Relative Enthalpy of Solid Beryllium Aluminate (Chrysoberyl), BeO · Al2O3, from 1175 to 2025 K, and of Liquid Beryllium Aluminate from 2170 to 2350 K

The relative enthalpy of solid beryllium aluminate BeO · Al2O3 from 1180 to 2025 K and liquid beryllium aluminate from 2170 to 2350 K was measured by “drop” calorimetry using an adiabatic “receiving type” calorimeter. The thermodynamic functions from 1175 to 2025 K and the enthalpy of melting at 2146 K are reported.


Introduction
Naturally occ urring BeO -Ah0 3 (c hryso beryl) has variable and appreciable amounts of impurities such as Cr, Fe, Si, Na, Li , K, and Ti [3,4,5).1 Little or no accurate work has been done on the thermodynamic properties of thi s material in its natural state_ The heat capacity of synth etic 1: 1 beryllium aluminate from 16 to 380 K and the re lative enthalpy from 273 to 1173 K have been previously measured at th e National Bureau of Standards [1 ,2]_ The present work has been undertaken to extend the range of accurate thermodynamic data on thi s material to near its melting temperature_ BeO -A1 2 0 3 is reported to melt at 2146 ± 10 K2 [6]. We have made so me enthalpy meas urements beyond this temperature in a welded capsule so that th e enthalpy of melting can be estimated _

. Sample
The BeO· Ah0 3 sample used in this work was prepared by Semi-Elemen ts In c. of Saxonburg, Pa.,3 by arc-fusion of a stoichiometric mixture of high purity powdered BeO and Ah0 3. The homogeneity of the lot has been adequately es tabli shed and the sample is from the same lot as described in references [1,2].
The fine material in the samples was removed by passi ng it thru a 16-mesh stainless steel screen. Occasional dark particles re maining on the screen were discarded_ After 2_5 years storage in a plastic bottle on a laboratory s helf the water conte nt was dete rmined to be 0.16 percent by the Mic roc hemical Analysis Section of the National Bureau of Standards. The sa mple was heated to 1325 K in a carbon-hydrogen-nitrogen analyzer. Th e water in the sample was se parated by a gas c hromatographic column and th e n de tec ted by thermoconduc tivity. This result is con sistent with th e 0.2 percent mass loss observed in our furnace under similar conditions . A ne w spectrochemical analysis of the sample showed small differences from the earlier ones [1,2]_ The results of the analyses are tabulated in table L Six samples designated A, B, C, D, G, and H were us ed in this work of which C and D were not analyzed because they duplicate A and unexposed samples, respectively. The only significant difference betwee n the exposed and unexposed samples is the small amount of container material found in the former. This could be due to abrasive action of the hard material on filling and emptying the container, chemical combination, or sublimation. After exposure to higher temperatures (1700 K and above) the surface of the crystals appeared slightly grayish and the fu sed sample showed patches of gray areas ; however , no difference in chemical composition between the li ght and gray areas could be de tected.
The samples are id e ntifi ed as in tables 1 and 2. A brief history of the samples is as follows: A. Heated in an un sealed molybdenum container. Total mass loss in two experime nts at 1700 K was 0.38 percent.
Heated in an unsealed molybdenum container. Mass loss on heating to 1700 K was 0.4 percent and additional loss on heating to 2000 K, 0.07 percent. There was no further significant change in mass.
e. Heated in an unsealed molybdenum container. Mass loss on heating to 1180 K was 0.25 percent with an additional loss of 0.1 percent on heating to 1700 K. There were no further significant changes. D. Heated in an unsealed molybdenum container.
Mass loss on heating to 1180 K was 0.24 percent.
G. Heated 6 hours in a platinum crucible in the flame of Meker burner at 1200 K before loading in a molybdenum inner container. During the sealing process by electron beam welding, the container lost 3.06 mg. Because of the extremely localized heating of the process, the mass loss was taken to be molyb· denum. No further significant mass changes were observed. H. Pretreated as in G but loaded in a tungsten inner container. During the welding process this container lost 2.70 mg. There were no further significant mass changes.

Containers
Tungsten and molybdenum, both 99.95 percent pure, were used as container materials. Two types of containers are used. The first type, which we call an outer container, is used at lower temperatures where sample mass losses are negligible. It is not sealed, so that the sample can be loaded into the container as small lumps and removed to determine a sample and container mass for each experiment. The second type, used at higher temperatures and throughout the liquid range, consists of the unsealed outer container and an inner container vacuum sealed by electron beam welding after adding a weighed amount of sample. This technique has the advantage that the mass of the inner container does not change and any significant changes in mass of the outer container can be ac-  counted for experimentally. It has the disadvantage that the experiment gives the combined enthalpy of the sample plus the inner container, for which a correction must be made.
To determine this correction, the enthalpy of a molybdenum sample, machined from the same rod used for the inner container, was determined in the same series of measurements and in the same outer container, whenever the enthalpy of an inner container with sample was measured.

Enthalpy Measurements
The method of enthalpy measurements and the apparatus used in this work [15] will be described briefly. After the capsule (full or empty) has reached temperature equilibrium in the furnace it is lifted from the furnace into a "receiving" type adiabatic calorimeter operating near room temperature. If the position, flight time, shutter sequence, emissivity, and the furnace temperature are the same, the difference in heat energy received by the calorimeter from the full and empty capsule is the change in enthalpy of the contents. An automatic servo-regulated lifting device is used to keep the position and flight time of the capsule the same. The furnace is inductively heated and a Leeds and Northrup automatic optical pyrometer monitors and controls the temperature of the graphite core or the bottom of the capsule by sighting on it through a prism at the bottom e nd of the furnace. A number of change s have been made since the previous description of the apparatus [15] and are described as follows.
When the apparatus was moved from Washington, D.e. to Gaithersburg, Md. to a laboratory in which the temperature is regulated to ±1 K, the new environment eliminated much of the problem associated with the effect of room temperature on the automatic optical pyrometer. This effect was further reduced by replacing some temperature-sensItIve germanium transistors with more s table silicon transistors.
A solid state referen ce voltage supply has replaced the mercury cell. The s tability of the furnace temperature depends directly on the co nstancy of this supply. The variations in the furnace temperature are now so small that they have a negligible effect on the measured heat « .02%).
For measureme nt of th e te mperature of the adiabatic calorimeter, a copper resistan ce th ermom e te r wound noninductively and ce mente d with an e poxy resin in a groove in the copper bloc k has re placed the platinum resistance th ermometer. Comparisons made betw~en the two thermome ters over a period of 3 years indicated that the coppe r th e rmometer was stable within th e imprecision of the meas ure me nt. Its resistance is about 80 fl and th e chan ge in resistance p er degree is about three tim es as large as the resis tance chan ge in the platinum thermome te r. It also h as the advantage of excelle nt th ermal contact with the calorim eter so that its excess te mperature due to heat gene rated by the thermome ter c urre nt is es timated to be 6 X 1O -5~ at 2 mA, co mpared to 2 X 10-3 K for the platinum thermome ter. The c hange in excess te mperature for ordinary variations in thermome ter c urre nt is now negligible. Elec trical calibrations of the adiabatic calorime ter conducted with the coppe r the rmom eter over a period of 2112 years in this laboratory now have an es timated standard de viation of 0.004 perce nt.
Recirc ulate d c hille d wate r at 10.5 °C is now used to cool the induction heate r and the furnac e e nds, and has replaced th e tap wate r and water economizer used in the old location . Since the power to maintain th e furnace at a preset te mperature does not c hange during the day, th e te mperature gradi e nt in the furnace is more stable.
The experime ntal procedure is now designed to account for mass gains of the outer container. Three or four individual experiments are made in a day and are ordered so that the first and last experiments are duplicate s. When the mass of the outer container c hanges between the first and last experiments, any difference in the total heat for these experiments, after appropriate corrections, is assumed to be proportional to the mass gain and intermediate expe riments are corrected according to the mass gain in eac h. In practice, the correc tion factor in joules per milligram is de termin ed by plotting de termination s for all experiments and drawin g a s mooth c urve through th e m. Above 2000 K the correction factor is virtually constant. The magnitud e of this correc tion ranges from negligible at te mperatures below 1600 K to 5 percent of the e nthalpy of th e liquid Be O . Ah03 a t th e higher temperatures . (The liquid s ample is about onehalf the mass of the solid sample. ) Masses are now de termin ed after each individual experime nt , whi ch co nsiderably slow s th e work but permits the e mpirical correction for each experiment. The advantage of the e mpirical correction is that it does not assume any partic ular c he mical process for the mass gain. The c hronological sequence of the furnace te mperatures for th e meas ure me nts on th e solid work was selec ted randomly. Th e meas ure ments in th e premelting region and in th e liquid phas e were run on late r dates afte r th e mac hining, e ngin eerin g, and welding proble ms were solved for the inne r co ntain er.
The sequence for the e mpty and full experim e nts was s taggered in order not to introduce a bias du e to gradual change in th e furnace in sulation.

2.4_ Results
Presented in table 2 are the res ults of the individual experim ents. The quantity of heat deliv ered to the calorime ter includes the s mall correction s for the  e nthalpy of the contain e r and its conte nts be twee n th e final calorime ter te mpe rature and 298.15 K. These corrections were at most 2 perce nt of th e measured he at so that th e effect of the un certainty in the data used in makin g the m [1 , 8, 9,10] is negli gibl e. Wh ere ve r the correc tion data were prese nted in calorie units, th ey were conve rted to joules by multiplyin g by the conversion fac tor 4.1840. In column 2 the larger fi gures for a given day are the meas ure d heats for a full caps ule and the smalle r figures refer to the e mpty capsule. T o account for the tun gs te n inn e r contain er in th e pre· melting and liquid range the correction data were taken from reference [7]. Th e e nthalpy for th e molyb· de num inn er co ntain er was meas ured along with th e BeO· Al 20 3 when thi s material was used, and is tabulated in the table along with th e other experim e nts for the day. Weighin g was don e in air and th e correc· tion for buoyan cy is based on a den sity of 3.71 gm/c m 3 for c hryso beryL Th e te mperature scale is IPTS 1968 [11 , 121. Equation (1) (see below) represents th e e nthalpy of solid BeO . Ah03; it was co mputed by the method of least squares [13]. Since the unce rtainty in the te mperature is greater at higher temperatures, the res ults of individual experime nts were weighted in· versely to the magnitude of th e molar e nth alpy. The coefficients of eq (1) we re calc ulated using the results re ported h erein with th e results of Ditmars and Douglas [2] and Furukawa and Saba [1]. The joining of the data se ts is s hown in fi gure 2. Equation (1) and the coefficients of the equati on are as follow s: The estimated standard de viation of the observed points from the s moothed curve is ± 0.142 pe rce nt for the range 1180 to 2100 K.

+ET + (F/2)T2+ (G/3)P+ (H/4)T4
Beyond 2125 K and up through 2137 K pre meltin g of chrysoberyl is evidenced by the sharp departure of the observed enthalpies from the s mooth ed solid and liquid c urves . (See fi g. 1.) Th ere is a gradual c han ge of th e dimen sions of the inn er containe r in this ran ge as well as at the hi gher temperatures as the sample is cycled to room te mperature . Pres umably, this is caused by the rapid ex pansion and co ntraction of c hryso beryL The tungs te n co ntain er ultimately frac· tured thu s limitin g the number of experime ntal points.
For th e liquid range the e nthalpy of c hryso ber yl can be re prese nted by th e equation: The root mean square deviation of a single deter· mination (3 individual experiments) from the smoothed curve is ± 0.16 percent.
Taking 2146 K on the International Practical Temperature Scale of 1968 to be the melting temperature [6], the enthalpy of fusion is calculated to be 171.5 kJ . mol -1 by extrapolating eqs (1) and (2) to this temperature. An uncertainty of ± 10 K in the melting temperature will have an effect on the enthalpy of fusion no larger than ± 0.10 percent. Extrapolation of the smoothed curves will introduce an uncertainty estimated to be ± 0.3 kJ . mol -1 at 2146 K.
A few measurements on a sample of molybdenum from the same rod used for the inner container have been made at 2033, 2095, 2125, 2200, and 2254 K. The results are listed in table 2 along with those for chrysoberyl. These experiments were carried out simultaneously because the best data found in literature [14] claim a maximum error of ± 1.2 percent. The results obtained are within 0.48 percent of the reported values.

Polynomial Curve Fitting for the Solid Phase
The usual method of fitting the enthalpy measurements to an empirical equation by the method of least squares [13] was employed to establish how well we can expect the curve to represent the observed data from 1180 to 2030 K. The estimated standard deviation of the observed enthalpies of the solid phase from a curve fit (not shown) of this work alone is ± 0.10 percent. Since acc urate thermodynamic data on this material at lower temperatures are available from earlier works [1 , 2], it was decided to make use of their results to extend the range down through 273 K. Certain conditions must be set to do this. First is that the he at capacity of the subs tance is well be haved and normal throughout the region of study. The re is no evidence that this is not so. The amount of impuritie s is small. The BeO and Be O . 3Alz0 3 phases were not detected.
Lang, Fillmore , and Maxwell [6] rede termined the equilibrium diagram of the beryllia-alumina s yste m and their results indic ate no ph ase tran sition in this te mperature range . References LI , 2] re port no unusual be havior in the heat capaciti es at lower te mpe ratures.
Sec ond is that the enthalpy and he at capacity curves are smooth fun ctio ns throughout thi s r ange. This is reasonably assured if th e fir st condition is sati sfi ed and if all the e n ergy, te mperature and mass measurements are co mpa red to the same s tandard s durin g calibration a nd observa tion s.
A third conditi on set on the c urve fit is that th e equation justifi es the accuracy of meas ure ments for the three studi es a t different te mperature ranges.
Equation (1) can be used down to 273 K with little or no loss in accuracy. Fi gure 2 compares the valu es of the heat ca pacities from equ a tion (1) with the present work and with those re ported in refe re nces [1 ,2].

Liquid Phase and the Heat of Fusion
Equati on (2) r e presents th e relative e nthalpy of c hrys obe ryl in the liquid phase for th e range 2175 to 2355 K. A polynomial of 2d degree was selec ted having least squares de vi ation and 95 p ercent confidence limits bec au se a s traight lin e re presentati on (us ually assigne d to e nthalpies for suc h a small te mperature range and s mall numbe r of observations) does not adequately re prese nt the observed values.
The uncertainty limits on the heat of fu sion of ± 3 .5 kJ . mol -1 inc hides 1.5 kJ . mol -1 for the extrapolation error of the solid c urve , 1.5 kJ . mol -1 for the extrapolation e rror of the liquid c urve, and an error of 0.5 kJ · mol -1 due to the co mbined effect of the te mperature unce rtainty a nd of the compromise in me rging our res ults with lower te mperature work. Not e nough observation s in the pre melting stage, 2025 < T < 2150, were made to give a de finitive explanation to its cause except to state that molybdenum and tungste n, the inner co ntainer, were detected in the post-measure me nt spectral analyses of the samples.

Errors
Ther e are three principle sources of error involved in the present calorimetri c me thod-on e , th e te mperature meas ure ments; two, the ene rgy measure me nts; and three, the sample purity and be h avior.
The s ta bility of both the solid sta te circ uitry a nd s t<..ldard reference la mp in the autom atic opti cal pyrometer was examined by re peated calibrations (5) 71 during the 4 years of usage. The uncertainty ranged from ± 4 K at 3000 K to ± 0.7 K at 1325 K (with the us ual precautions in frequent checks on optical alignme nt, foc us, and cleanliness). This compares closely with the ± 0.1 perce nt deviation that we obtained in the c urve fittin g.
The operational procedure was designed so that we co uld e valuate the imprecision of the energy measureme nts for the solid range. Thi s turned out s urprisingly simple because the furn ace te mperature can be controlled to ± 0.02 pe rcent durin g a day's work. By making duplic ate observati ons on the same day at on e furn ace te mperature, th e imprecision of the entire temper ature range of the solid phase was expressed as : where 5" = estimated imprecision n = number of observations ma de at differe nt te mpe ratures di = perce nt diffe rence of the two e nthalpy meas ureme nts at a given te mperature.
S pectroche mi cal analyses of exposed a nd un exposed c hryso ber yl s how very little differe nce in me talli c impurities. Molybde num found in the exposed sample (less th an 0.1 %) can only come from the contain er.
If we ass ume that the atomi c s pecific heat is th e sam e for the ele me nts involve d , the error in the e nth alpy would be less than 0.002 pe rcent. Although this s mall a mount introdu ces a bias to th e overall meas ure me nt, correction s were not applied because th e un certainty is overs hadowed by the greater un certainty in the furnace te mperature , because four samples we re used making it diffic ult to estimate the amount of molybde num impurity present in eac h experim e nt , and because th e weight loss es re ported in section 2.1 might not be entirely due to e vaporation of chrysober yl as we have assumed.
Considering all the errors that were di scussed we believe that other systematic errors encounte red in this measure ment are negligible compared to the estimated uncertainty of ±0.32 percent in the relative enthalpy of the solid phase.
The thermodynamic functions (see table 3) were prepared by routine smoothing and numeric al integration of the heat capacities from eq (1). The e nthalpy and entropy values at 273.15 K are from refere nces [1,2].
The authors gratefully ac knowledge the contributions from th e followin g me mber s of the NBS staff: P . Pfaff, .J. W. Bradle y, a nd R. R. Orwic k de veloped the mac hinin g, millin g and sealing techniques of the tun gste n and molybde num caps ules; R. A. Paulso n de termin ed th e moisture co ntent by gas c hromatog-raphy; V. C. Stewart and E. K. Hubbard examined the samples for impurities; M. L. Reilly developed and later modified the automatic data analysis procedure to fit our needs; E. Lewis, Jr. calibrated the automatic pyrometer and investigated the sources of errors in this instrument.