Measurement of Specific Heat Functions by Differential Scanning Calorimetry

M. J. O'NEILI The Perkin-Elmer Corp., Norwalk, Conn.

When a sample material is subjected to a linear temperature program, the heat flow rate into the sample is proportional to its instantaneous specific heat. By recording -dH this heat flow rate as a function of dt temperature, and comparing it with the heat flow rate into a standard material under the same conditions, t the specific heat of the sample is de- II termined as a fundion of temperature. II The method is illustrated by measure- I II ments on various samples in the tem- T2---l--- ' perature range 340" to 510" K., and agreement with literature specific heat values is demonstrated. The ultimate precision of the method is 0.370 or better, which approaches the Tk=-tFigure 1. Linear temperature program precision of adiabatic calorimetry. However, measurements may be made with samples which are four orders of magnitude smaller, and program transition heat effects may be obtained two sample holders, using platinum rates two orders of magnitude larger, by comparison of heat content values resistance thermometers and heating than those typical of conventional on both sides of the transition tempera- elements embedded in the sample calorimetry. ture, but this method is unreliable when holders. A secondary temperature the difference is small. control system measures the tempera- At temperatures above 350" K., ture difference between the two sample ETERMINATION of specific heat is specific heats in the absence of sharp holders, and adjusts this difference to D accomplished in two ways, de- transitions are obtained by differentia- zero by controlling a differential com- pending on the temperature range in tion of the algebraic function of T ponent of the total heating power. which the property is to be measured. which best fits the measured heat This differential power is measured and From cryogenic temperatures to ap- content data. It is evident that this recorded. proximately 350" K., adiabatic calorim- process can lead to percentage errors eters are used, while at higher temper- in the specific heat which are con- SPECIFIC HEAT DETERMINATION atures the drop calorimeter, using the siderably greater than the errors in the method of mixtures, is preferred. Rep- original measurements. The ad- In order to measure the specific heat resentative adiabatic calorimeters and vantages of a technique which would of a sample, the sample holder tempera- drop calorimeters have been described permit the direct measurement of ture is programmed as shown in Figure in detail in the literature (I, 4, 12). specific heat and determination of heat 1. To establish a base line, the pro- A common feature of these calorim- content changes by integration of the gram is carried out with no sample eters is that in order to achieve pre- specific heat function are clear. present; however, empty aluminum cision their applicability in routine foil sample containers are placed in the laboratory analysis has been seriously sample holders. Isothermally, the base compromised. Analysis time is pro- DIFFERENTIAL SCANNING CALORIMETRY line indicates the differential losses of hibitively long, large samples are re- A new instrumental method for the the two sample holders at the initial quired, and sample geometries must be direct measurement of specific heat has temperature. When the program begins, carefully controlled. been developed. In differential scan- there may be a small offset from the A more fundamental objection to ning calorimetry (DSC), the sample isothermal base line, caused by the these techniques concerns their pre- material is subjected to a linear tempera- thermal capacity mismatch between the cision at transition temperatures in the ture program, and the heat flow rate two sample holders and their contents. sample material. In the adiabatic into the sample is continuously When the temperature program ends, calorimeter, adequate resolution of measured; this heat flow rate is pro- the isothermal base line reappears. sharp transitions is possible only at portional to the instantaneous specific This procedure is then repeated, with extremely slow scanning rates, and with heat of the sample (7, 11). a weighed sample added to the sample a resultant loss in sensitivity and Two sample holders are mounted holder. The isothermal base lines are signal-to-noise @/A') ratio. In the symmetrically inside an enclosure which unaffected, since the sample has no drop calorimeter, heat contents re- is normally held at room temperature. influence on the power dissipation of the ferred to a standard temperature A primary temperature control system sample holder. However, there is an (usually 298.15' K.) are measured; controls the avcrage temperature of the additional off set from the programming

VOL. 38, NO. 10, SEPTEMBER 1966 1331 -dH dt

BASELINE

LtI_ I I""I~"'l*'",l Figure 2. C, calculation by ratio method STARTf UO 400 450 SO0 LTOP T- *K Figure 3. Base line, calibration, and sample analysis base line, owing to the absorption of heat by the sample. If the sample is result. However, these two parameters are the mass and specific heat of the entirely enclosed by the sample holder, may be eliminated from the calculation standard, and K is the ordinate calibra- every elementary volume within the if a material with a known specific tion factor, in cal. inch-' sec.-l sample must eventually arrive at the heat is used to calibrate the instrument. Dividing Equation 3 by Equation 4, program rate dT/dt prescribed by the Such a material is a-aluminum oxide, and rearranging terms: sample holder, after a transient effect, or synthetic sapphire, for which the the duration of which depends on the CP - m'y specific heat has been determined to five (5) size and thermal diffusivity of the significant figures in the temperature C,' my' sample. Therefore the heat flow rate range 0" to 1200' K. (3). into the sample is given by Figure 2 illustrates the method. Thus the calculation requires only the comparison of two ordinate deflections dT After the base line and sample programs, = mC,- a third program is run with a weighed at the same temperature. It will be at at sapphire standard. At any tempera- observed that the calculation would be ture T, the following equations apply: correct even if the ordinate calibration where dH/dt is the heat flow rate in and the program rate were temperature- calories second-', m is the sample mass dT dependent. In fact, the ordinate in grams, Cp is the specific heat in Ky = mC, - (3) calibration varies by less than 2% over calories gram-' O K.-l, and dT/dt is the dt the operating temperature range of the program rate in O K. sec.-l instrument. However, the program It follows that the area under the ld_T 5% Ky' = m'C, (4) rate may vary by as much as in a dH/dt curve between any two tempera- at 100" K. interval, owing to the inevitable tures is the change in heat content, as nonlinearities in the temperature shown by Equation 2: where y and y' are the ordinate de- calibration and in the temperature flections in inches due to the sample and control system. Thus Equation 5 the standard, respectively, m' and C,' represents the better method of calcula-

This illustrates the difference between scanning calorimetry and the drop calorimeter technique, where the heat content is the measured property, and the specific heat is obtained by dif- ferentiation. Although every part of the sample is programming at exactly the same rate eP dT/dt, the true temperature of the CAL. MOLE:' DE^' sample differs slightly from the indicated temperature of the sample holder, owing to temperature gradients which appear within the sample and at the interface between the sample and the sample holder. The gradient at the interface is always much larger than the gradient within the sample, and is one of the sources of error to be discussed later. In order to use Equation 1 in a specific heat calculation, the ordinate calibration and the temperature program rate must be known with at least TEMPERATURE *K the precision required of the final Figure 4. Specific heat of graphite, 39.7 mg.

1332 ANALYTICAL CHEMISTRY 4.0 4 X lo-' cal. sec.-', which was left uncorrected. The ordinate calibration is shown for reference. For each sample, C, was calculated at intervals of lo", using the method of 3.0 Equation 5, and the data were plotted against a temperature abscissa. Figures

4 and 5 show the calculated specific CP heat functions for graphite and GAL. MOLE? DEC' diamond. These samples are unusual, in 2.0 that their specific heats are quite small

and very temperature-dependent. In accordance with the suggestion of Maier and Kelley (6), the heat content and specific heat functions of such samples are usually represented by '+o+ '+o+ expressions of the form H(T) - H(T0) = 0 b 300 350 400 450 500 550 UT + 2 T2+ cT-' - d (6) TEMPERATURE OK Figure 5. Specific heat of diamond, 70.2 mg. C, = a + bT - cT-2 (7)

tion. For repetitive determinations at had a weight of 129 mg. The tem- The four coefficients are chosen so that the function described by a single temperature, Equation perature scale was calibrated with 1 Equation matches the measured heat might be used with a calibration factor, melting point standards. 6 but with a considerable loss of accuracy. The ordinate data were recorded content function as closely as possible. with a Leeds and Northrup Speedomax Table I shows the comparison between G 10-mv. recorder, with a chart speed the DSC data and literature values for EXPERIMENTAL of 1 inch per minute. A full scale these samples. The first literature The procedure described above was deflection corresponded to a differential function for each sample was calculated carried out with the Perkin-Elmer Model heat flow rate of 1.4 X 10-2 cal. set.-', from recent heat content measurements DSC-I, on a number of samples for except for one sample (AgNO,), where twice this sensitivity was used. between 298" and 600" K. (2, 9, IO), which specific heat functions have while the second is the equation given been measured by other investigators. by Kelley (5), covering a much wider RESULTS AND DISCUSSION A temperature interval from 340" to temperature interval. 510' K. was used for all but one of the measurements to be discussed, where a Figure 3 illustrates a typical base line, Equations 9 and 13 are linear ap- slightly smaller interval was used. sapphire calibration, and sample proximations to the DSC data, obtained The nominal program rate was 20" K. analysis. The base line shows a down- by the least squares method. For minute-'. scale capacity offset of approximately graphite, the greatest departure from At the beginning and end of each program there are characteristic transient behaviors of the base line, asso- ciated with the distributed thermal capacity of the sample holders. In order to give the initial transient behavior time to disappear, the temperature program was started at 320' K. The analysis time was approximately 15 minutes, including 2 minutes of isothermal recording at the initial and final temperatures. Between analyses, 15 minutes were allowed for the sur- rounding enclosure to return to its original temperature distribution. All samples were encapsulated in the aluminum foil dishes supplied with the 300 350 400 450 500 550 instrument, which weigh approximately TEMPERATURE *K 20 mg. with their covers. It was Figure 6. verified by calculation that the small Specific heat of gold, 657 mg. weight variations between these dishes would contribute a negligible error to the measurement. Table 1. Specific Heat Functions It is important to cover the sample (Cal. mole-' K.-1) holders with the metallic covers provided. This ensures that the isothermal Graphite Diamond base line is unaffected by the presence Literaturea 1.56 + 4.53 x 10-3~- 1.io + 5,i4x 10-3~- or absence of sample. A front panel 8.22 X 104T-2(Eq. 8p 1.11 X (Eq. 1l)d control is provided to adjust for the Literatureb 4.03 + 1.14 X IO-ST - 2.27 + 3.06 x 10-3~- 2.04 X 106T-2 (Eq. 10)~ 1.54 X 10aT? (Eq. 12)d unbalance between the sample holder DSC -0.03 7.12 X (Eq. -1.15+8.85X10-8T(Eq.13)d losses at any temperature; this control + Qp a 298400" K. was used to make the base lines at 320' 298-2500' K. for graphite, 298-1200' K. for diamond. and 510" K. coincide. See Figure 4. The sapphire heat capacity standard See Figure 5. was supplied with the instrument, and

VOL. 38, NO. 10, SEPTEMBER 1966 1333 At the transition and fusion temperatures for this sample, the apparent thermal capacity dH/dT is far greater 25.0 than mC,, and the calorimeter was e--- driven into saturation. This accounts ----- for the poor resolution of these transitions in the 55.9-mg. sample. In order to observe such transitions, smaller ePRESENT WORK samples should be used, as demonstrated by the second silver nitrate analysis cP 5.0 superimposed on the first one. This CAL./MOLE DEG. recording was made with a sample weighing 0.55 mg. As anticipated] the 0.0 ordinate deflection due to mC, is almost indistinguishable from the base line, whereas the fusion is well resolved, with 5.0 a S/.V ratio greater than 100. Better temperature resolution would be obtained at slower programming rates, at the expense of SIN ratio. ,,I ,111 Ill1 The a-P transition was not resolved any better with the smaller sample size, and disappeared entirely when the analysis was repeated. Further study of this behavior was considered to be outside the scope of the investigation. The last sample to be studied was a the literature (Equation 8) is 1.4%, at heat more clearly. The agreement with polycarbonate resin, which displays a 390" K. For diamond, the greatest the literature is within 0.7%. Figure 7 characteristic jump in specific heat at departure is 3.0%) at the same tempera- shows the data for silver nitrate; for the glass transition temperature. It is ture. These literature values are shown this sample the error approaches 2.5% in the analysis of phenomena such as as solid curves in Figures 4 and 5. at 430" K. this one that the direct measurement of The broken curves in Figures 4 and 5 The behavior of silver nitrate is shown specific heat is most valuable. With the represent the wide temperature interval in Figure 8. Although the sample was drop calorimeter method, the location approximations (Equations 10 and 12). programmed to a temperature well and magnitude of the transition would With only four coefficients available in above its melting point of 484" K., have to be inferred from a small change the empirical heat-content equation, specific heat calculations were made in the slope of the heat content function, the curve-fitting error must increase only for the a-phase, from the initial and a number of heat content measure- without limit as the temperature inter- temperature to 433" K., owing to the ments would have to be made at val is increased. anomalous behavior of the a-P temperatures close to the glass transi- Table I1 shows specific heat functions transition at this temperature. This tion. for pure gold, fully annealed] and for transition] unlike the fusion, was not The analysis can be made with a silver nitrate. Figure 6 shows the data reversible when the sample temperature scanning adiabatic calorimeter, pro- for gold and the literature data, with an was programmed back to 320" K., and vided that very slow scanning rates, expanded ordinate scale to show the there were some indications of rate- typically 20" K. per hour or less, are temperature dependence of specific dependent behavior. used. Figure 9 shows the analysis of a polycarbonate sample on the DSC-1, with a sample weight of 42.8 mg. Figure 10 shows the specific heat function i! calculated for this sample, and for i: Ii J ijI

3 II 0.002 CAL./SEC. !I dH f0.005 IdH dt dl i.." )I SILVER NITRATE POLYCARBONATE 42.8 MQ

i. , , , , , , , , , , , , . , ST**RT.J 350 400 450 LTOP 1- *I( 1- *K Figure 8. Silver nitrate analysis, showing influence of sample size Figure 9. Polycarbonate analysis

1334 o ANALYTICAL CHEMISTRY comparison the data from a recent determination with an adiabatic calorimeter (8). The agreement is within 2% below the glass transition temperature, and within 4y0 at higher temperatures. The close agreement may be fortuitous, since there probably were differences in structure or crystallinity between the two samples. CP a The present work indicates that the CAL. OM" OEO:' 0.40 I specific heat of this material increases POLYCARBONATE from 0.41 to 0.47 cal. gram-' ' K.-l in a I I transition temperature interval between PRESENT 420' and 430' K. The ordinate ac- -WORK curacy could be improved with faster --- LlTERATURE program rates or a larger sample, at the I I expense of temperature resolution. The exchange of temperature resolution for SIN ratio is inherent in scanning ''O 350 400 450 so0 calorimetric methods. One advantage of differential calo- TEMPERATURE 'K rimetry appears in the analysis of small Figure- 10. Specific heat of polycarbonate phenomena superimposed on a changing total specific heat. For example, the slowly varying component of the specific heat of the polycarbonate may be sup- justified only for measurements of the mately 100" K. sec. cal.-l, and is pressed in the readout by placing in the highest accuracy. reproducible within about 25%. Thus reference holder a suitable quantity of Returning to the nonsystematic there might conceivably be a difference a material which has a similarly varying errors, we consider first the ordinate of 50' K. sec. cal.-l between sample and specific heat without any transitions. noise level. This is specified by the standard coupling resistances, which at The step function in the polycarbonate manufacturer as less than 8 X 10-6 a heat flow rate of 1.6 X IO-* cal. sec.-l specific heat will then appear on a flat cal. sec.-l peak-to-peak. For a SIN would cause a total abscissa error of base line, and thus may be examined ratio of 100, the sample size andascan- 0.8" K. The resulting specific heat error with greater ordinate sensitivity. ning rate should therefore be chosen for depends upon the slope of the speci6c a heat flow of 1.6 X lo-* cal. sec.-l heat functions of the sample and In this case, the ordinate deflections may standard materials. If the true SOURCES OF ERROR be established with an uncertainty of temperature of the sapphire standard The specific heat measurement de- &0.5%, and their ratio therefore has an differs by 0.4' K. from the indicated scribed above is bawd on the comparison uncertainty of f 1.0%. temperature, the ordinate error will be of the heat flow rates into sample and Actually, this is a conservative esti- 0.04%, since the specific heat of sapphire standard materials subjected to identical mate of the possible error, since specific has a slope of approximately 0.1%' K.-1 temperature programs. The limiting heat functions vary slowly with in the temperature range covered by sources of error are the random noise on temperature, and a smooth curve may the DSC-1. The additional error due the measured ordinate deflection and be drawn which is a much better ap- to the sample temperature error of the reproducibility of the temperature proximation to the true ordinate de- 0.4' K. in the other direction may be program, which is essentially the ran- flection than implied above. For the estimated similarly. dom noise on the abscissa. most precise work, the analysis may be The magnitude of the abscissa error There are also systematic errors, such repeated one or more times, and the is directly proportional to the heat flow as those caused by ordinate non- data from successive runs may be rate into the sample, while the error due linearity and inaccurate temperature averaged. to the ordinate noise level is inversely calibration, which can be reduced to any The second nonsystematic error is proportional to the same heat flow rate. desired level at the expense of analysis due to the imperfect reproducibility of The overall error is minimized when the time. The ordinate linearity of the the temperature program. The re- operating conditions are adjusted so calorimetric readout is within I%, and producibility of the sample holder that the errors contributed by these two will not introduce an appreciable error temperature is of the order of 0.1" K., sources are equal. With careful if the sample size is chosen so that the which generates negligible errors in handling of samples and data reduction, ordinate deflections for sample and specific heat measurements. However, an uncertainty of &0.30/0 in specific reference materials are similar. The the true sample temperature differs heat may be realized. On the other temperature scale is calibrated with from the sample holder temperature hand, determinations of specific heat melting point standards, and the errors during a program, owing to the tempera- with an uncertainty no greater than of interpolation can be minimized by ture gradient across the finite resistance 3% may be made in little more than the calibrating at smaller intervals. These between the sample and the sample time required to weigh the sample and methods are time-consuming, and are holder. This resistance is approxi- scan its temperature through an interval of20' K. The experimental work described above lies between these two extremes; Table II. Specific Heat Functions the temperature scale was calibrated (Cal. mole-' "K.-1) with three standards over a range of Gold Silver nitrate 180" K, and the abscissa accuracy is Literature 5.66 + 1.24 X 10-*T 8.76 + 4.52 X 10-*T estimated to be within 1' K. There was DSC 5.71 + 1.23 X lO-'T 12.27 + 3.55 X 10-27' no attempt to match sample and standard heat flow rates, and there wm

VOL 36, NO. 10, SEPTEMBER 1966 1335 no averaging of data from successive (3) Furukawa, G. T., Douglas, T. B., (9) Stull, D. R., JANAF Thermochem- analyses on any sample. Under these McCoskey, R. E., Ginnings, D. C., I Data (1961). J. Res. Natl. BUT.Sld. 57, 67 (1956). Victor, A. C., J. Chem. Phys. 36, conditions, the accuracy of the specific (4) Ginnings, D. C., Corruccini, R. J., )3 (1962). heat functions determined abovc is Ibzd., 38, 593 (1947). Watson, E. S., O’Neill, M. J., estimated to be within &l.O%. (5) Kelley, K. K., U. S. BUT. Mines Jum itj!h^J.!.Bre?ner, N., ANAL. CHEM. Bull. 584 (1960). 36, lY66 (IYtj4). (6) Maier, C. G., Kelley, K. K., J. Am. (12) Westrum, E. F., Jr., Hatcher, J. B., LITERATURE CITED SOC. Chem. 54, 3243 (1932). Osborne. D. W..I- .I. Chem.- Phys. 21, 419 (1) Dauphinee, T. M., MacDonald, D. (7) O’Neill, M. J., ANAL. CHEM. 36, (1953). ’ K. C., Preston-Thomas, O., Proc. Roy. 1238 (1964). SOC.(London) 221, 267 (1954). (8) O’Reilly, 3. M., Karasz, F. E., Bair, (2) Evans, W. H., NBS Rept. 6928 H. E., J. Polymer Sci., Part C, Polymer RECEIVEDfor review March 29, 1966. (1960). Symp., No. 6 (1963). Accepted June 22, 1966.

Differential Thermal Analysis-Effluent Gas Analysis Method for Identification and Determination of Nitrides in Steel

W. R. BANDI, W. A. STRAUB, E. G. BUYOK, and L. M. MELNICK United States Steel Corp., Applied Research Laboratory, Monroeville, Pa. b A DTA-EGA technique has been de- to predict which compounds might were reported by Garn (8) in 1964. veloped for the determination of occur, but without knowledge of kinetics This work discloses the design and specific nitrides in residues extracted these predictions are unreliable, and test’ing of a DTA-EGA system that will from steel. The method can be used compounds are found in steel that would detect 10 pg. or more of nitrogen in to identify nitride phases in steel appear to be thermodynamically im- milligram quantities of residue extracted which are not identifiable by any possible. from steel. other analytical procedure. The pro- Optical and electron microscopy, cedure can be used to detect as little x-ray and electron diffraction, the EXPERIMENTAL as 5 pg. of nitrogen. Other corn- electron microprobe, chemical analysis, pounds present in the extracted resi- and combinations of these techniques DTA Apparatus. R. L. Stone due did not interfere with the nitro- have been used to gain analytical in- Model 12BC2. The DTA assembly gen determination. Above 10 pg. formation about compounds in steel. was modified for these experiments as an accuracy within 10% of the All of these are useful, but they have follows : amount present appears to be possible. limitations in terms of applicability. Copper tubing (l/s-inch 0.d.) was For instance, the resolution of optical soldered to the pressure regulator of microscopy is limited, and poor dif- the oxygen tank and a needle valve ETALLURGICAL literature shows fraction patterns are obtained when the capable of controlling the dynamic M that more than 30 nitrogen- particles are fine. (Particles of carbides oxygen flow at 3 ml. per minute was bearing compounds have been identified and nitrides as small as 100 A. have substituted for the gas controls in the been found in steel.) Furthermore, furnace platform. or postulated to exist in steels that are A modified sample holder assembly produced today. From consideration diffraction patterns of phases may not (Figure 1) was fabricated from Inconel. of the composition of these steels and be identified if the constituent is present Salient features of the design include a reference to the thermodynamics for the as less than about 5% of a residue ex- small effluent gas volume to attain the formation of nitrides, it appears possible tracted from the steel. Also, some desired EGA sensitivity, gas seals away that as many as 75 simple and complex carbides and nitrides have similar dif- from the heated area to ensure a mini- nitrogen compounds may exist in fraction patterns. mum gas leakage, and a stacked ther- various steel alloys now manufactured. Beeghly’s ester-halogen extraction mocouple arrangement to hold platinum These compounds are known to affect method (4) and methods for the deter- dishes containing the sample and reference material. The stacked thermo- the physical and mechanical properties mination of acid-soluble (6, 7) and/or couple is part of a bridge circuit contain- of steel. heat-treatable nitrogen (9-12) have ing the thermocouple beads. Although the effects of nitrides are at been used in many past metallurgical To facilitate use of the sample holder least partially known for simple steel- investigations of nitrides, but as the assembly, a hole was drilled through alloy systems, they have not been alloy system increases in complexity, the top of the DTA furnace. An as- extensively studied in complex ferrous the information gained by these methods bestos washer was placed on top of alloys mainly because of the lack of a is less specific. Therefore, for the past the furnace and around the sample good analytical method for determining several years we have been investigating holder assembly. To protect the gas which nitrides are present. At least the possibility of using differential seals from heat a split water jacket thermal analysis-effluent gas analysis made of copper was clamped around 25 nitride-forming elements are used in the tubing between the asbestos washer various types of steels and eight or 10 (DTA-EGA) to analyze for compounds and the gas seal. may be used in a single type. The that can be extracted from steel. Our EGA Train. The assembly for the problem is further complicated by the preliminary work with extracted res- determination of nitrogen in the efflu- fact that metal carbides, sulfides, or idues has been reported previously ent gas is shown in Figure 2. To oxides of the same elements may also be (1-3, 13). Also, preliminary experi- maintain a small gas volume, mini- present. Thermodynamics can be used ments with an EGA analytical train mum lengths of l/&nch 0.d. copper

1336 0 ANALYTICAL CHEMISTRY