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HEAT CAPACITY 
OF LIQUID BISMUTH 


FIRST TECHNICAL REPORT 


HOWARD BELL 
RALPH HULTGREN 


JULY I. I960 




SFP19 1960 

' _ 

JIPDR ' 


SERIES NO. 155 ISSUE NO. I 

CONTRACT NO. Nonr- 222 (63) 


UliUATERIALS U 

INSTITUTE OF 


^^70:ripr§ 

ESEARCH _ 

ENGINEERING 


ABORATORY 

RESEARCH 


UNIVERSiTV CF CA L ■> C F2 N I aERKE(l.EY 












HEAT CAPACITY OF LIQUID BISMUTH 


( 1 ) 


Howard Bell 


( 2 ) 


by 

(3) 

and Ralph Hultgren 


First Technical Report 
Contract No. Nonr-222(63) 


July 1, 1960 


Series No. 155, Issue No. 1 
University of California 
Berkeley, California 


(1) Report based on a thesis by Howard Bell submitted in partial 
satisfaction of the requirements for the degree of Master of 
Science in Metallurgy to the University of California. 

(2) Graduate Student, University of California, Berkeley. 

(3) Professor of Metallurgy, University of California, Berkeley. 



1 . 


ABSTRACT 

The true heat capacity of liquid bismuth was measured from within 
three tenths of a degree of the melting point (544. S^K) to 801. 8°K by a 
method of mixtures using a liquid bismuth calorimeter. The results show 
a decrease in heat capacity with increasing temperature. This is in agree¬ 
ment with a trend which has been observed for the heat capacities of other 
liquid metals. 

The results of the investigation are discussed in relation to the strucj- 
ture of the liquid. One conclusion reached is that there are associations 
similar to those found in the solid in the vicinity of the melting point which 
break up with increasing temperature. 



INTRODUCTION 


2 . 


The prospect of extensive use of atomic power reactors has made 
urgent the problem, of heat delivery from liquid coolants. The thermal 
diffusivity of a coolant is defined as the ratio of thermal conductivity to 
the product of specific heat and density. Liquid metals -which are chemi¬ 
cally stable at elevated temperatures and have a high thermal conductivity 
naturally play a major role in this field. As a result of its low melting 
point (544. 5“K) and low absorption cross section for thermal neutrons, bis¬ 
muth. is a possible reactor coolant. One of the important heat transfer pro¬ 
perties of liquid bismuth, specific heat, will be the subject of this investi¬ 
gation. 

Knowledge of the heat capacity of liquids is p, . o of interest since it 
may offer a sensitive measure of changes of str',<' 'ure. Some theories pre¬ 
dict that atoms in the liquid, when just above the melting point, are associated 
in quasi-crystalline arrangements. An abnormal metal such as bismuth, in 
which the solid and liquid states differ markedly both in structure and physi¬ 
cal properties, would be particularly subject to quasi-crystalline aggregations 
near the melting point, owing to the persistence in the liquid of forces acting 
on the atoms in the solid. These associations should be broken up by rising 
temperature, and this effect should be indicated by an anomalously high heat 
capacity. 

In most cases measurements of the heat capacity of liquid metals lack 
sufficient accuracy to determine any definite trend. The usual procedure is 
to pass a straight line through the scattered results of heat content measure- 



3 . 


ments, the slope giving a heat capacity which is constant with temperature . 

Precise measurements of liquid heat capacity have been carried out on only 

2 

a limited number of metals: lead, mercury, sodium, potassium, lithium , 

3 4 5 

tin ' , and indium . In each case the heat capacity was determined directly 
and found to decrease with increasing temperature. In several cases Cp. 
reached a minimum at a temperature somewhat s^bove twice the melting 
point, and increased thereafter. 

Direct measurements of the heat capacity of liquid bismuth have been 

6 7 8 

carried out by FOrster and Tschentke , Carpenter and Harle , and Person . 

FOrster and Tschentke found a decrease in Cp from the melting point to 

690‘’K.a;id increasing values thereafter but had considerable scatter, while 

Carpenter and Harle found decreasing Cp in the range 544. 5®- 640°K and 

Person reports a constant value of 7. 59 cal/deg. g-atom. Heat capacity 

g 

values have also-been determined from heat content data. Umino reported 
a constant value of 7. 80, while WQst and Meuthen^^ found a linear increase 
with temperature from 7. 1 at 544®K to 8. 76 at 1273®K. 

The present investigation is designed to accurately determine the heat 
capacity of liquid bismuth directly. The results should be an important con¬ 
tribution to the thermodynamic knowledge of bismuth and offer further evi¬ 
dence as to whether or not decreasing heat capacity is a characteristic of 
liquid metals. Data in the vicinity of the melting point should also offer an 
insight to the structural changes occurring during, the melting phenomena. 



APPARATUS 


4 . 


A liquid-metal solution calorimeter has been adapted for these measure- 

12 13 

ments. This apparatus has been described in detail elsewhere ’ ; there¬ 

fore only a brief description will be given here. 

The core of the apparatus is the liquid-bismuth bath, which consists 
of about 621 grams of liquid bismuth contained in a thin-walled molybdenum 
crucible. The crucible rests upon three sharp points of insulating refractory 
and is surrounded by a cylindrical nickel-plated copper jacket which weighs 
about ten kilograms. The jacket is heated by three series-connected Nichrome 
heating elements wound on an alundum tube at the sides and on ceramic disks 
at both ends of the jacket. A sensitive resistance-thermometer temperature 
controller makes it possible to prevent externally caused temperature drifts 
or fluctuations in the copper jacket either before or during a run. It is 
therefore possible to obtain constancy of the calorimeter temperatures to 
within less than ±0. 001° C prior to making a run. A series of nickel radiation 
shields provide insulation from the rest of the apparatus. 

The bath temperature is measured by a copper-constantan thermocouple 
extending into the center of the liquid bismuth inside a molybdenum protection 
tube. The jacket temperature is measured by a similar couple located in a 
vertical hole near the jacket wall ending at a point opposite the crucible. The 
couples have a common constantan leg making it possible to switch the leads 
appropriately to measure either temperature separately or the difference 

between the two. The jacket temperature is also measured by a platinum- 

platinum plus ten percent rhodium couple. 



5 . 


Thermocouple emf's are measured on a shielded White double poten¬ 
tiometer in connection with a moving coil reflecting galvonometer, meter 
scale and telescope. The sensitivity is such that a scale deflection of one 
mm. corresponds to a change of about 0. 015 microvolt (0. 00024° C) in the 
reading of the differential couple between the jacket and crucible. 

The upper part of the apparatus contains the dispenser unit from which 
specimens are ejected one at a tirrie into the bath. Specimens are solid pel¬ 
lets of pure bismi^th with diameters of 5-1/2 mm. or less. A thermocouple 

measures the specimen temperature prior to the drop. 

3 4 5 

Previous investigations ’ ' have found that the cold samples which 

are dropped into the bath can cause too low a temperature reading if they 

come into close contact with the thermocouple. To prevent error from this 

source a tantalum funnel was placed inside the crucible to act as a baffle. 

The units of the apparatus are supported in a vacuum-tight, water- 

-7 

cooled shell, which is evacuated to a pressure of 10 atmospheres during 
the runs. 


SAMPLE 

The bismuth used for both the bath and the pellets was supplied by 
Consolidated Mining and Smelting Co. This bismuth was 99. 9999% pure. 
A spectrographic analysis found only a trace of iron to be present as 


impurity. 



EXPERIMENTAL PROCEDURE 


6 . 


In preparing for the series of runs, bismuth was melted into a molyb¬ 
denum crucible. This step was carried out in an argon atmosphere to pre¬ 
vent oxidation of the bath. After the bath had cooled to room temperature it 
was removed from the furnace and placed inside the calprimeter. Crucible 
and contents were then raised to temperature. 

A run consisted of dropping a small bismuth pellet, initially at room 
temperature, into the bath of liquid bismuth. Previous to making a drop, 
readings cf both the jacket temperature and the difference in temperature 
between the jacket and crucible were taken. These readings were made for 
a period of approidmately twenty minutes to insure that steady-state condi- 
tios, in which the temperatures were constant to within ±0. 001“C, existed 
in the calorimeter. The temperature of the specimen was recorded just prior 
to its being dropped into the bath. After a drop, readings of the differential 
and jacket temperatures were taken at frequent intervals until temperature 
uniformity had been attained within the crucible. 

The heat transfer coefficient betw;een the jacket and crucible was deter¬ 
mined from measurements of the rate of return to steady-state conditions 
within the calorimeter after the reaction period. For the small differences 
of temperature involved ( ~ 1®C) the valid assumption was made that the net 
heat transfer between jacket and crucible followed Newton’s law. The heat 
transfer correction for the reaction period was then evaluated using estab¬ 
lished method;^, based on Newton’s law of heat transfer. 

The amount of heat absorbed by.the bismuth pellet was first calculated 



T. 

from the compiled heat content of bismuth^\ The heat content was later 
recalculated, taking the heat content at the melting point to be 4200 kcal/mole, 
by graphically integrating the experimentally determined heat capacity curve. 
The calculations were repeated until a self-consistent set of heat content and 
heat capacity values were obtained. 

The method of calculation used for the corrected temperature change of 

12 

the liquid bismuth was that described by Orr, Goldberg, and Hultgren .in 
their work with liquid tin. Corrections were made for the heat capacity of 
the molybdenum crucible and thermocouple protection tube, the tantalum fun¬ 
nel, the copper-constantan thermocouple, audits asbestos covering by using 

13 

the respective Cp values found in the literature . A typical calculation of 
the heat capacity is shown on the Sample Calcula1;ion Sheet in the Appendix. 

THERMOCOUPLE CALIBRATION 

The copper-constantan thermocouple that measured the initial tem¬ 
perature of the specimen was calibrated against a Bureau of Standards 

calibrated platinum-platinum plus ten percent rhodium couple. The Cu- 

constantan thermocouple that measured the bath temperature was calibrated 
at the melting point of bismuth, which was taken to be 544. 5°K. The couple 
was found to read 1.17® too high. The correction was assumed to be con¬ 


stant for all measurements. 



EXPERIMENTAL DATA 


8 . 


The experimentally determined heat capacities are presented in 
Table I. In each of the runs, Newton’s law was obeyed during the return 
of the crucible to the jacket temperature. 

The heat content at the melting point was assumed to be 4.200 cal/g-atom, 
a value in agreement with that reported by several investigators^^. The heat 
contents at other temperatures were obtained from the values of Gp deter¬ 
mined in this investigation. The selected values of heat contents and heat 
capacities are listed in Table n. 

Figure 1 shows the plot of Cp versus temperature obtained in this inves¬ 
tigation together with the data reported by other investigators. 


TABLE I 

Experimentally Determined Heat Capacity Data for Liqpiid Bismuth 


Cp 


Run No. 

T,*K 

cal/ deg. 

21 

801. 7 

6. 69 

20 

801.8 

6.72 

19 

755.2 

6.83 

18 

755.3 

6. 76 

17 

698. 1 

6.79 

18 

698. 1 

6. 86 

6 

653.4 

6.92 

5 

653. 4 

6.92 

4 

606. 3 

7.03 

3 

606. 8 

6.92 


Cp 

Run No. T, °K cal/deg, g-at, 


8 

577.4 

7. 13 

7 

577.4 

7. 13 

2 

55.8. 5 

7.22 

1 

55:8. 5 

7. 21 

11 

545.9 

7. 32 

10 

546. 6 

7. 29 

12 

545.4 

7. 28 

13 

545.4 

7. 33 

9 

546.6 

7. 30 

i5 

544. 8 

7. 34 

14 

545.2 

7.27 



8.0 



FIG. 1 HEAT CAPACITY OF LIQUID BISMUTH. 





10 . 


TABLE n 


Selected Data for Liquid Bismuth 


T, “K 

Cp 

cal/deg. g-at. 

^t"^ 298 
cal/g-at. 

544. 5 

(m. p.) 


4200 

550 

7. 27 

4240 

600 

7. 04 

4597 

650 

6. 93. 

4946 

700 

6. 85 

5290 

750 

6. 78 

56,31 

800 

6. 72 

5969 


NOTE: Heat content values are based on 4200 cal/grat. at 544. 5“K, 
which is selected from the literaturel^. 

DISCUSSION OF RESULTS 

The close agreement betiveen the measured values anc3 the results of 
Carpenter and Harle confirms the decreasing heat capacity oi liquid bis¬ 
muth with increasing temperature. The failure of Person and of F6rster 
and Tschentke to obtain either the correct trend or absolute values is 
believed to be due to errors in accounting for over-all conv&ctive and radia¬ 
tive heat losses. The fact that the data of Umino and of Wus;i;, Meuthen and 
Durrer disagree with the measured values is not surprising, since most 
heat-content data are too inaccurate to obtain even average v^alues of Cp. 

The anomalously high heat capacity of liquid bismuth just above the 
melting point adds credence to the belief that residual aggregates sijnilar 



11 . 


to the solid exist in that region. The dissolution of these associations with 

increasing temperature would account for the high Cp within a few degrees 

14 

of the melting point. Bublik and Buntar have interpreted their electron 
diffraction patterns as indicating that in this region liquid bismuth has a 
structure such that nearest neighbors are distributed in the same manner as in 
the solid. As the temperature is increasedj however, the structure changes 
to one of denser packing. This is just what would be expected if residual asso¬ 
ciations existed within a few degrees of 544. 5®K. The idea of residual aggre¬ 
gates has frequently appeared in the literature to explain the anomalous proper- 

^5 16 17 18 

ties of liquid bismuth within a few degrees of the melting point • > • ' 

These associations would also explain the fact that bismuth does not contract 

as much on melting as has been theoretically predicte i uy Saurevald and Teake 

Many models have been proposed that describe these residual aggregates 

as being pseudo-crystalline in the sense that they display a certain degree of 

local order, of the same type as that found in the solid. This is the case in 

20 

the model proposed by Bartenev . Other models of this nature include the 

21 22 
crystallite model of Ookawa and the cybotactic picture of Stewart and Benz 

The expressions derived from the models for the excess heat capacity near the 

melting point show only qualitative agreement with experiment, however. 

Impurities would have a great effect on the nature of these aggregates 


19. 


and on the manner in which they change with temperature. In the present 
investigation, it is felt that the high purity of the sample excludes the chance 
of any error occurring from this source. 



Whereas the breakup of aasobiations will account for the sharp drop 
in Cp near the melting point. thi« explanation does not apply to the gradual 
decrease in Cp observed at higher temperatures, since the residual associa- 

tiona have essentially disappeared within a few degrees of the melting point. 

23 

Byring in his treatment of liquid mercury attributes the decrease to a 
change in the potential function of the atoms in which turn affects the nature 
of the thermal motion of the atoms. At: the lower temperatures the thermal 
motion consists chiefly qf vibration, but increasing the temperature causes 
translational energy to become dominant. This results in a continual loss of 
degrees of freedom. Using this approach Eyring obtained a partition function 
for the liquid from which Cv could be obtained. His. values of Cv start at a 
value of 3E at the m elting point> in agreement with the law of Dulong and 
Petit, and decrease with increaaing temperature. A minimum in Cp is to 
be expected because of the continually increasing vatiue of (CprCv)* While 
this model will not account for the anomalously high values of Cp near the 
melting point, it shows good agreement with the high temperature values. 

No minimvun in the heat capacity was found, although the measurements 
extended to 800* K. If the trend that is followed by Hg. Na. and K is obeyed, 
however, a minimum value would be expected at a temperature about 2.3 
times the melting temperature or 1250*K. 



SUMMARY AND CONCLUSIONS 


13 . 


The true heat capacity of liquid bismuth was measured from 544. 8“K 
to 801. 8*’K by a method of mixtures using a liquid bismuth solution calori¬ 
meter. 

The following conclusions were reached: 

1) The anomalously high heat capacity within a few degrees of the 
melting point can be accounted for by assuming the presence of residual 
aggregates resembling the solid which are broken up with rising tempera¬ 
ture. 

2) The heat capacity of liquid bismuth decreases with increasing tem¬ 
peratures over the range studied. 

3) No minimum in Cp was observed although one may exist at a higher 


temperature. 



APPENDIX 


14 


Sample Calculation Sheet 
Run. No. 15 


Tin Pellet 


Weight = 0. 28524 g. 


Initial State 

Final State 

Temperature = 

= 982 pv 

Temperature = 13, 308. 55fiv 


= 24. 80‘>C 

-AT. = -13.21 

- Correction = 

= -0. 88 

t ... 

= 13, 295. 34/ljv 
= 272. 73°C 


23. 92°C 

273. 15 


-Correction = -1.17° 

T. = 
1 

297. 07°K 

271. 56° C 



T^ = 544. 71°K 

Ht “ H^gg = -6. 7695 cal/g-at. 
i 

Ht - H^gg = 4201. 6270 cal/g-at. 
f 

H - T 

= 4201. 6270 + 6. 

7695 = 4208. 3965 cal/g-at. 

T.)- 


AH = 4208. 3965 = 5. 7436 cal. 


Correction to Cp 

Material 

Gram Atoms ' 

Cp {call deg. g-at. ) cal/deg. 

Ta 

0.03906 

6. 24486 .2439 

Mo 

0.38210 

6.20810 2.3721 

Cu 

0. 00207 

6. 22704 .0129 

Ni 

0. 00056 

7. 78009 .0044 

Asbestos 

0. 109(gms.) 

0. 195(cal/deg. g.) .0213 



2.6546 


Temperature Change = 13. 209pv 
Thermocouple Constant = 56. 84|^v/deg. 

Amount of Bismuth in Bath - 3. 0051 g-atom 

1 9nQ 

(2. 6546 + 3. 0051 Cp) = 5. 7436 

56* o4 

Cp = 7. 34 cal/deg. g-at. 



15. 


I 


ACKNOWLEDGMENTS 

This work was conducted with the support of the Office of Ordnance 
Research, U. S. Army, to whom the authors wish to express their appre¬ 
ciation. The authors also wish to thank Mr. R. L; Orr and Mr, A. I. Kaznoff 
for their invaluable suggestions and discussions, Mr. Stanley Ross for his 
assist^ince with the experimental work, and Mrs. Ellen Abels for typing the 
manuscript. 



I 


REFERENCES 


16. 


1. K.K. Kelley, U. S. Bur., Mines Bull. 584 (1960). 

2. T.B. Douglas, Trans. A.S.M.E., 79, 23 (1957). 

3. H. Heffan, Master's Thesis, University of California (1958). 

4. R. L. Orr, private communication. 

5. A. Kaznoff, private communication. 

6. F. FSrster and G. Tschentke, Z. Metallk., 191 (1940). 

7. L. G. Carpenter and T. F. Harle, Proc. Roy. Soc. London, 136A, 243 (1932). 

8. C.C. Person, Ann. Chim. etphys., 128 (1848). 

9. S. Umino, Sci. Repts. Tohoku Imp. Univ., 15, 597 (1926). 

10. A. Wust, A. Meuthen and R. Durrer, Forsch. Gebiete Ingenieurw., 

204 , 1 (1918). 

11. Unpublished evaluations, project for evaluation of thermodynamic data for 

metals and alloys. Minerals Research Laboratory, University of 
California, Berkeley. 

12. R. Orr, A. Goldberg, and R. Huitgren, J. Sci. Instr,, 28, 767 (1957), 

13. A. Goldberg, Ph. D. Thesis, Uriiversity of California (1955). 

14. A. I. Bublik and A. G. Buntar, Fiz. Met. i Metallovedenie, 5, 53 (1957). 

15. A. Goetz, Phys. Rev., 193 (1930). 

16. A. Soroos, Phys. Rev,, M, 516 (1932). 

17. A. Knappwost, Z. Elektrochem., £7^, 618 (1953). 

18. P. Boydston, Phys. Rev., 3£, 911 (1927). 

19. F. Sauerwald and W. Teske, Z. anorg. Chem., 210, 247 (1933). 

20. G. M. Bartenev, Zhur. Tekh. Fiz., 1_7, 1321 (1947). 

21. A. Ookawa, J. Phys. Soc. Japan, 2, 108 (1947). 



17. 


22. G. W. Stewart and C. A.. Benz, Phys. Rev., 46, 703 (1934). 

23. J. F. Kincaid and H. %ring, J. Chem. P iys., 5, 587 (1937). 


t