permitted quicker cooling. In all cases the temperatures were measured at a point on the axis of and approximately in the middle of the specimen. The sample holder most commonly used was a high-density alumina block 2.5 cm in diameter with sample wells 15 mm deep and 4 mm in diameter. Bare-wire thermocouples, (0.25 mm), entered axially from the bottom. They were supported by a ceramic insulator except for ca. 2mm. The bead was positioned approximately at mid-height along the axis. The cavity was filled t o about bead level and the powder pressed down with a firm finger pressure. Sample was added to ca. 10-mm depth and pressed again. (At this depth general pressure could be exerted without displacing the thermocouple.) Finally, the cavity was filled and the material pressed again. The sample weight varied with the material because of the differing densities; they ranged from 0.48 to 0.97 grams. Special Modifications. Because of this investigator's awareness of the probability of supercooling, superheating, and kinetic effects, the experimental conditions were chosen so that these effects could be detected. The principal requirement was a time-based recorder moving at a reasonably high rate. An important adjunct was a method of spreading a small temperature range over the entire chart without losing accuracy of measurement. The two-pen strip chart recorder was modified slightly to provide a 32-inch/hr chart speed and millivolt spans of 1 or 5 mV to serve as the temperature span. The 1-mV span was used with platinum cs. platinum: 10% rhodium thermocouples and the 5-mV span with base metal thermocouples. By providing a n offset voltage from a millivolt potentiometer, the millivolt output from the sample thermocouple could be on scale during the heating transition and during the reversion no matter how severe the supercooling. The circuit is shown in Figure 1. For convenience and economy of chart paper, a switch on the temperature pen shaft causes the chart t o drive only while the temperature pen is on-scale. The programmer-controller was wired to reverse the program drive when the control thermocouple reached a pre-set temperature and to shut off the apparatus when the program temDerature was somewhat below room temperature. The (12) Leeds & Northrup Co., 4901 Stenton Ave., Philadelphia, Pa. (13) Apparatus Manufacturers, Inc., P.O. Box 184, Kent, Ohio.
rDEPARTURE
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1 HEATING
COOLING
TIME Figure 2. Representation of an endotherm and exotherm with the temperature trace The departure, intersection, and peak, measured from the temperature line, are given for each of the selected thermograms shown in Figures 3-13
---
TIME
-
Figure 3. Selected thermogram chart record for barium carbonate, rapid heating The data points are: Departure Intersection Peak
Heating 796.7 801.9 807.9
cooling 776 776 782
VOL. 41, NO. 3, MARCH 1969
449
T‘
Figure 4. Selected thermogram chart record for potassium chromate, slow heating The data points are: Departure Intersection Peak
Heating 662.7 664.7 667.5
cooling
666.6 665.4 664.5
TIME
-
Figure 5. Selected thermogram chart record for potassium nitrate, slow heating The data points are: Departure Intersection Peak 450
ANALYTICAL CHEMISTRY
Heating 130.5 131.8 135.5
cooling
124.8 124.0 122.8
TIME
-
Figure 6. Selected thermogram chart record for potassium nitrate, rapid heating The data points are: Departure Intersection Peak
programmer gears selected gave heating rates of 8.0 and 2.8 “C/min. These are the rates referred to as “fast” and “slow” heating. Experimental Procedure. Except for potassium nitrate, the sample materials were used as received; this was in accordance with the procedure set forth by the Committee. (The sources of the sample materials are listed in Appendix I.) Potassium nitrate was crushed (mortar and pestle) to a size which could be packed suitably. The specimen was transferred to the sample cavity in the block and pressed down firmly. (A specimen of calcined alumina was used as the reference material.) The furnace tube was set in place and the furnace chamber flushed with nitrogen. The flow of nitrogen was cut back to 15-20 ml/min at the start of the run. The temperature limit was set (on the recorder-controller) to about 20 “C above the transition temperature. The offset voltage was set on the millivolt potentiometer so that the transition temperature was near or slightly above midscale; this ensured that the reversion temperature on cooling would also be on scale. The switches establishing a heating-cooling program were set and the program was begun. At the termination of the program the sample was blown out of the sample cavity in preparation for the next run. Data. The data called for by the Committee are indicated in Figure 2. The average values of these points are shown for the several compounds in Table I. A complete tabulation is given in Reference 11. Figures 3-13 are tracings of portions of typical charts showing the endothermic and exothermic peaks. Although the data are shown to 0.1 “C, the reading accuracy, the recorder accuracy limits the relative accuracy within a run to ca. 0.3 “C. The accuracy of the potentiometer introduces a n absolute uncertainty of 0.5-0.8 “C, but within the set of data on a particular compound the relative uncertainty should be no more than 0.5”, because the error in setting the potentiometer should be quite repeatable.
Heating
cooling
128.8 129.2 133.5
124.2 123.5 123.0
DISCUSSION
The data clearly show that the experimental arrangement can provide good measurements of the several points considered to be of interest in a differential thermal analysis peak. They also show that only a few of the transitions behave ideally, that is, transform rapidly from one form to another depending solely on temperature. Supercooling (or superheating, as they are not easily distinguished) is common. If the behavior were ideal, the temperature in the center of the specimen at the endothermic and exothermic peak would be identical and equal to the thermodynamic transition temperature (7). (For systems in which the temperature is measured at the edge of the specimen, the break away from the base line should be the transition temperature; no other points have any clear significance.) The deviation from ideality is indicated by a lower transition temperature on cooling. In some cases there is a clear supercooling phenomenon; this is shown by the peak cooling being higher in temperature than the departure from the base line. The specimen has cooled beyond its transition temperature but once the change to the lowtemperature form has begun, the heat of transition raises the temperature of the specimen. This rise in temperature also accelerates the reversion so the peak shape is changed compared to the heating peak. While superheating is present in some cases, supercooling is clearly the principal deviation from ideality. Purely as an empirical measure of the deviation, the differences between the peak temperatures (averaged) on heating and the breakaway and peak temperatures on cooling are shown in Table 11. Considerable variation, as well as considerable magnitude, is immediately obvious. A fact which is less obvious and which is virtually hidden by standard methods of recording is the variation in behavior during heating. Nearly symmetric peaks and badly skewed VOL. 41, NO. 3, MARCH 1969
451
Figure 7. Selected thermogram chart record for potassium perchlorate, slow heating The data points are: Departure Intersection Peak
Heating
cooling
298.2 299.2 301.5
294.0 293.8 294.5
2
3 Q
m
W
3 C
3)
m
TIME
-
Figure 8. Selected thermogram chart record for potassium perchlorate, rapid heating The data points are: Departure Intersection Peak 452
ANALYTICAL CHEMISTRY
Heating
cooling
298.5 299.8 302.0
294.0 293.1 293.5
I
I
I I I
I
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I
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TIME
-
Figure 9. Selected thermogram chart record for potassium sulfate, slow heating The data points are: Departure Intersection Peak
I
TIME
Heating
cooling
577.6 580.0 582.0
581.1 580.7 580.0
-
Figure 10. Selected thermogram chart record for silicon dioxide, rapid heating The data points are: Departure Intersection Peak
Heating
Cooling
562.1 568.6 571.8
579.8 571.2 569.5 VOL.
41, NO. 3, MARCH 1969
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TIME
-
Figure 11. Selected thermogram chart record for silver sulfate, slow heating The data points are: Departure Intersection Peak
Heating
cooling
424.6 426.2 431.2
403.2 403.2 410.3
TIME
-
Figure 12. Selected thermogram chart record for silver sulfate, rapid heating The data points are: Departure Intersection Peak 454
ANALYTICAL CHEMISTRY
Heating
Cooling
424.8 429.8 436.0
402.6 401.8 410.6
TI M E
-
Figure 13. Selected thermogram chart record for potassium bisulfate The data points are: Departure Intersection Peak
peaks are both common, as are sharp breaks away from the base line and gradual deviations. The sharp break away from the base line suggests superheating, while the nearly symmetric peaks suggest a rate-controlled process or other variation from the simple zero-order thermodynamically reversible phase transformation. The slow-heating thermogram of potassium nitrate (Figure 5 ) shows irregularities which are partially-but not wholly-caused by the relatively large particle size of the specimen. By agreement, the specimens were to be used “as received,” and this material was in pieces ranging up to more than 1 mm across. Nevertheless, the cooling data agree well with data obtained on specimens crushed to about 200 k . The shoulder on the cooling curve shows that this transition is not simple. In larger crystals the phase change occurs in two steps (14). The rapid-heating thermogram of Figure 6 also shows the shoulder clearly on cooling. Only a little willingness and/or a straightedge enables perception of the shoulder on the heating peak, too. Potassium perchlorate shows a very pronounced shoulder on the cooling peaks as well as a skewing of the heating peaks. This is possibly a problem in heat transfer, but also possibly because of a rate-limiting process. Figure 11 was obtained at a relatively-low amplification to accentuate the distortion of the peak. In the conventional practice of obtaining peaks as near to fullscale as possible such skewing disappears. (The common practice of recording the differential temperature against the temperature rather than time also conceals the actual form of the peak because the (14) F. C. Kracek, J. Phys. Chern., 34, 225 (1930).
Heating
Cooling
175.8 176.5 175.2
140.8 140.5 142.3
temperature axis is changing more slowly during a transition than during steady-state heating.) Figure 12 shows a peak at higher amplification as well as heating rate. The skewing of the peak is far less perceptible, although none-the-less real. Figure 13 shows very clearly a case of superheating. The potassium bisulfate specimen was unique among these materials. Even the existence of one proven case suggests the possibility of superheating effects in other materials. Keeping in mind that the heat which can be given up is only the “surplus heat capacity” while the process using up the heat is a phase transition with a very considerable change in enthalpy without change in temperature, one may easily deduce that small superheatings would disappear in the face of the overwhelming absorption of heat. The existence of the temperature increment in a particular particle would not be apparent in the temperature signal because the thermocouple “averages” the temperatures of the particles in contact with the junction or bead. The Table 11. Apparent Supercoolinga of the Several Compounds Apparent Supercooling at Compound 2.8 “C/min 8.0 “Cimin Barium carbonate 60 “C 33 “C Potassium chromate 5.0 2.6 Potassium nitrate 9.1 9.5 Potassium perchlorate 7.2 7.8 Potassium sulfate 4.0 3.1 Silicon dioxide 0.9 1.8 Silver sulfate 14.8 17.4 a “Apparent Supercooling” is defined arbitrarily as the difference between the average peak temperatures on heating and on cooling. VOL. 41, NO. 3, MARCH 1969
455
superheating would more probably be seen as a delay in the start of the transition evidenced by a sharp break away from the base line, as in the case of potassium perchlorate (Figures 7 and 8). From the data shown herein, the known Solidl 2 Solidz phase transformations can be expected to show a wide range of behavior. Some, like silicon dioxide (quartz), potassium sulfate, and potassium chromate, show near-ideal behaviori.e., undistorted peaks and small apparent supercooling. Other transitions of similar quality probably will be found. On the other hand, the data also suggest that the near-ideal behavior will be exceptional. Four materials were rejected during the study by agreement among the committee, so, of twelve materials selected (by a committee of experts), only three show deviations which may be termed minor. The experimental technique is clearly useful for the observation of behavior during phase transitions and for detecting and measuring deviations from ideal behavior. It is quite improbable that any single expression will provide an accurate representation of Solidl 2 Solid2 curves; nevertheless, some information concerning the nature of the processes causing these dissimilarities should be obtainable from the deviations from the behavior of, for example, potassium sulfate.
APPENDIX I
Origins of materials tested for possible use as standards: KNOI Mallinckrodt A. R. Crystal KHSOd Merck Pro Analys Reagent KC104 Mallinckrodt A. R. Crystal Ag2SOa Prolabo R. P. (Rhone-Poulenc) Batch No. 66319 SiOz Fisher Scientific Co. Lot No. 762490 KzSO Micro Analytical Reagent (Hopkins and Williams) KZCrO4 AnalaR Grade Lot No. 0011540 BaC03 Merck Pro Analys Reagent AlZO3 (Reference) Aluminum Co. of America Tabular Alumina T-61 RECEIVED for review September 10, 1968. Accepted December 20, 1968. This work was supported principally by the Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio, through the Monsanto Research Corporation, Dayton, Ohio. The author is also grateful to the National Science Foundation for its partial support in equipment through an institutional grant and in time through research grant NSF GP-5060. Presented before the Division of Analytical Chemistry, 156th National Meeting, ACS, Atlantic City, N.J., September 1968.
A Single Scale for Ion Activities and Electrode Potentials in Ethanol-Water Solvents Based on the TriisoamylbutylammoniumTetraphenylborate Assumption Orest Popovych and Aloys J. Dill1 Department of Chemistry, Brooklyn College of the City University of New York, Brooklyn, N . Y . 11210 Medium effects for individual ions enable us to express standard electrode potentials and ion activities in different solvents on a single aqueous scale and to evaluate liquid-junction potentials at aqueous-nonaqueous interphases. Existing methods for the estimation of medium effects of single ions are summarized. In the present approach, the medium effect log m~ of triisoamyl-n-butylammonium tetraphenylborate (TAB BPha) is apportioned equally between the anion and the cation. On this basis, values of log m~ are estimated for H-, K+, CI-, TAB+, BPh,-, and picrate ions throughout ethanol-water range. In ethanol-water mixtures, the solvation energy of the proton is lower than in the pure solvents and passes through a minimum. Conventional EO’S in ethanol when referred to the aqueous SHE become positive by about 0.1 V. The residual liquidjunction potential between an ethanolic buffer and an aqueous KCI bridge is of the order of 60 mV.
As OF NOW there are no generally accepted solutions to the following interrelated problems : the establishment of a single solvent-independent scale for pH and for other ion activities, referred to their aqueous standard states; the formulation of a solvent-independent standard potential series having a single reference point E o H = 0 volts in water only; the evaluation of liquid-junction potentials at aqueous-nonaqueous interphases. By convention, the activity of a solute is referred to Present address, Paul D. Merica Research Laboratory, International Nickel Co., Sterling Forest, Suffern, N.Y. 10901 456
ANALYTICAL CHEMISTRY
infinite dilution in the given solvent as the standard state. Similarly, the emf series in any solvent has as its arbitrary zero the standard hydrogen electrode (SHE) in the same medium. As a result, there can be as many independent activity scales and emf series, as there are solvents. The key to the solution of the above three interrelated problems lies in the knowledge of medium effects for single ions. The medium effect, usually expressed in logarithmic form, is a measure of difference between the standard free energy of a solute i in water (&Oi) and in the given nonaqueous solvent (sGoi)(1-4): sGoi - wGoi = RT Inmy,
(1)
Subscripts s and w denote nonaqueous and aqueous standard states, respectively. For example, using a known medium effect for the proton in a given nonaqueous solvent, we could convert a conventional paH* value, referred to infinite dilution in that solvent, to its counterpart on a single paH scale, referred to the aqueous standard state: (1) R. G. Bates, “Determination of pH,” Wiley, New York, N.Y., 1964, Chapters I , 8. (2) R. G. Bates in “The Chemistry of Non-Aqueous Solvents,” J. J. Lagowski, Ed., Academic Press, New York and London, 1966, Chapter 3. (3) E. J. King, in “The International Encyclopedia of Physical Chemistry and Chemical Physics,” E. A. Guggenheim,J. E. Mayer, and F. C. Tompkins, Eds., Macmillan, NewYork, N.Y. 1965, Vol. 4. (4) 0. Popovych, ANAL.CHEM., 38, 558 (1966).
