The International Practical Temperature Scale of 1968 in the Region 90.188 K to 903.89 K as Maintained at the National Bureau of Standards

The reproducibility of the International Practical Temperature Scale of 1968 (IPTS-68) in the region 90.188 K to 903.89 K as maintained at the National Bureau of Standards is discussed. The realizations of the triple point of water, the freezing points of zinc and tin, and the boiling point of oxygen are described. The average of the standard deviations of the resistance measurements at the triple point of water of 213 platinum resistance thermometers received for calibration over a two-year period corresponds to ±0.15 mK. The standard deviations of the resistance ratio R(T)/R(0°C) obtained with check thermometers employed for monitoring the zinc, tin, and oxygen point measurements correspond to ±0.28 mK, ±0.30 mK, and ±0.16 mK, respectively; the results of repeated calibrations with five thermometers show comparable reproducibility at the tin and oxygen points but the reproducibility is worse by a factor of two at the zinc point. When suitably packed for protection from possible mechanical shock platinum resistance thermometers can be shipped by common carrier and retain their calibrations.


Introduction
.81 K ( -259_34 °C) to 903_89 K (630_74 °C) the International Prac ti cal T e mperature Scale of 1968 [1 ,2),1 referred to he reafter as IPTS-68, is based on nin e defining fixed points, the platinum resistance the rm ometer (PRT) calibrated at th ese fix ed points, and s pec ified inte rpolation e quation s to relate the tempe rature and the resistance ratio, where W* (T) is th e reference functi on defi ned by _ 20 [In W*( T) +3_28] jK

W(T) =R(T)/R(O°C),
where R(T) is the thermometer resistance at temperature T and R (0 °Cl is the resistance at O°c. The defining fix~d points are equilibrium states between phases of pure substances to which values of te mperature have been assigned. (The isotopic composition is generally specified wherever it may vary sufficiently to have a significant effect on the equilibrium tempera-ture_) The thermome te r resistor must be annealed pure platinum, supported in a "strain-free" mann er and ~lave a value of W(lOO °C) not less tha n 1.39250.  where n ~ 4. In the subrange 13_81 to 20_28 K, n = 3; 20_38 to 54_361 K, n = 3; 54_361 to 90_188 K, n = 2; and 90.188 to 273_15K, n = 4_ The coefficie nts k i are de te rmined by calibration at the fixed points and by the requirement that the first deriva tive, d6.W(T)/dT~ be continuous at the junction with the next hi gher subrange_ From 0 °C to 630_74 °C the values of te mperature t are defi ned by t = t' + 0.045 (10~ 0C) (10~' 0C -1) where t' is defined by fied in the text of the IPTS-68 the triple point of water, henceforth referred to as TP, is the most important. (The Thermodynamic Kelvin Temperature Scale is defined by assigning 273. 16 K to the temperature of the TP and the thermodynamic unit of temperature, kelvin, is defined as 1/273. 16 of the thermodynamic temperature of the TP [2].) The PRT temperature scale as defined by the IPTS-68 utilizes the resistance ratio, R(T)/R(O°C); consequently, the accuracy of every W(t') =R (t')/R (0 °C) = 1 +At' + Bt'2. (6)  Equation (6) is equivalent to t'={~ [W(t')-I]+o (10~'OC) (10~'oC+l)}OC, (7) where a=A+BXIOO°C (8) and 8(100°C)2

0=-A+BxlO00C
at the NBS, six observations were made on each cell (9) over a period of three days; the averages of temperatures observed on each cell were within ± 0.1 mK [5].
The thermometer constants R (0 °C), A, and B are determined from resistance measurements at the triple point of water, the steam point or the tin point, and the zinc point. The constants a and 0 are derived from the constants A and 8 according to eqs (8) and (9), respectively.
The accuracy of thermometry employing a well calibrated PRT depends primarily upon precise measurements of relative resistances to determine WeT) accurately. In the calibration of PRT's, there are required, in addition, accurate realizations of the de· fining fixed points to obtain the thermometer consta~ts. At the National Bureau of Standards (NBS) the defimng fixed points: the triple point of water, the tin point, and the zinc point are maintained and are employed regularly in the calibration of PRT's. The defining fixed points below 0 °C are "maintained" at present by reference standard PRT's of the capsule type. In an earlier paper, the NBS-IPTS-68 scale between 13.81 and 90.188 K maintained by the reference standard PRT's was described and the reproducibility of the calibrations in terms of the NBS-IPTS-68 scale, of capsule typ~ PRT's received for calibration during a 21f2-year period was shown [4]. The present paper deals with the calibration of long-stem type PRT's (and some capsule type PRT's in special holders) in the range. 90.188 to 903.89 K. The fixed points that are maintained, the method of calibration, and the reproducibility of the results are discussed.

Triple Point of Water
Of the thirteen defining fixed points 2 that are speci- Figure 1 shows the design of the TP cell employed at the NBS. The sealed borosilicate glass cell contains only ice, water, and water vapor. The thermometer well is constructed of precision bore tubing. The extension at the top serves as a handle or as a support, as shown in the figure. By suitably positioning the cell most of the "gas" can be trapped in the extension and the amount of air can be estimated from the size of the bubble , if any, that remains. (At room temperature when the TP cell is positioned with the bottom end up, the bubble trapped in the extension is under a hydrostatic head of water that corresponds to a pressure slightly higher than the vapor pressure of water. Hence, if the bubble contains only water vapor, it should collapse when the TP cell is turned bottom end up.) To prepare the TP cell for use, the cell is first cooled by immersing it in a bath of shaved ice for about onehalf hour or so. The cell is then mounted in the ice bath with the opening of the reentrant thermometer well above the ice-water level and the thermometer well is wiped dry, e.g., by using absorbent paper on the en~ of a rod or a tube. A mantle of ice is frozen around and Immediately next to the thermometer well by filling the thermometer well with crushed Dry Ice. The well is maintained full of Dry Ice for about 20 min, after which all of the Dry Ice is allowed to evaporate. (It is important to keep the well completely full of Dry Ice during the 20-min period. If the Dry Ice level in the well is allowed to fall several inches and then the well is refilled, the ice mantle is apt to crack. Although the crack often "heals," the desired triple-point temperature of the "inner melt" may not be achieved if a crack in the ice mantle later extends from the well surface into the surrounding liquid water of the cell. The impurities, if any, in the water are expected to become concentrated in the remaining liquid water that surrounds the ice mantle of the cell. This less pure liquid water should not be l. Polyurethan e sponge. K. Fine ly divided ice a nd wate r. thermometer resis tor.) 3 Usually de ndritic ice cr ys tals form around the bottom of the well on the introduction of the first few pi eces of Dry Ice. As more Dry Ice is in-3 1n a n expe ri rn e nt wh ere the ice mantles of fiv e cells we re int entionall y c ra c ked duri ng th e 'pre pa rat ion of the cell s. t he TP te mpe ratures o bse rv ed fCST the cell s did not differ s ignific a ntl y, if at all. from t he te mpera tu res that we re o btai ned when t he cell s were pre pa red without c rac ki ng t he ma ntles. This indic at es that th e c rac k hea led suffi cie n tl y. so t hat it did not ca use th e wate r out s ide the ma ntle to mix wi th th at in t he inn er me lt or tha t the watero( the T P cell is hi ghl y pure. troduced to fill the thermome ter well, a clear coating of ice form s around the well and gradually grows to about 7-mm thi c kn ess durin g the 20 min the well is maintain ed full of Dry Ice_ About 1-mm additional thickness of ice is form ed whe n th e re maining Dry Ice, after the 20-min period, is allowed to eva porate . Also, the ice mantle around the bottom e nd of th e well, whe re the thermome te r coil is normally located, becom es somewhat thi c ke r (see fi g_ 1). Afte r th e Dry Ice is co mple tely gone the cell is lowered deepe r into the ice bath and th e thermome te r well is allowed to fill with ice water.
Durin g the 20 min whe n the thermome te r well is maintained full of Dry Ice, there is a strong te ndency for the wate r to freeze solidly across at the top surface of the water in the cell. I[ this layer of ice form s a strong bond with th e thermometer well and the oute r cell , sub sequ ent freezin g of the water below this layer can de velop enough press ure to possibly rupture the glass cell. 4 Th erefore, whe ne ver a layer of ice is about to bridge (or has bridged) be tween th e thermome ter well a nd th e oute r cell wall , th e oute r cell wall near th e upper water s urface should be warme d to melt the s urface ice. This may be accomplis hed by raisin g th e cell out of th e ice bath bri e fl y and warming the cell near the unwanted ice with the hands while ge ntly s haking the cell side ways to was h and , therefore, melt th e ice with the warmer water of th e cell. Durin g thi s time the Dry Ice le vel in the thermometer well should not be allowed to fall too low.
I[ th e cell is raised hi gh e nough to see the mantle durin g th e freezin g proces s, the magnifi cation by the cylinder of water will give th e appearance that the ice mantle is thick e nough to contact the outer wall although the mantle may actually be muc h thinne r (l or 2 mm thi c k).5 During the freezing of the mantle, if the cell has e nough vapor s pace, the cell m ay be mome ntarily inverted , while kee pin g th e Dry Ice from fallin g out of the thermome ter well, to see the ma ntle without the effect of magnification and, therefore, see the true thickness of the mantle. The cell s hould be inverted only when the thermome ter well is cold e nough so that the ice mantle would re main fast to the wall and, therefore, would not float upward against the " bottom" of the cell. I[ the cell is inverted afte r the inne r melt is made the ice mantle will float upward to the bottom of the cell and the chemical composition of the inner liquid would be expected to be altered by the oute r liquid_ 6 The temperature of the water-ice interface of a n inne r melt is the fixed -point temperature of the TP cell. The inner melt is formed by inserting a solid glass rod at ambient temperature into the thermometer well of the TP cell filled with ice-bath wate r ; there by, a thin 4 On occasions whe n a la ye r of ice form ed ac ross t he top, th e in te rn a l press ure thai was form e d broke th e ice laye r in stead of th e glass cell. Th e wa te r t hat esca ped th rou gh the brea k in t he ice imm edi a tel y becam e a n " ice fount a in ." $ T he wa te r le vel in the cell serves as a n indicato r of wheth e r a n adeq uate (or a n excess ive) amou nt of ice i~ form ed around t he th e rmom e te r we ll 6 Of th e fiv e 'I' P cell s wh e re the inne r a nd th e out er wat e r we re inte ntiona ll y mixed by alt ern a tely in ve rtin g a nd upright ing t he cell s. t he TP te m pe ratu res t ha t we re observed for four of t he cell s we re esse nt ia lly t he sa me as those be fore mi xi ng. For the fifth cell th e T P te mpe ra t ure aft e r mi xin g was about 0.04 to 0.05 mK lowe r th an be fore mix in g !51 .
layer of ice adjacent to the thermometer well is melted. The existence of this inner melt is tested by giving the cell a sharp rotatory impulse about the axis of the well and observing if the ice mantle spins or moves freely around the thermometer well. The TP cell usually equilibrates to essentially constant temperature within 30 min to 1 h. after preparation using Dry Ice. In most applications at the NBS the TP cell is prepared at least one day prior to use.
-During storage of the TP cell in the ice bath, the frozen mantle of ice grows slowly and irregularly until it contacts and attaches itself to the outer walls of the cell. The cell is occasionally removed from the ice bath and the excess ice melted by warming with the hands or with water. (As mentioned earlier the extension on the type of TP cells used at the NBS serves as an indicator of the amount of water frozen in the cell. When the water level reaches the vertical extension, the amount of ice formed is usually considered excessive.) The growth of ice in the TP cell while stored in the ice bath can be reduced by insulating the TP cell with a sheet of plastic foam or by placing the TP cell in a Dewar flask which is in turn immersed in the ice bath_ By means of a suitable insulation and occasional melting of excess ice the same freeze of the TP cell may be used in an ice bath for a number of months withoug freezing a new mantle. Moreover, in the PRT calibration laboratory of the NBS the ice bath for the TP cells is installed inside a small freezer chest to reduce the melting of the ice and, thereby, reduce the frequency of replenishing of the ice in the ice bath.
The TP cell is employed with the PRT as follows. Referring to figure 1, a small soft plastic foam (J) is first placed at the bottom of the thermometer well to reduce the mechanical shock when the PRT is inserted. A closely fitting aluminum bushing (I) about 5 cm long is placed above the foam to reduce the external self heating of the PRT (see sec. 4 on self heating). The bushing is constructed of aluminum instead of the heavier copper so that the bushing would gently sink to the bottom on top of the foam when it is inserted into the thermometer well full of water. The bushing has a tapered hole at the top to gently center the PRT when it is inserted into the thermometer well. To avoid upward displacement of the bushing by a "pumping" action when the PRT is inserted, the bushing is not too close fitting with the PRT sheath. To eliminate the effect of the room radiation (particularly the ceiling lights) a heavy black felt cloth (A) is placed over the top of the cell and ice bath except for a hole through which the PRT is inserted_ 7 The PRT is precooled in the ice bath that surrounds the TP cell before it is inserted into the cell. A polyethylene plastic tube (B) helps to guide the PRT gently into the thermometer well. Before the final measurements on the PRT are made the thermometer current is on continuously for at least 5 min (with the Mueller bridge nearly balanced) for the thermometer to come to temperature equilibrium.
The temperature of the water-ice interface of the inner melt where the PRT resistor is immersed (more precisely, the location of the mid-point of the resistor) is slightly lower than the temperature of the TP. The temperature depression is 7 X 10-6 K per cm of water column [2]. The depth of immersion of the PRT is taken to be the distance betwee n the upper water -surface of the TP cell to the mid-point of the PRT resistor. The TP cells in use at the NBS have well depths of 32 cm or 36 cm, the TP cells with 32 cm wells being the most common and most recent. The depth of immersion of the PRT is about 29 cm or 33 cm, which corresponds to the temperature depression of the TP of 200 ILK or 230 ILK, respectively; therefore, the temperature of the TP cell at the mid-point of the PRT resistor is either 0.00980 °C or 0.00977 °C, depending upon the immersion depth of the TP cell being used.
The value of R (0 °C) is obtained by converting the observed values of R(TP) employing equation (6) (see sec_ 1, Introduction)_ Because of the small value of t' atthe TP (t = 0.OO980°C == t' or t = 0.00977 °C == t'), the term containing t 12 is negligible and the average value of A (3.98485 X 10-3 °C -1), found for PRT's calibrated at the NBS in the past years, is employed in the conversion. The unce rtainty in the adjustments of the .value from R (TP) to R (0 °C) in this manner is less than ± 1 X 10-8 R (0 °C) for PRT's that meet the IPTS-68 specification that W (l00 °C) be not less than 1.39250. Hence, in obtaining R(O °C) from R (TP), the uncertainty contributed by this procedure is negligible.

Zinc Point
In place of the normal boiling point (NBP) of sulfur or the sulfur point the equilibrium state between the solid and liquid phases of zinc at 1 standard atmosphere (henceforth referred to as the freezing point of zinc or the zinc point) was recommended as a defining fixed point with the value of 419.505°C on the IPTS-48 (Revised 1960) [7 , 8]. The presently used IPTS-68 assigns the value 419.58°C to the freezing point of zinc. Prior to 1966 the sulfur point was maintained at the NBS for the calibration of PRT's; however, since 1966 the zinc point has been maintained instead of the sulfur point. 8

Zinc-Point Cell
The freezing-point cell employed to realize the zinc point is illustrated in figure 2_9 A bank of suc h cells assembled from zinc samples (SRM-740) of greater than 99.9999 percent purity is available for the calibration work. The freezing points of these zinc-point cells agree within ±0.1mK. The residual resistivity ratios (the ratio of the electrical resistan ce at 273 K to that at 4 K) of specimens taken from zinc bars from which the SRM 740 zInc samples were pre pared ranged from 33,000 to 38,000 [9], indicatin g that the zinc samples have very high purity.
The zinc samples had bee n pre pared from a startin g material that was selected from a lot of electrolytic zinc of 99.99 + percent purity. Th e material was vacuum distilled twice and zone re fin ed with 20 passes. After the leading and trailing e nd s of th e zone re fin ed bars were cropped, they were homoge nized and cas t in fused quartz boats in the form of se micylindri cal bars about 5 cm across t he Rat side. The bars (a9proxi· mately 61 cm long) were deliv ered to the National Bureau of Standard s -Office of Standard Reference Materials (NBS-OSRM) individually sealed in argon· filled polyethylene bags. The zinc samples (1250 g) for each of the freezing-point ce ll s were received from th e NBS -OSRM in the form of two half cylinde rs (eac h about 8 cm lo ng) sealed in a polyethylene bag. The samples had bee n c ut from the bars with a carbid e tipped tool ; th e y were th e n e tc hed in high-purity dilute nitri c acid, rins ed with di stilled water, and air dried.
Because of th e r e lative ly hi gh vapor press ure of zinc at its meltin g point {about 13 Pa (0.1 Torr) [lOpO} , th e zinc samples were melted into the hi gh-purity graphite crucibles by indu ction heating under purifi ed argon at mosp here. The graphite thermo me ter well was then in serted a nd the cell was asse mbled in the form shown in fi gure 2. Details of the asse mbly procedure are the sam e as those describ ed for tin in references [11,12].

. Furnace for the Zinc-Point Cell
Th e des ign of the furnace e mployed with zinc · point cell is shown in fi gure 3. The furnace core co nsists of cylindrical bloc ks of aluminum [top (G), center or mai n (L), a nd bottom (Tn Th e space s urroundin g th e core is packed with Fiberfrax insulation. Th e te mpe rature of the cen te r core (L) is controlled by means of an absolute thermocouple a nd the main heater (0). The te mperatures of the top (G) and bottom (T) bloc ks are controlled relative to the ce nter bloc k te mpe rature by means of differe ntial th e rmocouples and heaters [(F) and (U), respectively] in the blocks. The electric power to the heaters is controlled automatically from the indication of the corres ponding th ermocouples.

.3 Preparation of Zinc-Point Freeze
Liquid zinc is found to s upercool only 0.02 to 0.06 °C. On the day prior to th e zin c-point calibration of the PRT's the furn ace co ntrol is set at a te mperature about 5 °C above the zin c point and the zinc sample is melted overnight. The followin g morning afte r inserting a monitorin g PRT in th e cell, the furnace control is re set to a te mperature a bout 4°C below the zin c point. After th e PRT indicates that recalescence has occ urred and abo ut 10 min have passed , the monitorin g L. C ra phite cru cible.
M. Ins ul ati on , F'iberfrax pape r. PRT is removed and two borosilicate glass rods are inserted successively into the thermome ter well for about 3 min each to induce an inner freeze immediately next to the thermometer well. Also, th e furnace control is reset to a temperature 1 °C below th e zinc point-After withdrawin g the second borosilicate glass rod, the cnld monitoring PRT is in serted into the thermometer well. By following this procedure freezes of 12 to 14 h. durations are obtained . With cells assembled usin g SRM-740 zinc s tandard th e c han ge observed in the fre ezin g point while th e first 50 pe rce nt is frozen is less than 0.2 mK.

I-
The resistance of th e monitoring or c hec k PRT is determined approximately 45 min after inserting it cold into the zinc-point cell. (Meanwhile the tes t PRT is being pre heated in an auxiliary furnace held about 20°C above the zin c point-) Afte r co mpletion of the measurements on the chec k PRT it is re moved from the zinc-point cell and the tes t PRT is withdrawn from the pre heatin g furnace and quic kly inserte d into the zinc-point cell so that th e th ermome te r te mperature during the in sertion would be slightly below that of the cell. (The PRT is in serted sli ghtly colde r than the cell temperature to avoid meltin g and loose ning th e solid zinc mantle arou nd th e thermometer well.) When the PRT is preheated to a te mperature close to that of the cell te mpe rature it reac hes te mperature equilibrium within a few minutes (see fi g. 35, Monograph 126 [12]). The resistance readings of th e test PRT are started about 15 min after inserting it into the zincpoint cell. (Meanwhile, the second test PRT is being preheated in the auxiliary furnace.) After co mpletion of the meas ure ments on the firs t test PRT, it is replaced in the zinc-point cell by the second tes t PRT. A maximum of six tes t PRT's are calibrated in any single zinc freeze. After the last test PRT is calibrated it is replaced with the pre heate d chec k PRT. This secO'nd reading with th e c hec k PRT mu st not differ from the first reading by more than 0.5 mK; if the differe nce is larger, the meas ure ments on so me of the test PRT's th at were calibrated last will be repeated using another zinc freeze. The test PRT's on which the meas ure ments are to be repeated are decided on the basis of th e elapsed tim e si nce the start of the freeze and th e chan ge in the freezing temperature that is observed with the check PRT.
Because of the effect of the hydrostati c head of liquid zin c, the temperature at the height where the mid-point of the PRT sensor is locate d in the zincpoint cell is slightly hotter th an th e equilibrium freezing temperature of zinc at 1 atm press , re as defined in the IPTS-68. (The effect of the hydrostatic head is 27 p,K per cm of liquid zinc [2].) For the NBS zinc-point cell the height of the liquid zinc column above the mid-point of the sensor is 18 c m ; the refore, the temperature at the height of the mid-point of the PRT sensor is 419.5805 0c.

Tin Point
The equilibrium state between the solid and liquid phases of tin at 1 standard atmosphere (231.9681 °c, henceforth referred to as the freezing point of tin or the tin point) is an alternative to the normal boiling point of wate r (steam point) as a defining fixed point on the IPTS-68. Prior to 1966 the steam point was maintained at the NBS for the calibration of PRT's; however, sin ce 1966 th e tin point has been maintained in-' iI s tead of th e steam point-

.3.1. Tin-Point Cell
The freezing-point cell e mployed to realize th e tin point is designed similar to the zinc-point cell (see fig.  2). A bank of tin-point cells assembled from tin samples (SRM-741) of nominally 99.9999 percent purity is available for the calibration work. Th e freezing points of these cells agree within ± 0.1 mK [11]. The res idual resistivity ratios of specimens take n from tin bars from which SRM-741 tin samples were prepared vari ed from 28,000 to 43,000 [13], indicating that the tin samples have very high purity.
The tin samples had bee n pre pared by initially electrolyzing comm ercially re fin ed tin and zon e refinin g the electrolyzed produ ct by at least 20 zone passes. Th e purified samples were homogenized and cast into se micylindrical bars about 5 c m across th e flat side and about 60 c m long. Each of th e tin samples (1300 g each) were received from the NBS-OSRM in th e form of two half cylinders (each about 10 cm lon g) sealed in a polye thyle ne bag. The sa mples had bee n c ut from the bars with a carbid e tipped tool. To re mov e s urface co ntamination they were etc hed first in 40 percent hydroc hloric acid solution and the n in a solution of 40 percent hydrochloric aci d plus 10 perce nt nitric acid; they were washed in di stilled water and in e thyl alcohol and air dried.
The tin samples were melted into th e hi gh-purity graphite crucible by induction heatin g unde r hi gh vacuum. (The vapor press ure of tin at its melting point is estimated to be about 6 X 10-2 1 Pa [10].) The graphite thermome ter well was then in serted and the cell was assembled in the form similar to that of the zinc cell shown in figure 2. Details of the assembly procedure are given in references [11,12] .

Furnace for the Tin-Point Cell
The design of the furnace employed with the tin-point cell is the same as that used with the zinc-point cell (see fig. 3). Initially the sleeve (H) for enhancing the thermal contact between the heat shunts (G, fig. 2) of the tin-point cell and the furnace was aluminum; however, in recent measurements an Inconel sleeve, similar to that used in the zinc-point furnace, has been used in the tin-point furnace.

Preparation of the Tin-Point Freeze
Liquid tin has been found to s upercool as much as 25°C, dependin g upon the temperature a nd le ngth of time the metal was allowed to remain melted . Impurities (e.g., Fe) seem to reduce th e degree of supe rcool [14]. If the freeze were initiated with the tin-point cell in the furnace, the furnace block temperature could not then be raised fast enough to avoid excessive freez· ing of tin. Therefore, the tin freeze is initiated by employing the "outside nucleated freeze" technique described by McLaren [15]. The tin sample is melted overnight in the furnace held at a temperature about 3°C above the freezing point. In the morning after inserting a monitoring PRT in the thermometer well, the furnace control is reset down to a temperature 1 °C below the tin point. (A different monitoring PRT is used with the tin·point cell from that used wtih the zinc· point cell, so that any possible effect on the PRT when used at another fixed point would be avoided. As with the zinc·point cell the monitoring PRT used with the tin·point cell serves also as the check PRT.) When the monitoring PRT indicates that the tin sample has cooled to near the freezing point, the cell is withdrawn from the furnace and held out in room temperature. When the PRT indicates that the sample has started to reca· lesce, the cell is quickly reinserted into the furnace. Following this procedure a freeze duration of 12 to 14 h is obtained. With the tin·point cells containing SRM-741 tin standard, after about 5 percent of the initial "freeze," the temperature change in the following 50 percent of the freeze is less than 0.1 mK. The resistance of the monitoring or the check PRT is determined approximately 45 min after reinserting the tin·point cell into the furnace. (Meanwhile a test PRT is being preheated in an auxiliary furnace held 20°C above the tin point.) After completion of the measurements on the check PRT it is removed from the tin·point cell and the test PRT is withdrawn from the preheating furnace and quickly inserted into the tin·point cell so that the thermometer temperature during the insertion is slightly above that of the celL In actual practice it is not certain whether any melting or any additional freez· ing occurs upon insertion of the PRT. In either event the preheated PRT reaches temperature equilibrium within a few minutes (see fig. 31 Monograph 126 [12]). The resistance readings of the test PRT are started 15 min after inserting it into the tin·point cell. (Mean· while the second test PRT is being preheated in the auxiliary furnace.) After completion of the measure· ments on the first test PRT it is replaced in the tin· point cell by the second test PRT. As with the zinc· point cell a maximum of six test PRT's are calibrated in any single tin freeze. After the last test PRT is cali· brated it is re placed with the check PRT. The require· ment of the second reading of the check PRT is that it shall not differ from the first reading by more than 0.5 mK; if the difference is larger, the measurements on some of the test PRT's that were calibrated last will be repeated using another tin freeze. The test PRT's on which the measurements are to be repeated are decided on the basis of the elapsed time since the start of the freeze and the change in the freezing temperature that is observed with the check PRT.
Because of the effect of the hydrostatic head of liquid tin, the temperature where the midpoint of the PRT sensor is located during measurements in the tin·point cell is slightly higher than the equilibrium freezing temperature of tin at 1 atm pressure as defined in the IPTS-68. (The effect of the hydrostatic head is 22 ILK per cm of liquid tin [2].1 For the NBS tin·point cell the height of liquid tin column above the midpoint of the PRT sensor is 18 cm; therefore, the temperature at the midpoint of the PRT sensor is 231. 9685 0c.

Normal Boiling Point of Oxygen
The calibration of the PRT's at the normal boiling point of oxygen (-182.962, oxygen point) is realized by reference to the NBS-1955 temperature scale adjusted to correspond to the IPTS-68 (see refere nce [4] for the discussion of this NBS-IPTS-68 scale between 13.81 and 90.188 K maintained on capsule· type reference standard PRT'sl. The temperature (hotness) assigned to the oxygen point is also main· tained by long·stem type reference standard PRT's which are intercom pared with the capsule type PRT reference standards. Calibrations near the oxygen point are obtained by intercom paring the test PRT's with a long·stem type reference standard PRT in the apparatus shown in figure 4. Eight thin·walled Monel tubes (A1 extend into the copper block (P); five tubes are 7.9 mm o.d. to accom· modate regular long·stem type PRT's , one is 10.3 mm o.d. for 9 mm PRT's, and two tubes are 12.7 mm o.d. to accommodate capsule type PRT's in holders. The tubes are soldered to the copper block as well as to the copper flanges at the various stages of the apparatus shown in figure 4. The thermometer stems are sealed at the top of the wells by a molded band of soft silicone rubber. The thermometer wells are filled with helium gas to a pressure that is slightly above atmospheri c (see helium gas distributing manifold (D) in fig. 4) . The helium gas enhances the thermal contact between the thermometer and the wall of the well and redu ces the chance of cQndensible gases entering the wells.
The apparatus is prepared for calibration by evacuat· ing through (1) and immersing in liquid nitrogen to the level shown in figure 4. The copper block (P) and shields (F and L) are cooled by admitting nitrogen gas and/or liquid nitrogen through valve (K) just below the liquid nitrogen surface. The cool nitrogen vapor flows through coils (N) attached to the two top shields and to the copper block and exits through (B) to a large·capacity vacuum pump. When the temperature of the copper block (P) is cooled nearly to the oxygen point, the valve (K) is closed and the nitrogen in the cooling coils is removed by pumping. The temperature of the copper block is adjusted to within 1 K of the oxygen point [either by heating or, if necessary, by opening valve (K)] and the two shields are controlled at the temperature of the block. (Calibrations of the PRT's are performed within 1 K of the oxygen point.) When the temperatures of the copper block and the two shields are nearly the same, the inner shield is allowed to " float " without electric power input. The outer shield is controlled relative to the temperature of the copper block by means of differential thermo· S. Tube to va c uum p ump to d raw liquid nitroge n through coo lin g tubes.
e. Tube to he lium gas s uppl y.
D. Ma nifold for di s tributin g; h e lium gas to th e th e r mo me te r we lls.
G. Liquid nitroge n . H. Liquid ux yge n. (Not e mpl oyed i ll com pa ri so n ca li bra ti o ns. ) I. Va l}Or-press ure tube. to <liffc rc llti al pressure di a phragm a nd ma nome ter.
.I . High vac uum lin e. K. Va lve t o co nlrollh e li q uid nitroge n input for coo lin g.
I" T op heat shi elds. to control,her molll cte r we ll and th e rm ome te r ste rn Ic mpe ra lUres. M. Hea ters. N. Coo lin g lubes ( thin -wall Mo ne l).
P . Co ppe r bloc k. co uples and shield heate rs. T he flo ating shield te nds to dampe n t he effects of tem perature gradi e nts a nd short term variations in th e con trol of the outer shi eld. The e lectric power in the s hield heaters is co ntrolled a utomatically fro m the emf outp ut of th e th er mocouples. T he PRT's a re tempered where th e tubes pass through li q uid nitroge n a nd where th e two shi elds a re soldered to th e t ubes (A) before e nterin g th e cop pe r block (P).
In the calibration of th e PRT's the resistance measure men ts are carried out on th e test PRT and t he refere nce standard P RT simulta neo usly usin g t wo M uell er bridges. Meas ure me nts are made as rapidl y as possible with the co mmutatin gs witchingor der NRRNNRRN of the Mueller bridges. As a part of the calibra ti on process the refe rence sta ndard PRT is c hec ked by comparin g with a second refere nce s ta ndard P RT. The te mperature at whi ch th e resistance of the test thermome ter is observed is calcula ted fro m th e observed resista nce of th e refere nce s tandard P RT and its R vers us T relation. (Actu ally, th e analysis is performed in term s of th e W vers us T relati on.)

Resistance Measurements
Th e resistan ce meas ure me nts are perform ed with Muell e r brid ges. Th e brid ge is basically an e qualarm Wh eats tone bridge with modifi cation s to permit co mmutation of th e four PRT lead s so that th e lead res ista nces can cel wh e n two bridge readin gs are ave rage d. Other modifi cation s in clud e a provi s ion for adju s tin g th e ratio arm s to e qua~t y a nd a provi sion for commutatin g the ratio arm conn ec tions a t th e same time th e PRT lead s are commutated , so th at s mall de viati ons from unity of th e rati o arm s would be negli gi ble. (For de tails of the bridge design see refere nce [12].) A galv a nome ter ph otocell amplifi er plu s a secondary " di s play" galvan ometer are used for balan ce de tection. Under fa vora ble circ uit conditi ons th e unbalan ce can be detected within a few na novolts.
In th e process of de termining th e resistance of the PRT the bridge c urrent is re versed to eliminate th e effects of any spurious emfs. The current reve rsal method also doubles the apparent null detector se nsitivity. The observations are made to the neares t 10 J.LO in the following sequence of commutator switch positions: NRRN. (At the oxygen point, observations in this sequence are obtained twice.) The Mueller bridges are calibrated once a year. (previously the bridges were calibrated twice a year.) First the bridge is internally calibrated for linearity in terms of the resistance X(1O} of the 1-0 dial switch. The resistance of a standard resistor (close to 10 O), which had bee n calibrated in terms of the absolute ohm maintain ed at th e NBS , is then measured usin & th e bridge 11. These data are used to obtain correction s to th e nominal valu es of th e switc h positions in term s ()f the absolute ohm. Bridge calibrations are obtained to 10-7 0 for th e I-ohm dial switc h and for the lower dial switches and to 10-6 0 for 10 and 100-ohm dial switches_ For details of the Mueller bridge calibration see the appendix of reference [12]_ A small residual unbalance exists in the Mueller bridge even with all measuring switches set on zero because of the resistances of the leads that connect the resistor network and the resistances of the switch contacts_ The W aidner-W olff elements [16] contribute also to the residual resistance_ In the bridge design a resistor (about 0.98 n) is placed in series with the O.I-ohm decade resistors (which operates "subtractively," see reference [12]) to balance the remainder of the residual resistance of the W aidner-Wolff elements in the adjacent arm and the necessary copper connecting wires in the bridge when all switches are set to zero_ The deviation from balance is the "bridge zero." The bridge zero is subtracted algebraically from the dial readings of all measurements. Because of the changes in the switch contact resistance and changes in the temperature of some bridge components the bridge zero varies during the day. Each day the bridge is used the wiping contacts of the switches are exercised, the mercury contacts are cleaned and the mercury replaced, and the bridge zero is read and estimated to 10-7 O . During the day two or three bridge zero measurements are obtained.

. Se lf-Heating Effects
The measurement of the PRT resistance involves passing an electric current through the resistor. The Joule heating (or i2R heating) raises the temperature of the resistor, its support, and its leads above that of ,the surrounding until a steady state condition is reached where the Joule heating equals the rate heat is dissipated to the surrounding medium. (If the temperature of the surrounding medium remains or becomes constant, e.g., as in a fixed-point cell, a steady PRT resistance reading can be attained. Otherwise, the PRT resistance will continue to change depending upon the Joule heating in the PRT resistor and upon other sources of energy exchange of the system.) The time required to reach the steady state condition depends upon the thermal diffusivities of the thermometer components and of the surroundings and upon the thermal resistances between them. In some situations as much as 5 min or longer may be required to reach the steady state condition. The magnitude of the self heating depends upon the Joule heating and upon the rate of heat transfer from the PRT resistor. At a given temperature the heat conduction from the thermometer resistor to the outer surface of the protective sheath remains essentially constant since the geometry and the thermal conductivity of the thermometer components usually remain unchanged with use. However, the heat conduction from the outer surface of the thermometer sheath to the surrounding medium depends upon the degree of thermal contact of the thermometer with the "surrounding heat sink." Therefore, the heat conduction · external to the thermometer depends upon the conditions of use. The self heating that is intrinsic to the thermometer is referred to as the internal self heating of the PRT. The self heating that is associated with the heat conduction external to the thermometer is referred to as the external self heating. The combined self heating is referred to as the total self heating. The total self heating may be expressoo as a resistance change or as a temperature change corresponding to the resistance change and, strictly speaking, at a given temperature and specified surroundings.
At low electric power leJds the total self heating is very nearly linear with respect to the power that is generated in the PRT resistor. At the NBS, measuring currents of 1 and 2 rnA are usually used with PRT's of R (0 °C) of about 25 0 to determine the total self heating. If R 1 is the resistance reading at a current of il and R2 is the reading at a current of i2, the resistance Ro at zero current is given by For i l and i2 of 1 and 2 rnA, respectively, The total self heating of the PRT is described also in terms of the change in the observed resistance caused by the change in the Joule heating or the change in the observed resistance caused by the change in the square of the electric current in the PRT. In this paper this latter coefficient of total self heating will be referred to as the total selfheating effect. Referring to eq (10), the total self-heating effect is given by (R 2 -R I) / (i~ -in. At the NBS the total self-heating effect is expressed as 0/ (mA)2. As given in eq (10) the product of this coefficient and the square of the current being used gives the total self-heating of the PRT_ A typical steady-state profile of the radial temperature distribution that is expected to result from a ture drop beyond the outer surface of the PRT immersed in th e ice bath. However, in th e TP cell ( fig. 6) the PRT is not in direct contact with the heat sink and, therefore, there is an addition al te mperature drop from the outer s urface of the PRT to the water-ice interface (heat sink) of th e inner melt whe re the temperature is very nearly that of the TP exce pt, as previously mentioned in sec tion 2.1, for the effect of th e hydrostatic head of water. The external self heating of the PRT in the TP cell is th e diffe re nce between the total self heati ng of the PRT in th e TP cell an d in the ice bath. At the NBS, unless r equested oth erwi se, the PRT's are calibrated with a co ntinuou s c urre nt of 1 rnA. The calibration (or the observed resistance) is related to the te mperature of the outer s urface of th e protectiv e sheath of the PRT adjacent to the resis tor. In the TP cell this te mperature corresponds to th e te mperature of the water-ice interface at the level of imm ers ion of the PRT adjusted for the external self heatin g of the PRT. In the calibrations at the other fixed points (tin, zinc, and oxygen) the observed resistan ces of the PRT at a continuous current of 1 rnA are also correlate d with th e te mperature of the outer surface of the PRT, i. e., the te mperature of the fix ed poin t is adjusted for the external self heating of th e PRTin the fix ed -point a pparatus. Therefore, to e mploy the PRT calibrations ob tain ed at th e NBS directly in temperature meas ureme nts, a co ntinuou s c urrent of 1 rnA mu st be used and the PRT must be in good thermal co ntact with the syste m of whi c h the temperature is bein g dete rmined so th at th e external self he ating is negli gible. Otherwise , a correction mu st be made for the external self heating. Wherever the highest accuracy is desired or the external self heating is difficult to determine, the two-c urrent method (described earlier) should be used to obtain the zero current value of the PRT resistance. Again the calibration of the PRT must have been determined for zero thermometer c urrent.

Thermometer Immersion
A PRT is sufficiently immersed in the bath when there is no net heat flow between the se nsor and it s environment (i. e., the environment external to the bath) through the thermometer leads and the s heath that extends from the region of the sensor. The adequacy of thermometer immersion can be readily chec ked by measurements at two or three different depths of immersion, allowing for the difference in temperature of the bath at different depths. If the temperatures at different depths do not agree within the desired limits , then the immersion of the PRT is inad equate.
The required immersion (or the heat co nduction along the PRT stem) can be reduced by choosing materials of poor thermal con ductivity for the leads from the PRT sensor and for the PRT sheath and by keeping their cross section as small as practicable. The thermometer sensor and its leads (gold or platinum for standards-type PRT) should make as good a thermal contact as possible with the s heath . The convection in the thermometer exchange gas should be localized (e.g., by means of baffles). In use, as previously emphasized, the thermal contact between the PRT sheath and the system of interest should be made as good as practica· ble. Figure 7 illu strates the case where th e PRT sheath is in good thermal contact with the bath (ice-bath heat sink); the figure shows on a logarithmic scale the difference between the ice-bath temperature and the indicated temperature as a function of immersion for twoPRT's of different sheath materials and internal construction. (The measurements s hown in figs. 7 and 8 are zero-current values.) For thermometer G, the temperature difference between the thermometer and the bath is reduced by a factor of 10 for eac h 3.3 cm increase in immersion; for thermometer M, the temperature difference is reduced by a factor of 10 for each 1.4 cm increase in immersion. The relation may be approximated by where oT is the desired limit of immersion error, 0 is the difference between the ambient temperature and the bath temperature, N is the change in the immersion that is required to change the temperature difference relative to the ice point by a factor of 10, and D is the immersion that is necessary to limit the immersion error to oT. Thus, in the case of the thennometers shown in figure 7 with the ambient temperature of 25°e, in order for the immersion error to be 0.025 mK or less, the thermometer must be immersed enough so that the temperature difference of 25°e is reduced by six orders of magnitude; i.e., thermom-eter G must be immersed 19.8 c m and thermometer M must be immersed 8.4 cm in the ice bath. Figure 8 shows the immersion characteristics of the same thermometers G and M in a TP cell where the thermal contact betwee n the PRT sheath and the heat sink is slightly inferior than in the ice bath. The immersion c haracteristics of both PRT's are different from those in the ice bath, particularly for thermometer M where the total immersion must now be about 13.5 cm instead of 10 cm in order for the temperature' difference between the observed value and TP temperature to be 0.01 mK. For thermom eter G the total immersion required remains nearly the same. The reduction in the thermal contact (see fig. 6) is caused principally by the thermal resistance of the layer of water in the thermomete r well and of the glass wall of the well. The relation between the radial and vertical heat flow condition s for thermom eter G was not affected as much as in thermometer M by immersion  at 3 and 6 cm up from the bottom should be about 21 and 42 ILK, respectively, higher than that at the bottom. The relatively small effect of the hydrostatic head in the TP cell may be obscured by the variations in the total self heating (see sec. 4 on self.heating effects) because of th e variations in the thermal con· tact of the PRT in the TP cell when the verticalloca· tion of the PRT is adjusted. Hence, it is essential to carry out two·current measurements and obtain the zero-current resistance readings, which eliminates the effects of self heatin g, to test th e effect of hydrostatic head of water in the TP cell. (At the NBS, as mentioned previously, the PRT's are immersed 29 or 33 cm depending upon the depth of the thermometer well of the TP cell.) The adequacy of immersion in the tin-point cell or the zinc-point cell can be c hec ked by th e same procedure as employed with th e TP cell. In th e case of the tin-point cell 12  The plot sh o ws the relations hip betwee n th e loga rithm o f relative teml~erature. and the depth of thermometer imme rs ion. Comparison with fi gure 7 s hows that the I~mers~on cha racteristics of the thermometers are poorer in the triple-point cell than those In the Ice bath. This deb'Tadation in th e immersion c haracteristics is caused by the higher re sistance to radial heat How in th e triple· point ce ll.
in the TP cell. The radial heat conduction within thermometer G is relatively low ; hence, the change in thermal contact from that in the ice bath to that in the TP cell does not result in a large change in the immersion characteristics of the PRT. However, in the case of thermometer M with relatively good radial heat conduction the lower radial h eat conduction in the TP cell caused the immersion characteristics of thermometer M to become poorer.
The adequacy of immersion of the PRT in a TP cell can be best checked by measurements at three depths of immersion, e.g., at the bottom, 3 cm up, and 6 cm up from th e bottom. If the immersion is adequate at the bottom and at 3 and 6 cm up from the bottom, the PRT readings should track the effect of th e hydrostatic head of water in the TP cell, i.e. , the readings block) is adequate the readings at two levels of immersion in the copper block should be essentially the same.

PRT Calibration Procedure
Unless specifically instructed otherwise by the owner of the PRT, all long-stem type PRT's that are received for calibration at the NBS are first annealed for about 4 h in a tube furnace held at 480°C. After annealing, the PRT's are removed from the furnace and allowed to cool in air at the ambient conditions. (Henceforth, unless indicated otherwise, the long-stem type PRT that meets the IPTS-68 specifications [2] will be referred to as SPRT. The platinum resistance thermometers in general will continue to be referred to as PRT.) The calibration measurements are then obtained at the fixed points in the following sequence: TP, zinc point, TP, tin point, and TP. As mentioned earlier, the 12 At the NBS th e lin -po int cell is used without th e inn e r freeze immedi ate ly ne xt to the therm o met e r well. Beca use of the liquid-solid int erface no t be in g close to the therm ome te r well the te mpe rature gradi e nt e xpecte d from th e c hange in press ure with d e pth is so me what obsc ure d ; th e tempe rature obse rved at 3 and 6 em up fr om the bott om is ver y nearly the sa me as that at th e bott o lll . Howe ve r. the te mperature o bse rved at th e bOll o m is esse ntially the sa me as th a t o bser ved at th e bOil o m with an inn er freeze immediat ely nex t to the well. SPRT's are usually calibrated in groups of six. The six SPRT's are first successively calibrated at the TP, then at the zinc point, and so forth. The calibration at the oxygen point is carried out by the comparison method, employing reference SPRT's which, as mentioned earlier, are periodically checked to be consistent with the oxygen point maintained on the capsule type reference PRT's that are used to maintain the NBS-IPTS-68 scale in the region from 13.81 K to 90.188 K [4]. After the oxygen point calibration, another measurement is made on the SPRT at the TP. (Henceforth, for convenience, the four SPRT resistance readings at the TP will be referred to as R (TP) (, R (TP) z, R (TPh, and R (TP) 0, respectively, and, when necessary, the values of R(O °C) obtained from these values of R (TP) will be given the corresponding subscripts.) Whenever the change in the resistance of the SPRT at the TP is greater than what corresponds to about 0.75 mK during the course of calibration the complete calibration process, including the initial annealing at 480°C , is repeated. In some thermometer designs the changes in the R (TP) readings have been found to be on the average greater than in other designs. For these SPRT's a change in resistance at the TP corresponding to 1 mK is allowed.
Above O°C, the constants A and B of eq (6) arti obtained by simultaneous solution from the resistance measurements at the TP, the zinc point, and the tin point. The values of the resistance ratio W(T) corresponding to those at the zinc point and the tin point are calculated using the values of R (TP) obtained after the measurements at the metal fixed points; i.e.,

W(Zn)=R(Zn)/R(O°C)z and W(Sn)=R(Sn)/R(O°C}r.
(For the calculation of R (0 °C) from R (TP), see section 2.1.) Employing eqs (5) and (6) and the constants A and B, tables of Wet) are calculated at integral values of t from O°C to 631°C for SPRT's with a fused quartz sheath or from 0 °C to 500°C for SPRT's with borosilicate glass or stainless steel sheaths. If a SPRT is also calibrated at the oxygen point, the constants A4 and C4 of the deviation function (see eq (4)): are calculated from the relations: (14) and where a*(=3.9259668XlO-3°C -I) is the a that corresponds to the IPTS-68 reference function [2]. From eq (2) where (17) Tables of Wet) are calculated at integral values of t from -183°C to O°C using eq (13), the constants A4 and C4 , and the reference function (eq (3)). The above relations for the SPRT are extrapolated to -200°C for those laboratories that employ the normal boilin g point of nitrogen instead of that of oxygen in calibrating other PRT's. (In such tables the values of t below -183°C are fictitious and serve primarily as artifices for calibrating other PRT's for use above -183°C.) When the SPRT is calibrated only at the TP, tin point, and zinc point, the tables of Wet) start from -50°C. The extrapolation of Wet) downward to -50°C is obtained by assuming a value for C4 ( = 1.7 X 10 -140 C -4) . in the deviation function (eq (13)). The variation in C 4 of SPRT's is not more than ± 1 X 10-14°C -4. By differentiating eq (13) and substituting -50°C for t there is obtained: Since dt/dl1W at -50°C is about 247 °C, the uncertainty in the tabulated value of We-50 °C), because of the assumed value of C4 , corresponds to 0.05 mK, which is negligible. During the course of calibration large c han ges in the SPRT resistance can arise from a number of sources. If the SPRT is insufficiently annealed prior to the measurements at the zinc point, the R (TPh reading can be smaller than the R (TP)( reading because of some annealing that could occur at the zinc point. Also, if the SPRT were "bumped" against an object during or after removal from the annealing furnace but prior to the R (TP)I reading, the R (TPh reading would be expected to be smaller than the R (TP)( reading on account of the extra strain resistance that was introduced by the bumping of the SPRT but was later partially removed by annealing at the zinc point. On the other hand, if the SPRT were bumped immediately after the R (TP)( reading, all of the extra strain resistance introduced by the bumping is most likely not removed by annealing at the zinc point; therefore, the R (TPh· reading could then be expected to be slightly higher than the R (TP) ( reading. If any large strains are introduced into the SPRT just prior to the R (TP)z reading, the R (TP)z reading should be larger than the R (TP) I reading. If any strong bumping occurs after the R (TP)z reading, the R (TPh and the R (TP) 0 readings should reflect the effect. If the platinum wire were wound too tightly around the coil form, strains can be introduced when the SPRT is cooled to the oxygen point and the R (TP) 0 reading could be relatively higher than the other R (TP) readings. Any changes in the R (TP) readings smaller than what correspond to 0.75 mK are considered to arise from the general instability of the SPRT an d the limit of precision of routine calibration measurements. Obviously, errors of observations, includin g errors of recording of data, will be superimposed upon the final data.
Berry [17] recently reported that with PRT's containing oxygen 13 in the protective sheath the R (TP) readings , following the annealing at 450°C, in creased up to 3 or 4 ppm when exposed to temperature s of 200 to 250 °C over a period of seven days. Depending upon the PRT an increase of 1 to 3 ppm is s hown to occur within the first hour of exposure to 200 to 250°C. Accord in gly, the R (TPh readin gs would be expected to be higher than th e R (TP) 1 and R (TP)z readings, the increase being dependent upon how lon g the PRT was in the tin-point cell. It will be shown later that in general the observed R (TPh readings are indeed somewhat higher than the R (TP) 1 and R (TP)z readings in SPRT calibrations. This oxygen-activated thermal effect on th e resistance of the PRT seems to impose a limitation on the precision that can be obtained with PRT's. However, a change of 3 ppm in the R (TP) readin gs correspo nds closely to 0.8 mK; such a large in crease in the R (TP) readin gs after the resistance readings at the tin point has seldom been observed. It seems that th e length of time (approximately 30 min includin g the t i me in the preheating furnace) th e SPRT is at the tin-point temperature during calibration is not eno ugh to convert the SPRT to a noti ceably higher value of the R (TP). 14 Work is plan ned to investigate further this recently observed oxygenactivated thermal effect.
Capsule type PRT's are calibrated as received without annealing. The PRT's are in stalled in holders shown schematically in figure 9 for calibration in the 13 Dry air is sealed in th e protec tive s heath of most S PRT's. M OS I capsul e-type PRT's have he lium gas wilh a small a mount of oxyge n seated in th e ca psul e . Wh e re pure he lium gas was initiall y used. it is I)Ossible th at t he gas would e ve ntuall y beco me co ntaminated with so m e oxyge n .
14 In an ea rli e r in ves ti gati on o n th e freezin g point of tin [11] th e S PRT th a i was e mployed was initia ll y an nealed at 480°C. Before th e inl er com pariso n meas ure me nt s of lin -point s were sta rt e d th e S PRT was probabl y us ed in preliminar y expe rim ent s at th e tin poi nt for a total of abou t 6 h. The s ubseque llt meas ure me nt desc ribed in refere nce [11] s hows th at R(TP ) in creased by an a mo unt correspo ndin g to a bo ut 0. 01 to 0.02 mK pcr 1 h a nd 40 min exposure at th e lin point. A. Elastomer tubin g to helium gas source.
S. Thin (0.1 3 mm ) wall stainless steel tubin g for purging the hold er with he lium gas before the vac uum tubing co nn ector (I ) is sealed. C. Leads to meas urement equ ipm en t ( Mueller bridge ). D. Sections (brass) of mechanical ti e·down , soldered to the stainless purge tube. for guidin g and fa stenin g th e incomin g the rmomet er leads. E. Hard wax for holdin g and sealin g th e 0. 13 mm gold leads that extend down to the thermom eter.
C. Thin wall sta inl ess steel tube ( 11.1 mOl o. d. X 0.11 mm wall ) closed at the bottom.
The coefficient A is obtained from the measurements at the TP and the tin point and from the average value of B. Assuming that there is no measurement error at the tin point, The relative values of R (TP) 's show certain tenden· cies; e.g., R(TPh is more often lower than R(TP)Io approximately twice as often lower than higher. 15 However, R (TP) T is more often higher than both R (TP) I and R (TP) z, almost twice as often higher than lower. R (TP) 0 is more often higher than R (TPh, approximately It as often higher than lower. These observations suggest that either in cooling from the annealing temperature of 480°C some strains are quenched in, which are removed when heated at the zinc point, or else that the additional heating at the zinc point, following the heating at 480°C for4 h, caused more annealing of th e PRT. However, the latter seems more consistent since the work of Berry [18] suggests that in cooling rapidly from 500°C only about 0.1 ppm of R (0 DC) of strain resistance (a change that corres' ponds to 0.02 mK) can be quenched in. The observation that values of R (TP) T were twice as often higher than those of R (TP) I and R (TP) z seem to support the work of Berry [17] that when an annealed SPRT is exposed to temperatures of 200 to 250°C the R (TP) increases 3 or 4 ppm over a period of seven days. Since R (TP) 0 is It times as often higher than it is lower than R (TPh, some SPRT's could have been slightly strained be· tween these two measurements.   " t:.

Check PRY's
As part of the calibration process at the NBS, separate check SPRT's are employed to monitor the constancy of the temperature of each of the fixed points. In the cases of the freezing-point cells of tin and zinc, although the metals employed in the cells are of high purity, the equilibrium temperature of the liquid-solid phases is somewhat dependent upon the relative amounts of the two phases. Usually the SPRT's are calibrated during the period in which the first 50 percent of the metal is being frozen. Of a group of SPRT's to be calibrated, the first and the last measurements in each freeze are obtained with the check SPRT. If the second reading on the check SPRT is lower than the first by what corresponds to 0.5 mK some of the SPRT's being calibrated, based on the time of the measurements that were obtained, are recalibrated employing a new freeze with the cell. The first and the last measurements on the new freeze are again obtained with the check SPRT. The comparison of the results of the repeat calibration with those of previous freeze will show whether SPRT's calibrated earlier in the sequence with the previous freeze should also be recalibrated.
The measurements with the check SPRT of every ne w freez e are co mpared with those of the previous freeze s. The c heck SPRT's e mployed with the zin c a nd tin point cells are usually about 1.5 a nd 2 h a t their respective fixed points during each freeze. Th e c heck SPRT for the tin point cell is near the tin point lon ger because of th e pre paration and ma nipula tion th at are followed for initiating th e freeze by withdrawing th e cell from the furnace well (see sec. 2.3).
For the oxygen point comparison calibration (see sec. 2.4) a second reference sta ndard SPRT is used as the check SPRT to monitor the consistenc y of the "working" reference standard SPRT. The value of W(02) obtained for the check SPRT is compared with those of pre vious calibrations.
With each of the readings of the c heck SPRT's at the fixed points th ere are also obtained readin gs at the TP. Thus, there is collec ted a his tor y of measure me nts with c heck SPRT's and fix ed points. zinc-point celL The symbols 0 and 6 indicate in most cases th e R (2n) readin gs at the beginning and end, res pectively, of a group of SPRT's that were calibrated.
Occasionally additional R (2n) readings h ave been obtained , the sequence bein g 0, 6 , 0, and (>. When th e firs t readin g ° is sus pected and th e second re ading 6 is obtained, th e symbols 6. and 0 indi cate th e beginnin g and e nd readin gs, res pectively, of a group of SPRT 's th at were calibra ted. Th e fourth readin g, in di-    [19] found that the reproducibility of W(lOO 0C) of five SPRT 's corresponded to 0.1 mK as long as the R (l00 °C) and R (0 0C) were observed with the platinum of the SPRT in the same oxidation state. The values of Wet) that are obtained in the NBS calibration procedure discussed in this paper corres· pond essentially to this requirement. Figure 15 shows  to ± 0.16 mK, which is significantly smaller than that found for W(Zn) and W(Sn) obtained with their respective check SPRT's.

Calibration of "MAP" Thermometers
As part of the NBS Measurement Assurance Program (MAP) on platinum resistance thermometry a set of three calibrated SPRT's has been furnished to participating standards laboratories of the nation. On receipt of the SPRT's the laboratory first determined R (TP) at 1 and 2 mA c urrents and then cali brated the SPRT's according to its regular laboratory procedure. After completion of th e calibration th e laboratory determined R (TP) at 1 and 2 mA c urrents just before shipping the SPRT's back to th e NBS. On return of the SPRT's to the NBS their R (TP) 's were first determined at 1 and 2 rnA c urren ts ; th ey were th e n annealed and recalibrated according to th e usual I  I  I  I  I  I  I  I    procedure. The SPRT's were then shippe-d to the next participating standards laboratory. The SPRT's were shipped cushioned in soft plastic foam inside a wooden box. When the SPRT's were at the various standards laboratories they were subjected to the annealing temperatures (450°C to 480°C) for 4 h and to the various temperatures (about -180, 0, 232, and 420°C) of the fixed points that were employed in the calibration. While at the NBS the SPRT's were annealed at 480°C for 4 h and then recalibrated. Therefore , in the interval between the calibrations at the NBS the SPRT's were exposed to temperatures over a wide range, including the higher temperatures where they were "annealed." The successive calibrations that were obtained at the NBS were examined to determine the reproducibility of the calibration and also to determine how well the calibrations of the SPRT's are figure 17.16 (The first three calibrations of thermometers A , B, and C and the first two calibrations of thermometer D were obtained before shipping them to the standards laboratories that participated m the MAP study.) The calibration sequence after the first calibration is indicated by the symbols 0, 6, 0,0, 9 , x, and •.
The flagged points indicate a second measurement using another freeze. There is a tendency for the values of W(Zn) to increase with use which was not the observation with the check SPRT 200 (see fig. 13). The calibration is noticeably more scattered at the zinc point than at the tin point or at the oxygen point. The deviations reflect the combined variations in the 16 After several successive cal ibrations the re lativ ely older thermometer A wa s cons id e red to be less stable than th ermom ete rs Band C. Thermome ter A wa s subsequ e ntl y replaced with thermometer D.
observations of R(TP) and of R(Zn), R(Sn), or R (02 ), the variations in R (TP) being amplified in W(Zn) and W(Sn) (see sec. 7.1). The deviations should reflect also the effect of handling of the SPRT's in the various laboratories and the effect of handling during shipment.  tainty of temperatnre measurement that can be achieved, under the various conditions to which the SPRT's were subjected, relative to the IPTS-68 maintained by the NBS. For example, the degree of repeatability of the measurements at the fixed points indicates the degree of retention of calibration by the SPRT. Since the standard deviations of the values of W (Sn) and W (0 2 ) are comparable and those of W (Zn) are about twice those observed with the check SPRT's, the calibration of the SPRT's have been retained close to the limit of calibration measurements at the NBS. The user of a SPRT that was calibrated at the NBS can look upon figures 18,19,20, and 21 to indicate the level of retention of c alibration (after annealing in a similar manner) and repeatability of calibration of a SPRT and, in the analysis of his temperature measure· ments, should combine the uncertainties shown in the figures with the uncertainties of his measureme nts to obtain his overall uncertainty relative to the NBS.

Repeated calibrations
As another test of reprodu cibility of th e NBS calibrations at the fixed points, a SPRT was repeatedly calibrated (includin g the initial annealing) in seven successive batches of calibratio ns. The sequence of calibration of this " test" SPRT (thermometer E) was varied within each hatc h of SPRT's that were to be calibrated for the c us tom ers so that the locati on of calibration on th e freezi ng " plateau " of the zinc· and tin-point cells was vari ed for the SPRT. The values of W that were obtained at th e zin c, tin, and oxygen points are com pared (relative to the firs t calibration in batch 74D) in figure 17 along with those calibrations obtained for thermometers A, B, C, and D that were used in th e NBS-MAP measurements descri bed earlier. The standard de viations of the measurements are sum· marized in table 1. The results show that the variations in the calibrations of th ermometer E are comparabl e to those obtained for thermometers A, B , C, and D; the refore, the additional han dlin g and " use" of th e NBS-MAP therometers did not see m to have a ffected the calibration of these SPRT's to a large exte nt. (These measureme nts were on only one the rm ometer E; other SPRT 's may show be tter or worse reprod ucibility. ) Figure 22 shows more clearly how the observations obtained with thermometer E changed with each calibration. The symbols 6., 0, and 0 are associated with the measurements at the zinc, tin, and oxygen points, respectively. The same symbols are used to represent the observations at the TP after the measure· ments at the above three fixed points. The symbol 0 represents the initial measurements at the TP after annealing the SPRT. The filled in symbols represent the values of W(t) at the corresponding fixed points. The plot shows that the values of the SPRT resistances tended to increase with each calibrationY However. the values of W(t) obtained at the fixed points do not show any definite trend. Figure 23 shows how the values of W(t) (in terms of equivalent values in t) vary relative to those of the first calibration. The meas· urements of the first calibration were slightly outside of those measurements obtained in the later series of calibrations. .

Discussion and Conclusion
The calibration data on 213 PRT's (mostly S PRT's) th at we re received over a two-year period show that the average of the sta nd ard deviations of R (TP ),s tha t were observed fo r each of th e th ermo meters corresponds to ± 0.15 mK. This indicates the preci sion of the NBS calibra tion meas ure me nts a nd the high reproduci bility of th e SPRT's at the T P a nd the high stability of the SPRT's even after bein g subj ected to te mpe ratures as hi gh as 420°C or as low as -183°C. The high reprodu cibility of valu es of W of the check S PRT's (serial nos. 199, 200, a nd 250) that are used for the zin c , tin , and oxygen points (poole d standard d eviations : ± 0.28, ± 0.30 , a nd ± 0.16 mK, respectively) shows tha t SPRT's can be employed in high-precision te mperature meas urements. [An error in R (TP) is amplified (or atte nuated) in the value of W a t the se fixed points by 2.6, 1.9, and 0.24 times , re spectively.] Th e high reproducibility also shows that the tin and zin c points and the reference standard SPRT for the oxygen point are highly stable. Although both the thermometer resistances and resistance ratios wer e found to c hange, the resistance ratios were more stable. The data on the check SPRT's were taken over a two-ye ar period ; measure ments ' over a longer period or pe rhaps other conditions are needed to de termine the useful life of a SPRT. 18 The values of W(Zn) of th e c heck SPRT used with th e zin c point are decre asin g sli ghtly with use_ An ann ealin g of I7 ln these meas urement s the sam e Muell e r brid ge calibra ti on was used. Ne it her th e hi sto ry of th e Mu elle r bri dge nor s ubseq uent ca lib rati ons ind ica te th at th e drift of th e bridge wa s respo ns ib le for the dri ft s hown in fig. 22. I II A SPRT is us ua ll y bro ken befo re in stabil iti es res ulti ng fro m grain gro wt h o r oth er defects ca use it to be " re tired.'" this SPRT at a higher te mperature (e.g., 480°C) may redu ce thi s tre nd. T he SPRT's th at were used in th e MAP study a nd in repeated calibrations were ann e aled at 480°C pri or to eac h calibration; the valu es of W(Zn) are eith er randomly scattered or are in creasin g sli ghtly with use.
The res ults wit h the SPRT 's used in the MAP s tudy show th at whe n th e thermometers are s hi pped in a s uitable protective co ntainer the calibration is retain ed. (The SPRT's have been s hipped an d received from a number of la boratories, so me located as far as across the contine nt.) The res ults show also that SPRT's can be em ployed reli ably in precise temperature meas ureme nts. Whe n these SP RT's were heated at 450°C or 480 °C for 4 h and calibrated at e ac h of the la bor atories (5) tha t participated in the MAP study and were heated again at 480°C for 4 h at th e NBS whe n th e SPRT's were returned from each of the laboratori es, th e calibrations did not ch ange by more tha n ± 1 mK. 19 The variations in the observed values of W re Aect the imprecision in the calibrations s uperimposed upon whatever changes that have occurred in the SPRT's. Th e largest scatte r was at th e zinc point, th e aver age of th e standard de viations b eing ± 0.6 mK. Th e average of the standard de viations of th e observed values of W of the SPRT's at the tin and oxygen points were ± 0.3 mK and ± 0. 2 mK , respectively. These sta ndard d e viation figures for th e tin and oxyge n point meas urements are compa ra ble to those obtain ed with th e c heck SPRT's whic h suggest th a t the treatm e nts to which th e MAP SPRT's were subj ected did not s ignificantly affect the thermometers anymore than if the SPRT's had remained at the NBS laboratory and been used. On the other hand, the standard deviation figure obtained on the MAP SPRT's at the zinc point is about twice as large as that obtained with the check SPRT.
The values of W that were obtained at the three fixed points in the repeated calibrations of a SPRT were similar to those obtained with the MAP SPRT's. Further work is needed to determine the source of larger imprecision at the zinc point.
The PRT calibration on the IPTS-68 is based on relatively few fixed point~. A small error (e.g., corresponding to 1 mK) at any of the fixed points can go undetected and cause large errors above the zinc point (see figures 18, 19,20,21, and 23). A fixed point near the upper limit of the PRT scale would be a sensitive means of detecting calibration errors at the tin or the zinc point; or if the PRT is to be used primarily at the higher temperatures, the freezing point of antimony (630.755°C) or the freezing point of aluminum (660.46 °C) could be included in the calibration [20] . Measurements at the freezing point of cadmium (321.108°C) could also serve to chec k the IPTS-68 calibration. Below O°C the triple point of xe non (-ll2 0c) co uld perhaps be developed for c heckin g the calibration.
The comparison calibration of test PRT's in terms of two or three reference standard PRT's, which are periodically "checked" on the IPTS-68 , can yield many calibration points that can be analyzed by a least squares method so that the contribution from an error in anyone observation would be negligible. Investigations are in progress to improve the calibration accuracy ofPRT's. The other notations have been retained.