Pulse Calorimetry and Transient Measurement of Thermal Properties at High Temperatures * BY AREDCEZAIRLIYAN National Bureau of Standards Washington D.C. 20234 U.S.A. Received 29th August 1973 A system is described for the transient (subsecond) measurement of selected thermal and related properties of electrically-conducting substances in the temperature range 1500K to the melting point of the specimen. The method is based on resistive self-heating of the specimen from room temperature to any desired high temperature in less than 1s by the passage of an electrical current pulse through it ; and on measuring and recording the experimental quantities every 0.4 ms with a full-scale signal resolution of one part in 8OOO. The system has been used to measure heat capacity electrical resistivity hemispherical total emittance normal spectral emittance and the melting point of selected refractory elements and alloys.The results of preliminary experiments have shown the potential application of the system to measurements of temperatures and energies of solid-solid phase trans- formations and heat of fusion at high temperatures. Most measurements of thermal and related properties at high temperatures employ steady-state or quasi-steady-state techniques. In all these techniques the specimen is exposed to high temperatures for relatively long periods of time (minutes- to-hours). When these techniques are extended to measurements above 2000 K many problems are created as the result of increased heat transfer chemical reactions evaporation diffusion loss of mechanical strength etc.Because of these limitations of the conventional techniques it has become necessary to develop transient techniques which permit the heating of the specimen and the measurement of the pertinent quantities in a very short time. The objective of this paper is to describe a system developed at the National Bureau of Standards for the transient measurement of selected thermal and related properties of electrically conducting substances in the temperature range from 1500 K to the melting point of the specimen. The system was initially developed for the purpose of extending the limits of accurate calorimetry to high temperatures. The results of extensive work have demonstrated that the technique can also be applied to investigations in various other areas of thermophysics.In this paper the emphasis is placed on the description of the measurement system primarily for calorimetric studies. However brief discussions of the extension of the technique to other measurements are also included to demonstrate the potentials of the transient measure- ment technique. The system has been successfully used to measure heat capacity electrical resis- tivity hemispherical total emittance normal spectral emittance and melting point of several refractory metals and alloys. The results of preliminary experiments have shown the feasibility of measuring heat of fusion temperatures and energies of solid-solid phase transformations and radiance temperature of electrical con- ductors at their melting points.* This work was supported in part by the U.S. Air Force Office of Scientific Research. 7 PULSE CALORIMETRY EXPERIMENTAL METHOD AND MEASUREMENT SYSTEM The method is based on resistive self-heating of the specimen from room temperature to any high temperature (in the range 1500 K to its melting point) in less than 1 s by the passage of an electrical current pulse through it ; and on measuring with millisecond resolution such experimental quantities as current through the specimen potential drop across the speci- men and specimen temperature. Formulation of the relations for properties in terms of the experimental quantities are given elsewhere. The measurement system consists of an electric power pulsing circuit and associated measuring and control circuits.A functional diagram of the complete system is presented in fig. 1. The details of the measurement system and its operational characteristics are given in earlier publications.'. In this section some of the important features are summarized. FIG.1.-Functional diagramof the system for the transient measurement of thermal properties. PULSE CIRCUIT The pulse circuit includes the specimen in series with a battery bank a standard resistance and a switching system. The battery bank consists of 14 series-connected2 V batteries each having approximately 1100A h capacity. A standard resistance (0.001 Q) is used to measure the pulse current through the specimen. An adjustable resistance (total resistance 30 ma) enables control of the heating rate of the specimen and the shape of the current pulse.The switching system consists of two series-connected fast-acting switches. The second switch is used as a back-up in the event the first one fails to open at the end of the heating period. SPECIMEN AND EXPERIMENT CHAMBER The specimen is a tube of the following nominal dimensions length 102 mm ; outside diameter 6.3 mm; and wall thickness 0.5 mm. A small rectangular hole (1 x 0.5 mm) is fabricated in the wall at the middle of the specimen to approximate blackbody conditions for pyrometric temperature measurements. For the above geometry blackbody quality of the sighting hole is estimated to be approximately 0.99. The specimen is mounted vertically 6 mm off-centre with respect to the axis of the experi- ment chamber to reduce the effect of internal reflections.The chamber wall as well as the specimen clamps are water cooled. Thermocouples are connected (electrically insulated) FIG.2.-Oscilloscope trace photograph of radiance of rapidly heating specimen. Dots forming the long horizontal lines correspond to radiances from the reference source. Equivalence of each major division is time 20 ms ; radiance arbitrary unit. To face page 91 A. CEZAIRLIYAN to the two end clamps to measure the specimen temperature before each pulse experiment. An expansion joint allows the expansion of the specimen in the downward direction. The potential probes are knife-edges made of the specimen material and are placed at a distance approximately 13 mm from the end clamps.The knife-edges define a portion of the specimen which should be free of axial temperature gradients for the duration of the experi- ment. The chamber is designed for conducting experiments with the specimen either in vacuum or in a controlled atmosphere. HIGH-SPEED PYROMETER Temperature of the specimen is measured with a high-speed photoelectric pyrometer which permits 1200 evaluations of the specimen temperature per second. The pyrometer alternatively passes precisely-timed samples of radiance from the specimen and a reference source (gas-filled tungsten filament lamp) through an interference filter (wavelength 650 nm bandwidth 10 nm) to a photomultiplier. During each exposure the photomultiplier output is integrated and is recorded.For measurements at temperatures above 2500 K calibrated optical attenuators are placed in the path of the radiation from the specimen. The pyro- meter target is a circular area 0.2mm in diameter. Typical results of the radiance from the sighting hole in the specimen as well as that of the reference lamp as seen by the pyro- meter as a function of time during a pulse experiment are shown in fig. 2. The details regarding the construction and operation of the pyrometer are given in the literat~re.~ DATA RECORDING SYSTEM Data corresponding to temperature current and voltage are recorded with a high-speed digita1 data acquisition sys tem which consists of a mu1 t iplexer ,analog- t 0-digi tal converter and a core memory together with control and interfacing equipment.All signals are brought to the multiplexer through differential amplifiers in order to avoid inaccuracies arising from common ground points. The multiplexed signals go to the analog-to-digital converter which has a full-scale reading of & 10V and a full-scale resolution of one part in 8192 (8192 = 213). Digital output from the converter consists of 13 binary bits plus a sign bit. This output is stored in a core memory having a capacity of 2048 words of sixteen bits each. The data acquisition system is capable of recording a set of signals corresponding to temperature voltage and current approximately every 0.4 ms. At the end of the pulse experiment information stored in the memory is retrieved in the form of numeric printing and punched tape using a teletypewriter.Since the laboratory has access to a time-shared computer it is possible to unload the memory directly to the computer bypassing the inter- mediate stage of punching paper tape. Oscilloscopes are used only to monitor the general pattern of the experimental results and to detect any anomalies. TYPICAL OPERATIONAL CHARACTERISTICS The operational characteristics of the system depend primarily on the electrical circuit parameters properties of the specimen and specimen maximum temperature. The system characteristics for typical experiments are as follows current 1300-2200A power 7000-1 5000 W heating rate 3000-8000K s-' heating duration 0.3-0.7s heating rate 10-100 cooling rate The above quoted figures are the results of typical experiments and do not represent the full capabilities of the measurement system.MEASUREMENT OF THERMAL PROPERTIES The system described in this paper has been used to measure heat capacity electrical resistivity hemispherical total emittance and normal spectral emittance of the refractory molybdenum,l tantal~rn,~ metals ni~bium,~ tungsten ; and the alloys tantalum-10 (wt. %) PULSE CALORIMETRY tungsten,' niobium-1 (wt. %) zirconium in the temperature range from 1500 K to near their respective me1 ting temperatures. Similar measurements were also performed on graphite in the range1500-3000K.'. lo In addition the melting points of niobium,l1 molybdenum,12 and tungsten l3 were also measured.HEAT CAPACITY Heat capacity is determined from the measurements of voltage current and temperature during the rapid heating period. A correction for heat Ioss from the specimen due to thermal radiation is made based on hemispherical total emittance determined during the same experiment. ELECTRICAL RESISTIVITY Electrical resistivity is obtained as a by-product from measurements of voltage current and temperature during the heating period. Before and after the pulse experiments specimen resistance at room temperature is measured using a Kelvin bridge. HEMISPHERICAL TOTAL EMITTANCE Hemispherical total emittance is obtained from data taken during the specimen heating period in conjunction with temperature measured during the radiative cooling period that follows the heating period.Only the data during the initial cooling period are considered to eliminate the effect of axial heat conduction on the results. NORMAL SPECTRAL EMITTANCE Normal spectral emittance is measured at the effective wavelength of the pyrometer interference filter (wavelength 650 nm bandwidth 10 rim). For this determination two rapid heating experiments are performed in which the pyrometer is first aimed at the blackbody radiation hole and then at the surface of the tubular specimen. The ratio of radiances (surface-to-hole) corresponding to the same specimen temperature is the normal spectral emittance. The same temperature in the two experiments is found by matching the measured specimen resistances. MELTING POINT During rapid heating of the specimen if the current is not interrupted the specimen temperature reaches its melting point and then collapses under gravitational forces.Melting 2750t 2750.6 K --**....**.........* **.*..-.* I 0 10 20 30 40 50 time arbitrary unit FIG. 3.-Variation of the temperature of a niobium specimen near and at the melting point. One time unit is 0.833 ms. A. CEZAIRLIYAN is manifested by a plateau in the temperature versus time function. Temperatures deter- mined from the pyrometer output for a niobium specimen are shown in fig. 3. By averaging the temperature points on the plateau the melting point is obtained. OTHER INVESTIGATIONS AND PRELIMINARY MEASUREMENTS In this section description and preliminary results of experiments are given for various thermal and related investigations at high temperatures.The same measurement system was used with some modifications. RADIANCE TEMPERATURE AT THE MELTING POINT Utilizing a specimen in the form of a strip it is possible to measure radiance temperature of a substance during rapid heating. The value of this quantity at the melting point is of particular interest. Fig. 4 shows the results of a typical experiment on a niobium specimen having the following dimensions length 102mm ; width 6.3 mm ;and thickness 0.25 mm. l1 The plateau indicates the melting of the specimen. The drop at the beginning of the plateau corresponds to the change in normal spectral emittance of the specimen as its melts. An initial high radiance temperature (peak of spike) indicates that normal spectral emittance of the solid surface is higher than that of the liquid surface.This is likely to be the case in general since solid surfaces regardless of the degree of polish depart from the conditions of ideal smoothness. The results of experiments on twelve specimens l4 performed under different conditions have demonstrated the constancy and reproducibility of the radiance temperature of niobium at its melting point. This may find applications in performing secondary calibrations on instruments and in conducting overall on-thespot checks on complicated measurement systems at high temperatures. The measurement of the radiance temperature at the melting point in addition to a separate measurement of the melting point yields the normal spectral emittance at the melting point.I--'i I I I 1 I f 2424K T . T J . 2410 1 I I I I I I FIG.4.-Variation of the radiance temperature of a niobium specimen as a function of time near and at the melting point. One time unit is 2.5 ms. TEMPERATURE OF SOLID-SOLID PHASE TRANSFORMATION Most solid-solid phase transformations can be detected by monitoring specimen tem- perature as a function of time as the specimen undergoes heating or cooling. For phase PULSE CALORIMETRY transformations that are constant or nearly-constant temperature processes the temperature versus time function exhibits a plateau during the phase transformation. The feasibility of the present system to measure temperatures of solid-solid phase transformations is demon- strated by preliminary measurements on iron.s For simplicity radiance temperature (instead of true temperature) of an iron rod during heating was measured as a function of time (fig. 5). The lower plateau indicates the solid-solid phase transformation (y -+ a) '700r--9 I650 -I600 -1550-1500-I I I I I 0 50 too 150 200 250 time/ms FIG.5.-Variation of the radiance temperature of an iron specimen as a function of time during its heating through the y +-6 phase transformation up to the melting point. and the upper plateau indicates melting of the specimen. From the measurements of voltage and current as a function of time it appears feasible to determine the electrical resistivity of the specimen and the energy imparted to the specimen during the phase transformation.After making a correction for the energy losses (mainly due to thermal radiation at high temperatures) energy of the phase transformations may be obtained. In the final measure-ments tubular specimens will be used. HEAT OF FUSION A preliminary experiment conducted on niobium l6 has demonstrated the feasibility of extending the capabilities of the present system to the measurement of heat of fusion of metals at high temperatures. The specimen was a composite made of three rectangular strips each having the following nominal dimensions length 75 mm width 6.3 mm and thickness 0.25mm. The middle strip was niobium and the two outer strips were tantalum. The specimen was pulse-heated from room temperature to approximately 200 K above the melting point of niobium.During the heating period current through the composite specimen potential drop across the specimen and radiance temperature (fig. 6) of the outer strip were measured. The plateau in radiance temperature corresponds to melting of the inner strip. Since the melting point of tantalum is approximately 500 K higher than that of niobium the outer strips did not melt during the entire experiment and acted as a container for niobium. The heat of fusion was obtained by integrating the power absorbed by the niobium strip over the duration of the plateau. Heat loss due to thermal radiation and energy absorbed by the outer strips were taken into consideration. The value obtained for the heat of fusion of niobium is 6,430 cal mol-1 (26,900J mol-l) which corresponds to an entropy of fusion of 2.34 cal mol-' K-l.A. CEZAIRLIYAN 1 1 I I I 8 9 3 2450' 2400 1 I J I RESULTS ESTIMATE OF ERRORS A summary of imprecision * and inaccuracy t of measured quantities and pro- perties is given in table 1. Tabulated values for imprecision represent averages of the results of several measurements on the four refractory metals (Nb Mo Ta W) corresponding to 2000K. Imprecision and inaccuracy of most quantities do not increase significantly at temperatures above 2000 K. At 3000 K inaccuracies of temperature and heat capacity are estimated to be 8 K and 3 % respectively. Details regarding the estimates of errors and their combination are given in an earlier publication.TABLE AND INACCURACY OF MEASURED QUANT~IESAND PROPERTTES * 1.-IMPRECISION (the values correspond to measurements at 2000 K) quantity imprecision inaccuracy temperature 0.5 K 4K voltage 0.02 % 0.1 % current 0.03 % 0.1 % heat capacity 0.6 % 2% electrical resistivity 0.1 % 0.5 % hemispherical total emittance 0.8 % 3% normal spectral emittance 0.3 % 3% (at 650nm) melting point 1K 6K * see text for definition of terms. *Imprecision refers to the standard deviation of an individual point as computed from the difference between the measured value and that from the smooth function obtained by the least squares method. Inaccuracy refers to the estimated total error (random and systematic).PULSE CALORIMETRY The estimates of errors in the measurement of other properties discussed in the previous section are not finalized yet. Preliminary estimates indicate that inaccuracy in the temperature of solid-solid phase transformation may be approximately the same as that for the melting point (6 K at 2000 K). Inaccuracy in heat of fusion may be 5 %. SOME RESULTS OF HEAT CAPACITY MEASUREMENTS AT HIGH TEMPERATURES As an example results for heat capacity of tungsten obtained using the present system in addition to those obtained by other investigators are shown in fig. 7. The results represent measurements using three different techniques namely "drop " "modulation " and "pulse ". There is no evidence for any bias with respect to a particular technique.The heat capacity results (smooth) for the elements niobium molybdenum tantalum and tungsten obtained using the present system are shown in graphical form in fig. 8 and are given in tabular form in table 2. It may be noted that the heat capacity results at high temperatures are considerably higher than the Dulong and 55 I I I I ----WORTHING (1918) 50 JAEGER (1930) HOCH (1961)..-..-KlRlLLlN (1963) -. -KRAFTMAKHER(1963) .-._ LOWENTHAL(1963) HElN (1968) LEIBOWITZ (1969) WEST PRESENT WORK f -5% f 25 I I I I I 1000 1500 2000 2500 3000 3500 temperature/K FIG.7.-Heat capacity of tungsten reported in the literature. For brevity the names of only the first authors are given in the figure.References to investigations presented in the figure may be found in the publication by Cezairliyan and McClure.6 The techniques that were used are as follows. Pulse Worthing Cezairliyan ; modulation Kraftmakher Lowenthal ; drop remainder. A. CEZAIRLIYAN Petit value of 3R. Some of the departure is due to cp-cv and the electronic terms. However they do not account for the entire departure. Heat capacity at high temperatures may be expressed by c,'= A -BIT2+ CT+ Ac (1) where the constant term A is 3R (24.943 J mol-l K-I) the term in is the hrst I I I I I I I 50 -U c 30 1 I I 1 I I 1 1I 1I - 1500 2000 2500 3000 3500 temperature/K FIG.8.-Hea t capacity (smooth) of niobium molybdenum tantalum and tungsten measured using the pulse calorimeter.TABLE &-HEAT CAPACITY (J m01-l K-') OF SOME REFRACTORY METALS AND GRAPHITE AT HIGH TEMPERATURES temp./K niobium molybdenum tantalum tungsten graphite 1500 29.48 24.14 1600 30.11 24.38 1700 30.73 24.61 1800 31.35 24.83 1900 32.02 33.97 30.66 25.03 2000 32.75 34.95 31.19 31.65 25.22 2100 33.57 36.07 31.71 32.49 25.41 2200 34.53 37.35 32.25 33.29 25.57 2300 35.64 38.77 32.83 34.08 25.73 2400 36.94 40.34 33.46 34.89 25.88 2500 38.46 42.06 34.17 35.72 26.01 2600 40.23 43.92 34.97 36.61 26.13 2700 42.28 45.94 35.89 37.57 26.24 2800 48.10 36.95 38.63 26.34 2900 38.16 39.81 26.43 3000 39.55 41.14 26.50 3100 41.39 42.62 3200 44.48 44.29 3300 46.17 3400 48.27 3500 50.63 3600 53.25 PULSE CALORIMETRY term in the expansion of the Debye function the term in T represents cp-c and first- order anharmonic and electronic contributions and the quantity Ac represents excess in measured heat capacity at high temperatures which is not accounted for by the first three terms.The coefficients B and C can be obtained from heat-capacity data at low and moderate temperatures (below 1000 K). 2000 2500 3000 3500 temperature/K FIG. 9.-Excess heat capacity Ac as defined by eqn (1) for niobium molybdenum tantalum and tungsten. Using eqn (1) and the measured heat capacity values the quantity Ac was com- puted for temperatures above 2000 K. The results are shown in graphical form in fig.9 and in tabular form in table 3. The estimated uncertainty in the computed Ac may be as high as 1 J mol-1 K-l. This is obtained from the combined uncertainties in the coefficients in eqn (1) and the measured heat capacities. TABLE 3.THE QUANTITY AC (IN J 11101-1 K-') IN EQN (1) FOR SOME REFRACTORY METALS IN THE RANGE 2000K TO NEAR THEIR RESPECTIVE MELTING POINTS temp./K niobium molybdenum tantalum tungsten 2000 2.03 3.70 1.08 2.07 2200 3.22 5.42 1.62 3.24 2400 5.06 7.68 2.31 4.37 2600 7.77 10.58 3.30 5.62 2800 14.23 4.76 7.18 3000 6.84 9.21 3200 9.70 11.90 3400 15.41 3600 19.93 Although vacancy generation becomes appreciable at high temperatures it is not likely that the high values are due entirely to vacancies. Higher-order terms in elec- tronic heat capacity and in lattice anharmonicity probably account for most of the excess heat capacity at high temperatures.More accurate theoretical work may produce a quantitative explanation of this phenomena. A. CEZAIRLIYAN DISCUSSION Delay at least until a few years ago in the development of accurate systems for the measurement of thermal properties may be attributed to a large extent to the lack of sophisticated instrumentation. Recent advances in electronics particularly in the area of high-speed digital data acquisition techniques have contributed im- mensely to the development of the system described in this paper. The system has been used successfully for the measurement of several thermal and related properties in the range 1500 K to the melting point of the specimen which for tungsten is 3695 K.The results of preliminary experiments have demonstrated the potential of the technique to extend the measurements to several other properties. In the temperature range 1500-2500 K the accuracy of measured properties by the present method and some of the accurate conventional techniques is approximately the same. However above 2500K,it becomes very difficult if not impossible to conduct accurate steady-state experiments ; thus the transient technique becomes a unique and indispensable tool for the measurement of thermal properties at high temperatures. Additional advantages of this technique are (i) the possibility of measuring simultaneously or consecutively several related properties and (ii) the possibility of conducting experiments to study time-dependent phenomena.The potential of the transient technique has not been completely explored. It shows promise in extending the measurements to (i) other thermal and related properties at high temperatures (ii) other electrically conducting high-temperature substances such as certain carbides borides nitrides and oxides and (iii) liquid metals and other electrically conducting liquids at hi& temperatures. A. Cezairliyan M. S. Morse H. A. Berman and C. W. Beckett J. Res. Nat. Bur. Stand. 1970 74A 65. A. Cezairliyan J. Res. Nat. Bur. Stand. 1971 75C 7. G. M. Foley Rev. Sci. Instr. 1970 41 827. A. Cezairliyan J. Res. Nat. Bur. Stand. 1971,75A 565. A. Cezairliyan J.L. McClure and C. W. Beckett J. Res. Nut. Bur. Stand. 1971,75A 1. A. Cezairliyan and J. L. McClure J. Res. Nut. Bur. Stand. 1971,75A 283. A. Cezairliyan High Temperature-High Pressures 1972,4,541. a A. Cezairliyan,J. Res. Nat. Bur. Stand. 1973,77A 45. A. Cezairliyan Proc. 6th Symp. Thermphysical Properties P. E. Liley ed. (Amer. SOC. Mech. Eng. New York 1973) 279. A Cezairliyan Electrical Resistivity and Thermal Radiation Properties of Graphite in the Range 1500 to 3000 K by a Pulse Heating Method in preparation. It A Cezairliyan High Temperatures-High Pressures 1972,4,453. l2A. Cezairliyan M. S. Morse and C. W. Beckett Rev. In?. Hautes Temp&. Rkfiact. 1970,7,382. l3 A. Cezairliyan High Temperature Sci. 1972,4,248. l4 A. Cezairliyan J.Res. Nat. Bur. Stand. 1973,77A 333. A. Cezairliyan and J. L. McClure A Pulse Heating Technique for the Study of Solid-Solid Phase Transformations at High Temperatures Application to Iron in preparation. I6 A. Cezairliyan A Pulse Heating Technique for the Measurement of Heat of Fusion of Metals at High Temperatures in preparation.