The effect of the conditions for the formation of an internal interface on the freezing point of zinc of

99.9999% purity for different intensities of the removal of heat from the zinc in the thermometer channel is

investigated. Comparative measurements without the formation of an internal interface were carried out.

The difference between the maximum values of the measured temperatures reached approximately 1 mK.

The reasons for these differences are considered.

Key words:freezing point of Zn, interface.

The authorization of the document [1] by the national metrological institutes and the preparation of comparison

tables for exhibition on an international level has given rise to increased discussion regarding estimates of the uncertainty of

the fundamental fixed-point temperatures of the ITS-90 International Temperature Scale. These estimates give the mean-

weighted value for key comparisons and, consequently, the deviations from it of results obtained in national laboratories.

Ultimately, they characterize the practical capabilities of individual metrological institutes. Estimation of the uncertainty of

the fixed points is a complex and nonunique process, which requires further analysis.

The key comparisons KS3 and KS4 [2, 3] showed that the differences between the results of measurements by

metrological institutes considerably exceed the overall uncertainties of the fixed-point temperatures presented by them. It is

obviously advisable to find and understand the reasons for the lack of agreement between the results and to estimate the

uncertainties. In our opinion, two methods are possible: either the optimum procedure for obtaining the fixed-point temper-

atures are subject to certain variations and they are not taken into account when estimating the uncertainty, or the estimates

of the individual components of the uncertainties are too low.

We will consider the uncertainties in the fixed-point temperatures [2]. Among the components of type B, the effect

of impurities predominates. Papers [4–6] are devoted to estimating it as well as discussions in the working groups of the

Consultative Committee on Thermometry. Three methods are at present proposed for this estimate: the so-called SIE and

OME methods, as well as the method in which samples of different purities are compared [5, 6]. Each of these methods has

its drawbacks.

According to [5, 6], the SIE method is preferable. This consists of summing the effect of the individual impurities

on the liquidus temperature of the material. The effect of each impurity is estimated by the product of the slope of the liq-

uidus line, obtained from the phase diagram in the region of 100% of the main component, and the impurity content, known

from the certificate. This estimate, in our opinion, gives rise to serious questions: how and with what uncertainty are the

phase diagrams obtained, particularly in the range of impurities of the order of units of 10–4%? In this case, the following

situation arises. Metrologists make considerable efforts to determine the fundamental fixed-point temperatures as the equi-

Measurement Techniques, Vol. 47, No. 11, 2004

AN ANALYSIS OF THE CONDITIONS FOR THE

FORMATION OF AN INTERNAL INTERFACE

AND THEIR EFFECT ON THE FREEZING

POINT OF ZINC

A. G. Ivanova and A. Yu. Il’in UDC 536.5.081.088

Translated from Izmeritel’naya Tekhnika, No. 11, pp. 43–45, November, 2004. Original article submitted May 12,

2004.

0543-1972/04/4711-1096©2004 Springer Science+Business Media, Inc.1096

librium temperature of the phases of the pure material. Optimum methods of realization have been developed for this pur-

pose and the purest materials are used as well as precision thermometers and measurement bridges,and the estimate of the

result obtained is verif ied by phase diagrams with an unknown uncertainty. This is like a closed circle. Can it be ascertained

what must be determined more accurately?

In the key comparisons KC3,the majority of national metrological laboratories (10 out of 14) estimated the com-

ponents of the effect of impurities for the freezing point of Zn using the OME method. As was shown in [4], the use of this

method leads to an estimate of this component that is too high. The method of estimating this component compares samples

of different purity in no way connected with the assumed definition of the measured quantity, i.e., the temperatures of the

fundamental fixed points. Hence, this result is treated in a complex way as a component of the uncertainty.

Hence, basing ourselves on the proposed methods of estimating the most significant component of the uncertainty

of type B [4–6],we arrive at the conclusion that estimates of it and, consequently, the overall uncertainty of the KC3 results

also,are not too low.

When discussing the results of the KC3 key comparisons,it was suggested that heat transfer along the thermome-

ters could affect the disagreement between the data obtained by laboratories. However, this is unlikely, since the consider-

able times for which the freezing areas,which were observed in the comparisons,existed, confirm that the temperature field

in the ovens was very uniform and, consequently, there was no appreciable heat transfer along the thermometer.

It follows from the above that closer attention needs to be paid to the individual assumptions of the optimum method

of realizing the temperature of the fixed points [7],which may lead to unjustified estimates of the uncertainty. The analysis

of the main components of the uncertainty arising from the effect of impurity [4–6] is based on the fact that the use of the

method of obtaining the fixed-point temperature with the formation of an internal freezing front and by measuring the first

25% of the area enables the temperature of the “liquidus” of the material to be determined. The construction of modern

ampoules for the fixed points,particularly closed ampoules,does not convince us that an internal interface has been formed

and is maintained. This indicates that the measured temperature may correspond to any temperature in the liquidus–solidus

phase transition interval. The purpose of the present paper is to investigate the effect of the conditions for the formation of

an internal interface on the zinc fixed-point temperature for different intensities of heat removal in the thermometer channel.

The intensity of heat removal was varied by introducing rods made of materials with different thermal diffusivities into the

thermometer channel at different times.

We chose to investigate the freezing point of Zn. In the experiments,we used an open ampoule with zinc of

99.9999% purity. The crucible of pure graphite had an internal diameter of 36 mm and a height of 24 mm,and an internal

diameter of the thermometer channel of 12 mm. The mass of zinc was about 900 g. The measurements were carried out

using standard platinum resistance thermometers of Russian manufacture and a Guideline 9975 precision bridge. The oven

had three heaters and an automatic system for maintaining the chosen conditions.

The uniformity of the temperature field around the ampoule for different melting and freezing durations was esti-

mated from the fact that the product of the temperature difference between the heater and the phase transition and the dura-

tion of the phase transition should be constant. This follows from the heat-balance equation

Q = αF(Th – Tph)τ = const,

where Q is the quantity of heat required for complete phase transition and is equal to the product of the mass of zinc and the

heat of phase transition,α is the heat transfer coefficient between the zinc and the heater, F is the total surface of the metal,

Th and Tph are the heater temperature and the phase-transition temperature, and τ is the duration of the phase transition.

The temperature gradient in the thermometer channel during the freezing period corresponded to the dependence of

the temperature on the hydrostatic pressure.

The fixed point of zinc was obtained using the recommended method [7] for a freezing duration of 10–16 h. The

procedure for initiating an internal freezing interface was varied from experiment to experiment using rods of different ther-

mal diffusivity and by immersing them for different times in the channel. When choosing the rods we followed the practice

of national metrological institutes,as presented in the KC3 report [2]: standard platinum resistance thermometers and quartz

and ceramic rods with an immersion time of 1–5 min.

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When considering and analyzing the initial parts of the zinc freezing areas,we bore in mind the results of thermal

calculations of the initiation process and certain estimates characterizing the zinc freezing process. The rate of freezing of

the zinc corresponds approximately to the velocity of motion of the interface of 0.75 mm/h for long areas and 1.5 mm/h for

short areas.

By calculating the temperature to which the rods were heated for a specified time of immersion in the thermometer

channel,taking their thermal diffusivities into account,we were able to estimate the amount of heat removed by them from

the zinc, and the amount of crystallized metal as a result of this removal. The error of this calculation was about 20%.

Finally, we obtained the following estimates:a standard platinum resistance thermometer after five minutes can ini-

tiate crystallization of the order of 5 g of zinc, a quartz rod in the same time can initiate crystallization of 30 g of zinc, while

a rod of stainless steel can initiate crystallization of 70 g of zinc. If we assume that, as a result of the initiation a uniform

layer of zinc crystals is formed on the surface of the thermometer channel,this will correspond to a layer thickness of 0.1 mm

when using a resistance thermometer, 0.6 mm when using a quartz rod and 1.1 mm when using a rod of stainless steel. The

calculations were carried out for an open crucible, i.e., when there was only an air gap and the graphite wall of the ther-

mometer channel between the zinc and the rod. For closed ampoules,the amount of crystallized zinc under the same initia-

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t, min

12

4

5

6

3

t, min

12

4

5

6

3

Fig. 1. Zinc freezing curves.

Fig. 2. Initial parts of the zinc freezing curves.

tion conditions will be less due to the additional thermal resistance produced by the quartz envelope and, as a consequence,

less removal of heat.

The results obtained enable us to estimate the possibility of continuous interfaces forming on the walls of the crucible

and the thermometer channel at the beginning of the crystallization stage. If a layer of metal not less than 1 mm thick is formed

by the continuous interface, the use of a metal rod immersed in the channel for five minutes will provide effective initiation.

The total zinc freezing areas of different duration for different methods of initiation are shown in Fig. 1, while the

initial parts of these areas are shown in Fig. 2.

As follows from Figs. 1 and 2,the most continuous and stable freezing areas (curves 1, 2) are obtained after initia-

tion using two stainless steel rods with an immersion time of 3 min. They correspond to the highest freezing temperature.

This can be explained by the fact that the intensive removal of heat by the two rods promoted rapid growth of pure zinc crys-

tals on the surface of the thermometer channel and led to the formation of a closed continuous interface around it. This inter-

face remained throughout the whole freezing process,and the thermometer recorded its temperature.

Curves 6 in Figs. 1 and 2 relate to freezing without initiation with a duration of 16 hours, i.e., with a velocity of

motion of the external interface of the order of 0.75 mm/h. As can be seen,the formation of an external interface and the

establishment of thermal equilibrium in the ampoule take about four hours. The maximum value of the temperature of this

curve differs from curves 1 and 2 by 1 mK. Curves 3–5represent the freezing areas obtained with different initiation: curves

3 and 4 are with one metal and one quartz rod, respectively, and curve 5 is with one resistance thermometer. As regards the

value of the temperature, they occupy an intermediate position between the curves described earlier. The use of a resistance

thermometer, according to earlier estimates,does not give rise to the formation of a closed internal interface, but as a conse-

quence of the removal of heat from the crystals growing on the walls of the crucible, it accelerates the establishment of ther-

mal equilibrium. The difference in the recorded temperatures can presumably be explained by the incomplete formation of

the internal interface and the effect of the external interface on the results of measurements.

It has been shown experimentally that different conditions of initiation of the internal interface lead to changes in

the zinc solidification curve and the recorded temperature. The maximum disagreement between the temperatures for initi-

ation and without it amounted to 1 mK. The most probable reasons for the changes would seem to be the conditions under

which the internal interface is formed, i.e., its presence or absence. This fact requires a different approach to estimating the

components of the uncertainty arising from the effect of impurities.

REFERENCES

1. Mutual Recognition of National Measurement Standards and of Calibration and Measurement Certificates Issued

by National Metrology Institutes, BIPM, Sevres (1999).

2. B. W. Mangum,G. F. Strouse, and W. F. Guthrie, CCT-K3: Key Comparison of Realizations of the ITS-90 over the

Range 83.8058K to 933.473K, NIST Technical Note 1450 (2002).

3. H. G. Nubbemeyer and J. Fischer, CCT on Key Comparison 4: Comparison of Local Realizations of Aluminum and

Silver Freezing Point Temperatures,Draft A, PTB, Berlin, (2001).

4. B. W. Mangum et al.,“On the influence of impurities on fixed point temperature,” Document CCT 99 11, submit-

ted to the 20th Meeting of the Comite Consultatif de Thermometrie (1999).

5. B. Felmuth,J. Fischer, and E. Tegeler, “Uncertainty budget for characteristics of SPRTs calibrated according to the

ITS-90,” Document CCT/2001-002, submitted to the 20th Meeting of the Comite Consultatif de Thermometrie

(2001).

6. E. Renaot and G. Bonnier, “Combined standard uncertainty. SPRT calibration according to the ITS-90,”

DocumentCCT/2000-17, submitted to the 20th Meeting of the Comite Consultatif de Thermometrie (2000).

7. B. W. Mangum et al.,“Optimal realization of the defining fixed points of the ITS-90 that are used for contact ther-

mometry,” Document CCT/2000-13, submitted to the 20th Meeting of the Comite Consultatif de Thermometrie

(2000).

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