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THE UNIVERSITY OF ALBERTA 


GROUP VI ELEMENTS IN FUSED LiCl-KCl 

by 



FRANZ G. BODEWIG 


A THESIS 

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES 
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE 

of 

DOCTOR OF PHILOSOPHY 


DEPARTMENT OF CHEMISTRY 


EDMONTON, ALBERTA, CANADA 
Spring, 1970 








































21 

































THE UNIVERSITY OF ALBERTA 


^ /£ ?7o 


FACULTY OF GRADUATE STUDIES 

The undersigned hereby certify that they have read, and 
recommend to the Faculty of Graduate Studies for acceptance, a thesis 


entitled 



"GROUP VI ELEMENTS IN FUSED LiCl-KCl" 


submitted by FRANZ G. BODEWIG, in partial fulfilment of the 
requirements for the degree of Doctor of Philosophy. 






































































































Ill 


ACKNOWLEDGEMENTS 

The author wishes to thank Dr. J. A. Plambeck for his 
encouragement and especially for his readiness to discuss problems, 
usually on very short notice. 

The financial support of the National Research Council of 
Canada is gratefully acknowledged. 

This thesis is dedicated to my mother who contributed much 


which cannot be found on the following pages. 

















































IV 


TABLE OF CONTENTS 

Page 

Approval Page. ii 

Acknowledgements . . .. . . . . iii 

Table of Contents .iv 

List of Tables.vi 

List of Figures .vii 

PART I: Electrochemistry of S, Se, and Te in Fused LiCl-KCl 

ABSTRACT 1 

INTRODUCTION AND HISTORICAL . 3 

EXPERIMENTAL . 10 

Apparatus.10 

Solvent.10 

Chemicals . . . ..11 

Electrodes.11 

Cell Construction.13 

Procedure.14 

RESULTS .17 

I. Sulfur.17 

II. Selenium.30 

III. Tellurium.39 

DISCUSSION.41 


BIBLIOGRAPHY 


48 









































































































































V 


Page 


PART II: Spectrophotometric Investigations of Sulfur-Sulfide 
Solutions in Fused LiCl-KCl 

ABSTRACT . 51 

INTRODUCTION AND HISTORICAL . 52 

EXPERIMENTAL . 54 

Apparatus. 54 

Solvent. 57 

Chemicals. 57 

Electrodes . 57 

Procedure. 57 

RESULTS AND DISCUSSION . 59 

BIBLIOGRAPHY . 64 

APPENDIX I: Original data for S/S - and Se/Se - couples ... 65 

APPENDIX II: Computer programs for calculation of 

E° from Nemst equation and for least 
M 

square analysis 


72 









































































































, 

























































VI 


LIST OF TABLES 

Page 

Table I Standard e.m.f. determinations for the 

S/S~ couple . 21 

II Standard e.m.f. determinations for the S/S” 

couple, low concentrations . 23 

III Chronopotentiometric study of sulfide . 28 

IV Standard e.m.f. determinations for the 

Se/Se” couple . 38 
























































































































































Vll 


LIST OF FIGURES 

Page 

Figure 1 Temperature dependence of potential as a 

function of sulfide ion concentration . 18 

2 EMF of sulfide electrode as a function of 

sulfide concentration . 20 

3 Nernst plot for the S/S = couple (all data). 24 

4 Voltammetric curve for sulfur . 25 

5 Current-potential curves for sulfide solutions ... 27 

6 Chronopotentiometric constant vs. sulfide 

concentration . 29 

7 Voltammetric curves for selenium and tellurium ... 34 

8 Current-potential curves for selenide solutions ... 35 

9 Temperature dependence of potential as a 

function of selenide concentration . 36 

10 EMF of selenide electrode as a function of 

selenide concentration . 37 

11 Furnace for Cary Model 14 Spectrophotometer. 56 

12 Spectra of fused LiCl-KCl without and 

with sulfide. 60 

13 Absorbance as a function of sulfide concentration . . 62 

14 Absorbance as a function of sulfide concentration; 

low concentration detail from Fig. 13. 63 






























































. 

.bo. 











• jt 

























Vlll 


It seemed quite natural to many scientists, not all of whom 
had a philosophical mind, to suppose that it was possible for the 
material world to have become known quite independently of the rules 
of the functioning of our mind, and especially of the processes 
necessarily associated with our faculties of sensation and perception 
through which we gain our knowledge of it. That our scientific 
theories should be connected with the rules of the functioning of our 
mind, to the structure of our reason, to the concepts of which we 
dispose, that is certainly a point concerning which no scientist 
endowed with a mind, let it be ever so feebly critical, has naturally 
ever been able entirely to rid himself; the science of man is human 
and can never cease to be so; on this point there is no possible doubt. 


Louis de Broglie 













































1 


PART I: ELECTROCHEMISTRY OF S, Se, 

AND Te IN FUSED LiCl-KCl 

ABSTRACT 

Liquid sulfur has been coulometrically reduced in fused 
LiCl-KCl eutectic at 420°C. Nernstian behavior is observed for the 
cell 

C, S(l)/S = , LiCl-KCl//Pt ++ , LiCl-KCl/Pt. 

The standard potentials of the sulfur/sulfide couple at 450°C with 
respect to the appropriate standard platinum reference electrode are 
-1.008, -1.039, and -1.219V on the molar, molal, and mole fraction 
scales, respectively. Voltammetric studies showed an anodic wave at 
+0.03 V ascribed to 

2S + 2C1" -+ S 2 Cl 2 (g) + 2e~ 
and a cathodic wave at -0.92 V ascribed to 

S + 2e ■+• S . 

The diffusion coefficient of the (poly)sulfide ion was found to be 
( 2 

3.12 x 10" cm /sec at 420°C by chronopotentiometric measurements. 

The observed blue color of sulfur-sulfide solutions is ascribed to 
polysulfide ions. 

Liquid selenium has been reduced coulometrically in fused 
LiCl-KCl eutectic at 400°C. Nernstian behavior is observed for the 
for the cell 

C, Se(l)/Se = , LiCl-KCl//Pt ++ , LiCl-KCl/Pt. 

The standard potentials of the selenium/selenide couple at 450°C with 
respect to the appropriate standard platinum reference electrode are 
-1.141, -1.172, and -1.252 V on the molar, molal, and mole fraction 





















































’ 











scales, respectively. Voltammetric studies showed an anodic wave at 
+0.05 V ascribed to 

2Se + 2C1 - -+ Se 2 Cl 2 (g) + 2e 
and a cathodic wave at -1.07 V ascribed to 

Se + 2e -+ Se~. 

For tellurium an anodic wave at -0.15 V is ascribed to 

Te -> Te(II) + 2e~ 

and a cathodic one at -1.40 V to the plating of lithium into tellurium; 
the formation of free telluride does not appear to occur. The standard 
potential for the couple Te(II)/Te is estimated at -0.1 V. 












































■ 
















3 


INTRODUCTION 

The electrochemical behavior of molten salts and of solutes 
dissolved therein has been studied intensively in recent years and 
much information of practical and theoretical interest has been gained 
from these studies. The majority of the work has concerned itself 
with metal-metal ion systems. Little has been done regarding non-metals 
and their anions, with the exception of cases where the anion is part 
of the melt itself, such as the halogen-halide couple in various halide 
melts. It therefore appeared desirable to extend the electrochemical 
studies to other anions. The LiCl-KCl eutectic was chosen as solvent 
since this electrolyte has probably attracted most attention so far 
and certainly the most extensive e.m.f. series has been compiled in it. 
The investigations were started with the sulfide ion and later extended 
to selenide and telluride. 

An additional reason to undertake these studies was that fused 
salt cells with chalcogen cathodes have attracted considerable attention 
in recent years as a means of efficient energy storage. Little 
electrochemical research, however, has yet been done on these systems. 

In the present study potentiometry, voltammetry, and 
chronopotentiometry were used to obtain insight into the electrochemical 
behavior of sulfur, selenium, and tellurium in fused LiCl-KCl eutectic. 





































. . _ , I -» ■' • fi 






















































4 


HISTORICAL 

Research in the field of molten salt chemistry has expanded 
rapidly during the last two decades and substantial efforts have been 
made to compile the extensive knowledge of this subject. Several 
monographs have been published dealing with fused salt chemistry in 
general (1,2,3,4). References to literature publications concerning 
physical properties of fused salt mixtures have been compiled by the 
Fused Salts Information Center of Sandia Laboratory (5). References 
to electrochemical studies in general have been compiled by Janz (4) 
and Delimarskii and Markov (6), while Plambeck (7) has compiled e.m.f. 
data in various molten salts. Electrochemical techniques used in 
molten salts have been reviewed (2,3). 

The largest body of e.m.f. data exists in the LiCl-KCl eutectic 
which is a convenient solvent in view of its low melting point (352°C), 
large potential span (3.6 volts), and relative ease of purification and 
handling. Most common metals have now been investigated in this medium. 
Solutions of the metal ions are prepared by adding the' appropriate 
metal chloride to the solvent or by anodization of a metal electrode. 

This last process produces the lowest oxidation state of the metal 
stable in the solvent; higher oxidation states are obtained by further 
oxidation of the metal ion with an inert electrode such as a 
graphite rod. In all cases the solutions of metal chlorides in 
LiCl-KCl are ionic and solubilities are fairly high so that few problems 
arise with electrochemical investigations on these systems. 

































' 
















5 


Relatively little work has been done, however, with regard to 
non-metals. This may be due to the fact that many electrode reactions 
involving complex anions are difficult to interpret and construction 
of reversible electrodes presents formidable technical problems. Even 
in the case of simple anions the electrode reaction is often not 
reversible at convenient temperatures. It is then not possible to 
produce the anion by cathodization of the element, while addition of 
the anion to the solvent as its lithium or potassium salt presents the 
problems of obtaining and handling of small quantities of the pure salt. 
For instance, calcium and lithium carbide are known to dissolve 
ionically in fused chlorides (8) but it was not possible in the course 
of this study to produce carbide by cathodization of a graphite rod in 
LiCl-KCl at temperatures of up to 800°C. 

) 

Anions most commonly investigated are those that are 
constituents of the melt itself, e.g., sulfates (9), nitrates (10,11), 
and carbonates (12). Halides have been studied both as constituents 
of the melt (13,14,15,16) and as solutes in a variety of molten salts 
(13,17). In LiCl-KCl the hydrogen-lithium hydride electrode has been 
studied (18) in view of its possible use in thermally regenerative 
fuel cells and its standard potential has been estimated (7). 

Reversible sulfur, selenium, and tellurium electrodes in solid 
electrolyte cells were used by Reinhold (19) in order to obtain 
thermodynamic data of the silver chalconides. He performed e.m.f. 
measurements on cells of the type 

Ag/AgI(s)/Ag 2 X(s)/X where X = S, Se, Te 
between 150° and 350°C. The solid silver iodide serves as electrolyte 









' 






involving migration of silver ions. Since the overall cell reaction 
taking place on passage of current is represented by 

2Ag (s) + X + Ag 2 X(s) 

the standard molar free energy of formation of solid silver chalconide 
is calculated from the reversible cell e.m.f. by means of the 
relationship AG = -nFE. This work was repeated by Kiukkola and Wagner 
(20) in their studies of solid electrolyte cells. 

Voltammetric studies of sulfide in fused potassium and sodium 
chloride mixtures have been conducted by Rempel and Maikova (21) in 
order to establish a sequence of discharge potentials of some 
industrially important anions. The order of discharge found was OH", 
NO^", S - , S0^ = , Cl". This work and that of Delarue (22,23) clearly 
indicate that alkali sulfides form ionic solutions in alkali chloride 
melts. Delarue (22) studied sulfide solutions in fused LiCl-KCl 
eutectic by means of voltammetry with a platinum indicator electrode 
and obtained an anodic wave at E^. = -0.45 V with respect to the standard 
molar platinum electrode which he ascribed to the oxidation of sulfide 
to sulfur according to 

S S + 2e . 

Several redox reactions such as 

S = + I 2 -> 21" + S 

were also carried out in this solvent. In all cases the sulfide was 
added as Na 2 S*9H 2 0. No attempts to obtain the cathodic wave for the 
reduction of sulfur to sulfide were reported. His quantitative results 
are subject to criticism (see Discussion section below). 

Bell and Flengas (24) have investigated the concentration cell 















. 






1 :;?u 

, ,u $o nuiJi-nx> ) ^ u bod - e ‘ tpib; fo-*i l'' ■w* 30 











































7 

Ag/AgCl,Ag 2 S/AgCl/Ag 

in the temperature range between 450° and 700°C. Their e.m.f. and 
conductivity measurements indicated that dilute solutions of silver 
sulfide in silver chloride are ideal and completely ionized. 

While the investigations on the liquid sulfur electrode in 
LiCl-KCl for the present study were in progress Thompson and Flengas 
(25) reported on a reversible sulfur vapor electrode in fused silver 
chloride. This electrode, used in the formation cell 

Ag/AgCl,Ag 2 S/S 2 (g), C, 

followed the Nemst equation with respect to the partial pressure of 
sulfur in the range between 0.001 and 1.0 atm and to the silver sulfide 
concentration at a fixed sulfur vapor pressure in dilute silver sulfide 
solutions. Hie cell reaction on passage of current is 

2Ag + |S 2 (g) Ag 2 S (solution) 

so that thermodynamic data of silver sulfide dissolved in silver chloride 
could be obtained from e.m.f. measurements. 

The literature on selenium and tellurium in fused salt media 
is scanty. The deposition potential of tellurium from solutions of 
tellurium dioxide in fused AlC^-NaCl-KCl at 218°C has been determined 
by Verdieck and Yutema (26). Since this potential was obtained from 
current-voltage curves by means of a three electrode system it is 
comparable to an e.m.f. measurement. There is, however, uncertainty as 
to the oxidation state of the electroactive tellurium species in 
solution (7). 

The free energy of formation of Li 2 Te lias been determined by 
Foster and Liu (27) using the cell 












































t 































8 


Li^BiCs), Li in Bi(1)/LiCl-LiF/Li in Te(l), Li 2 Te(s) 

The potentials of the secondary reference electrode, Bi saturated with 
Li^BiCs), had previously been measured against the Li reference 
electrode (28) so that the e.m.f. of the above cell could be converted 
to that for the cell 

Li(l)/LiCl-LiF/Li in Te(l), Li 2 Te(s). 

The free energy of formation of solid Li 2 Te was calculated from the 
e.m.f. of this cell. 

A similar cell has been used by Liu and Angus (29) to obtain 
thermodynamic properties of the bismuth-tellurium alloy Bi 2 Te 3 and to 
investigate the bismuth-tellurium phase diagram by e.m.f. measurements. 
The cell employed was 

Bi(l)/BiCl 3 ,LiCl-KCl/Bi-Te. 

Advances in molten salt technology have resulted in efforts 
to develop energy conversion or storage cells employing fused 
electrolytes. Lithium has most frequently been used as anode material 
because of its low electronegativity and low equivalent weight. Many 
elements have been investigated as cathode material, such as chlorine 
(30) and bismuth (31). However, sulfur, selenium, and tellurium seem 
to combine many desirable characteristics such as relatively high 
electronegativity, low equivalent weight, ease in handling, and simple 
cell construction. At Argonne National Laboratory selenium (32), 
tellurium (33), and sulfur (34) cathodes have been used in conjunction 
with a lithium anode to construct cells with high power and energy 
densities. The electrolyte used was the ternary eutectic of 
LiF-LiCl-Lil (mp 341°C). On discharge the cell reaction is the 







■ 














































9 


transfer of lithium from the anode to the cathode forming a lithium 
chalcogen compound at the cathode. A very interesting feature of 
these secondary cells is that recharge is possible within 15 minutes 
while on discharge current densities between 10 and 13 A/cm^ can be 
obtained. 










































EXPERIMENTAL 


Apparatus 

Potentials were measured with a digital voltmeter (Model 
3440A, Hewlett-Packard) . Coulometric generations employed a Model IV 
Coulometric Current Source (E.H. Sargent and Co.)- An Anotrol Model 
4100 Potential Controller modified to operate with a Model 4510 linear 
scan unit (Magna Electronics) was used for voltammetric investigations. 
Chronopotentiometric investigations employed a Model 6824A power 
supply-amplifier (Hewlett-Packard) in a constant current configuration 
controlled by appropriate mercury-wetted relay switching circuitry; 
measurements were recorded on a Hewlett-Packard Model 175A oscilloscope 
equipped with 1750B and 1781B plug-in units and a Model 196B camera 
using ASA 3000 Polaroid film. 

The temperature of the 3" diameter vertical tube furnace was 
controlled by a Model 3120-SCR-477 temperature controller (Marshall 
Products Co.). For the Lindberg Hevi-Duty Model 54381A furnace a Model 
59344 temperature controller was employed. Temperatures were measured 
with a chrome1-alumel thermocouple calibrated at the melting point of 
zinc. 

Solvent 

■ - — V 

The LiCl-KCl eutectic solvent (59.5 mole% LiCl, mp 352°C) was 
prepared by the method of Maricle and Hume (35) modified as described 


below. 







































■ 




















11 


A total of 600 g of the component salts was mixed and melted 
without previous drying. Chlorine gas dried over magnesium perchlorate 
was bubbled through the melt for 2 hours. After purging the melt with 
nitrogen for 4 hours, magnesium ribbon was introduced to displace any 
heavy metal ions. Subsequently, chlorine was again introduced to 
oxidize any magnesium metal that may have dissolved in the melt, 
followed by nitrogen. The molten eutectic was transferred to large 
test tubes in charges of 120-140 g inside a drybox purged with nitrogen. 
The test tubes were sealed and stored for future use. 

Chemicals 

Reagent grade LiCl (Fisher Scientific Company) and KC1 (Fisher 
Scientific Co. or Shawinigan Chemicals) were used. Selenium (99.99%) 
was obtained in 1/4" x 2" rods from A. D. Mackay, Inc. Tellurium 
(99.999%) was obtained from Atomergic Chemetals Co. The sulfur 
(sublimed; Fisher Scientific Co.) was dried at 100°C prior to use. 
Graphite electrodes were Special Spectroscopic Electrodes 1/8" in 
diameter (National Carbon Co.). Nitrogen was purified over hot copper 
turnings and dried by passage through a magnesium perchlorate column. 
Argon was dried by passage through a magnesium perchlorate column and 
two traps cooled by a dry ice-acetone bath. 

Electrodes 

A reference electrode based on the Pt(II)/Pt couple 
(0.03-0.04 M) was generated coulometrically for each experiment by 
anodization of a 3 cm 2 Pt foil sealed into Pyrex tubing; a current 
density of 7 mA/cm 2 was employed. All potentials were measured 






. 








. 








‘ II 























12 

against this reference electrode and are reported with reference to 
the Pt(II) (1.0 M)/Pt standard molar platinum electrode (S.M.P.E.) 

(36), conforming to the IUPAC "Stockholm" sign convention (37). 

The boiling point of sulfur (444°C) being very close to the 
temperature of 450° at which the e.m.f. data were desired, it was 
necessary to work either with a vapor electrode or a liquid electrode 
and extrapolate from higher or lower temperatures to 450°. The liquid 
electrode appeared simpler [ref. (25) then not being available], and 
the sulfur electrode used consisted of an isolation compartment with 
a pool of liquid sulfur floating on the melt. Electrical contact with 
the pool was made by a graphite rod attached to Nichrome leads well 
above the sulfur pool. Sulfide was initially added to the compartment 
as Li^S, but this proved unsatisfactory due to hydrolysis and 
difficulty in transferring known amounts to the compartment. The 
addition of sulfide by cathodic coulometric reduction of the sulfur 
pool proved more satisfactory and was used for all experiments reported 
here. Precautions were taken to ensure that an excess of liquid sulfur 
was always present, and more was added as necessary. 

The selenium electrode consisted of a small Pyrex cup (7 mm 
diameter, 5 mm long) containing pieces of selenium. Contact with the 
selenium (liquid at operating temperature) was made with a graphite 
rod attached to Nichrome leads well above the melt level. The Pyrex 
cup rested on the bottom of the isolation compartment and was totally 
immersed in the melt. 

The tellurium electrodes were made by melting lumps of 
tellurium in a 4 mm Pyrex tube under argon. A tungsten wire was 








-■ * - 

' 

ajkti.1' \n J' .•*.,!» will' Ml<Hi ■ < 1 *&*■ ** 1 '' 





























































13 


inserted into the liquid tellurium which was then allowed to solidify. 
The electrode was removed by carefully breaking the glass. 

A graphite rod in an isolation compartment was used as the 
counter electrode. 

The electrodes used in the chronopotentiometric investigations 
of the sulfide system were gold wires (0.05 cm in diameter) suspended 
in the melt or rhenium wires sealed in glass. Other metals such as 
tungsten or platinum were unsatisfactory because they became coated, 
presumably with insoluble sulfide. The geometric area of the gold 
electrode was calculated from its diameter and depth of immersion, 
that of the rhenium electrode from its diameter and the length of 
metal exposed. 

Cell Construction 

_ - „ . „ > 

The electrolytic cell consisted of a Pyrex crucible inside a 

glass jacket that could be connected to a vacuum pump by means of a 
Pyrex cap. A 75 mm 0-ring joint connected the jacket to the cap. 

The outer jacket could also be closed off with a machined Teflon 
stopper with holes for up to five isolation compartments, a thermo¬ 
couple, and a nitrogen inlet tube. The isolation compartments were 
made of Pyrex sealing tubes with 10-20 micron frits (D porosity; Ace 
Glass Inc.) and protruded through the Teflon stopper. A hole below 
the Teflon stopper allowed entry of nitrogen into the otherwise closed 
compartments to equalize pressure. 

The cell for the selenium and tellurium experiments was 


essentially the same, except that five 14/20 ground-glass joints were 
blown on the cap which were used to insert the thermocouple, the 












































. . 






*. 

I I it II ■ • w 













14 


electrodes, and an argon inlet tube. 

The remainder of the electrolytic cell and glassware 
preparation have been described previously (38). 

Procedure 

The crucible containing the frozen eutectic, isolation 

compartments, and electrodes was placed inside the outer glass jacket 

of the electrolytic cell. Transfers of frozen eutectic to the crucible 

were made inside a dry box under nitrogen. 

The 3" diameter tube furnace was used for the experiments with 

sulfur; the Lindberg furnace for those with selenium and tellurium. 

I. Sulfur - The temperature of the cell was raised slowly to 

420-430°C under vacuum in order to thoroughly dry the glass equipment 

and electrode before fusion of the eutectic. The compartments were 

allowed to fill with eutectic during a further 8 hours at this 

temperature. Finally, purified nitrogen was introduced and allowed to 

pass over the melt during all experiments. After addition of sulfur 

to the compartments the sulfide concentration was successively increased 

2 

by coulometric reduction of sulfur. The current density was 8 mA/cm . 
The reduction product was blue in color (see below). The sulfide 
electrode e.m.f. was measured against the same reference electrode for 
each run which normally included three different sulfide compartments. 

The thermoelectric potential between the graphite and 
platinum electrodes was found to be +1.5 mV with respect to the platinum 
electrode in the temperature range of 400-450°C. All e.m.f. values were 
corrected accordingly. 











. 






. 

' 



























15 


II. Selenium and tellurium - The temperature of the cell was 
slowly raised to 370°C under vacuum in order to dry the glass equipment 
and electrodes before fusion of the eutectic. After fusion of the 
eutectic, argon was introduced and bubbled through the melt during all 
experiments. The compartments were allowed to fill with eutectic 
during a period of 8-10 hr. The selenium or tellurium was added as a 
final step. Ionic species were generated by anodization or 
cathodization of the selenium or tellurium. The cells were operated 
at 400 ± 2°C to minimize loss of volatile materials from the melt, 
which was still the most serious problem encountered in the 
investigation. The electrode potentials were measured against the 
platinum reference electrode. The thermoelectric potential of the 
graphite and leads was measured as +10 mV with respect to platinum. 

It was essentially invariant with temperature from 400° to 450°. The 
potentials were corrected for this effect. 

In all cases the potentials were converted from the 
experimental temperature to 450°C using experimentally determined 
potential-temperature relationships (see below). This extrapolation 
to 450°C was done since all e.m.f. data in fused LiCl-KCl are reported 
at this temperature (7). 

The voltammetric studies were done by the method of current- 
voltage curves in three electrode cells: a platinum reference, an 
indicator, and a graphite counter electrode, each in a separate 
isolation compartment. The amount of solvent in each isolation 
compartment was determined by a potentiometric chloride titration; 
when necessary, sulfide or selenide was removed from aqueous solution 

























‘ 












































16 


by acidification with nitric acid. The concentrations of S’", Se~, 
and Pt ++ ions were determined from the coulombs passed and the solvent 
volume as described previously (36). 

Least square calculations were carried out on the University 
of Alberta IBM System/360 computer. The programs used are given in 
the Appendix. 































17 


RESULTS 

I. SULFUR 

Potentiometry 

Five runs were carried out, with new compartments, electrodes, 
and eutectic charge used in each. A total of 89 concentration-potential 
data points were taken over the range 400-440°C, each point the mean of 
two potentials measured 15 minutes apart. In general the e.m.f. became 
constant, to within 0.5 mV, 15-30 minutes after coulometric reduction 
of sulfur had been terminated and did not change more than 1 mV over 
a period of several hours. The temperature of the melt was recorded 
at the time of each potential measurement. The effect of temperature 
on the e.m.f. was determined for various sulfide ion concentrations 
with both increasing and decreasing temperature. Plots of measured 
potential against temperature were linear over the range 400-440°C for 
a fixed sulfide ion concentration. Plots of AE/AT against the logarithm 
of the molar concentration of sulfide (as moles S“/liter of eutectic at 
450°C) were linear over the concentration range 0.03-0.5 M as shown in 
Fig. 1. All data are given in the Appendix. Least square analysis 
gave, for the temperature dependence of the cell 

(-)C,S(1)/S = , LiCl-KCl//Pt ++ , LiCl-KCl/Pt(+), 

AE/AT = +0.124 Log[S = ] -0.520 mV/°C 
with a relative standard error of 4.4% in the slope and of 1% in the 
intercept. This equation was used to extrapolate all measured 
potentials to 450°C. Linear Nernst plots were obtained for these 





































































. 


























CHANGE IN CELL POTENTIAL, mV/ 


18 



Fig. 1. Temperature dependence of potential as a function 
of sulfide ion concentration. Line is that given 
by least-squares analysis. Points indicated by 
triangles not included in least-squares analysis. 



















































































































19 


extrapolated potentials over the concentration range 0.03-0.5 M 
sulfide. Less stable potentials were obtained at lower sulfide 
concentrations. A typical plot of potentials against the logarithm of 
sulfide concentration (Fig. 2) shows that Henry's law is obeyed over 
the concentration range studied. A summary of all runs is given in 
Table I; the original data are given in the Appendix. Least square 
analysis of all points gave a standard potential (molarity scale) at 
450°C of -1.008 V with a standard deviation of 0.002 V. This 
corresponds to values of -1.039 V and -1.219 V with the same standard 
deviation on the molality and mole fraction scales, respectively (56), 
all potentials being with respect to the appropriate standard platinum 
electrode. The slope of the Nemst plot was -0.0772 V/log unit with 
standard deviation of 0.0015, corresponding to a value of 1.86 ± 0.04 
for the number of electrons taking part in the reaction. This is in 
good agreement with the theoretical value of 2 expected for 

S + 2e S . 

The above results were later checked on lower sulfide 
concentration (0.0017-0.032 M). A separate counter electrode was not 
used; the current from the coulometer was passed through the sulfur 
and platinum electrodes so that the concentrations of the platinum ion 
in the reference electrode compartment increased with each increase in 
sulfide concentration. The platinum ion concentration was therefore 
approximately equal to the sulfide concentration at a particular 
potential measurement and ranged from 0.0016 to 0.032 molar. The 
e.m.f. dependence on temperature was determined for each concentration 
and plots of measured potential against temperature were again linear. 














. 

„ V * - ' 

























’ 





■ 
































LOG OF MOLAR SULFIDE CONCENTRATION 


20 



Fig. 2. Electromotive force of sulfide electrode (vs.S.M.P.E.) 

as a function of sulfide concentration in a typical 
Temperature (extrapolated) 450° C. 


run. 






















































21 


Table I* 


Standard e.m.f. determinations for the S/S - couple 


Sulfide 

Molarity 

No. of 
points 

E° (V) 

M 

Standard 
deviation (mV) 

Exper. 
n 

0.093-0.15 

6 

-1.010 

1.3 


1.81 

0.095-0.15 

6 

-1.008 

6.7 


1.80 

0.054-0.25 

7 

-1.012 

0.7 


1.75 

0.037-0.21 

7 

-1.012 

0.8 


1.80 

0.045-0.20 

7 

-1.015 

1.3 


1.72 

0.045-0.22 

6 

-1.007 

0.4 


1.98 

0.036-0.18 

6 

-1.009 

1.6 


2.02 

0.071-0.43 

7 

-1.004 

0.2 


2.09 

0.055-0.20 

5 

-1.007 

0.9 


2.03 

0.19-0.48 

5 

-1.006 

0.3 


2.19 

0.092-0.28 

5 

-1.007 

0.2 


2.13 

0.035-0.26 

7 

-1.004 

0.9 


1.79 

0.030-0.32 

8 

-1.002 

0.6 


1.83 

0.046-0.31 

7 

-1.004 

1.3 


1.72 

Least square 
analysis of 
all points 

89 

-1.008 

1.5 


1.86 

* two e.m.f. 

readings taken at each 

point 15 

minutes 

apart, 

except for 

run 1? temperature converted to 

4 5 0 ° C; 

all 

potentials 

given with 

respect to 

S.M.P.E.; 

each entry is a 

separate compartment, 

the first two being run 1 and the 

remainder . 

other runs 

with three 

compartments per 

run. 



























. 
















































































































































22 


These plots were used to extrapolate all potentials to 450°C. Standard 
potentials calculated from these extrapolated values are given in 
Table II (for original data see Appendix). 

A plot of all points is given in Fig. 3 where the line drawn 
is the one obtained from least square analysis of the points of Table I. 


Voltammetry 

Voltammetric scans of the pure eutectic melt with a graphite 
electrode gave the curve denoted by circles in Fig. 4. The potential 
was increased in the reduction direction and the current was measured 
after it had become constant (generally 5-10 sec.) After addition of 
sulfur to the compartment, the curve denoted by triangles in Fig. 4 
was obtained. For the cathodic rise, which is ascribed to the reaction 

S(l) + 2e" -» S = , 

extrapolation of the lower part of the curve to zero current gave 
-0.92 ± 0.02 V for the "decomposition" potential (mean and std. dev. 
of 5 experiments), in agreement with the potentiometric measurements 
cited above. The anodic wave is ascribed to the reaction 

2S(1) + 2C1" -* S 2 Cl 2 (g) + 2e" 

which Delarue (23) estimated to occur at about -0.05 V. The 
"decomposition" potential determined in this study is +0.03 ± 0.02 V 
(mean and std. dev. of 5 experiments). These measurements were carried 
out at 420 ± 2°C as were all other voltammetric and chronopotentiometric 
studies reported here. 

Voltammetric curves were also obtained in compartments in 
which sulfur was present and sulfide had been generated coulometrically 





' 













. 

• • 




* 







23 



Table II 

Standard e.m.f. determinations for the S/S~ Couple, 
low sulfide concentrations* 


Sulfide 

Molarity 

Potential Sulfide Electrode 
vs. S.M.P.E. (V) 

e m < v > 

0.00316 

-0.8176 

-0.9970 

0.00789 

-0.8521 

-1.0030 

0.0126 

-0.8687 

-1.0049 

0.0221 

-0.8905 

-1.0093 

0.0316 

-0.9027 

-1.0104 

0.00171 

-0.7772 

-0.9757 

0.00274 

-0.8024 

-0.9862 

0.00428 

-0.8236 

-0.9935 

0.00684 

-0.8373 

-0.9926 

0.0106 

-0.8540 

-0.9966 


*First five entries are run 1, remainder run 2. 
Temperature converted to 450°C. 
















































' 

































































LOG OF MOLAR SULFIDE CONCENTRATION 


24 



Fig. 3. Electromotive force of sulfide electrode (vs.S.M.P.E.) 
as a function of sulfide concentration. 

(extrapolated) 450°C. 


Temperature 

















































































































































































■ 

































































26 


at concentrations ranging from 0.1 to 0.5 M. Two typical curves are 
shown in Fig. 5, obtained from two different sulfide concentrations 
in the same compartment. Identical straight lines were always obtained 
regardless of the direction of voltage change as long as precautions 
were taken to prevent significant change in the sulfide concentration 
between measurements. These precautions included stirring and, when 
necessary, oxidation or reduction such that the zero-current potential 
remained within 3 mV of its original value. The slopes of these lines 
ranged from 10-15 ohms and represent the cell resistance. These curves 
show the sulfur/sulfide couple to be reversible under these conditions. 

Chronopotentiometry 

One set of measurements was made with an uninsulated gold wire 

O 

indicator electrode (diameter 0.055 cm, area 0.43 cnr), others with 
rhenium wire (diameter 0.062 cm, area 0.34 cm ) sealed in Pyrex so as 
to isolate it from the liquid sulfur pool. A total of 67 anodic 
chronopotentiograms were obtained. Each contained a single transition 
whose E(corrected for IR drop) was within 30 mV of the equilibrium 
e.m.f. for that sulfide concentration. The times for this transition, 
which is ascribed to 

S S + 2e , 

were measured and the results are summarized in Table III. All separate 
value of ix^/A, except those obtained at 93.6 mmol/1 sulfide, were 
subjected to least square analysis; this produced the linear plot of 
i T 2 /A against concentration shown in Fig. 6. This linearity indicates 
that the transition is diffusion-controlled and that the Sand equation 

























. 

' 












































(v w ) iNaaanD diqohivd (v w ) lNaaaro diqonv 




























































Table HI* 

Chronopotentiometric Study of Sulfide 


28 


Sulfide 

Concentration 

(mmol/1) 

No. of 
Points 

Mean ii'V A( 3 
(amp cm sec'^ mole - !) 

Standard 

Deviation 

23.2 

7 

349 

20 

27.9 

6 

335 

12 

37.2 

8 

331 

6 

51.1 

9 

321 

20 

65.1 

8 

299 

10 

37.4** 

7 

348 

25 

51.5** 

7 

352 

13 

74.8** 

8 

316 

6 

93.6** 

7 

281 

• > 

9 

* medium, fused 

LiCl-KCl 

eutectic at 420 1 2°C; 

current 


2 

density range, 26-101 mA/cm ; each point taken at a 
different current density. 

** rhenium electrode; otherwise,gold electrode. 


























































































- 





















ir 1 / 2 /A) x TO 3 , amp sec 1/2 / cm 2 


29 



Fig. 6. Variation of chronopotentiometric constant it^-/A 

* 

with sulfide concentration, showing obedience to 
Sand equation. Solid circles, single points; 
solid rectangles, multiple points, with number 


given. 
















































30 


ix 2 = ■=rTT 2 nFACD2 

is obeyed by the sulfur/sulfide system with both rhenium and gold 
electrodes. From the slope of the line in Fig. 6 and the Sand 
equation, the diffusion coefficient of the diffusing sulfide species 
was calculated to be 3.12, std. dev. 0.11, x 10" 6 cm 2 /sec at 420 ± 2°C. 
This value is almost an order of magnitude smaller than the smallest 
value reported for a divalent metal ion, Pb ++ , which is calculated as 
1.3 ± 0.2 x 10"^ cm 2 /sec at 420°C from literature data (39), indicating 
that the diffusing species is a somewhat larger entity, perhaps a 
polysulfide ion S~. There appears to be a trend towards smaller 
ix^/AC values with increasing sulfide concentration (Table III), but 
it is doubtful whether any significance can be attached to this in 
view of the standard deviations of these values. 

t 

Some of the curves indicated a very ill-defined second 
transition whose E T /4 was estimated as -0.08 ± 0.05 V and which we 
therefore ascribe to 

2S + 2C1" -> S 2 C1 2 + 2e". 

No measurements of the transition time were possible due to poor 
definition and the proximity of chlorine evolution. 

Some difficulty was encountered with deposition of sulfur on 
the electrode. It was necessary to strip off the sulfur produced in 
each chronopotentiogram cathodically and wait 10 minutes between 
polarizations for the solution to become uniform. Erratic results 
(extremely short transition times, probably due to blocking of 
electroactive surface) were sometimes obtained, apparently due to 
attachment of sulfur from the pool to the electiode. A small xesidual 












■ 























































31 


transition time was observed (intercept, Fig. 6), but it was much less 
than that reported by others (40) in fused salt media and can be 
ascribed to trace impurities and/or double-layer charging. 


II. Selenium 


Voltammetry 

The voltammetric curve obtained for selenium is shown in 
Fig. 7, denoted by triangles. In the absence of selenium and tellurium, 
the only electrochemical phenomena observed are anodic chlorine 
evolution (+0 o 3 V) and cathodic lithium deposition (>-2.1 V) as in 
previous work (36). 

The cathodic branch observed is ascribed to 

Se (1) + 2e ■+• Se . 

A red-brown color was observed leaving the electrode, until the entire 
compartment contents were colored when cathodic current was passed. 
Extrapolation of the linear part of the curve to zero current gave 
-1.07 ± 0.02 V for the "decomposition" potential, in good agreement 
with the potentiometric results given below. The anodic wave is 
ascribed to 


2Se(1) + 2C1" -> Se 2 Cl 2 (g) + 2e , 
analogous to the reaction 

2S(1) + 2C1" -> S 2 Cl 2 (g) + 2e" 

observed previously. The "decomposition" potential was +0.05 ± 0.02 V. 
Colorless gas bubbles were observed forming on the electrode at this 
potential and leaving the melt. No attempt was made to trap the gas 
since Se 7 Cl ? is reported as unstable at considerably lower temperatures 


















































< 


































32 


than those employed here. Stable potentials could not be obtained, 
as is expected when the species produced electrochemically volatilizes 
from the melt. 

Voltammetric curves were also taken with selenium electrodes 
in compartments in which selenide had been generated. Two typical 
curves are shown in Fig. 8. Identical straight lines were always 
obtained regardless of the direction of voltage change as long as 
precautions were taken to prevent significant changes in the ion 
concentration between measurements. These precautions included 
stirring and, when necessary, oxidation or reduction such that the 
zero current potential remained within 3 mV of its original value. 

The slope of these lines was approximately 15 ohms and represents the 

cell resistance. These curves show the Se/Se~ couple to be reversible 

) 

in this solvent system. 

Potentiometry 

Three complete experiments, each involving multiple cells, 
were carried out with new compartments, electrodes, and eutectic charge 
used in each. A total of 52 data points were taken at 400 ± 2°C. For 
each point, the e.m.f. became constant, within 0.5 mV, 30-90 min. after 
completion of coulometric reduction of selenium and stirring. The 
potential was thereafter constant, within 1 mV, over several hours. 

The effect of temperature on the e.m.f. was determined in 
several experiments over the temperature range 380-420°C, with both 
increasing and decreasing temperature. The measured potential was, for 
a fixed selenide concentration, linearly dependent upon temperature. 





























. 















33 


All data are given in the Appendix. A plot of AE/AT against the 
logarithm of the molar concentration (as moles Se /liter of eutectic 
at 450°C) was linear (Fig. 9). Least square analysis of this plot gives 

AE/AT = +0.123 log [Se = ] - 0.510 mV/°C, 
with a relative standard error of 6% in the slope and 1.5% in the 
intercept, for the temperature dependence of the cell 

(-)C, Se(l)/Se = , LiCl-KCl//Pt(II), LiCl-KCl/Pt (+). 

This equation is identical to that obtained for the analogous sulfide 
cell within experimental error. It was used to extrapolate all 
measured potentials to 450°C. 

These extrapolated potentials gave linear Nernst plots over 
the concentration range 0.015 - 0.35 molar selenide. A typical plot 

of potentials against the logarithm of selenide concentration (Fig. 10) 

) 

shows that Henry’s law is obeyed over the concentration range studied. 

A summary of all runs is given in Table IV; the original data are given 
in the Appendix. Least square analysis of all points gave a standard 
potential of -1.141 V for the Se(l)/Se~ couple (molarity scale) at 
450°C, with a standard error of 0.002 V. This corresponds to values 
of -1.172 V and -1.252 V, with the same standard error, on the molality 
and mole fraction scales, respectively (11), all potentials being with 
respect to the appropriate standard platinum electrode. The slope of 
the Nernst plot was -0.0660 V/log unit with a standard error of 0.0014, 
corresponding to 2.17 ± 0.05 electrons taking part in the reaction. 

This is in agreement with the theoretical value of 2 expected for 
Se + 2e~ -* Se - . 

Stable potentials could not be obtained on anodization of 




- 

' 

. 

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34 



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ANODIC CURRENT (irtA) CATHODIC CURRENT jmAj 


35 



Fig. 8. Current-potential curves for different selenide 

concentrations in the same compartment. Reference 
potential SMPE, temperature 400°C. 






































































































CHANGE IN CELL POTENTIAL , mV/°C 


36 



LOG OF MOLAR SELENIDE CONCENTRATION 


Temperature dependence of potential as a function 
of selenide ion concentration. Line is that given by 
least-squares analysis. Temperature range 380-420°C. 


Fig. 9. 






















































































LOG OF MOLAR SELENIDE CONCENTRATION 


37 



POTENTIAL AGAINST S.M.fiE.,(volts) 


Fig. 10. Electromotive force of selenide electrode 

(vs. SMPE) as a function of selenide concentration 
in a typical run, showing obedience to Henry's law. 
Temperature (extrapolated) 450°C. 






























































































38 


TABLE IV 

Standard e.m.f. determinations for the Se/Se~ couple* 


Selenide 

Molarity 

No. of 
Points 

(volts) 

Standard 

Deviation 

(mV) 

Exper. 
n 

0.015-0.10 

7 

-1.136 

2.6 

2.22 

0.024-0.24 

9 

-1.141 

1.1 

2.27 

0.018-0.16 

9 

-1.144 

1.2 

2.21 

0.029-0.32 

9 

-1.143 

2.4 

2.08 

0.029-0.33 

9 

-1.140 

2.8 

2.10 

0.039-0.35 

9 

-1.143 

2.3 

2;io 

Least square 





analysis of all 

52 

-1.141 

1.5 

2.17 

points 





* values corrected to 

450°C and SMPE; 

each entry 

is a 

separate compartment, 

the first being 

run 1, the 

next two 


being run 2, and the remainder being run 3. 























































































- * * • 








' 


. 



















39 


selenium electrodes, for the reasons discussed above. 

III. Tellurium 

Voltammetry 

The voltammetric curve obtained for tellurium is shown in 
Fig. 7, denoted by circles. 

The cathodic branch observed is ascribed to the formation of 
stable lithium-tellurium intermetallic compounds whose limiting 
composition is L^Te (27); the reaction written as 

Te (s) + 2Li + 2e Li^Te(s) 

is probably an oversimplification. The potential characteristic of 
this reaction was -1.40 ± 0.02 V. Liquid alloys were observed to form 
on the tellurium rod on cathodization beyond this potential. Such 
alloy formation on cathodization has been observed in previous studies 
of the Li-Te system (27,41). The anodic wave is ascribed to 

Te + Te(II) + 2e". 

An orange-brown color was observed leaving the electrode upon 
anodization. The "decomposition" potential for this reaction was 
-0.15 ± 0.03 V, in good agreement with the potentiometric measurements 
given below. 

Potentiometry 

Attempts were made to measure the standard potential of the 

Te(s)/Te = couple. These attempts were unsuccessful because the 

solubility of "Li 2 Te" in the LiCl-KCl eutectic in the presence of 

_ 3 

excess tellurium is very low; even an attempt to produce 2 x 10 M Te 
resulted in the formation of liquid on the surface of the tellurium 
























* 






















. 








40 


electrode. The potentials obtained in this manner were quite stable. 
They correspond, after correction for reference electrode, to those 
observed by Foster and Liu (27) for very tellurium-rich alloys of 
lithium and tellurium in a similar system, and therefore cannot be 
considered as true tellurium/telluride electrode potentials. 

Anodization of tellurium produced an orange-brown solution. 

Long needles of tellurium were observed extending from the electrode. 

The potentials measured were unstable, however, and drifted in the 
negative direction continuously after anodization was completed. At 
the same time, the color of the solution slowly disappeared. A yellow 
powder sometimes condensed in the cooler top of the isolation 
compartment. This behavior would be expected if a volatile species 
such as TeCl 2 (b.p. 327°C) escaped from solution at 400°. The 
experiment was repeated at 375° but the species formed still volatilized 
from solution. 

Attempts to produce meaningful Nernst plots from the potential 
data for this system were unsuccessful. The slope varied between 0.067 
and 0.134 V/log unit. Since 0.033 V/log unit would be expected for a 
four-electron process, the ionic species produced should be Te(II) 
rather than Te(IV). From these plots and the voltammetric curves the 
standard potential (molarity scale) of the Te(II)/Te(s) couple is 
estimated as -0.10 ± 0.03 V, placing it between Rh(III)/Rh and 
Ir(III)/Ir couples in this medium (7). Attempts to further oxidize 
the Te(II) species at a graphite electrode were unsuccessful. 

































' 

































41 


DISCUSSION 

The standard molar potential difference between the sulfur 
and lithium electrodes, using data for lithium (7) and sulfur, is 
2.252 V at 450 C. This is in good agreement with the open circuit 
potential of about 2.3 V obtained from the Li/S secondary cell at 385°C 
(31) for which the ternary eutectic of LiF-LiCl-Lil was used as 
electrolyte. 

It is not possible to compare the potential data for the cell 

Ag/AgCl, Ag 2 S/C, S 2 (g) 

studied by Thompson and Flengas (25) with the results of this work 
since Ag 2 S is completely miscible with AgCl but practically insoluble 
in the LiCl-KCl eutectic. Comparison would necessarily involve 
extrapolation of e.m.f. data and, more important, ignore a change in 
solvents. Potential data are experimentally accurate only within the 
concentration range where measurements were made and values extrapolated 
over several orders of magnitude on the concentration scale must be used 
with caution. Furthermore, the potential span between two couples may 
change from one solvent to another, especially if the electroactive 
ionic species are different in the two solvents. 

Thermodynamic functions of metal sulfides in the LiCl-KCl 
solvent cannot be calculated from the potential data. For the cell 

M/MCI , LiCl-KCl/LiCl-KCl, Li ? S/C, S(l) 
n ^ 

to cm 

employed in this study, the overall cell reaction may be written as 



















' 

‘ 






















































42 


2/n M + S(l) + 2/n M n+ + S~ 

(I) (II) 

if it is assumed that the and S ions do not take part in the 
transport of electricity and the activity of the Cl" and (Li + , K + ) ions 
are equal in solutions (I) and (II). The latter will hold in very 
dilute solutions. Any calculation, however, would refer to a 
hypothetical solution since most metal sulfides are quite insoluble in 
the melt and the metal and sulfide ions are here in two separate 
solutions. This difficulty could be overcome by constructing a cell 
of the type 

M/MS, LiCl-KCl/LiCl-KCl, MS/S(1), C 

(I) (II) 

Now, however, another problem may arise, viz. that of different metal 

> 

sulfide solubilities in solutions (I) and (II) due to the presence of 
liquid sulfur in solution (II). There is evidence (see below) of 
complex formation according to the equation 

S“ + nS + S- +1 

This would increase the sulfide solubility in solution (II) and render 

any cell potential measurement useless for a calculation of the free 

energy change of solid metal sulfide formation. Addition of sulfur to 

solution (I) is of course out of the question since it would quickly 

react with the metal electrode until no metal is left. 

The present voltammetric studies appeared to be in disagreement 

with those of Delarue (22), who attributed an anodic wave in sulfide 

solutions at Ei = -0.45 V to the reaction S" -> S + 2e . His melt was 

2 

not purified nor was an inert atmosphere used, and the sulfide was added 



















































































43 


as Na^S• 911^0 and an alkaline earth chloride. The necessity of 
scrupulously anhydrous and oxide-free melts has been discussed (35,42) 
and it originally appeared that impurities in his melt might account 
for the discrepancy. On duplicating his experiment with a purified 
melt and a platinum stationary microelectrode, it was found that the 

voltammetric curves were not reproducible but that waves of Ei near 

2 

-0.45 V were sometimes obtained. The poor reproducibility was 
unaffected by addition of sulfur, CaC^, and/or water. The equilibrium 
potential at the microelectrode was always near -0.9 V. The platinum 
surface immediately became dark on immersion in a melt containing 
sulfide. The discrepancy between this work and that of Delarue appears 
to be due to formation of a surface layer, probably PtS, on the platinum 
electrode in his work. It has not been possible to obtain reproducible 
voltammetric results with platinum electrodes in melts containing 
sulfide. 

Delarue (22) has observed the formation of S 2 CI 2 in this 
solvent when a strong oxidizing agent was added to melts containing 
sulfur. The anodic wave, which is observed voltammetrically and, with 
less reproducibility, in the chronopotentiometric studies, is therefore 
ascribed to the reaction 

2S(1) + 2C1" -> S 2 Cl 2 (g) + 2e~. 

From the data of Lewis and Randall (43) the free energy change 
for the reaction 

% 

2S(1) + Cl 2 + S 2 Cl 2 (g) 

is calculated to be -12.6 kcal/mole S 2 CI 2 at 420 C, while from the 
present voltammetric curves one calculates -12.4 ± 0.9 kcal/mole S 2 CI 2 



























.■ ‘' i,: si 


' 


' 





























44 


at the same temperature, in excellent agreement. Attempts to trap and 
identify the gaseous product were, however, unsuccessful. 

It has long been known that sulfur produces a blue color in 
certain solvents. This has been observed in fused KSCN (44,45) and 
fused LiCl-KCl (46). The nature of the colored sulfur species has not 
been established, and the following experiment was therefore performed. 

Chlorine was generated in a compartment on a graphite electrode 
to remove any remaining traces of impurities which could reduce sulfur 
to sulfide ion. The chlorine was then removed by repeated alternation 
of vacuum and nitrogen purging. Sulfur pieces, obtained by heating 
sublimed sulfur to 200°C and cooling under vacuum, were added to the 
melt. No blue color developed even after 1 hour. When sulfide was 
then generated by cathodic coulometry the blue color developed close 
to the electrode surface. On stirring the color spread throughout the 
compartment and was clearly visible at a concentration of about lCT^M 
calculated as sulfide ion. Further cathodic generation intensified the 
color. The color disappeared when chlorine was generated or when the 
potential of the graphite electrode was held at -0.3 V with respect to 
the S.M.P.E., both resulting in oxidation of sulfide to sulfur. The 
color also disappeared under vacuum after about 2 hours and reappeared 
on addition of sulfur to the melt. It appears impossible to explain 
these results, which indicate that both sulfide and sulfur are 
necessary to produce the blue color, other than by postulating that 
the color is due to a polysulfide ion formed by sulfur and sulfide, 
i.e., S = + xS -> S^ +1 (blue). The molar absorptivity is so high, 

16,600 (44), that a small amount of trace impurities present in 






- 

. 




















45 

the fused LiCl-KCl (46) could reduce enough sulfur to sulfide to 
produce the color. 

The situation in the fused KSCN system is more complex 
(44,45,47). The following reaction was proposed (44) at a temperature 
of about 400°C 

xKSCN -> xKCN + S x 

and the conclusion drawn (44) was that sulfur itself produces the blue 
color. The reaction 

S + 2CN" -* S = + (CN) 2 

might also take place, however, even though it has been reported in 
the literature (see ref. 44) to occur only above 500°C. If this is 
the case then both sulfur and sulfide are present and can cause the 

blue color in agreement with the present experimental findings in the 

> 

LiCl-KCl system. 

The standard molar potential difference between selenium and 
lithium electrodes, using literature data for lithium (7) and the result 
of the present study for selenium, is 2.163 V at 450°C. This is in 
good agreement with the open-circuit potentials of 2.3-2.4 V obtained 
from the Li/Se secondary cell between 350° and 400°C (32), and implies 
that at nearly full charge the selenium electrode potential of that 
cell may well be determined by soluble Se in the electrolyte rather 
than electrode composition. The free energy of the reaction 
2Se (1) + Cl 7 -* Se Cl (g) can be estimated as -11 kcal/mole from the 
voltammetric curves. No literature data could be found with which to 
compare this valuej it seems reasonable, however, as it is similar to 
that for the formation of gaseous S 2 CI 2 as determined above. 

















■ 

' 





46 


The Li/Te secondary cell is reported (27,33) to have an 
open-circuit voltage of 1.7-1.8 V which is in agreement with the value 
of 1.9 V obtained from the voltammetric curves of the present study. 

As would be expected, the electrochemical behavior of sulfur 
is quite similar to that of selenium. Tellurium, on the other hand, 
exhibits some metallic character and does in first instance produce a 
soluble cationic species, presumably Te , on anodization; the 
lithium-tellurium compound formed on cathodization is markedly less 
soluble in the LiCl-KCl solvent than the corresponding sulfur and 
selenium compounds. 

It is a moot point whether sulfur and selenium react directly 
at the cathode according to 

X + 2e~ -* X = 

) 

or whether lithium is plated into the sulfur (selenium) pool forming 
the lithium compound which later dissolves and dissociates according to 

2Li + + X + 2e“ -»■ L^X 
and L^X ** 2Li + k 

The overall result is the same in both cases and no clear distinction 
between the different mechanisms is possible. 

For tellurium the reaction taking place is apparently 
2Li + + Te + 2e" -* Li^Te 

as deduced from experimental observations. However, due to the low 
solubility of Li 2 Te the reaction may still be in first instance 

Te + 2e~ -> Te - 

and the liquid tellurium compound may only be formed after its 
solubility has been exceeded. 



















. 

















































47 


There is a significant point raised in the present work related 
to lithium-chalcogen cells. For both sulfur and selenium a soluble 
chalconide species determines the potential of the chalcogen electrode 
under the conditions of the present study. Such a species, whether X~ 
or L^X, can be expected to be present in lithium-sulfur (34) and 
lithium-selenium (32) cells and to diffuse to the lithium electrode if 
cell construction so permits. This will lead to reduced cell efficiency 
and eventual cell failure. This problem appears to be less significant 
in the lithium-tellurium system due to lower solubility of the telluride 
species produced. For this reason the Li/Te secondary cell (33) seems 
more promising as a high power, high energy battery although it produces 
a lower terminal voltage than the analogous sulfur or selenium cell. 





















. r 'n. it 






- 


































































48 


BIBLIOGRAPHY 

1. G. Chariot and B. Tremillion, Les Reactions Chimiques dans les 
Solvants et les Sels Fondus , Gauthier-Villars, Paris (1963). 

2. M. Blander, Ed., Molten Salt Chemistry , Interscience Publishers, 

New York (1964). 

3. B. R. Sundheim, Ed., Fused Salts , McGraw-Hill Book Co., New York 
(1964). 

4. G. J. Janz, Molten Salts Handbook , Academic Press, New York (1967). 

5. P. V. Clark, Fused Salt Mixtures , SC-R-68-1680, Sandia Laboratories, 

Albuquerque, New Mexico (Dec. 30, 1968). 

6. lu. K. Delimarskii and B. F. Markov, Electrochemistry of Fused Salts , 
A. Peiperl, Trans., R. E. Wood, Ed., Sigma Press, Washington, D.C. 
(1961). 

7. J. A. Plambeck, J. Chem. Eng. Data, JL2_, 77 (1967). 

8. D. R. Morris and J. R. Harry, Proc. of the Conf. on Industrial 

Carbon and Graphite, London, p.36 (1965). 

9. K. E. Johnson and H. A. Laitinen, J. Electrochem. Soc., 110 , 314 

(1963). 

10. H. S. Swofford, Jr., and H. A. Laitinen, J. Electrochem. Soc., 110 , 
814 (1963). 


11. 

H. 

E. 

Bartlett 

and 

K. 

E. Johnson, 

J. Electrochem. 

Soc. , 

114, 64 (1967). 

12. 

H. 

E. 

Bartlett 

and 

K. 

E. Johnson, 

J. Electrochem. 

Soc. , 

114, 457 


(1967). 

















































































■ 







































49 


13. J. W. Pankey and H. A. Laitinen, J. Am. Chem. Soc., 81, 1053 (1959). 

14. S. N. Flengas and T. R. Ingraham, Can. J. Chem., 35 , 1139 (1957). 

15. R. G. Verdieck and L. F. Yntema, J. Phys. Chem., 46, 344 (1942). 

16. R. Wehrman and L. F. Yntema, J. Phys. Chem., 48, 259 (1944). 

17. U. Anders and J. A. Plambeck, Can. J. Chem., 47_, 3055 (1969). 

18. J. A. Plambeck, J. P. Elder, and H. A. Laitinew, J. Electrochem. 
Soc., 113 , 931 (1966). 

19. H. Reinhold, Z. Elektrochem., 40 , 361 (1934). 

20. K. Kiukkola and C. Wagner, J. Electrochem. Soc., 104 , 379 (1957). 

21. S. I. Rempel and E. M. Maikova, J. Appl. Chem. USSR, 25 , 631 (1952). 

22. G. Delarue, Bull. Soc. chim. France, 906 (1960). 

23. G. Delarue, Bull. Soc. chim. France, 1654 (1960). 

24. M. C. Bell and S. N. Flengas, J. Electrochem. Soc., Ill , 567, 

575 (1964). 

25. W. T. Thompson and S. N. Flengas, Can. J. Chem., 46_, 1611 (1968). 

26. R. G. Verdieck and L. F. Yntema, J. Phys. Chem., 48_, 268 (1944). 

27. M. S. Foster and C. C. Liu, J. Phys. Chem., 70_, 950 (1966). 

28. M. S. Foster, S. E. Wood, and C. E. Crouthamel, Inorg. Chem., _3, 

1428 (1964). 

29. C. C. Liu and J. C. Angus, J. Electrochem. Soc., 116 , 1054 (1969). 

30. D. A. Swinkels, J. Electrochem. Soc., 113 , 6 (1966). 

31. H. Shimotake and E. J. Cairns, presented at Electrochem. Soc. 
Meeting, Dallas, Texas, May 1967; Ext. Abstracts of the Ind. 
Electrolytic Div. , 1-5, 3_, 4 (1967). 

32. H. Shimotake and E. J. Cairns, presented at Electrochem. Soc. 
Meeting, Boston, May 1968; Ext. Abstracts, No. 282. 























' 

' 


- 

















































. 































50 


33. H. Shimotake, G. L. Rogers, and E. J. Cairns, presented at 
Electrochem. Soc. Meeting, Chicago, Oct. 1967; Ext. Abstracts 
of the Battery Div., J-l, 12 , 42 (1967). 

34. H. Shimotake and E. J. Cairns, presented at Electrochem. Soc. 
Meeting, New York, May 1969; Ext. Abstracts, No. 206. 

35. D. L. Maricle and D. N. Hume, J. Electrochem. Soc., 107 , 354 (1960). 

36. H. A. Laitinen and C. H. Liu, J. Am. Chem. Soc., 80_, 1015 (1958). 

37. T. S. Licht and A. J. de Bethune, J. Chem. Educ., 34 , 433 (1957). 

38. H. A. Laitinen and J. A. Plambeck, J. Am. Chem. Soc., 87 , 1202 

(1965). 

39. C. E. Thalmeyer, S. Bruckenstein, and D. M. Gruen, J. Inorg. Nucl. 
Chem., 26_, 347 (1964). 

40. H. A. Laitinen and H. C. Gaur, Anal. Chim. Acta., 18_, 1 (1958). 

41. J. A. Plambeck and C. C. Liu, unpublished data. 

42. H. A. Laitinen, W. S. Ferguson, and R. A. Osteryoung, J. 

Electrochem. Soc., 104 , 516 (1957). 

43. G. N. Lewis and M. Randall, Thermodynamics, 2nd Ed., p.684, 
McGraw-Hill Book Co., New York (1961). 

44. H. Lux and H. Anslinger, Chem. Ber., 94, 1161 (1961). 

45. R. E. Panzer and M. J. Schaer, J. Electrochem. Soc., 112 , 

1136 (1965). 

46. J. Greenberg, B. R. Sundheim, and D. M. Gruen, J. Chem. Phys. , 

29_, 461 (1958). 

47. G. Metzger, Report CEA-2566, Commissariat a l'Energie Atomique, 
Centres d’Etudes Nucleaires, Saclay, irance, Nucl. Sci. Abstr., 

19, 1333 (1965). 








- 






' u 

' 
















. 

’ 








































51 


PART II: SPECTROPHOTOMETRIC INVESTIGATIONS OF 
SULFUR-SULFIDE SOLUTIONS IN FUSED LiCl-KCl 

ABSTRACT 

The spectrum of a sulfide solution in fused LiCl-KCl eutectic 
with excess sulfur present has been determined at 400°C. One broad 
peak is observed with the maximum absorbance at 585 my. A plot of 
absorbance against sulfide concentration, where the sulfide was 
generated coulometrically in the spectrophotometric cell, showed that 
Beer’s law is obeyed at sulfide concentrations less than about 
2 x 10" 5 molar. The molar absorptivity of the absorbing species was 
found to be 4,600 1 mole ^ cm 





























































* j 











































52 


INTRODUCTION 

As discussed above in Part I, the solution of sulfide ions 
in molten LiCl-KCl eutectic is blue in color if an excess of sulfur 
is present as a liquid pool floating on the melt. The blue color 
intensifies when more sulfide is added to the solution but disappears 
when the sulfur is pumped off, indicating that it is possibly due to 

I 

a polysulfide species. 

It appeared interesting to obtain the spectrum of this 
sulfide species and to investigate whether or not Beer’s law is 
followed when the sulfide is generated coulometrically. 























53 


HISTORICAL 

General aspects of molten salt spectrophotometry will not be 
discussed here since several reviews have been published on this 
subject (1,2). 

The spectrum of molten KSCN has been published (3) and the 
blue color observed has been ascribed to sulfur (see Part I). An 
absorbance maximum was observed at 605 my between 250° and 450°C and 
below 250°C an additional one appeared at 415 my. The molar 
absorptivity for the 605 my maximum was estimated to be between 16,600 
and 30,000. 

A spectrum of molten LiCl-KCl eutectic saturated with sulfur 
has been published (4) and the blue color of the solution has been 
attributed to dissolved sulfur. The maximum absorbance was at about 
600 my between 400° and 600°C. No value for the molar absorptivity 
was reported. 

















































* 


































































54 


EXPERIMENTAL 


Apparatus 

Spectra were recorded on a Cary Model 14 spectrophotometer. 
Potentials and currents were measured with a digital voltmeter 
(Model 3440A, Hewlett-Packard). Two 45 V batteries in series were 
employed as current source from which currents between 50 and 500 yA 
were drawn through a resistor network. 

The spectrophotometric cell consisted of square Pyrex tubing 
(Vitro Dynamics) of inside dimensions 22 x 10 mm with a top connected 
to it be means of a 34/45 ground-glass joint. Four 10/30 ground-glass 
joints were blown on this top which were used to insert a thermocouple, 
a gold foil electrode, an isolation compartment with a tungsten 
electrode, and an inert gas inlet tube. The isolation compartment for 
the anode was made of Pyrex sealing tubes (5D; Ace Glass Inc.). Part 
of this cell is shown in Fig. 11. The cell path length was 10 mm. 

After several attempts a furnace was constructed that 
operated satisfactorily and fitted into the Cary sample compartment. 

It is shown in Fig. 11. Previously published oven designs did not 
allow insertion of the relatively large Pyrex cell used in the present 
study. Problems were also encountered in obtaining the uniform 
temperature necessary over a melt column of about 5 cm. The present 
design, which uses a large aluminum cylinder, accomplishes this; the 
temperature gradient in the unstirred melt was less than 2 over a 




























' 
















































Fig. 11 Furnace for Cary Model 14 Spectrophotometer 


1 Brass water jacket 

2 Water inlet and outlet 

3 Semicylindrical aluminum reflectors 

4 Semicylindrical heating units, parallel, each 290 
watts, length 4", i.d. 2 3/8" (Fisher Scientific 
Co. ) 

5 Stainless steel crucible, 59 mm dia. 

6 Aluminum cylinder, 58 mm dia. 

7 Square 22 x 10 mm (i.d.) Pyrex cell 

8 Quartz window in water jacket, 20 mm dia. 

9 Opening in aluminum cylinder, 7 x 17 mm 

10 Insulation 

11 Pyrex wool 

12 Isolation compartment with tungsten electrode 

13 Pyrex tube for thermocouple 

14 Gold foil electrode making contact with sulfur 
pool 


56 



J I I 1 

5 cm 


I 1 

0 


























































































































































57 


vertical distance of 5 cm. The temperature of the oven was controlled 
by a Model 226 2-Mode solid state controller (API Instruments). The 
regulating thermocouple (not shown in fig.11) was placed close to the 
heating elements. 

Solvent 

After preparation of the melt as described in Part I it was 
filtered through a Pyrex frit (B porosity; Ace Glass Inc.) before 
freezing and storage. 

Chemicals 

The chemicals used were described in Part I. Helium was used 
as inert gas. It was passed through three cold traps cooled with 
liquid nitrogen; the last cold trap contained activated carbon. 

Electrodes 

A gold foil electrode (Johnson, Matthey £ Mallory Ltd.) was 
used to generate the sulfide from a sulfur pool. The anode consisted 
of a tungsten spiral in an isolation compartment which prevented 
mixing of anode and cathode products. 

Procedure 

The.frozen eutectic was transferred to the cell and allowed 
to melt under a helium atmosphere. Once molten the eutectic was again 
treated with chlorine gas after insertion of the isolation compartment 
and the Pyrex tube for the thermocouple. After 10-15 minutes the 
chlorine was removed by purging with helium which was passed afterwards 
over the melt for the remainder of the experiment. I he sulfide was 














' 

« 










































































































58 


generated with a gold electrode in a sulfur pool floating on the melt. 
The current used was about 100 yA. After each coulometric generation 
the solution was made uniform by stirring it with the isolation 
compartment. The temperature of the melt was 400 ± 2°C. Spectra were 
recorded with a scanning speed of 25 A/sec. The concentration of the 
sulfide was calculated from the measured current, time of generation, 
and volume of melt obtained as before from a potentiometric chloride 
titration (5,6). 

















' 

< 




























59 


RESULTS AND DISCUSSION 



The spectrum of the solvent with a sulfur pool floating on it 
is the lower curve in Fig c 12„ The zero point on the absorbance scale 
is taken arbitrarily since the reference light beam passed through air c 
It shows no peaks between 400 and 800 my, contrary to an earlier report 
by Greenberg, Sundheim, and Gruen (4). In the present work no blue 
color develops when care is taken in the purification of both the melt 
and the inert gas. Impurities present in the melt might have reduced 
enough sulfur to sulfide to have produced the blue color observed in 
the earlier work (4) 0 The spectrum after addition of sulfide to the 
melt is also given in Fig. 12. Only one maximum is observed at 585 my, 
not two as reported earlier (4)„ 

Spectra of solutions with increasing sulfide concentrations 
were recorded at 400 ± 2°C 0 The absorbance at 585 my was measured as 
indicated in Fig. 12„ For several experiments these absorbances were 
plotted as a function of the time of coulometric sulfide generation at 
constant current. In all cases the extrapolated lines passed through 
the origin 0 This indicates that the linear background line drawn under 
the upper curve in Fig. 12 is the zero absorbance line. It should be 
noted that the "zero absorbance" line shift from that of the solvent 
plus sulfur when sulfide was added to the solution. lhis was observed 

in all experiments. 













































I 

* 















. 































60 



in 

CM 


in 

CM 

o 


in 

CM 

in 


in 

CM 

^r 


in 

CM 

co 



T5 

0 ) •• 

CO d) 

3 > 

4-1 3 
3 
•• U 
CD 

> 3 

!-l CD 

3 • 

U C4 CD 
Cd U 
Cl *H 
0) 4-1 

|§ • H 

O 4J 3 
hP *H CO 

CD 4-1 
• > O 
& O 

tn rd O 
3 *H 
CD tP+J 
H c nj 
QJ -H Cl 

> 4-> CD 
rd rd 3 
£ O CD 

i—I tJi 

4-1 4-1 
O U 

l—I -I—I 

3 c 3 
0 0-3 
•H Cl, (D 


C4 CD '—i 
3 4-13 
4-1 rH o 
3 O 
cd ui 

tj) 

tnjee 

cd 4-> -H 
•H [3 
CD £ O 

O rH 

d h i—i 

rd o o 

JQ « 4-1 
3 I 

OrHO) 

wu g 

rQ -H rd 

<! 3J in 


CM 
I —I 

tr> 

•H 

Pm 



I 















































• * 




































61 


A typical plot of absorbance as a function of sulfide 
concentration is shown in Fig. 13. Concentrations up to about 
2 x 10 molar followed Beer's law accurately; the plot for these 
low concentrations is given in Fig. 14 on a larger scale. Negative 
deviations occurred at higher concentrations. The cell path was 
measured as 1.00 cm. From this and the slope of the line of Fig. 14 
the molar absorptivity of the absorbing species was calculated 
to be 4,600 1 mole cm for sulfide concentrations up to 
2 x 10 molar. Lux and Anslinger (3) estimated this coefficient 
to be 16,600 or higher but this value was arrived at under the 
assumption that the absorbing species is S2„ Furthermore, it is not 
clear how these authors determined the zero absorbance line from 
which the absorbance was measured 0 The present value is therefore not 
strictly comparable with their value, especially in view of the fact 
that the fused salts used are significantly different,, 

It is not yet clear whether the negative deviations from 
Beer's law are due to chemical or physical interaction between the 
absorbing species or to other effects such as light scattering. 
Nevertheless, spectrophotometric measurements could be used to 
determine the solubility of metal sulfides in fused LiCl-KCl in the 
presence of excess sulfur 0 Suitable calibration curves would, however, 

be required. 

It should be pointed out that it was quite difficult to prevent 
reduction of some sulfur to sulfide in every experiment. Fuithei 
improvement in the purification methods for the melt and inert gas 
would help to ensure more easily reproducible results. 





. 

- 























62 


\ 


O 

CN 



3DNV9^0SaV 


MOLAR SULFIDE CONCENTRATION (xlO 5 ) 


























63 



MOLAR SULFIDE 
CONCENTRATION (xlO 5 ) 


Fig 


14 


Absorbance as a function of sulfide concentration; 
low concentration detail from Fig. 13. 











































































































64 


BIBLIOGRAPHY 

1. M. Blander, Ed., Molten Salt Chemistry , Interscience Publishers, 

New York, 1964. 

2. B. R. Sundheim, Ed., Fused Salts , McGraw-Hill, New York, 1964. 

3. H. Lux and H 0 Anslinger, Chem. Ber., 94 , 1161 (1961). 

4. J. Greenberg, B. R. Sundheim, and D. M. Gruen, J. Chem. Phys., 

29, 461 (1958). 

5. H. A. Laitinen and C. H. Liu, J. Am. Chem. Soc., 80_, 1015 (1958). 

6. E. R. Van Artsdalen and I. S. Yaffe, J. Phys. Chem., 59, 118 (1955). 






































































































APPENDIX I 


65 


SUIT IDF F ME DATA 


COLUMN 1 
COLUMN ? 
COLUMN 3 
COLUMN 4 
COLUMN 5 
COLUMN 6 


SULFUR ELECTRODE EMF VS. RFF. ELECTRODE (V) 

T F M P F R AT UP E CENT I0PAD E 

MICRO EQUIVALENTS OF SUFFICE GLNERATI D 
mmolL CHLORIDE IN SUIEICE COMPARTMENT 
MICRO EQUIVALENTS OF IT ION TV REF. EL. COMPARTMENT 
MMOLE CHLORIDE IN KEF. EL. COMPARTMENT 


PLANK ENTRY INDICATES SAME VALUE AS 1AST PR I NTED VALUE 


-0.8477 

421.0 

400.00 

64.055 

2 CO.00 

70.769 

-0.8S10 

42 C. 8 

440.00 




-0.8551 

42 C . 6 

490.00 




-0.8575 

421.3 

540.00 




, -0.8603 

421.5 

590.00 




f - C.8633 

421,5 

650.00 




-0.8454 

421.C 

400.CO 

62.54 0 



-0.8507 

4? 0.8 

440.CC 




-0.8549 

42 0.3 

490.00 




-0.8567 

4 2 1.3 

54C. CC 




-0.8593 

421.5 

590.00 




-0.8611 

42 1.5 

640.0 0 




-0.8252 

A 9 1 0 

24 0. CO 

65.872 

r . p. p p ■ 

6 W U t V* N. 

7 r> 7 a 

i / ♦ n. r 

-0.8257 

42 C. 4 

240.CO 




-0.8336 

42 1.0 

3 00. C 0 




-0.8333 

4 2 1.0 

3 00 • GO 




-0.3440 

42 0.6 

/ , "V, PA 




-0.8441 

42 C. 8 

40'G. 00 




-0.8515 

42 0.6 

500.00 



. 

-0.8514 

42 0.6 

500.00 




-0.8627 

42 0.4 

7CO.00 




-0.8629 

42C.4 

700 . 00 




-0.8720 

42 0.2 

9C0.00 




-C .8729 

418.8 

9 0 C . 0 C 




-0.8783 

4 18.5 

1 ICO.CO 




-0.8785 

417. 8 

1100.00 




-C.8143 

421.0 

160.00 

64.712 



- C . 8 1 4 5 

42 0.4 

160.OC 


• 


-G.8317 

4 2 1.0 

26C.CC 





-0.8313 421.0 
-0.8389 420.6 
- 0 . 83-1 8 42.:. 4 
-0.8461 42b.6 
-0.8461 420.6 
-0.8535 42C.4 


-0.8535 

42 0.4 

500.C 0 

-C.8645 

4 2 C . 2 

700.00' 

-0.8649 

41 8.8 

7C0.CC 

-0.8733 

4 18.5 

900.OC 

-0.8733 

41 7. 8 

900.00 


260. 

CC 

32C . 

OC 

32 0. 

c 

o 

4 00 . 

6 G 

4 CO. 

OC 

5 00. 

CO 



























































■ 


- 






































■ 

















































































































































































66 



-0 . 8184 

421.0 

200.CC 

66.378 





- 0.0 1 8 5 

42 0.4 

200.00 






-0.8340 

42 1.3 

3 CO. 00 






-0.8 330 

4 2 1.3 

360.00 






-0.8386 

42 0.6 

34 6. CO 






-0.8387 

42 0. 6 

340.00 






-0.8444 

42 0.8 

400.00 






-0.8443 

420.6 

400.00 






-0.85?7 

42 0.4 

500.00 






-0.85?6 

4 2 0.4 

500.00 






-0.8639 

42 0.4 

7,02.4 0 






-0.8640 

4 1 9 . C 

7C2.40 






-0.8723 

418.5 

900 .CO 






- 0.6723 

417. 6 

5 •_ 0 . 0 0 






-0.8307 

4 19.3 

200.00 

65.972 

i\> 

o 

ft 

o 

o 

75.185 



-0.8308 

4 19.5 

200. C C 






-0.8433 

4 1 8.5 

300.00 






-0.8431 

418.8 

300.00 






-0.8511 

420.2 

4'T . CC 






-0.8511 

421.0 

400.00 






-0.8633 

4 2 0.6 

60C.CC 






-0.8634 

418.5 

6C0.0C 






-0.8 72 7 

418.3 

800.00 






-0.8726 

416.5 

800.00 






-0.8790 

418.8 

1000.00 





/ 

-0.8786 

4 19.3 

1CC0.CC 






-0.8257 

419.5 

16C.42 

65.948 





-0.8257 

^ 1 9.3 

i60 • 42 



) 



-0.8410 

418.8 

240. CO 






-0.8412 

4 18.8 

240.00 





s 

-0.8498 

42C . 2 

340.00 






-0.8 50 1 

42 0.0 

340.00 






-0. 8571. 

420.2 

460. C C 






-0.8582 

418.8 

460.00 






-0.8682 

418.5 

640.0 C 






-0.8682 

418.8 

640.00 






-0.8742 

418.8 

0CC.OC 






-0.8737 

419.3 

SCO. CO 






-0.8457 

419.5 

300.00 

62.34C 





-0.8457 

419.5 

300.00 






-0.8545 

418.8 

400. GO 






-0.8543 

416.8 

400.00 






-0.8621 

4 2 0.2 

540.00 






-0.8623 

42 0.0 

540.00 






-0.8730 

420.6 

001.72 






-0.8742 

418.8 

801.72 






-0.8831 

418.5 

1 IOC.00 






-0.8831 

418.8 

1 100.00 






-0.8897 

418.8 

14C0.CC 






-0.8893 

419.3 

14C0.00 






-0.8965 

4 1 9 . C 

1 8 C 0.0 C 






-0.8965 

416.3 

1 8C0.CC 






-0.8365 

423.3 

240.00 

65.165 

2C0.00 

74.630 



-0.8367 

422.5 

240.CO 






i 

o 

. 

00 

> 

-T' 

421.5 

340.00 




• 
































































• 









































































67 


-0.8463 

421.5 

340.00 



-0.8564 

422.0 

460.00 



-0.8553 

421.8 

460.00 



-0.8 6 6 6 

42 1 . 5 

640.00 



-C .8655 

42 1.8 

640.00 



-0.8756 

421.5 

900.00 



-0.8761 

420.8 

9CC.C0 



-C .8747 

4 2 2.5 

8 00.C 0 

62.365 


-C.8745 

4 2 3.3 

800.00 



-C.8810 

421.5 

1000.CO 



-0.88 1C 

4 2 1.5 

1000.00 



-0.8859 

422.0 

12 CO.00 



-0.8858 

4 21.8 

1 1 00.90 



-0.8940 

421.5 

16C0.00 



-0.8939 

421.8 

16CQ.0C 



-0.8999 

421.5 

2COO.00 



-0.90O4 

42 0. 8 

2000.CO 



-0.8545 

4?2 . 8 

4 00.C C 

64.155 


-0.8540 

42 3.3 

40C.CC 



- C • 8644 

421.8 

560.00 



-0.8644 

421.8 

560.CO 



-0.8706 

42 2.3 

700.00 



-0.8705 

422.0 

700.CO 



-0,8777 

421.8 

9C0.CC 



- 0.8775 

421.8 

900.00 



-0.0857 

421.5 

1200.00 



O P ci /. 1 
w » Q cj i 

42 C . 8 

1 O p n p r\ 
i c. L- 'j • \j yj 


) 

-0.8117 

419.0 

16C.00 

66.450 2CC.CC 

6 7 • 0 0 C 

-0.8117 

418.5 

160.0C 



l -0.8260 

4 18.5 

240.60 



-0.8255 

41 7. 8 

240.CO 



-C.8410 

41 6 . 8 

360.CO 



-0.841i 

417.3 

36C.C0 



-0.8489 

41 7.5 

460.00 



-C.8487 

417.5 

460.OC 



-0.8602 

418.5 

660.40 



-C.860 1 

41 8.5 

660.4C 



-0.8684 

418.3 

060.00 



-0.8683 

418.3 

860.OC 



-0.8775 

4 17.3 

1 16 0 . C C 



-0.8772 

41 7. 8 

1160.00 



v, -0.8C70 

419.3 

120.00 

58.775 


f -0.8211 

418.5 

180.00 



-0.8210 

418.3 

18C.CC 



-0.8362 

417.8 

280.00 



-0.8350 

42 0.2 

280.CO 



-0.8491 

41 7.3 

400.00 



-0.8490 

417.3 

400.00 



-0.8595 

417.5 

560.CC 



-C.8595 

41 7. 3 

560.GO 



-0.8685 

418.5 

76 0.00 



-0.8685 

418.5 

760.00 



-0.8 ?55 

4 18.0 

960.OC 



-0.8756 

4 18.0 

960.00 



























































. 





























■ 





























' 









































































































68 


-0.8035 

41 7.8 

1260.CO 

-0.8 83 5 

417.8 

1260.00 

-0.8149 

418.3 

200.00 

-0.8145 

4 18.0 

200.00 

-0.8324 

42 0.2 

320.00 

-0.8322 

42 C. 2 

320.00 


6 4.7 7 5 


-0.8458 417.3 44C.CC 

-0.8455 417.5 440.00 

-0.8504 417.3 66C.C0 

'- 0.8599 41 7.0 66 0. 6 0 

-C.8676 4]8.3 860.00 

_- 0.867 5 4 1 8.3 860 . 00 

-0.8749 417.8 1080.00 

-0*8.746 4 L 7.8 10 8 0.0 C 

-0.8815 417.5 1360.00 

-0.8813 417.3 1366.CO 



TFMPERAT'JFP D FP FN OF NCF PF CFU °f'T F N T T AL , SOLO 1 1 


COLUMN 1 LUG OF MOLAR SULFIDE CONCENTRATION! 
COLUMN 3 CHANGE IN CELL POTENTIAL, MV/DE 0 


PT ION CONG. IN PFF. EL. APPROX. C.04M 


-1.538 

-0.718 

-1.215 

-0.661 

-1.143 

-0.667 

( -0.971 

-0.637 

-0.854 

-0.629 

-0.740 

-0.610 

-0.578 

-0,588 

-0.480 

-0.577 

i — 0 • 6 4 8 

-0.6P4 

r -0.745 

-0.605 

-0.369 

-0•564 

-0.323 

-0.569 

















































' 


































































































































69 


SULFID 

r 

EME DATA, 

LOW C UNOENTP ATI ON5 


GUI U M N 

1 

SULEUR 

ELECTRODE EOF VS. REF. CLFCTR03E (V) 


COLUMN 

2 

T EMPEPATUPE CENT I OR ARE 


COLUMN 

3 

M I CP 0 

EQUIVALENTS UF SUM IDE GENERATED 


COLUMN 

4 

MM 01 L 

CHLORIDE IN SULFIDE COMPARTMENT 


COLUMN 

5 

MMOL L 

CHLORIDE IN PEE. EL. C 0 M P A R T M F 1 


MICRO 

EQUIVALENTS 

PT ION IN REE. EL. COMPARTMENT E DUAL 


MICRO 

EG. SULFIDE 


BLANK 

ENTRY INDICATES SAME VALUE AS LAST PRINTED VALUE 


-C.6856 


39 8.3 

20.00 93.92 97.42 


-0.6695 


4 14.5 



-0.69?4 


390. 8 



-0.7C84 


3 73.3 



-0.6960 


3 8 8.0 



-0.688 5 


39 7. 0 



-0.7271 


41 7.4 

50.CO 


-0.7422 


40 0.5 



-C .7529 


3 8 (• 



-0.7628 


3 7 5.0 



-0.7412 


4 01.3 



-0.7518 


424.5 

8C.0C 


-0.7790 


o o r\ 

• 


-C.7908 


3 76.8 



-0.7714 


40 1.2 



-0.7955 


415.0 

140.00 


-0.8142 


389. 5 



-0.8288 


36 9.0 



-0.8077 


399.0 



-0.8150 


419.0 

200.00 


-0.8326 


39 3.3 



-0.8446 


3 76. G 



-0.8245 


4 05.8 



-0.6183 


411.3 

1C.DC 86.67 91.80 


-0.6098 


419.8 



-0.6278 


40 2.0 



-0.6419 


39C .0 



-0.6405 


42 3.8 

16. GO 


-0.6765 


385.3 



-0.6690 


395.8 



-0.6554 


41C.0 



i 

o 

• 

-p* 


3 8 6.5 

25.00 


-0.6933 


40 0. 5 



-C.6841 


412.0 



I 

o 

• 

o 


424.3 



-0.7C05 


42 6. 8 

40.00 


-0.7133 


411.8 



. -0.7263 


396. 8 



-0.7366 


38 5.3 



-0.7577 


389.3 

60.00 


— 0 • 74 80 


40 1.6 



-0.7372 


414.5 



-0.7306 


42 3.8 




















































‘ 






























































































































































































































70 


S F Ll hi (' 

F 

EMF HAT A 


COLUMN 

1 

SELENIUM ELECTRODE EMF VS. 3 F F . FirOTPl6F (\f \ 

COLUMN 

9 

r. 

TEMPERATURE CEL 

I GRADE 

COLUMN 

3 

MI CRC 

EQUIVALENTS OF SbLENIDE GENERATED 

COLUMN 

4 

MMOL E 

CHI OR IOE 

IN SELF NI0 E COMPARTMENT 

COLUMN 

6 

MICRO 

EQUIVALENTS OF PT ION IN REF. EL. COMPARTMENT 

COLUMN 

6 

MM OLE 

CHLGRIDE 

IN REE. EL. COMPARTMENT 

BLANK E 

MTKV INDICATES SAME VALUE AS LAST POINTED VALUE 

-0.9876 


39 8.4 

200.00 

76.213 2C0.0C 94.047 

-0.9900 


3 9 8.2 

250.CC 


-0.99?8 


39 8.4 

300.00 


-1.0COO 


3 9 8. 7 

400.00 


-1 .CC72 


3 9 8.7 

5CO.CO 


-1.0193 


39 7.6 

750.00 


- 1 .0283 


3 9 8.5 

1CCC.00 


-).0374 


3 9 8.6 

1400.00 


- 1.0433 


39 7.7 

18CC.CC 


-0.9780 


39 8.4 

15C.CG 

76.66 3 

-0.9823 


39 8.2 

2 0 C » 0 C 


-0.9847 


3 9 8.4 

250.CC 


-0.9934 


398. 1 

360.CC 

> 

-1.0CC9 


3 9 8.2 

45C.CC 


- 1.0143 


397.6 

700.00 


-1.0219 


39 8.5 

900.CC 


- 1.032 7 


3 9 8.6 

1300.00 


-1.0410 


39 7.7 

1700.00 


-0.9786 


39 8.4 

150.00 

77.769 

-0.9832 


3 9 8. 2 

200.CO 


-C.9865 


398.4 

250.CC 


-0.9951 


39 8.7 

35C .00 


-1.CC32 


398.2 

450.00 


-1.0161 


39 7.6 

700.CC 


-1.0237 


39 8. 5 

9C0.CC 


- 1 . C 3 4 3 


39 8.6 

1300.CC 

• 

-1.0424 


3 9 7.7 

1700.00 


-0.9701 


398. 8 

ICC.00 

82.791 200.CO • 90.975 

-0.9812 


398. 2 

150.00 


-0.9890 


398.2 

200.00 


-0.9978 


3 9 8.7 

275.CO 


-1.0032 


399.0 

35C.CO 


-1 . 0 C 9 6 


399.3 

450.00 


- 1. C 1 68 


3 9 8.7 

6 0 0 . 0 0 


-1.0215 


3 99.7 

750.OC 


-1.C252 


399.2 

900.00 


-0.9806 


396.0 

125.00 

7 3. 78° 

-0.9855 


3 9 6.2 

175.00 


-0.9924 


398.2 

225.CC 


-0.9983 


398. 7 

2 75.OC 

_ _ _____ , _„______—....-.—-. . .... * 




















































































- 




























































■ 


























: 

















. 































































































71 


-1.0C7C 399*0 40C.00 

-1.0134 399.3 5CO. 00 

- 1.0215 39 8.7 7CC.0C 


-1.0279 

-1.0335 

-0.9500 

399.7 

399.2 

3 94.7 

950.00 

1250.00 

75.00 

74.712 

125.00 

83.79? 

-0.9578 

-0.9668 

-0.9726 

395.5 

393.5 

395.5 

100.00 

135.00 

2CC.CC 




-0.9815 

39 5.0 

275.CO 




-0.9926 

3 94.2 

400.00 




-C.9996 

3 94.2 

505.00 





tempera tunc s '• i '‘ t• "i- cell r m , ^ 

wmmmwm9****&w***m»m m * m m.-+ , ■**** * **:’* » mwojttmtim **w*wr 


cntuMfj l 

COLUMN 2 


LOG OF MOL A c < SEl.ENIDF CONGE : T ? A T n 

CMAMGC IN CELL POTENTIAL-, NV/DLORtE 


PT ION 

CGNC. IN REF. EL. APPROX 

-0.521 

-0.572 

-0.574 

-0.579 

-0.559 

-0.574 

-0.712 

-C.6 CO 

-C.874 

-0.629 

-1.066 

-C.64? . 

-1.280 

-0.657 

-1.573 

-0.697 

-1.544 

i 

o 

• 

O 

o 



















































. 





. 












































































































. 
























ooooo ooorvooooooooooo o o r> o o ooo 


APPENDIX II 


72 


NERNST EQUATION LEAST SQUARES PROGRAM USING LSQ1 (FORTRAN) 

IMPLICIT PEU*8 ( A-Ht C-Z ) 

REAL*4 TITLE (20) 

DIMENSION A (20,15), B(20,l), X(500) f Y(500,1), W(500), $UM(1), 

XPESID(500,1), EVAL(500), STD(15), XX1(50). Xl(50), CTEMP(500), YTE 
XRM(500 ) t P ELDV(15), RELDEV(500), C0NCTM(500), SP0T( 500) 

X , S T D P 0 T (500 ) , YY( 500) 

EQUIVALENCE (YTERM,STDPOT)»(YY(1) »Y ( 1 ,1 ) ) 

DATA R/8.3143/, F/96437.0/, T/273.16/, BASECH/O.43429448/ 

10 CONTINUF 


SET OF SUMMATIONS TO ZERO 

IREJ=0 
NR F J = 0 
MORFN = 0 
NiTOT = 0 
T0TAL1 = 0. 
il RF AD ( 5,305) TITLE 
WRITE (6,1100) TITLE 


C 

c 

c 


PROGRAM CONTROL CARD 
N = N0• HF POINTS IN EACH SET 


I F 

I F 
I F 


I P 
IP 
I P 


c n 

L. W 


o 


rj A DU 


i « i 


EO .1 
EQ . 2 


G < 
GRAPH 
GRAPH 


SUBROUTINE 
SUBROUTINE IS 
SUBROUTINE IS 


n a \ i r* r\ 
G H L L L. I J 


CALLED 

CALLED 


AND LEAST SQUARE LINF IS 


ALSO PLG T T ED 

IF N1.NE.0 PROGRAM WILL CALCULATE POTENTIALS AT CONCENTRATIONS 
SPECIFIED ON INPUT CARDS 

IF IC.NE.O ON ALL BUT LAST DATA SET, ALL DATA SETS ARE COMBINED 
TO CALL GRAPH ONLY ON LAST DATA SET IP=1 
IF IF.NE.O ON LAST DATA SET (ALL OTHERS IR=0) REJECTION OF POINTS 
WILL TAKE PLACE 


IQ AND IT ARE DUMMIES 


READ (5,1000) N, IP, Nl, IC, IR, IQ, IT 
IF (N.EQ.O) STOP 
TOT A L 4 = 0. 

TOTAL 5 = 0. 

TOTAL6 = 0. 
m - 

DATA CARD FOR INDICATOR ELECTRODF COMPARTMENT 
ZN CHARGE CF ION IMCL. SIGN 

CONC NUMBER OF MOLES OF CHLORIDE IN COMPARTMENT 

DENS DENSITY CF MELT IN G PER LITER 

ZMMW MEAN NGL. WEIGHT CF MELT 
BASICT TEMP. OF MELT IN CENTIGRADE 

R EAD(5,2 OCO) ZN, DUMMY, CONC, DENS, ZMMW, BASICT 
































































■ 












. 

' 























































* 












. 












ASSUMPTIONS MADE BY PROGRAM FOR THE LICL-KCL FUTECTIC 

IF (BASICT.LE. 0.0) BASICT = 450.00 
IT (ZN.EQ.O.O) ZN = l.o 
IF (C n N C . L E . 0.0 ) CONG = 0.1000 
IF (DENS.LE.0.0) DENS = 1648.00 
IF (ZMMW. L c .0.0) ZMMW = 65.5900 

data CARD FOR RFP. ELECTRODE COMPARTMENT 
StOJV NUMBER OF EQUIVALENTS OF REF. ICN GENEPATED 
SCONC NUMBER CF MOLES OF CHLORIDE IN REF. COMPARTMENT 
SN CHARGE OF REF. ION INCL. SIGN 
APnT STD. ROTE NT IAI OF REF. ELECTRODE COUPLF 
ORIGEQ NUMBER OF EQUIVALENTS USED TO GENERATE ION OF LOWER 
OXIDATION STATE WHEN PROGRAM IS USED FUR IONS OF TWO sol 
OXIDATION STATES ' 


READ (5,2000) SEQIV, SCONC, SN, APOT, OR IGEQ 

WRITE (6» 5 100) SN, ORIGEQ, CONC♦ DENS, ZMMW, BASICT 

IF (SCONC.LE .0.0 ) SCONC = CONC 

IF (SN.LE.Q.O) SN = 1.0 

NCHECK = MOREN + 1 

N S U M - N + MORE N 

WRITE (6,^100) 

FIRST CALCULATION LOOP 

) 

DO 33 I = NCHECK,N$UM 

DATA CARD FOR INDICATOR ELECTRODE 
EOIV NUMBER OF EQUIVALENTS OF ION GENERATED 
V EMF VS REF. ELECTRODE IN VOLTS 
CTEMP<!) TEMP. IN CENTIGRADE 
W(I) WEIGHTING FACTOR OF POINT 

READ! 5,2000) EQIV, V, CTEMP(I), DUMMY, DUMMY, W ( I > 

IF (CTEMP(I) .EQ.O.O) CTEMP(I) = bASICT 
IF (W(I).EQ.O.O) W(I) = 1.0 

WRITE (6,4000) EQIV, V, W(I), CTEMP(I), DUMMY, DUMMY 
YTERM(I ) =V 

TOTAL6=T0TAL6+(CTEMP(I)+T) 

CONCTM(I) = (EQI V*DENS) / ( CABS(ZN)*CONC*ZMMW) 

IF (ORIGEQ.NE.O.O) C ONCTM{I )=(EOIV/ZN)/(OR I GEO-(EQIV/ZN)) 
X(I) = DLQG10(CCNCTM<I)) 

AVTEMP = TQTAL6 / DFLOAT{N) 

TOT AL1 = TOT AL1 + T0TAL6 

REFERENCE ELECTRODE CALCULATION LOOP 

DO 4? I = NCHECK, NSUM 
STEMP = C T E M P(I ) + T 

SCNCTM = (SEQIV * DENS) / (SN * SCONC * ZMMW) 

SPOT(I) = APOT + ((R*STEMP) / (SN*F))*DLOG(SCNCTM) 

T0TAL4 = T0TAL4 * SPOT(I) 

Y( I ,1) = S POT(I ) + YTERM(I) 



























































■' 











































































































O o o 


74 


C 

C 

C 


c 

c. 

c 


c 


AVSPGT = T0TAL4 / DFLOAT(N) 

ERROR AND DEVIATION CALCULATION LOOP 

SPTDEV=Q.O 
IF(N.LE.l) GO TO 4 4 
DO 43 I = NCHECK, NSUM 

43 TOTALS = TOTALS + (((AVSPGT - SPOT(I))**2)/<DFLOAT(N)-l.0)) 
SPTDEV = DSQRT(TOTALS) 

44 WRITE (6,3100) APOT, SCONCt SEOIV, SCNCTM, AVSPDT, SPT 
XDEV, AVTFMP 

IF (NX•EQ•0) GO TO 46 
N1T0T = N1T G T + NI 
N1 = NHOT - NX + 1 

DATA CARDS FOR CASE Ni.NE.O 


READ (3,2000) (XX1(I), I = Nl, N1T0T) 
DO 45 I = Nl, NlTOT 
45 X i ( I ) = DLOGLOtXXI(I ) ) 


46 MOP FN = NSUM 

IF (IC.NE.O) GO TO 11 
AVGTMP = TGTAL1 / D F L 0 A T(NSUM) 
50 TOTAL2 = 0.0 


TOTALB = 
DO 60 I 
STDPOT( I 
TOTAL 3 = 
60 TOTAL? = 
X l . 0 ) ) 


0 . 

1 , NSUM 

= Y(I,1) “ ((R*(CTcMP(I) 

TOTAL? + (STDPOT(I )*W(I)) 
TOT AL? 4- ( ( ( CTEMP ( I ) 4- T 


T) ) /(ZN*f) 5 *(X(I } /BASECH 
AVGTMP))/(DFLOAT(NSUM) 


TMPDEV = DSQRT(T0TAL2) 

AVGSPT = TOTAL? / DFLOAT(NSUM - NREJ) 


END OF CALCULATION LOOPS 

t 

CALL LS 01 (X,Y,W , RES ID,NSUM,SUM,1,A,B,M) 

STDERR = DSQRT(SUM(1)/DFLOAT(NSUM - NREJ)) 

EXPEPN = (R * AVGTMP) / (B{2,1> * F * BASECH) 

DO SO I = 1 , M 

STD ( I) = DSQRT(SUM(1 ) ( I , 1)/DF LOAT ( NSUM - NREJ - M - 1)) 

80 FELDV( I) = STD( I ) /B( 1,1) 

TOJA LI ^ 0. 

DO 90 I = 1,NSUM 

TOTAL 1 = T0TAL1 4- ( ( ( AVGSPT-STDPOT ( I ) ) **2 ) *W ( I ) ) 

E VAL ( I ) = RES ID (1,1) 4- Y ( I , 1 ) 

90 RELDEV(I) = RESID(I,1) / Y(I,1) 

SPOTDV = DSQRT( TOT At. 1 / DF L OAT ( NSUM-NRE J- 1)) 

IF (IREJ.GT.C) GO TO 170 
IF ( IREJ.GT .NSUM) GO TO 190 

100 WRITE (6,3 000) NSUM, IP, N1 TOT, IP, IQ, 1C, NPEJ, IT 

WRITE (6,5100) AVGTMP, TMPDEV, EXPERN, ZN, AVGSPT, SPOTDV 
WRITE (6,5000) (B(I,1), STD(I), RELPV(I), I = 1,M) 




' 








* 















' -n f i • ? 1 % oi i 



























o o o o o 


75 


WRITE (6,6000) SUM 


WRITE (6,6100) STDERR 
WRITE (6,6200) 

00 160 I = 1,M 

160 WRITF (6,6000) (A(I,J), J = l,M) 

WRITE (6,^000) (W(I), CONCTM(I), X(I), SPOT(I), Y(I,1), 
XFVAL(I), RES 10(1,1), RELDEV(I), STDPOT(I), I=1,NSUM) 


PLOTTING OPTION 

HORIZONTAL AXIS IS POTENTIAL AGAINST STD.RFF. IN VOLTS 
VERTICAL AXIS IS LOG CF IONIC CONCENTRATION 
X= EXPERIMENTAL POINT 
C *= LEAST SQUARES LINE 

C 0 INDICATES OVERLAPPING POINTS 

IF(IP.NE.O) WRITE(6,1100) TITLE 

IF( IP .NE .0 ) CALL DGRAPH(NSUM,X,YY,EVAL,YY,IP,0.0,0.0,0.0,0.0,61) 

C 

IF (IR.LE.O) GO TO 190 
IF (IRFJ.GE.NSUM) GO TO 190 
IF ( IREJ .GT .0) GO TO 180 
WSTOR E =W(1 ) 

W(1) - 0.0 

IR F J = 1 
NR E J = 1 
GO TO 50 

170 NREJ = NREJ + 1 

IF (NREJ.GE.(NSUM-2 ) ) GO TO 190 

IF (DABS(RESIO(IREJ,1)).GE.2.576*$TD£RR} GO TO 100 
NREJ = NREJ - 1 
W(IREJ) = WSTORE 
180 IREJ = IREJ + 1 
WSTORE = W(IREJ) 

W( IREJ ) = 0.0 
GO TO 50 

190 IF (N1T0T.LE .0) GO TO 10 
00 196 I = 1,Ml TOT 

194 EVAL(I) = POLY(XI(I ) , M, R, 1, 20, 1) 

WRITE (6,800 0) (XXI (I), XHI), EVAL(I), I = 1, N1T0T) 

GO TO 10 

805 FORMAT (20A4) 

1000 FORMAT (1216) 

1100 FORMAT (1 HI,2 0A4) 

2000 FORMAT (6C12.5) 

2100 FORMAT (84HJ REF. CHARGE ORIG.EQUIV. C3NC. DENSITY 

X MEAN MPL.WT. BASE TFMP. /(1HJ1P6D14.5//)) 

3000 FORMAT (48Hi LEAST SQUARE NERNST PLOT USING LSQ1 / 

X 3HJN = I3,5H I P=I 2 » 6H N1 = I2,6H IR=I2,6H 10=12,6H IC 

X=I2,8H NREJ=I2,6H IT=I2) 

3100 FORMAT (80HJ INPUT DATA FOR AND CALCULATED VALUE OF 

XTHE STANDARD POTENTIAL /105HJ SCALE POT. SOLV. CONC. 

XEOUI VALENT S CONC. TERM STD. POT. STD. DEV. AVG. TEMP. 

X /(1HJ1P8D14.5//) ) 


4000 FORMAT 
4100 FORMAT 

(1HJ1P8D14.5) 

(86HJ EQUIVALENTS 

POTENT IAL 

WEIGHT 

TEMPERATU 

XRE 


/ ) 































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. 














































76 


5000 FORMAT (62HJ COEFFICIENT ERROR RELATIV 

XE ERROR/(1HJ3F20.8)) 

5100 FORMAT (82HJ AVERAGE TEMP. DEVIATION EXPER. N THEOR. N 

X MEAN STD. DEV. /(1HJ1P8D14.5)) 

6000 FORMAT (36HJWEIGHTED SUM OF SQUARED DEVIATI0NS=1PD13.5) 

6100 FORMAT (2 9HJST AN HARD ERROR OF ESTIMATE =1PD13.5) 

6200 FORMAT (13HJERROR MATRIX) 

7000 FORMAT (124HJ WEIGHT MOLARITY X REFERENCE 

X POT. POTENTIAL EVALUATION RESIDUAL RELATIVE DEV. STD. 

XPOT./(1HJ1P9D14.5)) 

8000 FORMAT (43HJ MOLARITY EXTRA X EVALUATION /(1HJ1P3D1 

X 4.5 ) ) 

END 


C. 

C 


C 

C 


SUBROUT INF LSQ1(X,Y,W,RES ID,N»SUM,L,A,3 , M) 

IMPLICIT REAL*8(A-HtO-Z) 

DIMENSION X(500)t Y(500,1),RES ID(500 * 1 >,A(20,15),B(20,1),C( 500,15), 
XSUM(1) ,W(5 00 ) 

COMMON C 


DO 1 I 

C ( I , 1) 

DO 2 J 
DO 2 I 

C(I,J) 
DO 3 I 
DO 3 J 

A ( I , J ) 
DO 3 K 
A<I,J) 
DO 4 J 
DO 4 I 
B ( I , J ) 
DO 4 K 
B(I ? J) 


1, N 

1 . 000000000 


2,M 

1 » N 


+ C (K, I ) * C(K,J) 


C (1 , J - 1 ) - x ( I ) 

If M 
1 , M 

0.000000000 
1 , N 

A ( I , J ) 

1 , L 
If M 

0.000000000 

1»\ 

B ( I , J ) + C ( K , I ) * Y ( K , J ) * 
CALL MAT INV (A,M,B,L f DETERM ) 

DO 6 J = 1 , L 

SUM(J) = 0.000000000 

DO 6 I = 1 , N 

P E S I 0 ( I , J ) = P0LY(X(I)fM f B f Jf20fi) - 
SUM(J) = SUM(J) + RE SID(IfJ )**2*W(I) 
RETURN 
END 


W ( K ) 


W(K) 


Y(I,J) 
































































































































ooo ooo ooo oooo 


77 


MATRIX INVERSION WITH ACCOMPANYING SOLUTION OF LINEAR EQUATIONS 
SUBROUTINE MATINV!A,N,B,M,DETERM) 


IMPLICIT REALMS(A-H,0-Z) 

DIMENSION IPI V 0 T{2 0) , A(20,20), B(20,* ) , INDEX(20,2), PIV0TI20) 
COMMON PIVOT,INDEX, I PIVOT 

EQUIVALENCE (IRCW,JROW), tICOLUM,JCOLUM), {AMAX,T,SWAP) 

INITIALIZATION 

DETFRM = 1.000000000 
DO 20 J = l , N 
20 IPIVUT(J) = 0 
DO 5 50 I = 1»N 

SEARCH FOR PIVOT ELEMENT 

AMAX = 0.000000000 
DO 105 J = 1,N 
IF(IPIVOT(J) - 1) 60,105,60 
60 DO 100 K = 1,N 

IF { IPIVQT{K) - .1 ) 80,100,740 
80 IF(DABS(AMAX ) -DABStAtJ,K))) 85,100,100 
8 5 I ROW = J 
ICOLUM = K 
AMAX = A(J,K ) 

100 CONTINUE 
105 CONTINUE 

IP!VOT( ICOLUM) = I PIVOT(ICOLUM) + 1 

INTERCHANGE ROWS TO PUT PIVOT ELEMENT ON DIAGONAL 

IF (IRON - ICOLUM) 140,260,140 
140 DETERM = -DETERM 
DO 2 00 L = 1 , N 
SWAP = A(I ROW,L) 

A(I ROW,L) = At ICOLUM,L) 

200 A{ICOLUM,L) = SWAP 
IF (M) 260,260,210 
210 DO 250 L = 1 ,M 
SWAP = 3(IR 0 W,L) 
b(lROW,L) = B(ICOLUM,L) 

250 B(-ICOLUM, L) = SWAP 
260 INDEX!1,1) = IRCW 

INDEX!1,2) = ICCLUM 
PIVOT(I) = A(ICOLUM,ICCLUM) 

DLTERM = DETERM ❖ PIVQT!I) 

C DIVIDE PIVOT ROW BY PIVOT ELEMENT 

C 

At ICOLUM, ICCLUM ) = 3 . 000000000 
DO 3 50 L = 1 , M 

350 A! ICOLUM,L) = A(ICOLUM,L)/PIVOT!I ) 




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o o o 


78 


IF (M) 380,380,360 
3^0 00 370 L = 1,M 

370 d(ICOLUM,L) = B<ICOLUM,L)/PIVOT(I) 

C 

r REDUCE NPNPIVCT ROWS 

C 

880 DO 5 80 LI. = 1,N 

IF(L1 - ICOLUM) 400,550,400 
400 T = A(L1,ICOLUM) 

A(LI,ICOLUM) = 0.0 
DO 450 L = I,N 

450 A(LIrL) = A(L1 , L ) - A{ICOLUM,L) * T 
IF (M) 550,550,460 
460 DO 500 L - 1,M 

500 B(U,L) = B(L1,L) - B{ ICOLUM, L) - T 
550 CONTINUE 

INTERCHANGE COLUMNS 

DO 710 I = 1 , N 
L = N + 1 - I 

IF (INDEX!L , 1) - INDEX(L,2) ) 630,710,630 
630 JRQW - INDEX(L,X ) 

JCOLUM = INDEX(L » 2 ) 

DO 70 5 K - 1 , N 
SWAP = A(K,J R 0 W) 

A(K , JROW ) = A<K,JCCLUM) 

A ( K , J C () i_ U F ) = SWAP 
705 CONTINUE 
710 CONTINUE 
740 RETURN 
END 


REAL FUNCTION POLY<X,M,CGEFF,J,MR,MC) 
IMPLICIT REAL*8(A-H,0-Z) 

DIMENSION COEFF(MR,MC) 

POLY = 0.0 
DO 1 N = 1 , M 
MA=M-N+1 

1 POLY = POLY * X + COEFF(MA,J) 

RETURN 

END 















































































































c 

c 


79 


SUBROUTINE DGRA PH( N, X I,YI,YPI,YOI,NYL,XL INC,XLOR*YLINC, VLOR♦L) 

C 

C 

C N: INTEGER GIVING THE NO. OF POINTS IN THE X-LIST (EQUALS THE NO. 

C OF POINTS IN EACH Y-LIST) 

C 

C X: REAL*4 X-VECTOR 

C 

C Y,YP,YQ: 3 REAL*4 Y-VECTORS. ALL Y(T) ,YP(I ) , YQ( I ) SHARE THE SANE 

C X ( I ) . 

C 

C NY: INTEGER GIVING THE NUMBER OF Y-VECTORS TO BE ACTUALLY PLOTTED. 

C IF 1, Y IS PLOTTED; IF 2, Y AND YP ARE PLOTTED; IF 3, Y,YP,AND YQ 

C ARE PLOTTED. IF NY<1 OR NY>3, PROGRAM ASSUMES 1. 

C 

C XINC: P F A L * 4 X-INCREMENT. IF O.O, SCALE IS CALLED, AND WILL GIVE 

C A FAIRLY REASONABLE SCALE. IF NEGATIVE, THE ENTIRE AVAILABLE 

C SPACE (121 BY LINES) WILL BE FILLED. 

C 

C XOR: REAL *4 X-CRIGIN. IGNORED UNLESS XINOO.O. 

C 

C YINC: RFAL*4 Y-INCREMENT. IF 0.0, SCALE IS CALLED. IF NEGATIVE, 

C EACH Y-VECTOR IS SCALED SEPARATELY. 

C 

C YOR: REAL*4 Y-ORIGIN. IGNORED UNLESS YINOO.O. 

C 

C LINES: INTEGER GIVING THE MAXIMUM LENGTH OF THE GRAPH. IF LINES 

C IS LESS THAN 10, IT WILL BE ASSUMED TO BE 61 (ONE PAGE). IF THE 

C PROGRAM DETERMINES ITS OWN SCALE(XINC=0.0), THE MAXIMUM LENGTH IS 

C 500-1000 LINES, DEPENDING UPON THE RANGE. 

C 

C ACCEPTABLE CALL STATEMENTS ARE: 

C CALL DGRAPH(N,X,Y,Y,Y,1,0.0,0.0 ,0.0,0.0,61) 

C CALL DGRAPHtN,X,Y,YP,YQ,3,0.0,0.0,-1.0,0.0,201) 

C 

C THE PROGRAM PLOTS X IN THE VERTICAL DIRECTION AND Y IN THE HQR I- 

C ZONTAL DIREC T IQN (ACROSS THE PAGE). IF VALUES IN THE CALLING 

C SEQUENCE ARE RIDICULOUS, THE PROGRAM WILL EITHER RETURN OR MAKE 

C ASSUMPTIONS. ALL MEMBERS OF THE CALLING SEQUENCE WILL ALWAYS BE 

C RETUPNE-D UNCHANGED. 

C A POINT AT (X(I ) , Y( I ) ) WILL RE REPRESENTED BY AN X, ONE AT 

C (X(I),YP(I)) BY A *, AND ONE AT (X(I),YQ(I)) BY A + . IF TWO OR 

C MORE POINTS FALL WITHIN THE SAME PRINTING BLOC, AN 0 WILL BE 

C PRINTED; THERE WILL BE NO INFORMATION PROVIDED BY THE PROGRAM AS 

C TO WHICH POINTS ARE COINCIDENT. ANY POINTS OFF SCALE ARE IGNORED. 

C THE PROGRAM WILL NOT START A NEW PAGE OR PRINT A TITLE. 

C EXECUTION-TIME DIMENSIONING HAS BEEN USED AS MUCH AS POSSIBLE 

C IN THE PROGRAM. THE FOUR WORKING VECTORS, HOWEVER, HAVE BEEN 

C DIMENSIONED ARBITRARILY AT 20C. THIS CARD CAM READILY BE CHANGED 

C BY THE USER. 

C 

IF (N.LE.l) RETURN 
C 

































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80 


C IF THERE ARE MORE THAN 200 POINTS, THE FOLLOWING CARO SHOULD BE 

C CHANGED. 

C 

DIMENSION XI200), YI2G0),VP(200),YQI200) 

REALMS X I{N ) ,YI (N),YpI (N) ,YQI(N) 

INTEGER*2 EX,BLANK,STAR,PLUS,DASH ,VERT,ST,VEC(121 ) 

DATA EX/* X 1 /,BLANK/' '/,STAR/«*'/,PLUS/'+'/,DASHVERT/' | '/ 
LOGICAL SWT 
C 

C TRANSFER OR CALLING VALUES TO WORKING VALUES 

C 

NY = NYL 
XINC = XL INC 
XOR = XLOR 
YINC = YLINC 
YOR = YLCR 
LINES = L 
DO 1 I = 1 , N 
X( I> = XI ( 1 ) 

Y ( I ) = Y I ( I ) 

YP ( I ) = YPI ( I ) 

YQ(I) = YQI( I) 

1 CONTINUE 
C 

C SORTING OF WORKING VECTORS INTO ORDER OF INCREASING X. 

C 

NT = N-l 
ML = NT 

DO 3 I = 1 , NL 
SWT = .FALSE. 

DO 2 J = 1 , NT 

IF ( X ( J ) . L F . X ( J + 1 )) GO TO 2 
XTEMP = X( J > 

YTEMP = Y(J) 

YPTEMP = YP{J ) 

YQTEMP = YQ(J) 

X(J) •= X I J +1 ) 

Y ( J ) = Y ( J +1 ) 

YP(J) = YP{J+l) 

YQ(J) = YQIJ+l) 

X(J+l) = XTE^P 
YIJ +1 ) = YT C MP 
YP(J+l) = YPTEMP 
YQIJ+l) = YQTEMP 
SWT = .TRUE. 

2 CONTINUE 

IF I .NOT. SWT ) GO TO 4 

3 NT = NT - 1 

4 IF (LINES.LT. 10) LINES = 61 
C 

C BRANCHING FOR SCALING OPTIONS. 

C 

L = 0 

IF (X INC .L T .C .0 ) L = 


1 

















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iH 





















































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• 



















• 


















































































ooo ooo ooo ooo 


81 


5 

103 
102 
101 

104 


IP (NY.GT.3.CR.NY.LT.1) NY=1 


IP (XIjMC.GT.O.O.AND.XOR.GT.X(I) ) XOR = X ( 1) 

IF (X INC.LE.Q.O) CALL SCALE(X,X,X,0,XOR,XINC,LINES»N,L,BLANK) 


IP (Y INC . LT .0.0 ) 
IF (YIMC.GT .0.0) 
IF (YINC.EG. 0.0) 


GO TO 5 

CALL AX!YINC,YOR,BLANK) 

CALL SCALP(Y,YP , YQ* NY *YOR*YINC* 121,N,L,BLANK) 


IF (L.EQ.-l) RETURN 


YPOR = YOR 
YQOR - YOR 
YPIMC = YINC 


YQINC = YINC 


GO TO 104 

GO TO {101,102*103),NY 


CALL SCALE!YQ,YQ,YQ»1,YQOR,YQINC,121,N,L,PLUS) 
CALL SCALE!YP,YP,YP,1,YPOR,YPINC,121,N,L,STAR) 
CALL SCALE!Y,Y,Y,1,YCR,YINC ,121,N,L,EX) 

IP (L.EQ.-l) RETURN 

XVAL = XOR 


GRAPH PLOTTING SEQUENCE BEGINS. 

NL - 1 
N P - 0 

00 99 I = 1 , LI NES 


INITIALIZATION OF PLOTTING VECTOR. 

ST = BLANK 

IF (1.EQ.1.0R.(NL.GT.N.AND.(I+4)/5*5.EQ.I+4).0R.I.EQ.LINES)ST=DASH 
DO 6 J = 2,120 
VEC!J) = ST 

6 CONTINUE 

VEC(1) = VERT 

IF <(1+4)/5*5.E0.1+4) VEC!1) = DASH 
VEC!121 ) = VEC!1 ) 

IF (ST.NE.DASH) GO TO 8 
DO 7 J = 11,111,10 
VEC!J) = VERT 

7 CONTINUE 

CHECKING IF NEXT UNPLOTTED X-VALUES ARE WITHIN CURRENT RANGE. 

8 IF !NL .GT.N ) GO TO 12 
DO 10 J = N L,N 

IF ! (ABS(X(J ) - XVAL ) ) .LE. (XINC/2.0) ) GO TO 9 
GO TO 11 

9 NP = J 

10 CONTINUE 

11 IF (NL.GT.NP) GO TO 12 
LOADING OF PLOTTING VECTOR 
GO TO !201,202,203),NY 

203 CALL POSY!YQ,NL,NP,YQOR,YQINC,VEC,PLUS,N) 




■ 




















































































82 


202 CALL PO$Y(YP,NL,NP,YPOR,YPINC,VEC,STAR,N> 

201 CALL PO$Y(Y,NL,NP,YOR,YINC,VEC,EX,N) 

NL = NP +■ 1 
C 

c PRINTING OF PLOTTING VECTOR 

C . ... 

12 IF {(!+4)/5*5.EQ.I+4.0R.$T.EQ.DASH) GO TO 13 
WRITE (6,100) VEC 

GO TO 14 

13 WRITE (6,200) XVAL,VEC 

14 IF (ST.EQ.DASH.AND.I.NE .1 ) GO TO 15 
99 XVAL = XVA L + XINC 

100 FORMAT ( • • ,ilX , 121A1 ) 

200 FORMAT (’ *,1PEi1.4,121A1) 

15 RETURN 
END 


C 

C 

SUBROUT INE PCSY(Y,NL,NP,YOR,YINC,VEC,SAVE,N} 

C 

C 

C LOADS PLOTTING VECTOR WITH APPROPRIATE CHARACTERS. 

C 

DIMENSION Y(N) 

I NTEGER*2 S AVE,VEC(121),STAR,PLUS,EX,0 
DATA O/'O*/,S T A R/* * */,PLUS/ , + , / ,EX/ , X*/ 

DO 2 J = N L , N P 

YPS = 1.0 + (Y(J)—YCR)/YINC 

JY = I NT(YPS) 

IF ((YPS-AINT(YPSJ-C.5).GT.O.O) JY = JY +1 
IF (JY.LT.l .GR.JY.GT.121) GO TO 2 

IF (VEC(JY).EQ.EX.QR.VECIJY).EQ.STAR.OR.VEC(JY).EQ.PLUS.OR.VEC(JY) 
l.EQ.O) GO TO 1 
VfcC(JY) = SAVE 
GO TO 2 

1 VEC(JY ) =0 

2 CONTINUE 
RETURN 
END 

















































































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. 























































o o o o o o 


83 


C 

c 

SUBROUTINE SCAL E(Y,Y P , YQ,NY,YOR,YINC,LINE S,N, L » ST) 

C 

c 

IF (L.EQ.-l) RETURN 

DIMENSION Y(N)»YP(N)»YC(N)»ASCALE(5),YA(6) 

I NTEGER*2 ST 

DATA ASCALE/10.0,20.0,25.Ot40.Ot50.0/ 

ALINE = FLOAT!LINES) - 1.0 
BSCALE = 0.0 
NY1 = NY + 1 

BRANCHING TO DETERMINE RANGE• 

YMA X = YIN) 

YMIN = Y(1 ) 

GO TO (104,101,102,103),NY1 

101 DO 1 I = 1,N 
YM AX = A M A X1 ( Y M A X , Y ( I ) ) 

YM IN = AM I NilYMIN,Y(I )) 

1 CONTINUE 
GO TO 104 

102 DO 2 I = 1 , N 
YMAX = AMAX1(YMAX,Y(I),YP(I)) 

YM I N = AMIN1(YMIN,YI I),Y P(I ) ) 

2 CONTINUE 
GO TO 104 

10 3 DO 3 I = 1 T N 

YM AX = AMAX1(YVAX,Y(I),YP(I ) ,YQ(I) ) 

YM IN = AM I N H YM I N , Y ( I ) , Y P ( I ) , YO { I ) ) 

3 CONTINUE 

104 YRANGE = YMA X - YMIN 

IF (YRANGE.EQ.0.0) GO TO 10 
YOR = YMIN 
IF (L.EQ.l) GO TO 7 

DETERMINATION CF INCREMENT. 

YRLOG = ALGG10IYRANGE) 

J EX P = I NT(YRLOG) 

IF (YRLOG.LT.0.0.AND.FLGAT(JEXP).NE.YRLGG) JFXP = JEXP - 1 
DO 4 1=1,5 

SING = (ASCALEII))*YRANGE/10.0**JEXP 
IF ISIMC.GT.ALINE) SINC = SINC/10.0 
IF ISINC*10.0.LE.ALINE ) SINC = SINC*10.0 
IF (SINC.LE.ALINE) BSCALE = AMAX1(BSCALE,SINC) 

4 CONTINUE 

YINC = YP.ANGE/BSCALE 
C 

C * DETERMINATION OF ORIGIN. 

C 

YL = AL0G10(YINC) 

I EXP = INT(YL) + I 

IF (YL.LT.O.O.AND.FL0AT( I EXP) .NE.YL) IFXP = 


IEXP 


1 























































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84 


DO 6 1=1,2 

ORIG = 1Q.0**( 1-1)*AINT<YMIN/10.0**(IEXP+1-1)*1 .0001 ) 

TF (ORTG.F0.0.0 ) GO TO 5 

IF (YMIN.LT.0.O.OR.(YMIN/ORIG.LT.1.0001.AND.YMIN/ORIG .GT .0 
10RIG = ORIG - 10.0**(1-1) 

5 AY OR = 1O.O**IEXP*0RIG 

IF (((YMAX-AYOR)/YINC).LE.ALINE) YOR = AM IN1(YOR,AYOR) 

6 CONTINUE 

IF < .NOT. (Y.MAX.GT.0.0. AND.YMIN.LT.O .0 ) ) GO TO 8 
A = 10.0 

IF (NY.EO.O) A = 5.0 

ORIG = A*{AINT(-1.0001*YMIN/(YINC*A))*1.0) 

IF {(YMAX/Y INC+0RIG + 1.0).LE.ALINE) YOR = -YINC*ORIG 
GO TO 8 

7 YINC = YR ANGF/A LINE 

8 IF (NY.EO.O) GO TO 11 
C 

C PRINTING OF Y-SCALE 

C 

ENTRY AX(YINC,YOR,ST) 

DO 9 1 = 1,6 

Y A( I) = YOR + YINC*(20.0*FLOAT(I ) - 10.0) 

9 CONTINUE 

WRITE (6,500 ) ST,Y A 
GO TO 11 

10 L = -1 

500 FORMAT <« • ,IX,A1,3X,»Y-AXIS I S',3X,1PE11.4,5(9X, 1 PEI 1.4) ) 

11 RETURN 
END 


.9999Q)) 





' 

■ 











































85 


\ 


C 

c THIS IS A GENERAL PROGRAM FOR LEAST SQUARE POLYNOMIAL FIT 

C FORTRAN IV MODIFICATION OF UOl LSQI FOR 360 OPERATION ( 

C 

C DOUBLE PRECISION USED THROUGHOUT 

C 

C LIST OF SYMBOLS USED FOR INPUT 

C N= NUMBER OF POINTS 

C M= NO. OF COEFFICIENTS OF POLY 

C Nl= NO. OF ADDITIONAL POINTS AT WHICH EVALUATION OF FITTING 

C POLY. IS DESIRED. MAX. N1=50 

C. L= NO. Of DATA SETS TO BE FIT SIMULTANEOUSLY. L=l-4 

C IE V A L = SIGNAL TO OUTPUT. IF IEVAL>0, A TABLE OF THE INPUT 

C DATA WITH POLY EVALUATIONS AND RESIDUALS IS PRINTED 

C X= INDEPENDENT VARIABLE 

C W= WEIGHTING FACTOR. USE 1.0 FOR EQUAL WEIGHTING 

C Y= DEPENDENT VARIABLE 

C X1= EXTRA X AT WHICH POLY IS TO BE EVALUATED 

C 

IMPLICIT REAL*8(A-H,0-Z) 

DIMENSION A ( 20 »1 5) , 6(20,4), X(5Q0), Y(500,4), W(500), SUM(4), 

X RESID(500,4), STD(15,4), EVAL(500), XK50) 

C 

1 READ (5,1000) N, M, N1, L, I EVAL 
I F ( N ) i , I , 2 

2 DO 3 I = 1 , N 

3 READ (5,2000) X(I), W(I), Y(I,1),Y(I,2),Y(I,3),Y(1,4) 

IF (N1) 5,5,4 

4 READ (5,2000)(XI(I), I = 1,N1) 

5 CALL LSQl(X,Y,W,RESID,N,SUM f L,A,B,M) 

DEG = N - M - 1 

DO 6 I = 1 , M 
DO 6 J = 1 , L 

6 STD ( I , J ) =0 SOP. T ( SUM ( j ) * A(I,D/DEG) 

WRITE (6,3000) N, M, Nl, L 

DO 7 I = 1 , M 

7 WRITE (6,4000) (A(I,J), J = i,M) 

DO 3 J = 1, L 

WRITE (6,5000) <8(1,J), STD(I,J), I = 1,M) 

WRITE (6,6000) SUM(J) 

IF (IEVAL) 11,11,9 
9 DO 10 I = 1,N 

10 EVAL(I) = R E SID( I,J) + Y(I,J) 

WRITE (6,7000) (X(I ),W(I) ,Y(I , J>,EVAL(I ) ,RESID(I,J),I = 1,N) 

11 IF (Nl) 8,3,12 

12 DO 13 T = 1,Nl 

13 EVAL(I) = POLY(XKI) ,M,B,J,20,4) 

WRITE (6,8000) (X1(I), EVAL(I), I = 1,N1) 

8 WRITE (6,9000) 

GO TO 1 

1000 FORMAT (1216) 

2000 FORMAT (6D12.0) 

3000 FORMAT (48H1 LEAST SQUARE POLYNOMIAL FIT USINQ LSQI / 

X 3H0N=I 3,5H M=I 2,6H Ni = I2,5H L=12/13HOERROR MATRIX) 










































' 












































86 


4000 FORMAT UNO 1 P8D14.5 } 

5000 FORMAT <37M0 COEFFICIENT ERROR/(1H 

6000 FORMAT (36H0WEIGHTED SUM OF SQUARED DEV I ATIONS = 1 PD13 
7000 FORMAT (70H0 ' X WEIGHT Y 

X9N R FSI DUAL/(IH 1P5D14.5)) 

8000 FORMAT (29H0 EXTRA X EVALUATI ON/ ( 1H 1P2D14. 

9000 FORMAT ( 54H --r - -- -- -- -- -- -- -- -- - 
END 


PROGRAM CONTINUES WITH 
SUBROUTINE LSQl 
SUBROUTINE MATINV 
REAL FUNCTION POLY 
(SEE NERNST EQUATION LEAST 
SQUARES PROGRAM) 


1P2D20.7)) 

.5) 

EVALUATI