This dissertation has been microfilmed exactly as received 67-2446 GILBY, Stephen Warner, 1939- DETERMINATION OF THE RELATIVE THERMODYNAMIC PROPERTIES OF THE -- SYSTEM AT TEMPERATURES NEAR 1600° C.

The Ohio State University, Ph.D., 1966 Engineering, metallurgy

University Microfilms, Inc., Ann Arbor, Michigan DETERMINATION OF THE RELATIVE THERMODYNAMIC PROPERTIES

OF THE IRON-CHROMIUM-NICKEL SYSTEM AT

TEMPERATURES NEAR l6 0 0 °C ,

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio S ta te U n iv e rsity

By

Stephen Warner Gilby, B.S.

The Ohio S ta te U n iv e rsity 1966

Approved by

Department of M etallurgical Engineering ACKNOWLEDGMENTS

The author gratefully acknowledges the assistance of Dr. George

R. St.Pierre whose guidance and thoughtful comments aided greatly in the completion of this thesis. The experimental assistance of

Dr. Rudolph Speiser is also greatly appreciated. The author would especially like to thank Mr. Richard Reese for his able assistance in collecting and analyzing the mass spectrometer data reported in this thesis. The valuable assistance of Dr. Karl Svank is also acknowledged. The financial support of the American Iron and Steel

Institute and the International Nickel Company made this thesis p ossib le.

i i CONTENTS

Page

ACKNOWLEDGMENTS i i

TABLES iv

FIGURES v i

INTRODUCTION AND UTERATURE REVIEW 1

EXPERIMENTAL EQUIPMENT 25

THEORETICAL BASIS ia

EXPERIMENTAL PROCEDURE 5o

RESULTS AND DISCUSSION 77

APPENDIXES 1UU

BIBLIOGRAPHY 171

i i i TABLES

Table Page

1. The Relative Isotopic Abundances of the of . . . 29 Chromium, Iron, and Nickel.

2. Typical Analyses of the Iron, Chromium, and Nickel . . . 51 Used in this Research.

3. Nominal Compositions, Analysis Methods, and Temper- . . . 5U atures of the Alloys Studied in this Research.

U. Experimental Equilibrium Vapor Compositions in the . . . 78 Iron-Chromium Liquid System at l600°C.

5. A c tiv ities of Iron and Chromium in the Iron-Chromium . . 82 Liquid System at l600°C.

6. Experimental Equilibrium Vapor Compositions in the . . . 87 Nickel-Chromium Liquid System at 1600°C.

7. Activities of Nickel and Chromium in the Nickel- .... 92 Chromium Liquid System.

8. Experimental Equilibrium Vapor Compositions for Iron- . . 107 Chromium-Nickel Liquid Alloys at 1600°C, for Alloys with a Constant Chromium Concentration of 5 Atomic Percent.

9. Experimental Equilibrium Vapor Compositions for Iron- . . 108 Chromlum-Nickel Liquid Alloys at 1600°C, for Alloys with a Constant Chromium Concentration of 10 Atomic Percent.

10. Experimental Equilibrium Vapor Compositions for Iron- . . 109 Chromium-Nickel Liquid Alloys at 1600°C, for Alloys with a Constant Chromium Concentration of 20 Atomic Percent.

iv Table Page

11. Experimental Equilibrium Vapor Compositions for Iron-.... 110 Chromium-Nickel Liquid Alloys at 1600°C, for Alloys with a Constant Chromium Concentration of 30 Atomic Percent.

12. Activities of Iron, Chromium, and Nickel in the Iron-... 121 Chromium-Nickel Ternary System for Alloys with a Con­ stant Chromium Concentration of 5 Atomic Percent.

13. Activities of Iron, Chromium, and Nickel in the Iron-... 122 Chromium-Nickel Ternary System for Alloys with a Con­ stant Chromium Concentration of 10 Atomic Percent.

llu Activities of Iron, Chromium, and Nickel in the Iron-... 123 Chromium-Nickel Ternary System for Alloys with a Con­ stant Chromium Concentration of 20 Atomic Percent.

15. Activities of Iron, Chromium, and Nickel in the Iron-... 12i| Chromium-Nickel Ternary System for Alloys with a Con­ stant Chromium Concentration of 30 Atomic Percent.

16. Interaction Parameters in the Iron-Chromium-Nickel ..... 133 Liquid System at 1600°C.

17. Free Energy of Mixing Values at 1600°C for Iron- ...... 136 Chromium-Nickel Alloys with the Four Constant Chromium'Concentrations of 5, 10, 20, and 30 Atomic Percent.

v FIGURES

Figure Page

1. Iron-Chromium Phase Diagram ...... 8

2. Iron-Nickel Phase Diagram ...... lit

3. Nickel-Chromium-Phase Diagram ...... 17

I4. Iron-Chromium -Nickel Phase Diagram at l6 0 0 °C ...... 21

Bendix Time-of-Flight Mass Spectrometer ...... 26

6. Knudsen-Cell Furnace Assem bly ...... 31

7. Schematic Diagram of Knudsen-Cell ...... 32

8. Metal Vapor Pressure C ell ...... 36

9. Knudsen-Cell Assembly for Vapor Composition Analysis . 37

10. Variation of the Vapor Composition Function with Nl . 8l in the Iron-Chromium Binare at 1600°C. e

11. Hie Activities of Iron and Chromium in the Iron- . . . 83 Chromium Binary at l600°C.

12. Graph of the Equilibrium Vapor Compositions in the . . 89 Nickel-Chromium Binary at 1600°C.

13. Variation of the Vapor Composition Function with N^. . 91 for the Nickel-Chromium Binary at 1600°C. Nl

lit. The Activities of Chromium and Nickel in the Nickel- . 93 Chromium Binary at l600°C.

19. Second Law Determination of the Heats of Sublimation . 98 and Evaporation From Mass Spectrometer Intensity Data for Iron, Chromium, and Nickel.

16. Topical Graph of the Ionization Intensity Versus the . 105 Electron Energy of the Ionizing Beam for Monatomic Atoms.

v i Figure Page

17. Hie Equilibrium Vapor Compositions for Iron-Chromium^- . 112 Nickel Alloys at 1600°C, for Alloys with a Constant Chromium Content of 5 Atomic Percent.

18. The Equilibrium Vapor Compositions for Iron-Chromium- 113 Nickel Alloys at l600°C, for Alloys with a Constant Chromium Content of 10 Atomic Percent.

19. Hie Equilibrium Vapor Corrpositions for Iron-Chromium- . llll Nickel Alloys at 1600°C, for Alloys with a Constant Chromium Content of 20 Atomic Percent.

20. Hie Equilibrium Vapor Compositions for Iron-Chromium- . 115 Nickel Alloys at 1600°C, for Alloys with a Constant Chromium Content of 30 Atomic Percent.

21. Integration Paths from States (1) to (2) in Ternary . . . . 118 Iron-Chromium-Nickel A lloys.

22. Hie Activities of Iron, Chromium, and Nickel in the . . . 126 Iron-Chromium-Nickel System at 1600°C, for Alloys with a Constant Chromium Content of 5 Atomic Percent.

23. The Activities of Iron, Chromium, and Nickel in the . . . 127 Iron-Chromium-Nickel System at l600°C, for Alloys with a Constant Chromium Content of 10 Atomic Percent.

2li. Hie Activities of Iron, Chromium, and Nickel in the . . . 128 Iron-Chromium-Nickel System at 1600°C, for Alloys with a Constant Chromium Content of 20 Atomic Percent.

25. Hie Activities of Iron, Chromium, and Nickel in the . . . 129 Iron-Chromium-Nickel System at 1600°C, for Alloys with a Constant Chromium Content of 30 Atomic Percent.

26. Graph of Excess Free §nergy of Mixing for Iron-Chromium- 138 Nickel Alloys at 1600 C.

27. Variation of the Vapor Composition Function with N^ at . 163 l600°C, for Alloys with a Constant Chromium Contenxeof 20 Atomic Percent.

28. Variation of the Vapor Composition Function with N^ at . l6h 1600°C, for Alloys with a Constant Chromium C ontentof 20 Atomic Percent.

v ii Figure Page 29. Variation of the Vapor Composition Function with . . 165 at l600°C, for Alloys with a Constant Chromium r Content of 20 Atomic Percent.

30. Variation of the Vapor Composition Function with n Y . . 166 at 1600°C, for Alloys with a Constant Chromium Content of 20 Atomic Percent.

31. Variation of the Vapor Composition Function with NCr • * 167 at 1600OC, for Alloys with a Constant Chromium Content of 20 Atomic Percent.

32. Variation of the Vapor Composition Function with N^. . . 168 at l600°C, for Alloys with a Constant Chromium Content of 20 Atomic Percent.

33. Variation of the Vapor Composition Function with NY . . 169 at 1600°C, for Alloys with a Constant Nickel r Content of 10 Atomic Percent.

3li. Varitation of the Vapor Composition Function with . . 170 at l600°C, for Alloys with a Constant Nickel Content0 of 10 Atomic Percent.

v i i i INTRODUCTION AND LITERATURE REVIEW

The determination of the thermodynamic properties of alloys is an important activity in the fields of metallurgy and chemistry. From the practical point of view, a knowledge of the thermodynamic properties of alloys allows one to adjust processing variables to optimize the refin­ ing process. The experimental determination of the thermodynamic prop­ erties of alloys is very important in the development and verification of theoretical models. Also, experimentally determined thermodynamic properties can be used to check the accuracy of equilibrium phase diagrams of alloys and to predict phase boundaries at temperatures in which it is difficult to establish equilibrium conditions.

The alloy system studied in this research forms the basic conpo- nents of the industrially important stainless steels and nickel-base alloys. The stainless steels are used primarily in applications re­ quiring high mechanical strength combined with corrosion resistance and a bright surface finish. The nickel-base alloys are used primarily for their excellent strength at elevated tenperatures and their oxidation resistance. Each of the elements, iron, chromium, and nickel, is in the first series of transition elements in the periodic table and is characterized by the presence of an unfilled 3d electron shell. The elements iron, chromium, and nickel have melting points of 1536°C,

1 1900°C, and lU53°C respectively. For a temperature of 1600°C, the vapor pressure of chromium is approximately four times higher than the vapor pressure of iron, and eight times higher than the vapor pressure of nickel. The principal oxide of chromium, Cr^O^, is thermodynamically the most stable and the oxide of nickel, NiO, is the least stable of the three elements studied in this research. For a temperature of 1600°C and a residual vacuum of 1 x 10"^ ran Hg, only chromium w ill oxidize from reaction with in the residual vacuum; iron and nickel w ill not.

The carbides of chromium are thermodynamically stable at 25°C, but the carbides of iron and nickel are not. However, each element has an appreciable solubility for in the liquid state. The solubility of in liquid chromium is quite high compared with its solubil­ ity in either liquid iron or liquid nickel. Dissolved nitrogen lowers the apparent melting point o f chromium greatly. Great care must be taken in the preparation and melting of high chromium alloyB to either prevent or eliminate the contamination of the resultant alloys with carbon, oxygen, and nitrogen. If the pure metals are free from serious contamination by oxygen, carbon, and nitrogen, the melting of high chro­ mium alloys in a good vacuum is an excellent way to prevent contamina­ tion of the melt.

The measurement of thermodynamic properties of liq uid iron- chromium-nlckel alloys near 1600°C presents many difficult experimental problems, partly because of the reactivity of chromium with oxygen, nitrogen, and most refractory m aterials. Before the literature review the concept of thermodynamic activity should be explained. The activity, can be mathematically expressed as

where 5^ is the chemical potential or the partial molal free energy of component i in the solution and is defined as the partial derivative of the Gibbs Free Energy of the solution with respect to the quantity of component i at constant temperature, pressure, and quantity of a ll other conponents present in the solution. F? is the standard partial molal free energy for component i. The standard state is generally chosen as the pure component or the conponent in the infinitely dilute state of the solution. Thus the activity of conponent i is a measure of the difference between the standard state partial molal free energy and the actual partial molal free energy of conponent i in a given state. The activity of i is always relative to the chosen standard state and is not an absolute quantity. From the measurement of the a c tiv ity and i t s variation with the absolute temperature, most thermodynamic properties of the a llo y can be determined. These derived properties such as en­ thalpy and entropy of solution are also relative to the chosen standard states for the activities.

■HA11 thermodynamic symbols used in this thesis are consistent with the accepted nomenclature of The Metallurgical Society of the American Institute of Mining, Metallurgical, and Petroleum Engineers. There are several methods used to experimentally determine activ­

ities. Each method has its inherent advantages and disadvantages as to the ease and accuracy of the activity determinations. In general, each method is best suited for a particular type of alloy and a particular

temperature range. The three main types of experimental methods to de­ termine activities are these

1. Equilibration with a second phase in which the thermodynamic properties of the second phase are known.

2. Electromotive c e ll measurements in which the E. M. F. generated by a concentration-type cell is a direct measure of the activity of one conponent in the alloy.

3. Equilibrium vapor pressure methods in which the partial vapor pressure of a conponent in an alloy is directly related to the activity

of that conponent in the alloy.

The f ir s t two methods require that only one conponent in the a llo y par­

ticipate in the equilibration or electrode reaction. This fact requires

that the other conponents in the alloy be of sufficient chemical dissim­

ilarity to prevent their participation in the reaction. In general,

this requirement lim its their use in detexmining thermodynamic proper­

ties of the chemically similar transition metals. Also the electro­

motive cell technique is generally limited to tenperatures below the

liquidus tenperatures of the alloys studied in this investigation. The third method i s the most widely used method for high temper­ atures and alloys whose components are chemically sim ilar. Hie vapor pressure method and a variation of i t were used exclu sively in th is in­ vestigation to measure the activities of each component in the liquid alloys. The activity of conponent i in the alloy can be defined as the ratio of the partial pressure, p^, to the pure vapor pressure of conpo­ nent i, pj°, at the same temperature. The standard state of component i i s the pure conponent i in i t s equilibrium form at the given temper­ ature. The only requirement of this definition is that the vapor phase in equilibrium with the alloy and the pure metal be essentially an ideal gas.

ftiere are several methods used to measure vapor pressures. Hie particular method employed depends primarily on the magnitude of the vapor pressure. If the vapor pressure is above approximately 1 x 10 atmospheres i t can be measured by s ta tic manometers; however, the vapor pressures of the metals and alloys studied in this research do not reach this pressure until the temperature is well above their melting points.

For vapor pressures ranging from lCT^ to lCT^O atmospheres, rate of sub­ limation or evaporation, rate of effusion, or transpiration methods must be employed. The rate of sublimation or evaporation method was f ir s t devised by Langmuir. In th is method the rate of sublimation or evapo­ ration from a free surface into a high vacuum is measured from the 6 weight loss of the metal or alloy heated in a vacuum chamber. To employ th is method, the surface area of the sample exposed to the vacuum must be known and the accommodation c o e ffic ie n t, CX, must eith er be known or assumed equal to unity. The accommodation co efficien t, (X , i s defined as the ratio of molecules that stick to the surface to the total number that strik e the surface. Speiser and Johnson (1) have reviewed th is technique. I t i s a nonequilibrium method and may be subject to k in etic obstacles which may result in a nonequilibrium vapor pressure determination.

The effusion method was first suggested by Knudsen (2). This method measures the rate of effusion or random escape from an isothermal enclosure through an orifice into a high vacuum. The vapor escapes from a cell where it is assumed to be in equilibrium with the solid or liquid material in the cell. There are several important requirements that must be met in order to obtain random escape through the o r ific e which w ill be discussed in detail later. The effusion or Knudsen method is the most widely used technique to measure low pressure because it is e sse n tia lly an equilibrium method and requires no knowledge or assump­ tions about the accommodation coefficient.

The transpiration or carrier gas method employs an inert gas that is passed over the material and becomes saturated with the vapor of the material and is subsequently analyzed to determine the amount of mate­ r ia l in a given volume of inert gas. This i s a direct method to determine the vapor pressure but suffers from the dependence of the apparent vapor pressure on the flow rate of the inert carrier gas over the material.

A ll o f the above vapor pressure measuring methods su ffer from the fact that the vapor pressure is an exponetial function of temperature.

For the metals and temperatures under investigation in this research a variation of 1°G causes the equilibrium vapor pressure to change by approximately 1 .3 percent. Because i t i s d iffic u lt to measure and con­ trol temperatures at 1600°C, serious errors may be introduced into a c tiv ity measurements by vapor pressure methods.

Hie phase diagram for the Fe-Cr system from H ellawell (3) appears in Figure 1. The important features of the phase diagram are the wide range of solubility of the body-centered-cubicoC-phase, the minimum in the solidus and liquidus lines at NCr * .23, and the appearance of a sigma phase below 800°C with the approximate composition FeCr. Mechan­ ically, this sigma phase resembles a brittle intermetallic compound.

The minimum in the liquidus indicates that the deviation of the activ­ ities from ideal solution behavior is less positive in the liquid alloys than in the solid alloys. If we interpret the sigma phase as a misci- bility gap we might expect positive deviation from ideal solution be­ havior to exist in the solid alloys. However, if we consider the sigma phase to be an intermetallic compound we might expect to observe U Temperature, 1900 1800 1700 1600 1300 1500 1200 1400 1100 1000 0 0 9 700 800 800 600 I U E IRON-CHROMIUMFIGURE . 1 PHASE DIAGRAM 0 - ^ ------850 10 20 1510 20 etn pit: hoim 19° Io, 36°C 5 1 Iron, ; 1898°C Chromium, points: Melting 20 040 30 30 40 hoim a/o / a Chromium, hoim w/ /o w Chromium, 820 50 50 48 a +

Temperature, 9 negative deviation for the solid alloys. In general, one is not justi­ fie d to make a sp ecific prediction about the thermodynamics of a binary system from the phase diagram alone. This can be confirmed by comparing the deviation from id ea l solution laws exhibited by the Fe-Cr and Fe-V solid alloys. The phase diagrams are almost identical. The melting points of V and Gr are within 10°C of each other, and V and Cr are chem­ ic a lly sim ilar. Both phase diagrams exhibit a minimum in the liquidus and solidus lines on the iron-rich side of the binaries, and both ex­ hibit CV-phase formation. Several investigations on the solid alloys of the Fe-Cr system, Kubaschewski and Heymer (ii), McCabe et a l. (5 ),

Vintaikin (6), and Beese (10), have shown that positive deviations from id ea l behavior occur. However, investigations by Saxer (7) and Myles and Aldred (8) of solid Fe-T alloys show strong negative deviation from ideal solution behavior.

There have been five independent activity investigations on solid

Fe-Cr a llo y s. McCabe, Hudson and Paxton (5) measured the a c tiv itie s of

Cr and Fe by a conventional Knudsen-cell, weight-loss procedure in the temperature range 1200-1250°C. They found a slight positive deviation of the to ta l vapor pressure from ideal solution behavior. However, they were unable to analyze the composition of the vapor phase and, therefore, were unable to compute the activities without assuming the alloys formed a regular solution. Vintaikin (6) measured the activities 10 o f Cr in so lid Fe-Cr a lloys from NCr * .20 to NCr ■ .75 over a tempera­ ture range of 1100° to lit00°C. The Knudsen-effusion technique was coupled with a radioactive (Cr-^) determination to calculate the vapor pressure of Cr over the alloys and the pure metal. In this method, the vapor effusing from the orifice was condensed on a target, and the condensate was then dissolved in acid solution to determine the 51 Cr concentration by radiometric analysis. This procedure was very useful because of the small amount of condensate resulting from the low vapor pressure of Cr below llt00°C. At 1350°C and NCr ■ .213, Vintaikin found that the activity coefficient, ^ Cr, is 1.75 and at NCr ■ .1*11* that yQr is 1.65. From the temperature dependence of the Cr activity data he found that the integral heat of mixing, was positive with a maximum value of 1000 calories/m ole at NCr ■ .65. Kubaschewski and

Heymer (li) studied so lid Fe-Cr alloy s at a temperature of 1350°C for a llo y s ranging from N(jr ■ .05 to NCr * .70. They employed the Knudsen- cell procedure coupled with a radioactive isotope, Cr-^, to measure the partial pressure and activity of Cr. They found at 1350°C and

NCr - .0828 that ^ 0,. • 1.85 and for NCr - .295 that y Cr - 1.36. These authors (ii) estimate the maximum error in their activity to be +22 percent at NCr" .20. Jeannin, Mannerskantz, and Richardson (9) measured the a c tiv ity of Cr in Fe-Cr a llo y s from lQljO0 to 1300°C for compositions ranging from NCr » .021 to NCr " .320. The alloys were equilibrated with -water vapor mixtures and C^O^. They found a c tiv itie s that agree w ell with the work of Kubaschewski and Heymer (ii).

Reese (10) investigated the Fe-Cr system from lUOO° to 1700°C for com­ p osition s ranging from NQr ■ .01 to Nqj. ■ .65. The same Bandix non­ magnetic, time-of-flight mass spectrometer used in this thesis was used by Reese. The method involves measuring the ion intensities of Fe and

Cr which effuse from a Knudsen-cell source into the ionization region of the mass spectrometer. The ion intensities are directly proportional to the vapor pressure of Fe and Cr that exist in the Knudsen-cell. There­ fore, the activities can be computed from the ratio of the ion intensity of the component in the alloy to the ion intensity of the pure com­ ponent. The method w ill be discussed in more d e ta il la te r . Reese found the system exhibited positive deviation from ideal behavior. At 1U00°C

Reese found that YCr ■ 1.35 at NCr ■ .056, aid at NCr ■ .278 that

Y cj. ■ 1.12. The over-all agreement between the five investigations on the solid Fe-Cr alloys is fairly good considering the experimental dif­ ficulties encountered in measuring low vapor pressures at elevated temperatures.

Die published investigations on the liquid Fe-Cr alloys above

1600°C are in much wider disagreement. The earliest reference by Chen and Chipman (11) infers that the Fe-Cr liquid system is very near ideal.

More recently lyubimov and Granovskaya (12) measured the activities of

Fe and Cr in the liquid alloys at temperatures between 1670° and l82U°C for alloys ranging from N^r * .02 to “ .65. The method used was the

Langrmiir rate of evaporation technique in which they employed the radio- active isotope, Cr-’-*-, to measure the vapor pressures of pure Cr and Cr in the liquid Fe-Cr alloys. The procedure consists of evaporating the liq u id a lle y s, in a high vacuum, from an open alundum crucible and collecting the escaping vapor phase on the water cooled walls of the vacuum furnace enclosure. The weight of the condensate was obtained from weighing the condensation jacket before and after the run. The weight of Cr in the condensate was determined by radiometric analysis using a Geiger counter. The weight of Fe in the condensate was deter­ mined by difference. The p a rtia l vapor pressures of Cr and Fe were

determined from the Langmuir relation assuming that the accommodation

co efficien ts were unity. They found that the Fe-Cr liq u id system ex­ hibits positive deviation from ideal behavior. They also found that the

solution becomes more nearly ideal as the temperature is raised from

1670°C to l82h°C. At 1670°C and N^r - .10 they found ^ to be 2.2

based on a pure solid Cr standard state. At “ .25 they found ^Cr

to be 1.7. Wada et al. (13) investigated the liquid Fe-Cr system at a

temperature of 1630°C for Cr concentration ranging from Ngr ■ .01 to

N^, " .UO. They used approximately the same method as Lyubimov and

Granovskaya (12). However, they collected only a portion of the total

vapor coming from the open crucible, by condensing the vapor on small d iscs. Since they did not c o llec t a l l the vapor coming from the free liquid surface, they were unable to compute an absolute vapor pressure of Cr. Biey employed an indirect method assuming a regular solution model to calculate the a c tiv ity of Cr. They concluded from th is in­ direct approach that the Fe-Cr liquid system is a regular solution ex­ hibiting negative deviation from ideal behavior. Reese (10), in the same investigation, discussed previously for the solid Fe-Cr system, studied the liq u id Fe-Cr system to a temperature o f 1700°C. He found that the liquid alloys also exhibit positive deviation from ideal be­ havior. At 1600°C and NQr * .107 he found y to be I.J 4. for a pure solid Cr standard state. At 1600°C and NQr ■ .278 he found to be 1 .18. The phase diagram for the Fe-Ni system from the work of Floyd(lli), is shown in Figure 2. The important features to note are the wide solu­ bility limits of the face-centered-cubic V~phase, the peritectic re­ action, and the minimum in the liquidus and solidus lines.

For solid Fe-Ni alloys Oriani (15) determined the activity of Fe from 657° to 908°C for iron-rich alloys ranging from Npg * .93 to

Npe ■ .1&. He equilibrated pure Fe and Fe in the Fe-Ni alloys with hydrogen-water vapor mixtures and wustite, FeO. He found the activity o f Fe to be ideal over the conposition range studied. Kubaschewski and von Goldbeck (16) determined the activity of Fe by the same method employed by Oriani (15). They measured the a c tiv ity of iron from

Npe = 1.0 to Npe * .31 for tenperatures between 727° and 927°C. Though 800 U Temperature, 1500 1400 900 300 400 700 300 600 I U E IRON-NICKELFIGURE . 2 PHASE DIAGRAM 0 20 10 0 20 10 Melting pointi: Iron, 1536°C ; Nickel, 1453°C 1453°C Nickel, ; 1536°C Iron, pointi: Melting 0 0 0 60 30 40 30 IRON-NICKEL rn a/o o / a Iron, rn w/o w Iron, 0 0 0 100 90 80 70 + « y 90 100 2800 2600 1200 1000 1400 1600 600 800

Temperature, u* 15 th eir resu lts scatter somewhat, they concluded that the iron a c tiv ity was e sse n tia lly id ea l. Lyubimov and Granovskaya (17) determined the activities of Fe and Ni between 1190° and H*30°C using equilibrium vapor compositions determined by a magnetic focusing mass spectrometer. They determined the activities of Fe and Ni from the vapor compositions in essentially the same manner used in this dissertation. They found the solid Fe-Ni system to be nearly ideal. Smith, Paxton, and McCabe (18) date mined the vapor pressure and activity of Mn in Fe-Ni-Mn ternary alloys at 959°C by a Knudsen-cell, weight loss method. 3hey concluded that the Fe-Ni solid system exhibits strong negative deviation. To cal­ culate the activities of Fe and Ni in the Fe-Ni binary they had to em­ ploy Darken*s (19) ternary integration method and extrapolate from 20 percent Mn to the Fe-Ni binary.

There have been two investigations an liquid Fe-Ni a llo y s.

Speiser, Jacobs, and Spretnak (20) determined the activities of Fe and

Ni at 1510° and l 600°C from Njjj^ * .10 to N ^ ■ .90. They determined the activities from a determination of the equilibrium vapor composi­

tions in the same manner that is employed in this dissertation. They found that the liquid system deviates negatively from ideal behavior.

At 1600°C they found ^ Ni to be .70 from « .10 to N ^ « .1*0, and

to be .1*0 at N^e " .10 and .90 at Npe « .1*0. They also found that the system became more nearly ideal as the temperature was increased from 1510° to l600°C. The temperature dependence of their a c tiv itie s 16 was used to calculate the integral heat of mixing, AH*1. They found

AHm to have a maximum value of -8000 calories/mole at N^ * .60.

Zellars, Payne, Morris, and Kipp (21) determined the activities in liquid Fe-Ni alloys at 1600°C, using the transpiration technique. They found results that agree very well with those of Speiser et al. (20).

They found a t 1600°C that Y Ni - .67 a t Njfe » .10 and .71 at Njfo » .1*0.

Also they found that Y fo “ at NFe " .10 and .95 a t »Fe * .1*0.

The investigations on the Ni-Cr phase diagram are in wide disagree­ ment. There is even disagreement on the basic form of the phase dia­ gram. The ea rlier work was done before pure Cr was available and i t i s known that minor impurities lower the melting point of Cr greatly.

Liquidus and solidus lines were determined before pure Cr was available.

Figure 3 shows two proposed phase diagrams for the Ni-Cr system. The lower diagram i s from the work of Williams (22). This diagram displays a simple eutectic plus an allotrqpic transformation for chromium near

its melting point. The face-centered-cubic Ni rich region has a large

so lid so lu b ility for chromium. Bloom, Putnam, and Grant (23) and Stein

and Grant (21*) found evidence for the existence of a high temperature

face-centered-cubic /3 ~Cr phase which undergoes eutecioid decomposition

at 12l5°C. The phase diagram based on the work of (23) and (21*) is

shown in the upper part of Figure 3.

Recently Wyder and Hoch (25), using high temperature X-ray diffrac­

tion techniques, investigated the Ni-Cr system and found no evidence of U Temperature, °C Temperature, 2000 1800 1600 1200 1400 1000 2000 1000 1400 1200 1600 1800 800 600 600 800 ___ "T 0 20 10 0 0 0 0 O 0 0 0 90 80 70 60 SO 40 30 20 10 FIGURE NICKEL-CHROMEUM . 3 PHASE DIAGRAM ' y 1 — — — etn pit: hoim 19° Nce, 43C 1453°C Nickel, ; 1898°C Chromium, points: Melting 30 T _ - .... 0 O 0 70 60 SO 40 r~ l l / / 45.2 hoim a/o o / a Chromium, hoim w/o w Chromium, hoim a/o / a Chromium, /o w Chromium, llq 1 r~ ■ r —. 1— 52 * + * 52 .. l2l5 080 60 30 ✓ ' 1340 a +y ~\ 60 <* + . r .. y 70 68 B - v s ' s I - 80 T a+ I a+ 4 s ------\ \ 90 ct+B / 90 I - / V / / 1600 - \ 100 100 100 100 - - _

3600 3200 1? 2400 ^ 2800 1200 1600 2000 3600 3200 2400 2800

1200 2000

Temperature, °F Temperature, 18 the face-centered-cubic y0-Cr phase or the reported eutectoid decompo­ sition. Foster (26) found that small additions of Cr to Ni caused a great lowering of the heat capacity of the resultant alloy* This was

concluded to be due to strong Ni-Cr in teraction s. However, Taylor and

Hinton (27) found no deviation in the heat capacity from Knopps Law at

HCr * -2S-

There have been four published thermodynamic in vestigation s on solid Ni-Cr alloys and each investigation found the same type of activ­ it y behavior. Grube and Flad (28) measured the equilibria at 1100° and

1200°C for the reaction, Cr (in alloy)g + 3/2 H 2° ( g) “ V 2 CrgO^ +

3/2 (g)* Kubaschewski and Schneider (29) calculated thermodynamic properties from their data. For a temperature of 1200°C they found that

Ycr increased from . 2U a t NC r “ 0 to 1.17 at NQr ■ .1+0. They found a negative entropy of formation for the alloys which they attributed to the negative thermal entropy found by Foster (26). Panish et al. (30) determined the E. M. F. of the electromotive cell,£br CrCl 2-NaCl-RbClJ

Cr-Ni (ai i 0y), at 750° and 965°C for Cr concentrations ranging from

NCr ■» .11 to NCr ■ .96. At 750°C they found that ^Cr increased from

.hS at Nqj, “ .112 to .9 0 at NCr » ,21b, then increased sharply as the m iscib ility gap at NCr ■ ,k0 was approached. Kubaschewski, Dench, and

Heymer (31) have investigated the Ni-Cr system between 1126° and 1327°C

for Cr concentrations of NCr ■ .10 to NCr ■ .70. They measured the partial pressure of Cr over the alloys using the Knudsen-cell method coupled with the Cr^ radioactive isotop e. They improved th eir method of radiometric analysis and orifice area measurement with respect to their previous work on the Fe-Cr system (k) and reduced th e ir maximum random error from 22 to 9 percent. At 1327°C they found that in­ creased from .6 0 at NCr ■ .10 to 1 .0 at NCr « .25, then increased sharp­ ly as the miscibility gap is approached at about NCr * .50. This re­ search involved as many as seven vapor pressure determinations on each alloy at a given temperature, along with an equal number of pure Cr vapor pressure determinations. Their reproducibility was about 10 per­ cent which agrees with their random error calculations. This method is probably the best yet attained for high temperature activity measure­ ments by Knuds en -cell vapor pressure measurements, but the error of

10 percent prevents the calculation of reliable heats of mixing from the temperature dependence of the a c tiv ity data. Vintaikin (32) has recently determined the vapor pressure and activity of Cr in Ni-Cr alloys in the temperature range, 1100° to 1300°C, using the Knudsen­ cell plus Cr^ technique. His results are similar to those of

Kubaschewski e t a l. (31). He fcund at 1200°C that y , increased from

.5 to 1.7 as N increased from .059 to .318. Cr There is no published work on the activities in the liquid Ni-Cr system. 2 0

Figure h is an isothermal section, at l600°C, for the ternary

Fe-Cr-Ni system constructed from the binary diagrams shown in Figures 1,

2, and 3 * The ternary section is only approximate, but the important feature to note is that all ternary alloys with less than 60 atomic per­ cent chromium are in the liquid state at 1600°&.

The only published thermodynamic investigation found on the Fe-Cr-

Ni system was by Lyubimov, Granovskaya, and Berenstein (33) • They measured the vapor compositions in the Fe-Cr-Ni liquid system at 1633°,

1682°, and 1737°C. They determined the vapor compositions along the constant Cr concentration lines of Nqp * .01*95, .259, and .372 from the

Fe-Cr binary, across the ternary field, to the Ni-Cr binary. They evaporated the liquid alloys from an open alundum crucible, in a vacuum, and condensed a portion of the vapor on a cooled plate. The condensate was then analyzed by quantitative spectrographic analysis.

For the N^r • .01*95 alloys they found that the Cr vapor composition,

Njr, was .58 in the Fe-Cr binary at 1633°C. With increasing Ni addi­

tions the Cr vapor decreased linearly until the Ni-Cr binary was approached, where it then dropped sharply to a value of N&. ■ .05 in the

Ni-Cr binary. The Fe vapor composition dropped linearly from Npe ■ .1*2

in the Fe-Cr binary to zero in the Ni-Cr binary at 1633°C. The Ni vapor

composition was found to change almost lin ea rly from Njj^ ■ .95 in the

Ni-Cr binary to zero in the Fe-Cr binary at 1633°C. The effect of in­

creasing the tenperature from 1633° to 1737°C was to decrease markedly 2 1

oO

CM 1,600

Q/

FIGURE 4 . THE IRON-NICXEL-CHF.OMIUM PEASE DIAGRAM AT 1600°C 22

v V the Cr concentration in the vapor from Nqp ■ .58 to NCr ■ .12 in the Fe-

Cr binary. This temperature effect decreased as the Ni-Cr binary was approached. There was little variation of the vapor composition with temperature in the Ni-Cr binary. The Fe vapor composition rose greatly with temperature near the Fe-Cr binary but showed no change with temper­ ature beyond 4 ± - .50. The Ni concentration in the vapor increased with increasing temperature for all alloys.

The vapor composition trends at the N^, • .25 and Njf#r ■ .37 lev els behave in essentially the same manner as those in the N^r ■ . 01*95 liquid alloys with two exceptions. The temperature dependence is practically zero and the Fe concentration in the vapor goes through a maximum as the

Fe-Cr binary i s approached and then drops in the Fe-Cr binary. The authors did not compute activities from this vapor oonposition data but concluded from estimates based cn ideal solution behavior that the

Fe-Cr-Ni liq u id system varies su bstantially from id eal in the temper­ ature range studied.

Though mass spectrometers are being employed today for many

different types of thermodynamic and k in etic in vestigation s, they have not been used for the specific determination of activities to any

sign ifican t extent. The meager use in th is application stems from two

reasons. First the mass spectrometer until only recently has been used primarily to identify and study the products of reactions or to measure the isotop ic composition of atoms and molecules. Secondly the deter­ mination of activities by a mass spectrometer requires two separate measurements and i t i s often very d iffic u lt to reproduce the same conditions in the mass spectrometer for both measurements. This w ill be discussed in d etail la te r . However, with the recent addition o f a

Knudsen-cell inlet system to the mass spectrometer, many thermodynamic investigations have been made that are of direct interest to the m etallurgist. Excellent reviews by Inghram and Drowart (3U) and White e t a l. ( 35) on the application of mass spectrometry to high temperature chemistry have been written recently. They point out that at present the measurements of the absolute vapor pressures of m aterials can be expected to be within a factor of two of the true value for a properly calibrated mass spectrometer. This error mainly stems from a lack of knowledge of the true ionization cross section of the material and the response of the electron multiplier to a given ion of the material.

Vintaikin, Gruzin, and Fedorov ( 36) have discussed the use of the mass spectrometer to determine the activities of metallic alloys. They employed a Knudsen-cell in le t system. Lyubitov (37) used a mass spectrometer to measure the activities of in solid silver- alloys at 800° and 900°C. Bieir results on the three alloys studied are within 10 percent of those reported by Qriani ( 38 ) using the electro­ motive cell method. In this investigation an open cell was employed to furnish the atomic vapor beam to the ionization region of the mass 2U spectrometer. Lyubimov and Granovskaya (17) measured the a c tiv itie s of

Fe and Ni in the Fe-Ni system from 1190° to lii30°C using a mass spectrometer with an open c e ll in le t system. However, they found that they could not sufficiently reproduce the mass spectrometer conditions to measure activities directly. They determined only the vapor compo­ sitio n s from which they computed the a c tiv it ie s . From th eir ion in ­ tensity data they found at ll*30°C and NNi ■ .792 that the vapor compo­ sition was Njj^ « .96. Since they found the system to be nearly ideal, th is im plies that the vapor pressure of pure Ni i s about s ix times hi^ier than pure Fe. The selected ratio, from Hultgren et al. (50), of pure Ni to pure Fe i s one to two, not s ix to one. EXPERIMENTAL EQUIPMENT

The thermodynamic a c tiv itie s reported in th is dissertation were determined by either a mass spectrometer or a vacuum induction vapor pressure cell. The mass spectrometer used in this research was a Bendix,

Model 12-101, tim e-of-flight equipped with an analog output system and a high temperature Knudsen-cell inlet system. The analog output system is used in the detection and display of the ion mass peaks produced in the electron multiplier section. The Knudsen-cell inlet system supplies the ionization region of the mass spectrometer with a molecular beam that is characteristic of the vapor phase existing in the Knudsen-cell.

Figure 5 is a photograph of the mass spectrometer. Detailed descriptions of this instrument have been reported by Wiley and McLaren (39) and

Harrington (1*0). The non-magnetic, tim e-of-flight mass spectrometer

consists essentially of an ion source where ions are produced by bom­ barding neutral molecules with a pulsed electron beam; a field free drift space, where the ions are separated with respect to their mass to charge ratio; and an ion detector. In this instrument both the ionizing electron beam and the ion beam are pulsed. An ion created at the begin- ing of each cycle is accelerated by a constant voltage into the field free d r ift space between the source and detector. The accelerating voltage is constant, thus equal kinetic energy is imparted to each ion of the same charge. Therefore, the final or drift velocity of each ion

2 5 FIGURE . BENDIX TIME-OF-FLIGHT MASS SPECTROMETER will depend only on its mass to charge ratio, The lightest ions w ill reach the detector first, followed by the ions of higher mass. Ihe model 12-101 Bendix Mass Spectrometer operates at a repetition frequency of 10,000 cycles per second. The first event in each cycle is the production of an ionizing electron beam from a heated filament.

Ihe electron beam is pulsed through the ionization region by a 0.25 microsecond positive pulse applied by an electron control grid which is normally biased negative. Ihe electron beam is magnetically collimated in the ionization region. Ihe energy of the electron beam is determined by the voltage difference between the d. c. potential on the tungsten filament and the last grid of the electron gun. The electron energy can be varied between 0 and 100 e. v ., During ionization, all parts surround­ ing the ionization region are at ground potential. Immediately after the electron beam turns off, the ions produced by the electron beams are focused into the accelerating region by a -270 volt focus grid. The time of this pulse is such that all ions of interest will pass through the grid into the final acceleration region. Next these -ions are accelerated into the field free drift tube by a -2800 volt pulse applied to the last grid of the ion gun. The ion detector is 100 cm down the

drift tube from this final accelerating grid. The ratio of the two fields on the focus grid and accelerating grid is such that two ions of the same mass and charge, initially at different positions in the ion 28

source, will reach the ion detector at the same time. The resolving

power of the instrument is determined primarily by this fact.

When the ion reaches the detector, it first strikes a cathode which

produces secondary electrons. The secondary electrons are then multi­ plied by a magnetic electron multiplier, which uses crossed magnetic and

electric fields plus special resistive coated glass strips. The crossed

electric and magnetic fields cause the electrons to cascade down the

glass plate in a cycloidal path; each time they strike the glass strip

they produce new secondary electrons. This am plifies the in it ia l ion

signal many tim es. The voltage waveform produced by the electron multi­ plier is displayed on a Tektronix Model $h3A. dual channel oscilloscope

synchronized with the mass spectrometer or recorded through an analog

output scanner by a Sanborn Model 1J>0 dual channel recorder. The dual

channel recorder was used for a permanent record of the ion in ten sity

data. The resolution of this mass spectrometer has been discussed by

Wiley and McLaren (39) and White et. al (35). The adjacent peak con­

tribution in the mass range of interest (50 to 60 a. m. u .) was negli­

gib le.

The isotopic percentages of the Cr, Fe, and Mi isotopes, determined

from the recorded ion intensity peak heights, are given in Table 1 to

indicate the accuracy and resolving power of the instrument. The ex­ perimental isotopic percentages listed In the third column of Table 1 29 TABLE 1

THE RELATIVE ABUNDANCES OF THE ISOTOPES OF CHROMIUM, IRON, AND NICKEL

Element Isotope Mass Percent Abundance Determined in this Investigation Reported Values ...... q * ) - . Cr 00 Lu7 U.3

Cr 52 82.8 83.7

Cr 53 10.0 9.5

Cr Bk 2.5 2.it

Fe Bk 5.8 5.8

Fe 56 91.6 91.6

Fe 57 2.2 2.3

Fe 58 O.U 0.3

Ni 58 68.3 ' 67.8

Ni 60 26.1 26.2

Ni 62 3.6 3.7

Ni 61 1.2 1.2

Ni 6JU 0.9 1.1 30 have not been corrected for the reported differences in the sensitivity of the ion detector to ions of different mass, because the correction i s small over a small mass range.

The high temperature Knudsen-cell furnace assembly, shown sche­ matically in Figure 6 , was connected to the mass spectrometer ionization source. The Knudsen-cell used throughout this research is shown sche­ matically in Figure 7. It consists of a split outer cell and a refractory thoria inner cell which contains the liquid alloys. Hie cell was positioned five or six cm below the ionization region and could be adjusted horizontally to maximize the flu x of neutral atoms in to the ionization region. The atomic beam effusing from the orifice in the

Knudsen-cell passes through several slits positioned between the Knudsen- cell and the ionization region. These slits collimate the beam greatly.

The tantalum outside cell was heated by electron bombardment from two heated 0.010" tungsten filaments* The electron bombardment was created by a 700 volt D. C. potential between the filaments and the tantalum

cell. An alternating current of 6 to 7 amperes heated the tungsten filaments so that electrons were thermally emitted. The filaments can

be vertically adjusted in the tower assembly, and this adjustment was made until the minimum vertical temperature gradient was achieved in the

c e ll. Temperature control of the c e ll i s accomplished by manually ad­

justing the tungsten filament current. The temperature of the Knudsen- 31-

PRISM view ing PORT t S H U T T E R ASSEMBLY

SOURCE

VALVE OPERATING o MECHANISM

CROSS

SHUTTER

VALVE

FILAMENT ■—CRUCIBLE --H E A T REFLECTORS

CRUCIBLE SUPPORT R O D S -

HEAT SHIELDS WATER COOLEO— JACKET -SPACER BLOCK WATER IN — _ WATER OUT

CRUCBLE SUPPORT TOWER

QUICK CONNECT CLAMP

- HOUSING ASSEMBLY

COVER V A C U U M — ' CONNECTION

-CONNECTOR

P O W E R —' CJASE HEAOER CONNECTION THE*MOCouf>L£ CRUCIBLE ADJUST FIGURE 6 . KNUDSEN-CELL FURNACE ASSEMBLY Top View Top View

V------7— ThoriG Lid >. / r i Tant a 1u m 1 I L T o p Thoria Liner 1 1"! " "1 1 i 1 i 1 I Ta n t a 1u m ' ! Side View i i ^ B 0 11 om L —| f= E ^ =

11 Tantalum Set Screw INNER CELL to Hold Thermocouple

-Tantalum Thermocouple Guide Side View .1/16" Ceramic Insulator to O U T E R CELL Hold Thermocouple FIGURE 7. SCHEMATIC DIAGRAM OF KNUDSEN-CELL VrojO 3 3

c e ll 'was measured by a W-5/6 Re/W~26$ Re thermocouple that was attached mechanically to the tantalum cell (Figure 7).

The orifice in the top of the tantalum cell was enlarged to .09V 1 to prevent any interference with the effusion beam from the inner thoria

cell. The thoria inner cell had the following dimensions: height,

1 .1*6 cm; outside diameter, 1 .1 2 cm; wall thickness, .058 cm; and o rifice

diameter, .051 cm. To compensate for the difference in thermal ex­ pansion between tantalum and thoria, the inside diameter of the tantalum

c e ll was approximately . 010" larger than the outside diameter of the

thoria cell.

The thermocouple was fastened in place and calibrated by measure­ ment of the thermocouple E. M. F. at the melting points of high purity

nickel (l!*53°C), iron (1536°C), and (1773°C). For this cali­

bration a small piece of the pure metal was placed in the bottom of the

thoria cell and another small wedge of the metal was placed in the

orifice of the thoria lid. The cell was heated until the small specimen

in the orifice was visually observed to melt. The visual observation

was made with an optical pyrometer through a special viewing port above

the Knudsen-cell. The c e ll was immediately cooled and removed, and

visual observation showed that the specimen in the top of the cell was

hotter than in the bottom. The whole procedure was repeated except on

the second t r ia l the c e ll was heated 10°C (as measured by the thermocouple) beyond the melting point of the specimen in the orifice.

After removing the cell from the tower assembly, a second visual ob­ servation established that the material in the bottom of the thoria cell had also melted. It was then concluded that a vertical temperature gradient of le s s than 10°C at the m elting point of iron (1536°C) had been established. A requirement of the Knudsen-cell is that the orifice temperature be at least as high as the temperature of the rest of the cell. Therefore the temperature gradient of less than 10°C, described above, was used in order to assure that the orifice temperature would be at least as high as the cell temperature. The temperature measurements were reproducible to + 2°C at the melting point of pure iron . The temper­ ature control was better than + $°C at a l l temperatures employed in th is research. The flight tube was evacuated with a diffusion pump equipped with a freon-cooled baffle and a liquid nitrogen cold trap.

The vacuum in the flight tube was better than 1 x 10"^ ram Hg as measured by a cold cathode Phillips gauge. A similar pumping system was used for the Knudsen-cell inlet system. This separate pumping arrangement allowed the inlet system to assume atmospheric pressure without raising the pressure in the entire spectrometer. With both pumping systems in oper­ ation, and the isolation valve open, a vacuum of 1 x 10“^ mm Hg or better could be obtained in the Knudsen-cell inlet system with the cell The mass spectrometer was used to measure the activities in twenty of the fifty-three alloys studied in this investigation. The experimen­ tal data for the remaining thirty-three alloys were obtained using a conventional Knudsen-cell technique. However, because of several difficulties, absolute vapor pressures were not determined. Instead, only the equilibrium vapor compositions existing above the alloys were determined by collecting and analyzing the effusing alloy beam from the

Knudsen-cell. Figure 8 is a schematic representation of the interior of the metal vacuum chamber used to collect the vapor phase effusing from the Knudsen-cell. The cell walls are constructed of brass, with water cooled copper coils surrounding the outside for cooling purposes. The vacuum is produced by two high-speed o il diffusion pumps in series, backed up by a mechanical fore pump. There is also a liquid nitrogen cold trap between the o il diffusion pumps and the furnace chamber. The pressure in the chamber is measured by a hot cathode ionization gauge.

The Knudsen-cells used in this phase of the investigation are shown schematically in Figure 9. They consisted of an outer cylinder of 0.02CP tantalum tubing with a 0 . 010" thick tantalum base which was pressed into the tubing to form the outside susceptor cell. Inside the tantalum cell is a close fitting thoria cell which contains the liquid alloys. The lid to the Knudsen-cell is a multiple type specifically designed to prevent excessive heat loss from the orifice area. The bottom lid is a flanged alumina lid which fits closely down into the thoria crucible. 3 6

Shutter

Cooling Coils

Pyrex Plate Lucite Knudsen Cell ■Transite To Cold To R.F. Trap and — — Oscillator Oil Diffusion^ Molybdenunrf, Pump Tripods

F ig u re 8. METAL VAPOB PRESSURE CELL 3 7

Tantalum Lid and Heat Shield

Alumina Lid Y77777Y7A V'/'//77ZZZZu

Tantalum Cell

Liquid Thoria Crucible Alloy

FIGURE 9. KNUDSEN-CELL ASSEMBLY FOR VAPOR COMPOSITION ANALYSIS The orifice in the alumina lid is molded into the lid before sintering.

The tipper lid i s made of tantalum sheet. The lid has a bottom section of 0 . 010” tantalum separated by a small air space from a 0 . 005” upper tantalum section. The lid is press fitted into the tantalum tubing in such a Kay that another air space is left between the alumina and the upper tantalum lid. This multiple upper lid acts as an effective radi­ ation shield; thus, preventing excessive heat loss from the area of the orifice. The upper lid is very important in preventing condensation of the vapor phase, in the Knudsen-cell, on the bottom of the alumina lid

\ and in the o r ific e of the alumina lid . The dimensions of the Knudsen- cell assembly are: height, 2.86 cm; outside diameter, 1.90 cm; orifice diameter, 0.178 cm; and orifice thickness, 0.251* cm. The Knudsen-cell assembly is supported in the middle of the induction heating coil by a tripod. Heating of the Knudsen-cell is accomplished by means of a 20 kilowat, U50 kilocycle Westinghouse oscillator. The work coil is brought through vacuum-tight insulators to the center of the cell. A cylindrical silica sleeve that fits closely to the inner diameter of the copper work coil is not shown in Figure 8 . This sleeve aids in reducing temperature gradients set up in the Knudsen-cell and prevents effusing vapor from impinging on the work coil. Above the Knudsen-cell orifice there is a heavily etched pyrex plate which is firmly attached to the water cooled upper furnace wall. The alloy vapor beam effusing from the Knudsen orifice is condensed on this etched pyrex plate. A Leeds and Northrup disappearing-filament optical pyrometer was used to measure the temperature. The Knudsen-cell orifice is viewed through an o p tica lly f la t viewing window above the c e ll. The window i s protected from the effusing beam by a magnetically operated shutter which is opened only for a temperature measurement with the optical pyrometer.

The small orifice in the Knudsen-cell provides a hohlraum so that emis- s iv ity corrections for the sample are not necessary. However, the opti­ cal pyrometer was calibrated by two methods in the temperature range of interest (lii50°-l600°C). First the pyrometer was calibrated by sighting through the optical flat into an orifice drilled into a graphite cell which was situated in the constant temperature zone of a tube furnace.

A calibrated platinum/platinum-13$ thermocouple was placed in

the graphite cell to record the temperature of the cell. In this way

the pyrometer was calibrated from 1300° to l600°C. Also the pyrometer was calibrated in the exact positions for the experiments by sighting

through the orifice of the Knudsen-cell onto a sheet of high purity

iron in which there were drilled small holes, This iron sheet rested

on the top of a pure iron sample of the same weight used for the actual

runs. The temperature of the Knudsen-cell was increased very slowly

in the range of the melting point of iron. The pyrometer reading was

noted when the iron sheet just began to melt. The holes drilled in

the iron sheet greatly facilitated the observation of the onset of melting. These two calibration methods agreed within 3°C at the melting point of iron (1536°C), which is about the degree of reproducibility of the pyrometer readings. The temperature gradient between the alumina

Knudsen-cell lid and the alloy surface was measured by placing a pure iron sheet on top of the pure iron sample and a pure iron str ip in the orifice. The temperature of the orifice for the Knudsen-cell assembly in Figure 8 was found to be 10°C lower than that of the sample surface in the Knudsen-cell. However, th is arrangement did prevent any ob­ servable condensation cm the bottom of the alumina lid.

Temperature control is the poorest feature of this vacuum furnace assembly. The temperature is controlled manually by adjusting the voltage to the plates of the rectifier tubes in the radio frequency oscillator. Fluctuations in the incoming line voltage and power factor make it necessary to continuously check and adjust the plate voltage in order to keep the grid and radio-frequency currents constant. With constant attention, the temperature can be controlled within +10°C at

1600°C. Temperatures as high as 1750°C and pressures as low as 1 x 1C)""^ mm Hg were consistently obtained with the apparatus described above. ^THEORETICAL BASIS

The relationships that are required to derive activities from mass spectrometer ion intensity data and equilibrium vapor composition data are presented in this section.

The relationship between the partial pressure of species i in the

Knudsen-cell and the ion intensity of a particular isotope in the mass spectrum for species i is given by the equation1,

+ H pi xi T— W where p^ is the partial pressure of the ith species in the Knudsen-cell,

I* is the relative ion intensity or ion current for a particular posi­ tively charged isotope of species i, T is the absolute temperature of the Knudsen-cell source, and is the sensitivity factor for the species in the mass spectrometer. Ihe factor k| takes into account the geometry of the Knudsen-cell source, the geometry of the ionization region, the ionization cross-section of species i (a function of the bombarding electron energy), the isotopic abundance of the particular isotope re­ corded, and the electron multiplier efficiency for the isotope of spedes

1 (a function of the masB, energy, charge, and electronic configuration

Equation (1) is derived and discussed in Appendix A. h2 of the ion striking the ion detector at the end of the flight tube).

The factor is assumed to be independent of temperature and pressure.

To determine the absolute pressure, p^, of species i in the Knudsen-cell source requires a determination of the constant k|. The methods for the determination of k-[ have been discussed by Inghram and Drowart (3U).

However, i t w ill be shown that the determination of k | i s not necessary fo r the determination of the a c tiv ity of a component, a^, in an alloy.

The activity of any component i in a multicomponent alloy is given by,

f i ai " f9 1 „o where f is the fugacity of component i in the actual state and f^ is the fugacity of i in a particular standard state. If the pressure in the system is sufficiently low, below 1 atmosphere, i t i s a good assump­ tion to equate the fugacity to the partial pressure. If the standard state is defined as the pure component i in its stable state, the activity is given by,

Pi » i - l f (3) where p^ is the partial pressure and p° is the pure component vapor pressure. Substituting equation (1) into equation (3) yields,

I i ki° T ai " Ij k{ T &) ftie temperatures are equal and equals k{° because both are for the same isotope of i in the vapor phase. Therefore equation (U) reduces simply to , _Ei_ ai ' ~ (5) where 1^ is the ion intensity of a particular isotope of component i in any multicomponent a llo y and 1° is the ion intensity for the isotope of the pure component at the same temperature. However, to obtain accurate activities from equation ( 5 ) one must successfully reproduce the mass spectrometer constant k-[, because the determination of 1^ and l£ re­ quires two separate mass spectrometer determinations.

Another important relation in mass spectrometry is the Clausius-

Clapeyron equation in terms of ion in te n sitie s . The p artial heat of sublimation or evaporation of component i is given by the equation,

^ P i - A % d(Vt> (6) where AH^ is the partial heat of sublimation or evaporation for compo­ nent i. A plot of lnpi versus l/T should be almost linear over a lim ited range of temperature. Taking natural logarithms of both sides of equation ( 1),

In I ±T - In k^ + m p-_ (7) if this equation is differentiated with respect to l/Tf d In I^T d In p^ ' d(i/T) JOTT (8) because k! i s assumed to be independent of temperature. From equations

(6) and ( 8 ),

d In I 3T -A H i -~307tr~ * — E- or,

d log I±T -AH± d(l/tf) " 2.303R ^

considering the pure component i,

d log ijT -£ji° d (l/¥ ) “ 2.303R where AH^ is the standard heat of sublimation or evaporation of pure

component i. Plotting log I^T versus l/T over a lim ited range of temper-

ature a straight line of slope ~A%/ 2 . 303R exPec^e^* In th is re­

search, equations ( 10) and ( 1 1 ) were used primarily to smooth the ex­

perimental ion intensity data. Least squares analyses on plots of log

I^T versus l/T were made to correct the experimental ion intensity data

to the best straight lines.

The other important mass spectrometer relation used in this research

is the relation between the ion in te n sitie s of the various components

and the equilibrium vapor compositions existing above the alloys in the

Knudssn-cell. The atomic fraction of a component in the vapor phase cf

an ideal gas is given by, where Pj is the total pressure, is the number of moles of component i in the vapor phase, and n^ is the total number of moles in the vapor phase. If equation (1) is substituted into equation (12) and it is noted that,

PT - (13) L then

(111) N i ■ Z w i

Therefore, to obtain Nj the individual sensitivity factor, k^, for each component must be determined. The relation used to determine n T in this research is,^

±/

For reasons that will be discussed later the activities of the a llo y s studied in the metal vapor pressure c e ll were determined from a knowledge of the equilibrium vapor compositions existing above the alloys and appropriate reference activities, without resorting to the more conventional determination of the partial pressure and pure

^Equation (15) i s derived in Appendix A. component vapor pressures of each component in the alloys. Speiser and

S t. Pierre (U2) have derived and discussed the necessary equations to determine activities from vapor composition data without a knowledge of the partial pressures or pure component vapor pressures. Lyubimov and

Granovskaya (17) have derived the same relations and applied them to solid iron-nickel alloys and iron- alloys. Speiser, Jacobs, and

Spretnak (20) have applied the vapor composition method to liquid iron- nickel alloys and obtained excellent agreement with the work of Zellars e t a l. ( 21) who measured the partial pressures and a c tiv itie s of iron and nickel in the same a llo y s.

The basic equation is the general form of the Gibbs-Duhem equation which may be written in the following forms

S^T - V^dPT ♦ ^>N?d ln a . » 0 (16) where is the mole fraction of component i in any condensed phase, q, and is the activity of component i in the condensed phase, q. The first term, S^dT, disappears under isothermal conditions, and the second term, V^dPT, is negligible because of the negligible absolute variation of the total pressure, PT, with composition at low vapor pressures.

Therefore equation (16) is reduced to,

S N?d In a « 0 (17) L The activity of each component in the condensed phase is related to the vapor pressure by, I f th® vapor i s assumed to be an id eal gas, then

• • • • (19) where is the mole fraction of component i in the vapor phase. Fran

(19 ) we can express the partial pressure of any component in terms of the partial pressure of any other component by,

(20 ) and the activity of each component may be related to the vapor composi­ tion and the relative vapor pressure of one component by,

Ni pj 3i " r»° Nj Pi .

Combination of equations (17) and (21) resu lt in the follow ing modifi­ cation of the Gibbs-Duhem relation:

(22)

Solving for p^ in equation (22) gives,

(23) which reduces even further to, Integration of equation (23) from n Y ^ to yields the ratio of the J J activities in the corresponding states,

dlnNj In a aj (2) nr (25) i

The path of integration of equation (25) is of no significance because only exact differentials are involved. Equation (25) allows for the determination of activities from a study of vapor composition correspond­ ing to condensed phase composition without resorting to the absolute measurement of vapor pressure.

For the single phase ternary alloys studied in this dissertation the most convenient foim of equation (25) is given by equation (26)^,

(2) r « t 2 ) r nt (2) n v ( 2 ) In ai In N1 l i ) dNg + (N N^dNj W N^ c r r + n : N h: n T rv(l) v (l) N N (26) L v where is the mole fraction of component i in the liquid phase and

is the mole fraction of component i in the vapor phase. The main

advantage of th is foim is that a ll terms in the integrals remain fin ite

in general and it is more accurate to extrapolate the terms in the

integrals to zero concentration of one of the components in the con­

densed phase. From equation (26) it can be seen that In order to

(26) is derived and discussed in Appendix B. (2) determine the activity of component 1 in state 2, a-^ , it is necessary to know a reference activity, in some reference state lj it is also necessary to know the variation of vapor composition with condensed phase composition along sane arbitrary path between state 1 and state 2. EXPERIMENTAL PROCEDURE

The fifty-three alloys studied in this research were prepared frcxn high purity iron, chromium, and nickel. Zone refined iron donated by

B attelle Memorial In stitu te and the American Iron and S teel In stitu te was used. The nickel was taken from a high purity carbonyl nickel rod donated by the International Nickel Company. The chromium, also donated by the International Nickel Company, was of vacuum grade. Typical analyses are given in Table 2 fo r each of the above m etals. Only the impurities above one part per million are listed for the zone refined iron. The major impurities in the chromium were iron, , carbon, and . Although an oxygen analysis was not furnished with the nickel and chromium it is possible that significant amounts of oxygen may have been present in both metals. The effects of impurities on the thermodynamic a c tiv itie s of the major components in these a lloys are discussed in Appendix C. I t i s concluded in AppendixC that the e ffe c t of impurities on the activity values of iron, chromium, and nickel is small compared with the experimental accuracy of the activities deter­ mined by th is investigation .

A ll pure metals were etched in su lfu ric acid and rinsed twice in acetone. A ll but the iron-chromium a llo y s were proportioned to produce a definite chromium content after melting. The chromium loss on melting $0 *1

TABLE 2

TYPICAL ANALYSES OF THE IRON, CHROMIUM, AND NICKEL USED

Iron Analysis

A nalysis Element ppm

Chromium 3»0 Cobalt ii.O 2.0 Phosphorous 3.0 Carbon 8.0 Oxygen 2.3 S ulfur 5.3

Nickel Analysis

A nalysis A nalysis Element EE2___ Element „.-PPm___ Carbon 10 Chromium 5 S u lfu r 10 Cobalt 5 10 Aluminum 10 Iron 6 10 S ilico n 7 5 Copper 10 3

Chromium ■ A nalysis

A nalysis Element Weight Percent

Chromium 99.55 Aluminum 0.025 Iron 0.21 S ilico n 0.11 Copper 0.01 Carbon 0.02 S ulfur 0.012 was determined by a preliminary investigation and the slight chromium loss was taken into account when the actual alloys were weighed and melted. All alloys were melted in high purity Morganite Alumina crucibles in the vacuum induction melting unit described in the experi­ mental apparatus section. The total alloy weight melted was 15 to 20 grams. Die a llo y s were held for 15 minutes at 1650°C under a vacuum of

5 x 10"^ mm Hg. The a llo y s were broken out of the alumina crucibles after melting and sanded on a silicon carbide belt to remove entrained alumina. The alloys were then etched in aqua regia to ranove all traces of oxidation and slag from the melting process. The alloys were next milled to obtain small chips for both chemical analysis and mass spectrometer investigations. The alloys investigated in the metal vapor pressure cell were not milled into chips; only drilling was done to obtain a sample for chemical an alysis. A ll a lloys were analyzed after melting to insure that the alloys were of the correct composition and had been held in the liquid state for a sufficient time to allow complete homogenization. It was found by chemical analysis that a few of the higher Cr alloys were not homogeneous after the first melting and these had to be remelted to produce a chemically homogeneous alloy. ALL alloys were analyzed by wet chemistry techniques. Pe was determined by

stannous chloride reduction followed by titration with dichro- raate with an internal indicator. Cr was determined by catalyzed oxida­

tion with ammonium persulfate and silver nitrate, followed by titration with ferrous ammonium sulfate and potassium permanganate. The nickel was determined by the standard dimethyl glyoxime gravitation analysis.

The relative error of these analyses is +.5 percent for each element.

The nominal compositions of the fifty-three alloys studied in this thesis are given in Table 3. Also listed in Table 3 is the method for the determination and the temperatures of the determination. The mass

spectrometer was used to investigate 19 alloys; 15 were ternary alloys near the iron rich comer of the ternary diagram. Bie other it alloys are either in the Ni-Cr binary or ternary alloys with 5 atomic percent

Fe. The vapor composition analysis method was used on 1;0 alloys, 21 were ternary a llo y s, 7 were Fe-Cr a llo y s, and 8 were Ni-Cr a llo y s. Both methods were used on 6 alloys as indicated in Table 3.

Mass spectrometer determinations

In all mass spectrometer ion intensity determinations the ion in­ tensity for a given isotope of Fe, Cr, or Ni is proportional to the vapor pressure of the component in the Knudsen-cell source through the

equation

+ ki Pi I± y (1)

where 1^ is the ion intensity of a particular isotope of component i,

the mass spectrometer constant for component i, and p^ the vapor pressure TABLE 3 Sh

NOMINAL COMPOSITIONS, ANALYSIS METHODS, AND TEMPERATURES OF THE ALLOYS STUDIED IN THIS RESEARCH

Iron-Chromium- System

Nominal Composition A nalysis Tempera 1 L T, N Method NCr Fe °C

O.Ol 0.99 Vapor Composition Analysis 1600 .05 .95 II ii ii it .10 .90 . II it ii n .15 .85 II ii ii ii .20 .80 II ti M it .30 .70 II n it it o.Uo 0.6 0 II ii ii ii

Nickel-Chromium System

Nominal Composition

Ncr % i A nalysis Temperature Method °C

0.01 0.99 Vapor Composition Analysis 1600 .03 .97 n ii ii it .05 ' .95 n it ti ti .10 .90 ii n ti it .10 .90 Mass Spectrometer 1600, 1650, 1700 .20 .80 Vapor Composition Analysis 1600 .20 .80 Mass Spectrometer 1600, 1650, 1700 .30 .70 Vapor Composition Analysis 1600 .hO .60 ii ii ti If 0.50 .50 n tt it II

Continued. SS TABLE 3—Continued

Iron-Chromium-Nickel System

Nominal Composition A nalysis Tempgrature „L N Method N i F e

0.05 0.05 0.90 Mass Spectrometer 1600, 1650, 1700 it .10 .85 ti ti n ti ii ti .15 .80 ii ti ii it ii .20 .75 it ti ii it it .30 .65 Vapor Composition Analysis 1600 ti .50 MS it it II ii .70 .25 ti it II n .80 .15 ii it II ti .85 .10 ti it II it .90 .05 ti it II

.10 .05 .85 Mass Spectrom eter 1600, 1650, 1700 It .10 .80 ii ti ii it it It .15 .75 it it ii ii 11 .20 .70 it 11 11 II It .20 .70 1600 It .30 .60 ii ii ii It .50 M o ii it ii It .70 .20 it ti ii It .75 .15 ii ii ii II .80 .10 ii ii ii It .85 .15 ti it ti

.20 Mass Spectrom eter 1600, 1650, 1700 .05 .75 * it .10 .70 ipor Composition Analj 1600 M .15 .65 Mass Spectrom eter 1600, 1650, 1700 It .20 .60 ii ti II II It It .20 .60 ipor Composition Anal} 1600 If .30 •5o ii ti it ii n .bo .Uo it it ii it it .60 .20 it it it ii it .70 .10 ii ti n ii it .75 .05 ti it ii ti 0.20 0.75 0.05 Mass Spectrom eter 1600, 1650, 1700

The alloy used in the mass spectrometer proved to be inhomogeneous and the results were discarded. 5 6 TABLE 3—Continued

Iron-Chromium-Nickel System

Nominal Composition

N A nalysis Cr N„.N i Temperature Fe Method °C

0.30 o.o5 0.65 Mass Spectrometer 1600, l65o, 1700 .10 .60 n ii II II II .15 .55 it II II II .20 .50 it It II II .30 .i*o Vapor Composition Analysis 1600 .1*0 .30 ti ii ii II .50 .20 it n ti II .60 .10 ii ii ii II .65 .05 ti ii ii II 0.30 0.65 0 .0 5 Mass Spectrom eter 1600, 1650, 1700 of component i in the Knudsen-cell. When the mass spectrometer constant* k^, can be reproduced the a c tiv ity of component i i s given by

Therefore the successful determination of activities is largely t determined by the successful reproduction of k^. The factors that contribute to the difficulty in reproducing k^ are believed to be

1. Temperature measurement and control.

2. Alignment of the Knudsen-cell orifice with the slits leading to the ionization region.

3. Knudsen-cell orifice area and length.

U. Alignment of the ion beam as it strikes the electron multiplier.

5. Electron multiplier efficiency and stability

The determination of accurate activity values from the ratios of alloy component intensities to pure component intensities is possible only when the above five factors are essentially the same for the alloy and pure component intensity determinations. Six months of preliminary work on the mass spectrometer were required before these factors could be consistently reproduced.

The temperature measurement problem was e ffe c tiv e ly solved by the design shown previously in Figure 6. The W-5$Re/W-26$Re thermocouple junction was press fitted into a small tantalum sleeve. The sleeve was 5 8 brought up through the bottom of the Knudsen-cell so that the top of the sleeve was flush with the bottom of the tantalum Knudsen-cell. The thoria crucible which contained the sample was in good thermal contact with the thermocouple junction. Also the tantalum sleeve caitaining the

thermocouple junction was tightly held in this position by a tantalum

set screw. This design eliminated the possible variation in thermo­

couple junction position that was experienced initially. The importance

of temperature measurement and control i s due to the exponential vari­

ation of the vapor pressure with temperature. For the transition metals,

a variation of 1°C at 1600°C changes the ion intensity by approximately

1.3 percent, which is a very large change considering the d iffic u ltie s

in the measurement and control of temperature at l600°C. The measure­

ment of temperature at the melting point of Fe (1536°C) was reproducible

to within +2°C by the thermocouple calibration method previously

described. The control of the temperature of the Knudsen-cell was

never conpletely solved. Electron bombardment heating is a rather un­

stable heating method. There is always the possibility of arcing which

was never completely eliminated. The only feasible method to control

the temperature and record ion intensities at the same time is to employ

two persons. One person would control the temperature to within ik°C

of the predetermined lev e ls between 1500° and 1700°C, while the other

would record intensity peaks when the temperature was within the li°C

range. It was attempted to take the same number of intensity peaks when the temperature was below the predetermined le v e l as when the temperature was above the le v e l. This would tend to reduce the temperature errors in the Intensity values due to the averaging of all the intensity peaks at a given temperature.

The Knudsen-cell orifice was aligned with the slits leading to the ionization source by first aligning the Knudsen-cell orifice with the slits in the heat shields while the tower assembly was removed from the mass spectrometer. After the tower assembly was fastened to the mass spectrometer the heated Knudsen-cell orifice was viewed through the optical system of an optical pyrometer. The orifice, if necessary, was centered in the middle of the slit leading to the ionization region by an adjustment screw in the tower assembly which horizontally moves the

Knudsen-cell. When the first predetermined temperature level was reached the adjustment screw was slightly changed in both directions to make certain that the maximum ion intensity was being obtained. It was found that the orifice could be aligned quite satisfactorily by the visual adjustment. The thermocouple, attached to the base of the tantalum outer cell, aided in holding the Knudsen-cell in a more rigid, reproducible position in the tower assembly.

The problem of reproducing the Knudsen-cell o r ific e area and length was eliminated by using the same thoria lid for all pure metal and alloy intensity determinations. The thoria lid was cleaned in hydrochloric 6 0 acid before each new run and dried to remove the acid and moisture. The thoria lid orifice diameter was checked periodically and found to have no measurable change in diameter.

The alignment of the ion beam as it strikes the first cathode of the electron multiplier is controlled by two magnetic fields. It was found that this alignment sometimes changed from run to run giving significantly different intensity values. Therefore, before any in­ tensity values were taken on a given run, the horizontal and vertical deflection controls were adjusted, if necessary, to give a maximum in ten sity.

The reproducible efficiency and stability of the electron multi­ p lier is very important, however changes in in te n sitie s caused by changes in the efficiency of the multiplier are impossible to separate from other effects. Therefore the contribution from this source is not known. The electron multiplier was periodically cleaned, and the manufacturer reports that if this is done the electron multiplier is very stable and reproducible. It was found that cleaning and adding fresh mercury to the mercury diffusion pumps was very important in preventing excessive background in te n sitie s in the 50 to 60 (a. m. u .) range. The dirty diffusion pumps also caused erratic variation in in ten sity peaks, which was possibly due to background in ten sity variations. Until now only the disadvantages in the mass spectrometer technique have been emphasized and perhaps they have been overemphasized due to inexperience with the instrument. However, there are many advantages to the mass spectrometer technique over conventional Knudsen-cell studies which must not be overlooked. The mass spectrometer i s capable, if properly calibrated, of determining the vapor pressure of all compo­ nents in the vapor phase and also the vapor composition. This is a distinct advantage over the conventional Knudsen-cell technique. The mass spectrometer allows one to determine the components that are effusing from the Knudsen-cell, while the conventional Knudsen-cell weight loss method usually can not. The vapor species effusing from the Knudsen-cell must be assumed in the weight lo ss method, and these assumptions have sometimes been proven incorrect by the mass spectrom­ eter. Another very important advantage to the mass spectrometer technique is the fact that a given run can cover a wide range of temper­ atures, whereas the conventional weight loss method can include only one temperature per run. The second law method of obtaining the heat of a gaseous state reaction by plotting InK versus l/T , where K is the equilibrium constant expressed by the I^T values from the mass spectrom­ eter data, is widely used in thermodynamic investigations because it is free from any serious approximations. 62

The mass spectrometer determination of the vapor composition effusing from the Knudsen-cell is made during one run by applying equation,

^ i/ (JT x (15) L The difficulties of reproducing the same mass spectrometer conditions are greatly reduced because in general these conditions remain the same during any one mass spectrometer run. The main factors that determine the accuracy of the vapor compositions are

1. Close control of temperature for all intensity determinations at a given temperature.

2. The accuracy of the relative ionization cross-sections used in equation (15).

3. The rela tiv e electron m ultiplier efficien cy fo r each component.

Factor 1 has been discussed and factors 2 and 3 will be discussed in the results section.

The established procedure for an experimental mass spectrometer run for either a pure metal or an alloy, with the above reproducibility problems in mind, was as follow s. The thoria crucible was ground to a height of 1.U53 + .002 cm. It was then filled with 2 * .1 grams of either pure metal or alloy. The thoria crucible was placed in the lower half of the split tantalum cell which was firmly in place in the tower assembly. The acid cleaned thoria lid was placed over the thoria cell and the upper tantalum half of the cell was placed over the thoria cell. The heat shields were centered over the orifice in the thoria lid, and the tower assembly was inserted into the mass spectrometer.

The tower assembly section was evacuated to the 10 ^ mm Hg range. The iso la tio n valve between the two vacuum systems was opened and the

Knudsen-cell was heated to a low temperature to degas the Knudsen-cell components. The temperature was slowly raised to the f i r s t temperatuxe of in terest. When the vacuum was below 2 x 10“** mm Hg, in the Knudsen- cell region, the Knudsen orifice was aligned to produce a maximum in­ tensity at a given temperature. The horizontal and vertical deflection controls were adjusted so that the ion beam coining down the flight tube produced a maximum in ten sity value* The in te n sity recordings at a given temperature were made by one man while the other controlled the temper­ ature. At least twenty intensity peaks were recorded for the isotopes of Fe, Cr, and Ni studied. After each isotope intensity determination was made the Knudsen-cell was shuttered off from the ionization region and the background in ten sity was recorded for the mass peak in questicn.

The pure metal intensity determinations were made at 50°C intervals be­

tween 11*00° and 1700°C. The electron energy used for ionization was always 50 e. v. for all pure metal and alloy determinations. The alloy

intensity determinations were made at 1600°, 1650°, and 1700°C. The

isotopes recorded for each of the three elements were the mass 52 isotope for Cr, the mass 56 isotope for Fe, and the mass 58 isotope for

Ni. Each isotope i s the most abundant isotope for the element. Table 1, listed previously, gives the experimental and reported isotopic abun­ dance for Fe, Cr, and N i. The mass 58 isotope of Fe was overlooked and a l l in ten sity measurements of 1 ^ ^ in the a lloy s include a mass 58 Fe contribution* The isotopic abundance of the mass 58 Fe isotope is only

.33 percent, however there is a significant contribution to the mass 58 peak from the Fe 58 isotope for alloys with low nickel concentrations.

This Fe 58 isotope contribution can be computed and w ill be explained in the results section. After a mass spectrometer ran was completed the in ten sity peaks fo r each isotope and temperature were averaged and the background in ten sity peaks, i f present, were also averaged. The back­ ground intensity was then subtracted from the total intensity and the remainder was attributed to the in ten sity of Cr^g, Fe^^, or Ni^g from the Knudsen-cell.

The intensity values for the pure metals IF°, Ic°, and IN°j and the intensity values for the alloys I , ICr, and 1^ were fitted to a least squares straight line of Log I^T versus l/T by a computer as described previously. This procedure smooths the data, however the actual ex­ perimental intensities for both the pure metals and the alloys deviated by a maximum of only ii percent from the straight line computed by the least squares technique. In general deviations from the computed straight line were on the order of 1 to 2 percent. The conditions that must be satisfied for the successful deter* mination of vapor pressures by the Knudsen-cell technique have been

enumerated by Speiser and Spretnak (U6), Dushman (U7), and Whitman (1*8).

The four most important criteria are

1. The mean free path of the gas in the Knudsen-cell must be

several times the diameter of the orifice; preferably ten times.

2. The ratio of the orifice area to sample area must be small; approximately 1 to 100.

3. The temperature of the Knudsen orifice must be at least as

high as the body of the Knudsen-cell and sample.

Ii. The mean free path of the residual gas outside the Knudsen-

c e ll must be large.

The last three requirements are well satisfied in this research. How­

ever only at the lowest temperature, l600°C, is condition (1) conpletely

satisfied. Pure Cr has a vapor pressure that is 3.5 times pure Fe and

7 times that of pure Ni. The mean free path to orifice diameter ratio

for pure chromium i s approximately 9 at l600°C, and drops to 3.5 at

1700°C. The mean free path to orifice diameter is 10 or greater for

both pure Fe and Ni for temperatures to 1700°C. The alloys with the

highest vapor pressure in this research are the 30 atomic percent Cr

alloys. The mean free path for the (30 Cr-70 Fe) alloy is approximately

16 at 1600°C and 5.5 at 1700°C. The observed effect of the above ratio 6 6 dropping below 10 i s to lower the flu x of atoms coming from the Knudsen- cell due to collisions in and around the orifice of the Knudsen-cell.

If the vapor pressure or ion intensity was appreciably lowered by this e ffe ct i t would be most obvious in the Log(lg° • T)versus l/T p lot for pure Cr. An examination of these plots from lUOO0 to 1700°C for three pure Cr runs show that the lowering effect may be present to the degree of 5 percent at 1700°C. This effect may also account for the observed low heat of sublimation values for pure chromium obtained in these in­ vestigations. This will be discussed further in the results section.

Vapor Composition Determination in the Metal Vapor Pressure C ell

The vapor composition analysis method was employed on fo rty a llo y s.

Figure 8 in the experimental apparatus section presented the important details of the vacuum induction furnace used to collect the vapor effusing from the Knudsen-cell. The attempts to accurately and re- producibly measure the absolute vapor pressure of the pure elements Fe,

Cr, and Ni by the conventional Knudsen-cell weight lo ss method, using the apparatus in Figure 8, failed for several reasons. First, the temperature measurement by the optical pyrometer is reproducible to no better than +3°C at 1600°C and the temperature control on many runs was only +10°C. This 10°C temperature error could result in a 13 percent error in the vapor pressure runs. Also there is a significant weight lo ss from the alumina Knudsen-cell lid during a 3 or 1* hour vapor pressure run. This empty cell weight loss is on the order of 10 percent of the total cell weight loss for a Fe vapor pressure determination.

The vapor composition must also be determined for the partial pressure determinations in the alloys. In order to obtain enough condensate from the Knudsen-cell for an accurate chemical analysis an orifice diameter of .176 cm was used. This orifice diameter is 3.5 times larger than used in the mass spectrometer Knudsen-cell. Therefore at 1600°C the mean free path to o r ific e diameter ratio fo r pure Cr would be only 2.6 which is significantly below the ratio of 10 that is required.

Because of the above reasons, absolute vapor pressures were not determined, instead only the compositions of the vapor effusing from the Knudsen-cell were determined. The vapor compositional method has several experimental advantages over the conventional Knudsen-cell weight loss method for determining activities. First, the vapor composition is not an exponential function of temperature as the vapor pressure is; in fact for alloys whose components have similar heats of vaporization, the vapor composition is only a slight function of temperature. For an alloy of 20 atomic percent Cr and 80 atomic percent

Fe the Cr vapor fraction was computed to change by only .3 percent when the temperature changed from 1600° to 1610°C. The p artial pressure of

Cr changes by 13 percent for this temperature change. Another important advantage is that the accurate measurement of the orifice diameter is of 6 8 no consequence. Also the fact that the mean free path to orifice diameter ratio is below 10 should have no effect on the vapor conposi- tion effusing from the orifice as long as the orifice area is much smaller than the projected surface area of the sample. Hie disadvantage of the vapor composition analysis method for activity determination is the fact that the method is not an absolute method like the vapor pressure method. Hbte vapor composition method requires an accurately known reference activity. The accuracies of the activities determined by this method depends on the accuracy of each vapor composition deter­ mination along the path of graphical integration chosen to evaluate the activities.

Hie success of the vapor composition method depends on three main processes. First, the vapor effusing from the Knudsen-cell must truly represent the vapor composition that exists in equilibrium with the alloy. This effusing vapor composition must be corrected for differences in effusion velocities to obtain the equilibrium vapor composition in the Knudsen-cell. Secondly, the effusing vapor must be efficiently collected in such a manner that the condensed vapor has the same conposi.- tion as that effusing from the cell. Finally, the composition of this condensed vapor must be accurately analyzed. The conditions that should assure that the effusing vapor represents the equilibrium vapor composi- tion have been met in this investigation. One important factor that has not been discussed is the choice of the refractory crucible used to contain the liquid alloys. Ihe Fe-Cr-Ni liquid alloys are very reactive with most environments, particularly the higher Cr alloys. 3he crucible material selected must be able to with­ stand rapid heating and the potential chemical attack by the liquid alloys for periods up to 5 hours at 1600°C. High purity alumina cruci­ bles were found to be appreciably attacked during the long holding times required by the runs. A definite layer of green or scarlet oxide formed over the liquid alloy surface. Ihis layer could impede the establish­ ment of equilibrium in the vapor phase of the Knudsen-cell. For this reason thorla crucibles were used in both the vapor composition investi­ gations and the mass spectrometer work. Thoria crucibles withstood attack by these alloys very well. 3he alley surface was always free from visible oxidation or crucible reaction after a run on all but the ij.0 and 50 atomic percent Cr alloys. On these three alloys there were patches of oxidation products on the alloy surface, however 50 percent of the alloy surface was still free from any visible oxide layer. Hie only disadvantage of the thoria crucibles was the tendency to crack upon cooling after the run, and on several occasions they cracked during a run. In general they did not crack on cooling until a low temperature was reached. The second process of collecting the effusing vapor is very im­ portant. In this work the vapor was condensed on a heavily etched py- rex plate. The back of the pyrex plate was in good thermal contact with the water cooled top of the brass cell as shown previously in Figure 8.

The most important function of the target is to condense all vapor atoms that strike it, also the condensate must be removed from the target for subsequent analysis. Tantalum sheet, copper sheet, and aluminum fo il were first used as condensing targets. These metallic targets condensed a ll the incident atoms, but i t was impossible to dissolve the condensed material without dissolving the target material also. The large amount of dissolved target material in relation to the small amount of con­ densate complicates the analysis of the condensate. The etched pyrex target proved to be an excellent material for three reasons. All atoms incident upon it were condensed, the condensate could be dissolved off the pyrex plate without dissolving the target, and the weight of the pyrex plate remained very stable through both the condensing operation and the dissolving operation; this fact made it possible to obtain a fairly accurate weight of the condensate. The etching of the pyrex plate was done by hydrofluoric acid; this etching helped in obtaining a more adherent condensate film . Several preliminary experiments indi­ cated that the pyrex target was condensing all the vapor impinging on it. In one experiment a hack saw blade was positioned almost in contact with the pyrex plate. Pure Fe was then evaporated onto the target from the Knudsen-cell assembly. Close examination of the Pyrex target revealed a very sharp outline of the hack saw teeth which indicates there was no excessive surface diffusion after condensation. Another argument in favor of the condensation of all atoms impinging on the target is the observed ratio of the wei^rt of the material condensed on the plate to the total material effusing from the Knudsen-cell. In all alloy vapor composition determinations the ratio was between .53 and .51*. This ratio of target weight pick-up to total weight loss can be computed from the knowledge of the target diameter and the vertical distance between the orifice and target. For a knife-edge orifice this ratio is 0.1*1, however the effect of a finite thickness orifice is to focus more material in the forward direction. From the theoretical equations of

Clausing (1*9) this ratio was computed to be .55 far an orifice diameter

to orifice thickness ratio similar to the ratio used in this investiga­ tion. The agreement between the experimental results and the theoret­ ical results from Clausing*s equations offers verification that the

pyrex target is condensing all the atoms that strike it. The final

experiment to assure that the condensed vapor composition was the same

as that effusing from the cell was to compare the vapor compositions ob­

tained from a (5Cr-95Ni) alloy for different target surfaces. In one

case the pyrex plate was precoated with a layer of pure Fe by evaporat­

ing pure Fe onto the pyrex plate from the Knudsen-cell. The Ni-Cr alloy vapor phase was then condensed on the Fe coated plate and the analyzed vapor composition was compared to the vapor composition from the same alloy obtained using the etched pyrex plate surface. The vapor compo­ sitions agreed within 1 percent, which is approximately the experimental accuracy of the chemical analysis of the condensate. The tests offered confirmation of the condensing efficiency of the pyrex plate because Fe should be an excellent condensing material for Ni and Cr because it has a very similar lattice parameter and most metals are known to condense other similar metal atoms without reflection or re-evaporation.

The other possible source of error in the condensation process is the preferential reflection or re-evaporation from the silica sleeve which is between the induction coil and Knudsen-cell. Ihis silica sleeve intercepts a significant portion of the effusing beam. If the hot silica sleeve does not condense all the atoms that strike it, there is the possibility that the reflected atoms will have a different average composition than the composition effusing from the Knudsen-cell.

A portion of these reflected atoms would strike and condense on the pyrex target. Extensive reflections from the silica sleeve seem un­ likely because of the agreement between the experimental value of the condensation ratio and the theoretical value from Clausing's work. However this preferential reflection or re-evaporation possibility was investigated. To check the p o ssib ility of any re-evaporation from the 73 silica sleeve the following experiment was performed. A silica sleeve with a heavy alloy, metallic deposit, was placed in the coil along with an empty tantalum Knudsen-cell. Ihe cell was heated to 165>0°C and held for 3 hours. The pyrex plate was examined and found to be free of any condensate. Therefore it was concluded that the silica sleeve does not become hot enough to re-evaporate a measurable quantity of the metal deposit. This does not rule out the possibility of preferential re­ flections from the silica sleeve however. This possibility was checked by analyzing the condensate on the silica sleeve and comparing it to the caadensate analysis from pyrex plate for the same alloy deter­ mination. The analyses agreed within 1 percent. This should eliminate the possibility of preferential reflections from the silica sleeve. It was concluded that the condensate on the pyrex plate was of the same composition as that effusing from the Knudsen-cell.

The final experimental procedure is the accurate chemical analysis of the condensate. The analysis of the condensate is difficult because of the small amount of condensate that is deposited on the pyrex plate.

The weights of the condensates ranged between 1;0 and 120 milligrams de­ pending on the alloy composition and holding time at 1600°C. The con­ densate had to be analyzed for a l l components because the to ta l weight

of the condensate could not be obtained to an accuracy of better than

+1 milligram. This was due to the large weight and size of the pyrex target in relation to the weight of the condensate. Since the weight of the condensate is small to begin with it -was undesirable to split the ternary condensate into three portions in order to analyze each portion for one of the components. The splitting technique would only reduce the accuracy of the analysis. Therefore an analysis procedure had to be found to analyze for a l l three components using one sample. Most cf the standard wet chemical analysis methods for Fe, Cr, and Ni are de­ signed for only one analysis and the chemicals introduced into the solution for one standard analysis interfere with the analyses of the other components. After many tests on different procedures using

standard Fe-Cr-Ni alloys, to check the accuracy of the analysis proce­ dure, the analysis procedure in Appendix D. was developed for the ternary condensates. 3he relative accuracy of this procedure was better

than 1 percent for 50 milligrams of the standard a llo y s. However, the

Ni analyses on alloys below 5 percent Ni or the Fe analyses on alloys

below 5 percent Fe were accurate to only 2 percent due to the very small

amount of Ni or Fe in the 50 milligrams of sample. All volumetric

apparatus was carefully standardized and the fractional balance weights

used were very accurate.

The accuracy of a ll activities calculated from the analyzed vapor

compositions depend strongly on the accuracy of the chemical analyses.

A check on the analysis is the fact that the total analyzed weight of Fe, Cr, and Ni was always 2 to 3 milligrams less than the weight of the condensate. Preliminary runs, using an empty Knudsen-cell assembly, established that the weight pickup of the pyrex plate was 2 to 3 m illi­

grams for a 3 hour run at 1600°C. This vapor condensate i s from the alumina lid because it is the only part that loses a measurable amount of weight during an empty cell run.

With the above discussion in mind the follow ing procedure was estab- lished for a vapor composition determination run. First, an empty

Knudsen-cell assembly was heated to 1650°C in the same vacuum induction

system to thoroughly outgas the assembly. The cell was removed from the

vacuum furnace and weighed, then the cleaned alloy was added and the

total assembly reweighed. The pyrex target was dried at 110°C and

weighed, after cooling in a dessicator. The Knudsen-cell was then

placed along with the pyrex target in the vacuum induction furnace and

evacuated to a pressure of 1 x 10“^ mm Hg with the aid of heating tape

around the outside of the brass furnace. The heating of the sample to

l600°C was done in 30 minutes. However, 25 minutes was taken to get to

1200°C and the final heating to l600°C was done in approximately 5

minutes. The vacuum never exceeded 2 x 10“^ mm Hg during this .

The temperature was sta b ilized at 1600°C and held for 2.5 to k .S hours

depending on the particular alloy composition being studied. The

temperature was determined with the optical pyrometer every 15 minutes and the grid and radio frequency currents of the oscillator were held at constant values. After completion of the run the pyrex target and

Knudsen-cell assembly were removed and placed in a dessicator. Later they were weighed to determine the condensate weight and the Khudsen- cell weight loss. The condensate was dissolved in the acid solution and the pyrex plate dried and reweighed to be certain its weight was the same as before the run. The dissolved condensate was then analyzed for the components present. The a llo y was also reanalyzed after the run be­ cause there i s a composition change during the run due to the differences in the vapor pressures of Fe, Cr, and Ni. The liquid alloy composition of the run was taken as the linear average between the in itial and final compositions. Hie averaging introduces negligible error because the composition change was small. The theoretical composition change, confuted from the in itial alloy weight, the Knudsen-cell weight loss, and the analyzed vapor composition was found to agree quite well with the experimental analysis after the run. Since Cr has the highest vapor pressure and Ni the lowest, the Cr concentration in the alloy decreases and the Ni concentration increases during the run. RESULTS AND DISCUSSION

The experimental results w ill be discussed in three sections:

(1) the Fe-Cr system; (2) the Ni-Cr system; and (3) the Fe-Cr-Ni system. The methods for calculating the activities w ill be presented and sample graphical integrations shown.

The liquid iron-chromium system

The equilibrium, vapor compositions were measured by analyzing the condensate from the Knudsen-cell as described in the section on experi­ mental procedure. The alloys studied ranged from N^r ■ .01 to N^r « .1*0.

The temperature of a ll insr estigations was 1600°C. The equilibrium vapor compositions are tabulated in Table U. The experimental vapor compo­ sitions are corrected for the differences in effusion velocities to give the equilibrium vapor composition in the Knudsen-cell. This correction is derived in Appendix E. The equation for the correction is,

where N^r is the equilibrium mole fraction of Cr in the vapor phase,

NV * is the mole fraction of Cr in the condensate, and M and ML are Cr Cr Fe the average molecular weights of Cr and F e, respectively.

77 78

TABLE ii

EXPERIMENTAL EQUIUBRIUM VAPOR COMPOSITIONS IN THE IRON-CHROMIUM LIQUID SYSTEM AT l600°C

"Sr NFe NCr NFe

O.OIOO 0.990 0.0385 0.9615

.0500 .950 .181 .819

.0963 .9037 .287 .713 CD 1-J • p- .852 .399 .601

.195 .805 ,h8$ .515

.295 .705 .619 .381

0.397 0.603 0.720 0.280 7 9

The a c tiv itie s o f Cr and Fe were calculated from the vapor compo­ sitions by the equations presented in the section on Theoretical Basis and Appendix B. The equations used were,

( 2)

(1) ■*( 2 )

The reference a c tiv ity for Cr, a ^ , i s from the mass spectrometer study of the Fe-Cr system by Reese (10). Reese’s work was part of the over­ all research program which included the results presented in this thesis.

The reference state chosen was the 30 atomic percent Cr alloy. This reference state activity was chosen for two reasons. First the activity of Cr determined by the mass spectrometer from a ratio of intensities should be more accurate, in general, for a higher Cr percentage such as the 30 percent chromium alloy. Secondly, the activity of Cr determined for the 30 percent and higher Cr alloys were more accurate than the lower percent Cr alloys because the mass spectrometer constant, k^, was reproduced better for the higher Cr alloys. The reference activity from Reese's work was a ^ • .3^8 for N^r “ .295 and the activity co­ efficient, is 1.18. The standard state for the Cr activity is 80 pure solid Cr at 1600°C. The reference activity for Pe, a ^ , is the activity of pure liquid Fe at 1600°C, which is unity for the pure compo­ nent activity scale used for all activities in this thesis.

The determination of both a„ and a„ involve the graphical eval- Cr Fe 6 1 uation of the integrals in equations (27) and (28). Figure 10 is the

T T i t plot of (Ncr/Ncr”NFe/Np ^ versus NFe used to graphically evaluate the integral in equation (27). The reference, N^. ■ .295, alloy is marked in Figure 10. The activities of Cr and Fe evaluated from equations (27) and (28) are presented in Table 5, along with the respective activity c o efficien ts. Figure 11 i s a graph of the a c tiv itie s lis te d in Table 5.

From Table 5 it can be seen that the activity of Cr in these liquid alloys shows a slight positive deviation from ideal behavior, and the

Fe activity is essentially ideal for all alloys studied. The result L that the activity coefficient of Cr for the Nqp ■ .01 alloy is lower than that for the Nqj. ■ .05 alloy is felt to be due to experimental

error in either the Nqj, ■ .01 or NQr * .05 alloy vapor composition. The accuracy of the Cr activities derived from the experimental vapor compo­

sitions is directly dependent on the accuracy of the reference Cr

a c tiv ity determined by the mass spectrometer. However, the Fe activity

is not dependent upon a mass spectrometer determination. There is an

alternate method to check the activities of Cr determined in this in­

vestigation. The equilibrium vapor composition is given by, -JO>CJ -JO>CJ ? h J - . Z I Z l- M Vapor Composition Function THE IRON-CHROMIUM VARIATIONFIGURE 10. OF THE BINARY VAPOR l600°C AT COMPOSITION FUNCTION IN WITH N^

- - -2.0 - - 0.8 0.2 0.6 0.4 0.2 . . 0.7 0.4 0.3 tm rcin e n pr e < apor, V in Fe Fraction Atom eeec Aly as pcrmeter Spectrom Mass Alloy Reference 0.5 0.6 0.8 0.9 *6

82

TABLE 5

ACTIVITIES OF IRON AND CHROMIUM IN THE I RON-CHROMIUM LIQUID SYSTEM AT l600°C

a b aCr 4 ■#r ®Fe 1 I

0.0100 0.990 0.0123 1.23 0.990 1 .0 0

.0500 .950 .0635 1.27 .9b8 1 .0 0

.0963 .90^ .111 1.16 ..908 1.01 CO • £ .852 .173 1.17 .857 1.01

.195 .805 .230 1.18 .806 1.00

°.295 .705 .3U8 1.18 .706 1.00

0.397 0.603 0.U70 1.18 0.603 1.00

a The standard state for all chromium activities is pure solid chromium at l600°C.

The standard state for all iron activities is pure liquid iron at 1600°C.

c This alloy is the reference mass spectrometer alloy used to calculate the activity of chromium. BINARY l600°C AT I U E 1 THEFIGURE ACTIVITIES 11. OF IRON AND CHROMIUM THE IN IRON-CHROMIUM

Activities of Components 0.7 0.5 0.8 0.6 0.3 0.2 0.4 0.9 0.2 . 0.4 0.3 tm rcin , N r, C Fraction Atom

0.5 Fe 0.6 0.7 Two Phase Region Phase Two 0.8 0.9 83 where and PpQ are defined by,

Per ‘ aGrPCr (30)

PFe “ aF e ^ e (31)

where p^, and ppQ are the vapor pressures of pure solid Cr and pure

liquid Fe* Substituting equation (30) and (31) into equation (29)

results in,

aCrP8r (32) aCrpCr + aFepFe

Equation (32) provides a method independent of the mass spectrometer to

compute the activity of Cr from the experimental vapor compositions. To

make this calculation the ideal activity of Fe based on this investiga­

tion was used. The pure component vapor pressures used were chosen from

the works of Kubaschewski and Heymer (U) for Cr and Z ellars e t a l. (21)

for Fe. These are the values chosen by Hultgren et al. (50). The

activities of Cr based on the above calculation method, using equation

(32), agree within 3 percent of the values obtained using the mass

spectrometer reference activity and equation (27). It should be noted

that if the standard state for the Cr activities was chosen as pure

supercooled liquid Cr at l600°C, the activity coefficient for Cr would L L be essentially 1.00 for all but the ■ .01 and NCr * .05 alloys.

This is because the vapor pressure of supercooled liquid Cr is approxi­

mately 17 percent greater than that for the stable pure solid Cr at l 600°C. Therefore the Fe-Cr liquid system is essentially ideal if the standard states are the liquid pure elements.

The results of this investigation agree with the mass spectrometer investigation of Reese (10), except for the activities of Cr for Cr con­ centration below NQr * .15. Reese's Cr activities are about 15 percent higher for the a llo y s below KCr " .1 5 . However, the a c tiv itie s of Cr, for the low Cr alloys, found in this investigation are much lower than those obtained by Lyubimov aid Granovskaya (12) using the Langrauir free L evaporation technique. Their Cr activity, at Ngr * .10, is about 90 percent higher than that found in this investigation. The negative deviation from id ea l behavior found by Wada e t a l. (13) was not con­ firmed. The activities of the liquid Fe-Cr alloys found in this inves­ tigation are lower than the activities of the solid Fe-Cr alloys as determined by the investigations previously cited. This result is suggested by the minimum in the liquidus and solidus lines in the Fe-Cr phase diagram.

The nickel-chromium liquid system

The equilibrium vapor compositions were measured by analyzing the condensate from the Knudsen-cell. Hie alloys studied ranged from L L Ngr * .01 to Ngr ■ .50. The temperature of a ll vapor composition deter­ minations was l600°C. Also the activities of Cr and Ni were measured directly by the mass spectrometer for two alloys, the * .10 and

N*jr = .20 alloys at temperatures of l600°, 1650°, and 1700°C. The experimental vapor compositions, corrected for differences in effusion velocities, are listed in Table 6. flnese vapor compositions have also been corrected to nominal Cr alloy compositions. This correction was very slight because the average Cr concentration was always within

2 percent of the nominal compositions listed in Table 6. Listed at the bottom of Table 6 are the equilibrium vapor compositions determined from the mass spectrometer intensity data for the two alloys investi­ gated by the mass spe ctr cane ter. The vapor compositions were calculated from the equations,

-.■■CT ^ . C c r Acr ,-g 2______(33) Icr/ (TCrACr-52 + " W (TNiANi-58

(5~NiANi-58 (3U) Icr/ $~Cr&Cr-52 + lNl/ <5NiANi-58 where ICr and Ij^ are the ion intensities for the mass 52 isotope of Cr and the mass 58 isotope of Ni, (J~Cr and <5 "~n i are the rela'fcive ionization cross-sections of Cr and Ni for singly charged ions from the paper of

Otvos and Stevenson (5l), and A^ ^ and Ajfi_cj8 are the isotoPic a b i­ dances of the mass 52 isotope of Cr and the mass 58 isotope of NI from the American In stitu te of Physics Handbook (1*1). The agreement between the two methods of vapor composition determination w ill be discussed in 87

TABLE 6

EXPERIMENTAL EQUILIBRIUM VAPOR COMPOSITIONS IN THE NICKEL-CHROMIUM LIQUID SYSTEM AT 1600°C

L L V ..V NCr VNi NCr Ni

0.010 0.990 0.0289 0.971

.030 .970 .0966 .903

.050 .950 .156 .81+1+

.100 .900 .309 .691

.200 .800 .580 .1+20 o o

• .700 .790 .210

.1+00 .600 .863 .137

.500 .500 .928 .0716

.100 a .900 .323 .677

0.200 3 0.800 0.599 0.1+01

a Equilibrium vapor compositions for these alloys determined by the mass spectrometer. 88 the Fe-Cr-Ni results section. Figure 12 is a graph of the vapor compo­ sitions listed in Table 6, also shown in Figure 12 are the vapor compo­ sitions based on the assumption that the solution is ideal. Die pure vapor pressure data for Cr and Ni were again taken from the data of

Kubaschewski and Heymer (U) and Zellars e t a l. (21). Note that the experimental and ideal solution curves intersect for both Cr and Ni.

This would indicate the possibility of both positive and negative activity behavior in the Ni-Cr liquid system. Die activities of Cr and

Ni were calculated from the vapor compositions by the equations,

A 2) (2) wv(2) r ml nl

- to-T7Tr ♦ (35) 3Cr N ^ 1 NCr NNi J(l)

w y ( 2 ) 1 n l v L In . In % , \ , Ni NCr , „.v . - n r * \ ^ ® or <3«) Ni % i \ Ni N0r

1 ^ (1> The reference a c tiv ity for Cr, a^ , was taken from the mass spectrom­

eter determinations on the Nqj, * .10 and N^r ■ .20 a llo y s. The same

results were obtained using a^' for the NQr ■ .10 alloy or the

NQr - .20 alloy. The reference activity, a ^ , for the N^ - .10 alloy

was .0$5l and the activity coefficient .55. The standard state for the

Cr activity is pure solid Cr. The reference activity for Ni, a^ P , was

unity for the pure liquid nickel standard state. I U E 2 GRAPHFIGURE 12. OF THE EQUILIBRIUM VAPOR COMPOSITIONS THE IN NICKEL- CHROMIUM BINARY C AT 1600 Atom Fraction in Vapor Phase 0.9 0.7 0.2 0.4 0.5 0.6 0.8 0.3 0.1 1 .0 0 0 0.1 0.2 . 0.50.4 0.3 tm Fr i , N i, N n tio c ra F Atom 0.6 EGEND - xei ental Experim - C i □ O Ni Vapor Composition Composition Vapor Based on Ideal Solution Ideal on Based ~- rmental n e erim p x -E N~ 0.7 0.8 0.9 1.0 89

The determination of a and a„ from the experimental vapor compo- Cr Ni sition data and reference activities involves the graphical evaluation of the integrals in equations (35) and (36). Figure 13 is a graph of

^NCr/Nv “^Ni/Nv. ^ versus NNi used to evaluate the integral for a ^ in equation (35). The reference alloy is indicated on Figure 13. The a c tiv itie s of Cr and Ni evaluated from these equations are lis te d in

Table 7 along with the activities of the two alloys determined by the mass spectrometer. Figure lU is a smoothed graph of the a c tiv itie s of

Ni and Cr at l600°C. Also the activity curves are projected up to and through the two phase, liquid plus solid region at 1600°C. The phase boundaries are taken from the work of Williams (22). Figure lh quanti­ tatively shows both the positive and negative activity deviations that were predicted qualitatively from the plot of the experimental and ideal

solution vapor composition curves shown in Figure 12. At the low Cr

concentrations of N^r ** .01, .03, .05, and .10, the Cr activity displays

strong negative deviation from ideal behavior. Hie activity coefficient

o f Cr in th is concentration range i s approximately .5. With increasing

Cr concentrations the Cr activity coefficient increases from .5 to 1.0

at N^ * .30, then increases to 1.3 at N^r » .50. The nickel activity

displays negative deviation for all alloys studied. The activity co­

efficient for Ni was .6? for the »Ki - .50 alloy. -ia H NCE - H O I M IA Y T 60C Ni THE NICKEL-CHROMIUM VARIATIONFIGURE . 3 1 OF THE VAPOR BINARY COMPOSITION 1600°C AT FUNCTION FOR WITH N^ > o z >

Vapor Composition Function z z

3 - -4 -2 -5 -6 eeec Aly s Seto eter Spectrom ass M Alloy Reference 0.2 0.3 Atom Fraction Ni in Vapor,N in Ni Fraction Atom 0.4

0.5

0.6 v 0.7 0.8 0.9 1 9

92

TABLE 7

ACTIVITIES OF NICKEL AND CHROMIUM IN THE NICKEL-CHROMIUM LIQUID SYSTEM

Temperature T L a b . » °C N„. nCr p Ni aCr ^ C r aNi V w i

1600 0.010 0.990 0.001*70 0.1*7 0.989 1.00

II .030 .970 .011*6 .1*9 .966 1.00

II .050 .950 .021*8 .50 . 91*6 1.00

II .100 .900 .0551 ° .55 .887 0.99

II .200 .800 .11*6 .73 .751 . 91*

11 .300 .700 .310 1.03 .587 .81*

It .l*oo .600 .1*35 1.09 .1*92 .82

It .5oo .500 .61*1* 1.29 .31*5 .69

Mass Spectrometer Activity Results

1600 .100 .900 .0551 .551 .891* .991* 1650 ii i i .0552 .552 .891* .991* 1700 it it .0553 .553 . 891 * .991*

1600 0.200 0.800 .11*8 .71*0 .71*8 .935 1650 i i II .153 .765 .751* .91*3 1700 i i It 0.157 0.785 0.759 0.91*9

a The sta n d a rd state for the chromium a c t i v i t i e s is pure solid chromium. b The standard state for the nickel activities is pure liquid n ic k e l. Q This chromium activity is the reference mass spectrometer activity used in equation (35). •FIGURE THE ACTIVITIES . 4 1 OF CHROMIUM AND NICKEL THE IN NICKEL-CHROMIUM BINARY C 1600 AT Activities of Components 0.3 0.8 0.9 0.5 0.2 0.4 0.6 0.7 0.2 0.3 Atom Fraction C r. N r. C Fraction Atom 0.4 Cr 0.5 Two Phase Region Phase Two 0.6 0.7 0.8 ------0.9 93

9U

As in the Fe-Cr system, the accuracy of the Cr activity in the Ni-

Cr system, computed from equation (35) > depends on the accuracy of the reference mass spectrometer Cr a c tiv ity . Again one can calculate the Cr activity independent of the mass spectrometer by the equation,

NcrCr — a p° + a — p°7 " (37) Cr Cr Ni Ni where the activity of Ni is from equation (36) using the experimental vapor compositions, and p£r and p ^ at 1600°C are from the work of

Kubaschewski and Heymer (it) and Zellars et a l. (21) resp ectively. Hie activities of Cr computed from equation (37) were found to agree within

5 percent of the values in Table 7, which are based on the mass spectrom­ eter reference Cr activity. The activities of the * .10 and N^r *.20 alloys were measured at 1600°, 1650°, and 1700°C by the mass spectrometer.

From Table 7 it can be seen that the activity of Cr increases with temperature as might be expected for an alloy displaying negative deviation. However, as w ill be discussed in the Fe-Cr-Ni resu lts section, little value can be placed on the absolute magnitude of this increase with temperature because the error in the a c tiv ity measurements i s greater than the change of a c tiv ity with temperature.

There are no reported thermodynamic investigations on liquid Ni-Cr alloys, however, there are four investigations on the activities of solid

Ni-Cr alloys: Grube and Flad (28) j Panish et al. (30)} Kubaschewski et al. (31); and Vintaikin (32). All investigations find that the activity coefficient of Cr increases from about .5 at low Cr concentra- L L tions to 1.0 between N^ ■ .20 and N^r * .30, and then increases sharply as the two phase region is approached. The nickel activity shows negative deviation until the two phase region is reached. This negative and positive deviation for the Cr activity is exactly analogous to the behavior found in this investigation for the liquid Ni-Cr alloys.

The Ni-Cr system exhibits a eutectic at N^r ■ .5U and 13l*3°C. The eutectic would favor positive deviation in the liquid alloys. Positive deviation is displayed by the Cr activity in the concentration region of the eutectic, however, the nickel activity shows negative deviation in the region of the eutectic. Foster (26) found that the additions of small concentrations of Cr to solid Ni lowered the heat capacity of the resultant alloy greatly. This is evidence for strong Ni-Cr interaction which is verified by the strong negative deviation of the Cr activity for the low Cr concentrations. The fact that the liquid Ni-Cr system exhibits the same Cr activity behavior is not unexpected. Fisher (52) reports that in general the structure and physio-chemical properties of liquid alloys near the melting point is similar to that of solid alloys. 96

Ihe iron-chromium-nickel system

Thirty-eight Fe-Cr-Ni alloys were studied in this investigation.

The nominal compositions, temperatures, and method of determination are listed in Table 3 of the section on experimental procedure. Briefly, the compositions studied were along four Cr levels of 5, 10, 20, and 30 atomic percent in the ternary. Along each Cr level, the Fe and Ni con­ centrations were varied between the Fe-Cr binary and the Ni-Cr binary.

The mass spectrometer was used to determine the activities and vapor compositions of 17 alloys and the remaining 21 alloys were studied by determining the equilibrium vapor composition by the condensate analysis method. Four ternary alloys were studied by both methods. Aside from the mass spectrometer determinations, the activity calculations from vapor compositions is more complicated than those in the binary Fe-Cr and Ni-Cr systems. These ternary calculations w ill be explained and illustrated carefully. The mass spectrometer calculations will be discussed first followed by the vapor composition calculations. How­ ever, the tables and graphs of the ternary data w ill include the ternary activities from both determination methods. 9 7

Mass spectrometer determinations

The determination and calculation of a c tiv itie s from mass spectrom­ eter ion intensity data have been discussed. The equation for the cal­ culation of activities was shown to be,

where 1^ is the ion intensity of component i for a particular isotope of i, and I? is the ion intensity for the pure element. The requirement t that the total instrument constant, k^, be essentially the same in both alloy and pure component mass spectrometer determinations was thoroughly discussed. The pure component intensity data of iron, chromium, and nickel were determined by averaging the resu lts from three independent determinations on each element. The averaging was done after the pure component intensity data was corrected to the best straight line of log l!?T versus l/T. The best straight line was determined by the method of least squares. The largest deviation between the three determinations was found to be approximately 8 percent, after each run was computer corrected to the best straight line. This is an indication of the constancy of the over-all mass spectrometer constant, k^, that was ob­ tained for the 9 pure component runs. Figure 15 i s a typ ical graph of log I°T versus l/T for a mass spectrometer run fo r pure Cr, Fe, and Ni. 9 8 5.0

LEGEND Pure Solid Chromium 4 . 8 O A Hs = 85 ,7 0 0

4 .6 A h s = 9 7 ,6 0 0

A Rure Liquid Iron A hv = 9 4 ,5 0 0 4 .4 ^ Pure Liquid Nickel A hv = 9 6 ,1 5 0 4 .2 Electron Energy =50e.v.

4 .0

3 .8 H Z 36 o

3 .4

3 .2

3 .0

2.8

2.6

2 .4

2.2 5.0 5.1 5.2 5.3 5 .4 5.5 5.6 5.7 5.8 5.9 6.0 l / T x I 0 4

FIGURE 15. SECOND LAW DETERMINATION OF THE HEATS OF SUBLIMATION AND \ EVAPORATION FROM MASS SPECTROMETER INTENSITY DATA FOR IRON, CHROMIUM,• AND NICKEL- The points shown are the experimental I°T values and the straight lines through the data were determined by least squares analysis. The heats of sublimation and vaporization, listed in Figure 15, are determined from the slope of the straight lines from equation (11). The heat of sublimation of Cr, given in Figure 15, is 5 percent lower than the value selected by Hultgren et al. (50). The experimental value of the heat of sublimation of Fe is 3.2 percent higher than the value selected by

Hultgren et al., and the heat of vaporization of Fe was 5 percent higher than the selected value. The heat of vaporization of Ni is l.U percent higher than the value selected by Hultgren et al. It was found in the previous investigation by Reese(10) that the heat of sublimation or vaporization could only be reproduced to within 3 or U percent by a

Second Law calculation based on mass spectrometer data. However, the determination of these heats of sublimation and vaporization was not the expressed purpose of this thesis. To make a more precise determination of these heats would require better temperature measurement and many more data points at different temperatures. Absolute vapor pressures were not determined in this research. Therefore, only the ratios of the pure component vapor pressures, obtained in this research, can be com­ pared with the same ratios from previous work. To compute a relative vapor pressure from the pure component ion intensity values we must use

equation (9-A) from Appendix A, 1 0 0

(9-A) 1 Aik'kiSQEj, where only A^, k^, and E^ are a function of the component studied. A^ is the relative isotopic abundance of the isotope of i studied; k^ is the instrument constant involving the ionization cross-section, (J"i> and the geometry of the ionization source; and is the multiplier efficien­ cy for the isotope of i studied. Therefore the relative vapor pressure of Fe compared to Ni is given by,

o X2 PFe AFe-56(SFeEFe-56 (38)

The differences in multiplier efficiencies was neglected in this inves­ tigation because the differences were found to be small for the several isotopes of Fe, Cr, and Ni. The relativ e isotop ic abundances are knowi quite accurately. The relative ionization cross-sections were taken from the paper of Otvos and Stevenson (51). These cross-sections are not obtained from experiments 1 determinations, but are computed from the assumption that the relative total ionization cross-section of atoms are given, to a good approximation, by the weighted sum of the outer, or valence, electrons of the atoms, where the weighting factors are the mean square radii of the valence electrons. Experimental cross-section data, using 75 e. v. electrons, for the rare gases, hydrogen, carbon, nitrogen, oxygen and mercury agree quite sa tisfa c to r ily with the th eoretical crcss- sections. Inghram and Drowart (3U) report that the theoretical values 1 0 1 of Otvos and Stevenson should be used u n til more theoretical and experi­ mental work has been done. The values of the relative ionization cross- sections are 28.0 for Fe, 28.1 for Cr, and 2i*.l* for Ni. Die values of

ApQ ££, ACr and ^ were given in Table 1. The ionization in­ tensities of the pure Fe 56 isotope, the Cr $2 isotope, and the Ni 58 isotope were 2.816, 9.719, and .875 respectively. From equation ( 38 ) and a similar one for PQr/p° » experimental ratios Ppe/p^ and p« / o were found to be 2.08 and 3.76 respectively. From the data of /p Fe Z ellars et a l. (21) for pure Fe and N i, and Kubaschewski and Heymer (1*) for pure Cr, we find the r a tio s , Ppe/p^ 311(1 p8r/pjj! » to be and

3.U2 respectively at 1600°C. The disagreement between these ratios is

5 percent for the Ppe/p° and 9 percent for the p°ry^o ratio, which is not excessive for high temperature vapor pressure measurements. Also the agreement would have been better i f the m ultiplier efficien cy correction and the correction for electron energy above the ionization threshold energy had been applied.

To compute the a c tiv itie s of Fe, Cr, and Ni we use the various forms of equation (5),

_ ^ - 5 6 ®Fe “ i 5------Fe-56

a - JCr-52__ Cr to (UO) Cr-52 It should be noted that the ionization cross-sections and the multiplier efficiencies for Fe, Cr, and Ni cancel out in equations (39), (UO), and

(111) because they are ratios of the same isotope. The intensities of

Fe, Cr, and Ni in the ternary alloys were measured at 166o°C, l650°C, and 1700°C. These values were corrected to the best straight line of log I^T versus l/T as discussed in the experimental procedure section.

However, the measurements of I^i gg in the alloys includes a contribution from the overlooked 58 isotope of Fe. The mass 58 isotope of Fe has a relative abundance of only 0.33 percent. But, this 0.33 percent abundant isotope contributes a very significant amount to the %j _58 peak at a low Ni concentration because the vapor pressure of Ni is lower than Fe, and Ni exhibits strong negative deviation in the ternary a llo y s. The 1 ^ contribution can be computed, with a fa ir degree of accuracy, from the measured value of the Fe 56 isotope in ten sity in the a llo y , and the isotop ic abundances of the mass 56 and 58 Fe isotop es.

The equation for this calculation is,

l F e - 5 8 ■ - f e f r AF9-s8 <«> where is the computed contribution of the Fe 58 isotope to the

Ni 58 in ten sity , IFe_cj£ the measured Fe 56 in ten sity value for the a llo y , and Ape-£Q and ^ the relative isotopic abundances. This calculated 1 0 3 correction was applied to all Ni 58 intensities for the alloy determina­ tions. This correction of ranSed from 25 percent for the

(5Ni-5Cr-9GFe) a llo y to 5 percent for the (2QNi-30Cr-50Fe) a llo y . There was no overlapping of isotopes for the Cr 52 and Fe 56 isotope intensity measurements.

In order to determine the vapor pressure of a solid or liquid com­ ponent using either the conventional Langmuir rate of sublimation method or Knudsen rate of effusion method, the molecular weights of the vapor species must be known. The mass spectrum of Fe, Cr, N i, and th eir alloys contained no measurable amounts of diatomic molecules such as Feg or

FeCr. Therefore, it is safe to assume that the vapor phase is predom­

in ately monatomic atoms of Fe, Cr, and Ni.

The equilibrium vapor compositions for the alloys studied with the mass spectrometer were computed from the ion intensities from equation

(15), I (15) L Bie corrected Ni 58 isotope in te n sitie s were used. The main factors

that determine the accuracy of the vapor compositions determined from mass spectrometer intensity data are these:

1. control of the temperature during all component intensity measurements fo r a given temperature j io U

2. accuracy of the ionization cross-sections taken from work of

Otvos and Stevenson (5l)j and

3. the error introduced by neglecting the effect of the multiplier efficiency, and neglecting the correction for the differences in elec­ tron energy above the threshold or ionization potentials for Fe, Cr, and Ni.

Each of these factors have been discussed with the exception of the difference in electron energy above ionization potential. The variation of ion intensity with the electron energy of the ionizing beam for monatomic atoms has the general form shown in Figure 16. The main features of this curve are: there is no ion intensity until the appearance potential or ionization potential is exceeded; then there is a region of linear increase in the ion intensity for approximately 20 e. v.; the curve then goes through a maximum; and then slowly decreases.

Therefore, neglecting all other contributions, components with different ionization potentials will have different ion intensities at the same electron energy. The ionization potentials for Cr, Fe, and Ni are 6.76,

7.90, and 7.63 e. v. from (53). If the electron energy used was between

10 and 30 e. v. it would have been justifiable to correct each intensity for the energy above the threshold energy. Since an electron energy of

50 e. v. was used the correction is not truly justified. 105

30

ELECTRON ENERGY ( e .v .)ENERGY ELECTRON 20 10 THE ELECTRON ENERGY OF THE IONIZING BEAM FOR M0NA1DMIC ATOMS M0NA1DMIC FOR BEAM IONIZING OF THE ENERGY ELECTRON THE FIGURE 16. TYPICAL GRAPH OF THE IONIZATION INTENSITY VERSUS INTENSITY IONIZATION THE OF GRAPH 16. FIGURE TYPICAL

•H IXISMLNI NOXIVZINOI 1 0 6

The liquid alloy composition was not found to measurably change during a mass spectrometer run as was found for the vapor composition analysis method. This i s because of the shorter duration of the mass spectrometer runs and the fact that the orifice area is about ten times smaller for the Knudsen-cell used in the mass spectrometer.

The equilibrium vapor compositions of the remaining 21 ternary a llo y s were determined by the condensate analysis method. These compositions have been corrected for differences in effusion velocities and a l l vapor compositions were corrected to the nominal Cr concentra­ tions of N^r ■ .05, .10, .20, and .30. The vapor composition data is presented in Tables 6, 9, 10, and U . Each table is for a given nominal

Cr concentration. The vapor compositions of four of the ternary alloys were determined by both the mass spectrometer and the condensate analysis method. The agreement between the two methods i s better than k percent. The agreement was also within li percent for the two a lloys in the Ni-Cr system that were analyzed by both methods. The same per­ centage error was found when comparing the Fe-Cr system vapor compo­ sitions from the condensate analysis with those from the mass spectrom­ eter work of Reese (10). In almost all cases the Cr vapor composition, y Ncr, determined from the mass spectrometer intensities was 3 to 5 per­ cent hi^ier than that obtained by the condensate analysis method. Since the condensate analysis method i s free from any important assumptions, it is felt that these determinations were more accurate. The error in 107

TABLE 8

EXPERIMENTAL EQUILIBRIUM VAPOR COMPOSITIONS FOR IRON-CHROMIUM-NICKEL LIQUID ALLOYS AT l600°C FOR ALLOYS WITH A CONSTANT CHROMIUM CONCENTRATION OF 5 ATOMIC PERCENT

T. L T, Determination 'V Tr XT c Method Np nJ NCr NFs Nx Cr Fe NNi o.o 5o 0.898 0.0518 Mass Spectrometer 0.189 0.799 0.0118

11 .855 .09U7 11 11 .191* .781* .0218

n .813 .137 it n .201 .768 .0318

it .71*7 .203 11 11 .212 .739 .01*91*

it .657 .293 Condensate Analysis .230 .681 .0855

it .24-60 .1*90 11 it .2 33 .560 .207

it .262 .688 11 it .251* .310 .1*36

it .156 .19k it ti .220 .177 .603

it .0988 .851 11 11 .212 .101* .681*

n 0.0528 0.897 11 11 0.182 0 . 01*92 0.769 108

TABLE 9

EXPERIMENTAL EQUILIBRIUM VAPOR COMPOSITIONS FOR IRQN-CHROMIUM-NICKEL LIQUID ALLOYS AT l 600°C FOR ALLOYS WITH A CONSTANT CHROMIUM CONCENTRATION OF 10 ATOMIC PERCENT

Determination N^ Method n J Cr Fe N*rNi Cr Fe 1 1 A

0.100 0.852 0.01*83 Mass Spectrometer 0.335 0.656 0.00869

it .792 .108 it tt .338 .61*0 .0211*

it .756 .11*1* it i i .355 .613 .0322

.. a .718 .182 it it .356 .599 .01*1*7

„ a .718 .182 Condensate Analysis .31*8 .607 . 01*51*

tt .607 .293 i i n .377 .51*7 .0758

it .1*15 .1*85 it it .1*05 .1*13 .182

it .208 .692 tt it .1*21* .199 .377

tt .157 .71*3 tt it .1*01 .11*0 .1*59

tt .105 .795 i i i i .383 .0922 .525 $ O o tt • 0.81*7 it it 0.335 0.01*55 0.620

a The vapor composition of this alloy determined by both methods. 109

TABLE 10

EXPERIMENTAL EQUILIBRIUM VAPOR COMPOSITIONS FOR IRON-CHROMIUM-NICKEL LIQUID ALLOYS AT l600°C FOR ALLOYS WITH A CONSTANT CHROMIUM CONCENTRATION OF 20 ATOMIC PERCENT

S3^ Determination S3

•H Method

NCr blfj-H (D NrCr

0.200 0.71+7 0.0528 Mass Spectrometer 0.539 0.1+53 0.00780 a ti .698 .102 Condensate Analysis .51+1 .1+1+2 .0165

u .662 .138 Mass Spectrometer .559 .1+15 .0260 b n .597 .203 11 tt .561 .1+03 .0361+ b >, II ti Condensate Analysis .563 .399 .0375

11 .506 .291+ 11 it .575 .361 .0638

11 .1+06 .391+ 11 11 .607 .297 .0951+ Co 1 —

II n it • .206 .591+ .631+ 1 .203

It .103 .697 11 11 .622 .0866 .292 b „ 0.051+5 0.71+6 11 11 .616 .0503 .331+ $ 0 b 0 00 it ti 11 Mass Spectrometer 0.637 • 0.313

The alloy run on the mass spectrometer was chemically inhomogeneous. b These alloy vapor compositions were determined by both m ethods. 110

TABLE 11

EXPERIMENTAL EQUILIBRIUM VAPOR COMPOSITIONS FOR IRON-CHROMIUM-NICKEL LIQUID ALLOYS AT 1600°C FOR ALLOYS WITH A CONSTANT CHROMIUM CONCENTRATION OF 30 ATOMIC PERCENT

Determination V Method NpGr Fe £Ni Cr Fe Nx

0.300 0.652 o.oltfl; Mass Spectrometer 0.668 0.326 0.00592

tt .605 .0951 ti it .677 .310 .0131

tt .551; . 1U6 11 it .712 .267 .0205

11 .508 .192 11 11 .708 .267 .0251

it .398 .302 Condensate Analysis .723 .227 .0503

n .307 ,393 it 11 .731; .183 .0829

it .205 .U95 11 11 .757 .128 .115

it .10U .596 11 ti .780 .0659 .1 5 1 ;

3 „ o.o5Ui 0 . 6U6 11 it .791; .036 3 .169 a I? 11 11 Mass Spectrometer 0.790 0.0370 0.172

a This alloy vapor composition was determined by both methods. the vapor compositions determined from the mass spectrometer can be rationalized by considering the effect of the neglect of the differences

in multiplier efficiency and the differences in energy above threshold

for Cr, Fe, and N i. From the data of Inghram and Hess (1*3), concerning

the inverse proportionality between the multiplier efficiency and the mass o f the ion, i t i s found that application of their resu lts would

lower the Cr vapor composition by approximately 2 percent. The ioniza­

tion potential of Cr is approximately 2.5 percent lower than Fe or Ni with respect to the ionizing electron energy of 50 e. v. used in this investigation. If 50 e. v. electron energy was in the linear region

discussed in Figure 16, the above fact would lower the vapor composition

of Cr by 2.5 percent. Therefore, the sum of these two factors could be

k to 5 percent; thus accounting for the observed disagreement between

the two methods of vapor composition measurement. However, the assump­

tion that the ionization cross-sections from Otvos and Stevenson (5l)

are correct is certainly not completely Justified. The author feels the

agreement between the two methods is good considering the high temperatures

and assumptions that were made. In fa ct th is agreement i s in part due

to the similarity in mass, electronic configuration, atomic radius, and

ionization potential of the elements Fe, Cr, and Ni.

Figures 17, 18, 19, and 20 are graphs of the data in Tables 8, 9,

10, and 11. Also shown in Figure 18 are the vapor compositions of Fe, ATOMIC PERCENT FORALLOYS ALLOYS C, 1600 AT THE WITH EQUILIBRIUM CONSTANT AFIGURE 17. VAPOR CHROMIUM COMPOSITIONS CONTENT FOR IRON-CHROMIUM-NICKEL OF 5

Atom Fractions in Vapor Phase 0.8, 021 .5 0 .9 0 .3 0 0.6 0.7 0 .9 5 Fe Fe 5 .9 0 05 Cr C 5 .0 0 0.4 02 .3 0 o acton N, N Ni, n tio c ra F tom A 0.4 LEGEND 0.5 r C 0.6 0.7 0.8 0 .9 0.95 0.95 .9 0 05Cr 5 .0 0 0 .9 5 Ni 5 .9 0 2 1 1 113

LEGEND

0 .9 A N

O N

0.8 □ N

Experimental Base on Ideal Solution 0.7 o c u> 0 .5 c o o a u. 0 .4 E o < 0 .3

0.2

0 0.1 0.2 0.3 0.4 0 .5 0.6 0.7 0.8 0.9 0.90 Fe Atom Fraction N i, N 0 .9 0 N i O.IOCr Ni O .IO C r

FIGURE 18. THE EQUILIBRIUM VAPOR COMPOSITIONS FOR IRON-CHROMIUM-NICKEL ALLOYS AT l600°C, FOR ALLOYS WITH A CONSTANT CHROMIUM CONTENT OF 10 ATOMIC PERCENT ATOMIC PERCENT FORALLOYS ALLOYS C, 1600 AT THEnEQUILIBRIUM WITH CONSTANT A FIGURE 19. CHROMIUM VAPOR COMPOSITIONS , CONTENT 20 FOR IRON-CHROMIUM-NICKEL OF

Atom Fractions in Vapor Phase 0.7 0.8 0.2 0.6 .9 0 0.4 0 .8 0 Fe Fe 0 .8 0 0 .2 0 Cr 0 .2 0 0.3 0.2 o i N , i N n tio c a r F tom A 3 0.4 .3 0 LEGEND .5 0 = 0.20 0.6 .7 0 20 Cr C 0 .2 0 Ni 0 .8 0 0.8

1 1 5

0.9

0.8

CO® v0.7 , ( _c0 > a ^

1 0.6 LEGEND o NT = 0 .3 0 > c in c o o £ 0.4 oE < 0 .3

0.2

0 0.1 0.2 0 3 0 .4 0 .5 0.6 0.7 0 .7 0 Fe Atom Fraction Ni,N 0 . 7 0 N i 0 3 0 Cr 0 .3 0 C r

FIGURE 20. THE EQUILIBRIUM VAPOR COMPOSITIONS FOR IRON-CHROMIUM-NICKEL ALLOYS AT 1600 C, FOR ALLOYS WITH A CONSTANT CHROMIUM CONTENT OF 30 ATOMIC PERCENT Cr, and Ni based on the assumption that the system forms an ideal solution. The pure vapor pressure data used to calculate the ideal solution vapor compositions are from Kubaschewski and Heymer (1*) and

Zellars et al. (22). Qualitatively Figure 16 would suggest that in the iron rich alloys the activity of Cr would exhibit positive deviation while the activity of Ni would exhibit negative deviation. In the Ni rich alloys the activities of both Cr and Fe would seem to exhibit negative deviation. Of course the activity behavior could also be predicted from the activities in the three binaries that form the ternary. Note that In all but Figure 20 the Cr vapor composition goes through a maximum as the Ni-Cr binary is approached then decreases into the Ni-Cr binary.

The activities of the 21 ternary alloys, not determined directly by the mass spectrometer, were calculated from the experimental vapor compositions determined by the condensate analysis method* using equation (26) in the Theoretical Basis Section. For the activity of

Cr equation (26) becomes, 1 1 7

In a l l cases the reference a c tiv itie s of Cr, Ni, and Fe were the a ctiv ­

ities determined by the mass spectrometer for the nominal ■ .20

alloys. The integration paths were along the four constant Cr alloy

concentration lines of Nqj. * .05, ■ .10, N^r * .20, and N^r ■ .30.

The four reference alloys have the nominal compositions of (5Cr-20Ni-

75Fe), (10Cr-2QNi-7QFe), (20Cr-20Ni-60Fe), and (30Cr-20Ni-5(Fe). These

reference mass spectrometer alloys were chosen for three reasons; (1) it was felt the accuracy of the activity of Ni was greatest for the 20

atomic percent Ni alloys because this was the highest Ni concentration

determined by the mass spectrometer and the contribution of the Fe 58

isotope is least significant for the 20 percent Ni alloys; (2) the vapor

compositions of two of the four reference alloys were determined by both

the mass spectrometer and the condensate analysis methods and the agree­

ment between the two methods was good; and (3) the integration path

passes only through alloys in which th eir vapor compositions were deter­

mined by the more accurate condensate analysis method. The integration

path was chosen along the constant Cr concentrations because the vapor

composition data was determined along these paths and no interpolation

of data was required. The integration paths from reference state (1)

to a given state (2) are shown schematically in Figure 21 for the four

integration paths in the ternary alloys. The calculations of the activities from equation (26) is discussed in more detail in Appendix F 1 1 8

Cr

0.30

0.20 --(I) (2)

0.10 (2) 0.05 (2)

F* 0.20 Ni

FIGURE 21. INTEGRATION PATHS FROM STATES ( l ) TO (2) IN TERNARY IRON-CHROMIUM-NICKEL ALLOYS 1 1 9 along with typical graphs used to evaluate the integrals in equation

(26).

Hie activities in the ternary states (2) were calculated at the same liquid alloy compositions at which the vapor compositions were determined. Also the data used to evaluate the terms in equation (26) were the experimental vapor compositions. The data was not smoothed in any manner. Therefore, the a c tiv itie s calculated from the vapor composition data should reflect any errors in the data.

The accuracy of the activities calculated from equation (26) depends directly on the accuracy of the reference activities determined by the mass spectrometer. However, the a c tiv itie s of Fe and Ni can be cal­ culated for a ll ternary alloys without the use of a mass spectrometer reference activity by using the activities of Fe and Ni in the Fe-Ni binary system as the reference activities in equation (26). The reference binary a c tiv itie s were taken from the work of Zellars et a l.

(21). This activity determination was very carefully done by the inert carrier gas method. The binary vapor compositions were computed from their pure vapor pressure and activity data. The only problem with the calculation for the Fe-Ni binary is the extrapolation of the ratio

NGr/Nv Jfrom ^Cr ” to Ncr “ °* extrapolation was made by plotting the experimental values of Nq^ v versus N ^ f 0r ternary allqj® with a constant Ni content for the Fe rich alleys, and N^ ,„v versus / Cr 120

NQr for alloys with a constant Fe content for Ni rich alloys. Ihese two

extrapolation methods were used because the integration path of equation

(26) was along a constant nickel concentration for the Fe rich alloys and

along a constant Fe concentration for the Ni rich alloys. The calcula­

tion of the activities of Fe and Ni from the reference Fe-Ni binary is

demonstrated in Appendix F.

The activities in the liquid Fe-Cr-Ni alloys are listed in Table 12,

13, 111., and 15. Die four tables are for the four Cr levels of N^r * .05,

■ .10, NQr « .20, and N^r * .30. Each table lists the temperature,

the liquid alloy composition, and the determination or calculation method used to obtain the activities. Due to limited space in the tables

the determination or calculation method is abbreviated. The three cal­

culation methods have been thoroughly discussed. The abbreviations re­

present the following calculation methods.

M. S.'aj_ and M. S. refer- to activities and activity coefficients that

were directly determined by the mass spectrometer, from the ratios of

alloy component ion intensities to pure c o m p o n e n t ion intensities.

M. S. Ref. a^ and M. S. Ref. refer to activities and activity co­

efficients that were determined from the equilibrium vapor compositions

by equation (26) in which the reference activity, a^^, was determined

d irectly by the mass spectrometer. In each table th is reference allo y TABUS 12

ACTIVITIES OF IRON, CHROMIUM, AND NICKEL IN THE IRON-CHROMIUM-NICKEL TERNARY SYSTEM FOR ALLOYS WITH a CONSTANT CHROMIUM CONCENTRATION OF 5 ATOMIC PERCENT

I M. S. M. S. M. S. M. S. Fe-Ni M. S. M. s . M. S. M. S. M.S. M. S. M. S. M. S. Fe-Ni R ef. R ef. Ref R ef. R ef. R ef. R ef. R ef. T°C & 4 ^ F e aFe *$Fe aFe aCr aCr $ r a Ni aNi / n i

1600 O.898 0.050 0.0518 0.915 1.02 0.0565 1.13 0.0570 1.14 0.0276 0.5 4 0.52 It it n 1650 .916 1.02 .0558 1.12 .0285 .55 tl ti 1700 " .918 1.03 .0549 1.10 .0292 .56

1600 .855 .050 . 09^7 .850 0 .9 9 1.03 .0561 1.12 .0571 1.14 .0491 .52 .52 M 1650 "" .855 1.00 .0536 1.07 .0510 .5^ 1700 n 11 11 .860 1.01 .0510 1.02 .0523 .55

1600 .813 .050 .137 .829 1.02 1.04 .0568 1.14 .0575 1.15 .0704 .52 .51 II 11 11 1650 .826 1.01 .0569 1.14 .0797 .58 II tt 1700 " .823 1.01 .0572 1.14 .0851 .62 a 1600 .7^7 .050 .203 .765 ' 1.02 1.05 .0583 1 .1 6 .106 .52 .55 tt tt 1650 " .763 1.02 .0587 1 . 1? .112 .55 tl tt tt 1700 0.762 1.02 0.0591 1.18 0.117 0.58

1600 .6 57 .050 .293 0.652 0 .9 9 1.05 .0583 1.16 0.169 0.5 8 .58 1600 .460 .050 .490 .421 .92 1.00 .0519 1.04 .357 .73 .71 1600 .300 .050 .650 .242 .81 0.8 5 .047 0 .9 4 .539 .83 .82 1600 .262 .050 .688 .19^ .74 .0446 .89 .600 .87 1600 .156 .050 .79^ .0987 .63 .65 .0344 .69 .738 .93 .95 1600 .0988 .050 .851 .0562 .57 .62 .0319 .64 .807 .95 .96 1600 0.0528 .050 .897 0 .0 2 5 4 0.48 0.51 .0264 .53 .876 .98 0.9 9 1600 - .050 .950 .0221 .44 .941 .99 1 b1600 - 0.050 0.950 J 0.0248 0.49 0.946 1.00 1

a This alloy la the reference mans apectroneter alloy.

b The activity valuee are from the nickel-chromium binary calculationa. TABUS 13

ACTIVITIES OF IRON, CHROMIUM, AND NICKEL IN THE IRON-CHROKIUM-NICKEL TERNARY SYS1EM FOR ALLOYS WITH A CONSTANT CHROMIUM CONCENTRATION OF 10 ATOMIC PERCENT

M. S. M. S. M.S. M. S. Fe-Ni R ef. R ef. Ref, M. S. M. S. M. S. M. S. M. S. M. S. V C !•!. S. Fe-Ni T°C NFe £ NN-Ni R ef. Ref. R ef. R ef. R ef. aFe *$Fe aFe 'jjpe a0 Cr Tfcr aCr ''fc r a Ni ^ N i aNi Y ni ^ N i 1.03 1600 0.852 0.100 0.0483 0.877 0.119 1.19 1.18 0.0260 0.50 0 .4 9 11 11 1.01 1650 " .859 .113 1.13 .0266 .55 It It .862 1700 " 0 .9 9 .107 1.07 .0289 .60

.100 .108 .99 1.03 1600 .792 .783 .110 1.10 1.16 .0563 .50 .51 1650 11 .. 11 .755 .95 .106 1.06 .0561 .52 1700 11 n M .729 .92 .103 1.03 .0579 .56

1600 .756 .100 ,166 .731 .97 1.02 .113 1.13 1.17 .0799 .55 .56 1650 11 .. II .735 .9? .106 1.06 .0776 .56 1700 II .739 0.98 .100 1.00 .0766 .52

a i6on .718 .100 .182 .717 1.00 1.03 .113 1.13 .111 .61 .60 1650 It 11 .721 1.00 .112 1.12 .112 .62 1700 „ II M 0.726 1.01 .110 1.10 .113 .62

1600 .607 .100 .293 0.612 1.01 1.06 0.112 1.12 0.177 0.60 .61 1600 .615 .100 .686 .372 0.90 0.95 .0968 0.97 .360 .70 .72 1600 .250 .100 • 650... .190 .76 .82 .086 .86 .509 .79 .82 1600 .208 .100 .692 .166 .69 .0816 .81 .561 .81 1600 .157 .100 .763 .0966 .60 .65 .0715 .72 .638 .86 .92 1600 .105 .100 •795.. .0597 .57 .63 .0652 .65 .697 .88 .94 1600 0.0530 .100 .867 0.0275 0.52 0 .5 5 .0532 .53 .767 .91 C.97

... 1600 _ 0.100 0.900 0.0551 0.55 0.0676 0.68 0.896 0.99 0.S25 J 0.92 122 a This alloy Is tha reference mass spectrometer alloy. TABU) Uj

ACTIVITIES OF IRON, CHROMIUM, AND NICKEL IN 3HE IRON-CHROMIUM-NICKEL TERNARY SYSTEM FOR ALLOYS WITH A CONSTANT CHROMIUM CONCENTRATION OF 20 ATOMIC PERCENT

Fe-Ni Fe-N: Ref, R ef. Ref, Ref, R ef. Ref, Ref, Cr R ef. >Fe lCr Cr

1600 0.0528 1.01 0.230 1.19 0.0267 0.50 1650 1.01 .219 0289 1700 1.02 ,209 1.09 0317 ll600 ,700 ,200 100 1.20

1600 662 ,200 138 ,235 1.18 1.20 £851 .62 1650 659 ,226 1700 ,660 ,218 1.09 ,0847

*1600 122 . ,200 ,203 .221 118 1650 ,603 1.01 ,229 ■ 120 1700 ,22S 122

1600 306■ 200 0 .2 2 0 0.191 1600 .906 ,200 ,218 269 1600 300 ,200 iOO ,292 ,213 1600 ,206 ,200 183 JOi ■938 1600 ,200 630 130 1600 103 ,200 697 .0866 1600 ■ 200 ,0525. 178 676169 ■ 90 628 0.90 1630 181 .682 1700 183 686

1600 0 .2 0 0 0.800 0.138 0.69 0.702 0.88

a The alloy run on mass spectrometer was chemically inhomogeneoua. H ro ^ This alloy is the reference maaa spectrometer alloy. t a b u ; 15

ACnVTilSS OF IRON, CHROMIUM, AND NICKEL IN H E IRON-CHROMIUM-NICKEL 1ERNARY SYS3EM FOR ALLOYS WITH A CONSTANT CHROMIUM CONCENTRATION OF 30 ATOMIC PERCENT

Fe-Ni Fe-Ni Ref, Ref. Ref. Ref. Ref. ‘Cr

1600 0.687 1.23 0.52 1650 1.02 1.19 ,0272 1700 ,0281

1600 ,606 i222. 342. 1650 1700 ,602

1600 ,300 1650 322 ,0838 1700 221 ■ 0820

‘1600 507 ■ 301 192 322. 105 3Z2 132.

0.189 322. .282 1600 322. 371 1600 ,300 141 .77 1600 104 321 ■ 78 1600 322 ■222. 0.77.79 0.78 1650 1.00 1700 1.01 0.80 1600 ,300 i222 2 S i '1600 0.300 0.700

* This alloy is the reference mass spectrometer alloy.

^ The activity values are from the nlckel-chrcnium binary calculations. 1 2 5 is the nominal = .20 alloy for the particular Cr content of the ta b le.

Fe-Ni ^ refer to activity coefficients of Fe and Ni that were deter­ mined from the equilibrium vapor compositions by equation (26) in which the reference activity, ap ), was the activity of Fe or Ni in the Fe-Ni binaiy. This reference Fe-Ni a c tiv ity data was taken from the work of

Zellars et al. (21).

Figures 22, 23, 21*, and 25 are graphs of the activities showi in the previous tables. In general the activities plotted on the graphs were determined either by the mass spectrometer or by using equation

(26) with a mass spectrometer reference activity. Table 12 and Figure

22 present the ternary activities for the 5 atomic percent Cr alloys.

The important features to note ares in the Fe rich alloys the activity of Cr is slightly positive; the Ni activity is strongly negative with an activity coefficient,'^^, of about .52; and the Fe activity is

essentially ideal. As the Ni content of the alloys increases the

activity coefficients of Fe and Cr slowly decrease below the ideal value of 1.0, and the Ni activity coefficient increases rapidly towards ideal behavior. As the Ni-Cr binary is approached the activity coefficients

of Fe and Cr decrease more rapidly to about .50 for the N^e * .05 alloy,

and the activity coefficient of Ni increases to almost 1.0. The agreanenb 126

LEGEND N p = 0 .0 5

0.9

0.8 □ a

— Ideal Behavior « 0.7 a>C c o f 0.6 oo o o« 0 .5 >

< 0.4

0 .3

0.2

0.2 Q 3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 0.95 Fe Atom Fraction N i, N 0.95 Ni 0.05 Cr 0 .0 5 Cr

FIGURE 22. THE ACTIVITIES OF IRON, CHROMIUM, AND NICKEL IN THE IRON- CHROMIUM-NICKEL SYSTEM AT 1600 C, FOR ALLOYS WITH A CONSTANT CHROMIUM CONTENT OF 5 ATOMIC PERCENT IU E 3 THE CHROMIUM, ACTIVITIES OF IRON,FIGURE 23. AND NICKEL THE IRON- IN CHROMIUM-NICKEL SYSTEM FOR ALLOYS 1600°C, AT WITH CONSTANT A CHROMIUM CONTENT ATOMIC 10 OF PERCENT

Activities of Componets .4 0 .3 0 .7 0 .5 0 0.6 0.8 .9 0 0.2 . OCr C O 0.1 Fe 0 .9 0 0.2 .3 0 tm acton NiN|- i,N N n tio c ra F Atom LEGEND a A 4 0.5 0 .4 0 da Beha or io av h e B Ideal 0.6 0.7 0.8 0 C r 10 . 0 Ni 0 .9 0 9 .9 0 7 2 1 I U E 4 THE CHROMIUM, ACTIVITIES IRON, OFFIGURE 24. AND NICKEL THE IRON- IN CHROI'HUM-NICKEL FOR ALLOYS SYSTEM , l600°C AT WITH CONSTANT A CHROMIUM CONTENT ATOMIC 20 OF PERCENT

Activites of Components .7 0 0.6 0.8 0.2 .3 0 .5 0 .9 0 0.4 80 Fe e F 0 .8 0 Cr C 0 2 0 0.1 0.2 o aton Ni N i, N n ractio F tom A 3 0. .5 0 .4 0 .3 0 LEGEND Cr 0.6 0.7 .0 Ni 0.80 20 r C 0 .2 0 0.8

128 129

LEGEND

0 .9

0.8

ideal Behavior 0 .7

a.

0 .5

> 0 .4

0 .3

0.2

0.2 0.40.3 0 .5 0.6 0 .7 0.70 Fe Atom Fraction N i- N V;. 0.70 N i 0 .3 0 Cr ’ Ni 0 .3 0 C r

FIGURE 25. THE ACTIVITIES OF IRON, CHROMIUM, AND NICKEL IN.THE IRON- CHROMIUM-NICKEL SYSTEM AT l600°C, FOR ALLOYS WITH A CONSTANT CHROMIUM CONTENT OF 30 ATOMIC PERCENT between the Fe and Ni activities determined from the three different methods i s good. The maximum disagreement is about 8 percent. This maximum disagreement occurs for the activity of Fe in the Ni rich alloys.

The activity of Fe calculated from the reference Fe-Ni binary is 5 to 8 percent higher than the Fe a c tiv ity calculated from the mass spectrometer reference. Also shown is the agreement between the activity of Cr in the Ni-Cr binary obtained from integrating equation (26) across the ternary to the Ni-Cr binary and the same Cr activity obtained from the

Ni-Cr binary calculations discussed previously. The Cr activity obtain­ ed by the ternary integrations is 10 percent lower than the value ob­

tained hy the Ni-Cr calculations. It was found in general the activities

of Fe, Cr, and even Ni, for alloys in or near the Ni-Cr binary, calcu­

lated from equation (26), using the mass spectrometer reference N^ * .20

a llo y , were from 5 to 10 percent lower than the a c tiv itie s obtained by

either direct mass spectrometer determinations, integrations from the

Fe-Ni binary, or determinations from Ni-Cr binary data only. I t cannot

be stated precisely that a set of activities calculated in one manner

is the most accurate, because the disagreement could be caused by

several reasons. However, it is felt that the higher activity values

obtained by the more direct or shorter integration paths are the more

accurate for the alloys near the Ni-Cr binaiy. This conclusion is based 131

on two reasons. First, the lower activity values were obtained from

long integration paths across the ternary and therefore a greater cumu­

lative error in the graphical integrations probably exists. Second, the

activity of Ni, calculated from integration across the ternary, from the

= .20 reference, is not as close to the ideal solution value as one would expect far these Ni rich a llo y s.

Hie temperature dependent activity data determined by the mass spectrometer is presented in the tables. The result that the activity

of Cr decreases towards id ea l with increasing temperature and the activity of Ni increases towards ideal with increasing temperature, for

the Fe rich alloys, is felt to be correct. However, the magnitude of

the change with temperature is often smaller than the precision of the mass spectrometer activity measurements. The heats of solution or

mixing, calculated from the temperature dependency of the activ­

i t i e s ranges rather randomly from -2500 to +1*000 calories/m ole. I t is

well established that small heats of mixing can not be determined

accurately from vapor pressure measurements, because the errors in the

measured vapor pressures and a c tiv itie s are greater than the a c tiv ity

changes with temperature. Hie heats of mixing, calculated from the

regular solution approximation, range from -200 to -500 calories per

mole for the iron rich ternary alloys. 132

The activity values obtained in this research for the N^ ■ .05

ternary alloys can be compared with the results obtained in the Fe-Ni

binary at l600°C from the work of Speiser, Jacobs, and Spretnak (20)

and Zellars et al. (21). These investigations found the activity co-

t L efficient of Ni was .66 at N^ “ 0, .67 at N^ * «10, and .69 at L L N * .30. The activity coefficient of iron was .1*0 at N„ * 0, .1*8 at Ni N^ * .10. and .70 at n £ * .30. From the data in Table 12 the activity Fe Fe coefficient of Ni is .52 at N^ ■ .10 and .58 at N^ ■ .30. The activity

coefficient of Fe is .59 at N^e ■ .10 and .83 at N^e ■ .30. Therefore,

from this research, the addition of Cr to Fe-Ni liquid alloys decreases

the activity of Ni in Fe rich alloys and increases the activity of Fe in

Ni rich alloys. Also from the data in Table 5, on the Fe-Cr system, it

is found that the addition of Ni to Fe-Cr alloys lowers the activity of

Cr for the NCr“ .05 alloys. Therefore the interaction between Ni and

Cr is negative for the Fe-rich ternary alloys. The interaction co­

e ffic ie n ts discussed in Appendix C can be calculated from the data in

Table 5, 7, aid 12, and the Fe-Ni binary data of Zellars et al. (21). ^ Ni ^ rjr The interaction coefficients £ Qr and can be calculated for iron

base a llo y s, where

C Ni » "d1*1 V cr P Cr , ^ In V N1 . For nickel base Cr — and Ni 0 Nm 0 Cr alloys the interaction coefficients and can be calculated, 133

, cCr ^ CFe _ ^^Vcr C Fe " t ancl CCr — ” ""t' 1 . Hie results are given a ^ r a % e in Table 16. Hiese interaction parameters are approximate due to the limited accuracy of the activity data, however the signs and the approximate magnitude are f e l t to be correct.

TABLE 16

INTERACTION PARAMETERS IN THE IRON-CHROMIUM-NICKEL LIQUID SYSTEM AT 1600°C

e g ■ - k -° Iron Base Alloys

£ c r ' - 2-5

££ «- .6 Nickel Base Alloys

E o" ■ +2' 7

At infinite dilution, should equal and should equal £ q®.

Hiis equality is approximately fulfilled for£Cr and £j.e> but it is not met for and Hie inequality could be due to lack of the infinite dilution requirement or to experimental errors in the binary and ternary data used to make the calculations. The inequality is probably due to both reasons. 13U

Table 13 and Figure 23 represent the ternary a c tiv itie s found for the 10 atomic percent Cr alloys. The only major difference in the

» .10 a lloys from the Nqp ■ .05 alloys is that the activity of Cr is less affected by the addition of Ni to the Fe-Cr alloys. Also the activities of Cr and Fe do not decrease quite as much for alloys approaching the Ni-Cr binary.

Table ill and Figure 2k represent the activities of the ternary alloys for the 20 atomic percent Cr alloys. The important difference from the previous Cr levels is the fact that the Fe and Cr activity co­ efficients do not decrease nearly as much as the Ni-Cr binary is approached. The activity coefficient of Fe for N^q ■ .05 has increased from .53 to .85 with a change in Cr concentration of N^r ■ .10 to L NCr * .20. The activity coefficient of Cr undergoes the same rapid increase toward ideal behavior. This same Cr activity behavior was found in the Ni-Cr binary.

Table 15 and Figure 25 represent the activities of the ternary alloys for the 30 atomic percent Cr alloys. The activity coefficient of Fe and Cr decrease only slightly as the Ni-Cr binary is approached.

In fact the activities of Cr and Fe are essentially ideal for the

(30Cr-65Ni-5Fe) alloy. The activity coefficient far Ni is .79 for this alloy. 1 3 5

Table 17 is a list of the free energy of mixing values for the alloys along the four constant chromium concentrations of 5, 10, 20, and

30 atomic percent. They are computed from the equation,

A l" - HT (HCrlnaCr ♦ NFelnaFe ♦ (U3)

The activities used in equation (U3) were the average of the values presented in Tables 12 through 1$, if there was more than one method used to calculate the activities. The alloy with the minimum free ener­ gy was the (30Cr-30Fe-iiCNi) a llo y . In Table 17, the excess free energy of mixing, F*3, is also listed for all alloys. The excess free energy of mixing is given by,

I " - RT(N0j> y Cr ♦ Nreln y Fe ♦ NNiln f a (to)

Figure 26 i s an iso-excess free energy of mixing diagram for the Fe-Cr-

Ni alloys studied in this investigation.

The agreement between the ternary Fe-Ni-Cr vapor compositions ob­ tained in th is investigation and those obtained by Lyubimov, Granovskaya, and Berenstein (33) is poor. The Cr vapor compositions determined by the above investigators were about 2 to 3 times higher in the Fe rich alloys and about 3 times lower in the Ni rich alloys. Their data would indicate a much larger positive deviation for the Cr activity, in the

Fe rich alloys, and a much larger negative deviation for the Cr activity,

in the Ni rich alloys, than found in this investigation. They obtained

the vapor condensate by evaporating from a free liquid surface contained 136 TABLE 17

FREE ENERGY OF MIXING VALUES AT l600°C FOR IRQN-CHROMIUM-NICKEL ALLOYS WITH THE FOUR CONSTANT CHROMIUM CONCENTRATIONS OF 5, 10, 20, and 30 ATOMIC PERCENT

INTERGRAL FREE ENERGY EXCESS FREE

•ft* CD NN1 Cr OF MIXING FM OF MIXIN

0.050 0.950 -690 + 1*6 it .898 0,0518 -1590 -id* n .855 .091*7 -2110 -227 ti .813 .137 -21*90 -296 it . 71+7 .203 -2970 -399 it .657 .293 -3510 -590 n .1*60 .U90 -3910 -723 i i .300 .650 -3630 -681* it .262 .688 - 31*80 -651* it .156 • 79k -281*0 -517 n .0988 .851 -2370 -1*1*7 it 0.0528 0.897 -1830 -336 0.050 - 0.950 -890 -155

0.100 0.900 — -1150 +60 11 .852 0 . 01*83 -1880 +30 II .792 .108 -2720 -278 It .756 .11*1* -3050 -365 II .718 .182 -3200 -300 II .607 .293 -3810 -1*81* II .1*15 .1*86 -1*270 -752 II .250 .650 -1*000 -812 II .208 .692 -381*0 -820 II .157 .71*3 -31*90 -730 II .105 .795 -3060 -639 II 0.0530 .8U7 -2510 -552 0.100 - 0.900 -1600 -387

Continued 137 TABLE 17— Continued

n J n 5. intergral free energy excess free energy Gr OF MIXING F*1 OF MIXING Fxs

0 .2 0 0 0.800 -1710 +151* .191* .751* 0.0528 -251*0 +11* .200 .700 .100 -301*0 -5 6 n .662 .138 -3350 -ill* n .597 .203 -3760 -210 it .506 .2 9k -1*170 -352 it . 1*06 .391* -14*1*0 -511 n .300 .500 -1*1*00 -570 ii .206 .591* -1*210 -61*9 it .150 .650 -3880 -585 i i .103 .697 -3590 -580 it 0.05U5 .71*6 -3130 -528 0 .2 0 0 - 0.800 -2390 -520

0.3 0 0 0.700 - -2060 +212 11 .652 0.01*71* -2660 +255 n .605 .0951 -3310 -7 11 .551* .11*6 -3660 -52 n .508 .192 -3920 -112 n .398 .302 -1*390 -331* n .307 .3 93 - 1*1*80 -1*21 n .205 .1*95 -1*31*0 -1*91* it .150 .550 -1*170 -51*2 n .101* .596 -3950 -585 n 0 . 051*1 .61*6 -3590 -610 0.3 0 0 - 0 .7 0 0 -2800 -529 Vv 'v* K* «Y-’-/''rv;Afr'v,_* . « i: ;< I { "C * J i 139 by an alumdum crucible. It is felt that the vapor composition obtained from collectin g the vapor phase effusing from a Knudsen-cell is a better method to obtain the true equilibrium vapor composition. The evaporation from a free surface into a vacuum can be affected by k in etic e ffe c ts , thus preventing the attainment of the true equilibrium vapor composition.

The absolute accuracy of the activities determined in this disser­ tation is difficult to evaluate because of the strong dependence on the accuracy of the mass spectrometer activity results. The difficulty in reproducing the over-all mass spectrometer constant, k|, was discussed thoroughly in the experimental procedure section. The fact that the pure component intensity data was reproduced within 5 percent has been mentioned. The mass spectrometer data for the iron rich alloys shows the activity coefficient of Fe to be 1 + .07. The true activity co­ efficient of iron must be near 1.0 for these iron rich liquid alloys.

The a c tiv itie s calculated by the several methods used in th is disser­ tation agree within 10 percent. This agreement is felt to be good considering the experimental difficulty in determining the activities of a ll components in these highly reactive ternary liquid alloys a t the elevated temperature of 1600° to 1700°C.

To the authors knowledge th is is the f ir s t published application of the equilibrium vapor composition method to the determination of activities in a ternary alloy. In fact, there have been few attempts to measure the a c tiv itie s of the m etallic components in liquid ternary transition metal alloys. The use of this vapor composition method has certain advantages as well as definite disadvantages. The main advantage is that the vapor composition can be determined more accurately than the absolute vapor pressures. Also the vapor composition is not strongly affected by temperature and Knudsen-cell conditions as is the absolute vapor pressure. The main disadvantages of this method are the vapor pressures of a l l components must be of the same order of magnitude in order to obtain accurate chemical analysis of the vapor composition; the graphical integrations involved can be somewhat erratic and tedious; and the accuracy of the a c tiv itie s obtained by th is method depends on the accuracy of the reference activities and the accuracy of each vapor composition along the integration path.

The application of the time-of-flight mass spectrometer to the measurement of activities in high temperature alloys is certainly a relatively untried application. There are many experimental and electronic problems with such activity measurements, but with improve­ ments in the heating methods of the Knudsen-cell inlet system it is felt that this method can become a very valuable tool. The advantages of rapid measurement and vapor phase composition determination warrants much more attention than has been given to date. It should be mentioned that, where it is practical, the difficulties of reproducing the mass spectrometer conditions can be overcome by using an inert material in the Knudsen-cell that w ill produce a vapor pressure independent of the other material in the cell. Then ratios of the intensities of compo­ nents to the intensity of the inert material can be used and this procedure w ill eliminate much of the reproducibility problems. However, no inert material could be found for the highly reactive liquid alloys studied in this dissertation. li|2

Summary

1. The iron-chromium system was studied at a temperature of 1600°C for chromium concentrations ranging from 1 to 1+0 atomic percent. The activity of chromium related to solid chromium was found to exhibit positive deviation from ideal solution behavior. The activity co­ efficient of chromium was found to be 1.25 at 1 atomic percent chromium.

The activity of iron was found to be ideal for all iron rich alloys studied.

2. The nickel-chromium system was studied at temperatures near 1600°C for chromium concentrations ranging from 1 to 50 atomic percent. The activity of chromium relative to solid chromium was found to exhibit negative behavior at the lower chromium concentrations and positive behavior for chromium concentrations greater than 30 atomic percent.

The activity coefficient of chromium was found to be approximately .50 at 1 atomic percent chromium, 1.0 at 30 atomic percent, aid 1.30 at

50 atomic percent chromium. The activity of nickel was found to exhibit negative behavior for all tiie nickel rich alloys studied. The activity co efficien t of nickel was found to be .70 at 50 atomic percent n ick el.

3. The iron-chromium-nickel ternary system was studied at temper­ atures near 1600°C. All alloys studied were in the liquid state at 1600°C

The ternary a llo y compositions studied ranged from the iron-chromium binary to the nickel-chromium binary along constant chromium concentra­ tion lines of 5, 10, 20, and 30 atomic percent. In the iron rich alloys the activity of chromium displays positive deviation similar to that found in the ircn-chromium binary. Die activity of nickel was found to exhibit strong negative deviation for the iron rich alloys. Die activity coefficient of nickel was found to be approximately .55 for nickel concentrations ranging from 5 to 20 atomic percent. Die activity coefficient of iron and chromium decrease with increasing nickel concen­ trations until they display negative deviation for the nickel-rich ternary alloys. With increasing chromium concentrations in the nickel rich alloys, the activities of iron and chromium increase toward ideal behav­ io r . ^ Ox* __ i;. Die interaction parameters, and (^Ni> were found to be negative for iron-base ternary alloys. However, their absolute magni­ tudes are not equal as predicted by theoretical considerations. Die

Qr and were found to be positive for the nickel-rich ternary alloys and their absolute magnitudes were approxi­ mately equal.

5. Within the experimental accuracy of the mass spectrometer measurements the vapor phase of iron, chromium, n ick el, and th eir alloys were found to consist of monatomic atoms. No polyatomic molecules were found within the above experimental error of the measurements. APPENDIX A

Derivation of equations used in mass spectrometer studies.

Hie relationship between the pressure in the Knudsen-cell of a species i and the ion intensity of a particular isotope of species i observed in the mass spectrometer was given by equation (1) as,

h m ( 1 ' a )

This equation is quite important and a derivation can be made with the following assumptions:

1) There are no surface diffusion contributions to the flux effus­ ing from the Knudsen-cell.

2) There is a low probability that a given atom of type i is ion­ ized.

3) There is no competition between atoms for the ionizing electrais.

Assumption 1 i s a good assumption for the ceramic lid s and large thick­ ness orifices used in this research. Assumptions 2 and 3 should be good for the low pressures of the alleys studied in this research. Hie follow ing symbols have the meanings:

1^, is the observable ion intensity for a particular isotope of compo­ nent ij 1UU 11*5

J^, is the flux of component i effusing from the Knudsen-cell orifice;

7i> is the residence time of component i in the ionization region;

A^, is the isotopic abundance of the isotope of component i;

Ei , is the multiplier efficiency for the ion of the isotope of component i ; and

is the effective length of the ionization region.

Hie general form of the icnization probability, ^ , must be such that at infinite residence times the ionization probability must be equal to unity. A form that satisfies this requirement is,

Die proportionality constant, k^, is an instrument constant that depends on the geometry of the ionization source, the ionization cross- section of component i, and the ionizing electron energy. If the residence time is short, as it is far high temperatures and relatively light molecules, equation (2-A) reduces to,

^ i " kiT i (3-A) The observed ion intensity for a given isotope of component i is propor­ tional to the flux of the isotope of component i, the ionization proba­ bility for this isotope, the length of time of the bombarding electron pulse,(J, and the multiplier efficiency for the isotope of component i.

The relation is given in equation (U-A). 12*6

I± » (JiAi ) ^ i (JEi (b-A)

From the Knudsen-cell relation us have,

„ „ Ji \[27TRTM^r (5-A) Pi ~Y~ V 1 where i s the flux of component i effu sin g from the o r ific e of the

Knudsen-cell, k is the Clausing correction factor for a finite thick­ ness orifice, and M is the molecular weight of component i.

Die residence time, ^, is simply given by the relation,

? i - (&-A) where v^ is the average velocity of the isotope of component i in the ionization region. From the kinetic theory of gases,

vi "Vr^- (7-A) substituting equations (3-A), (5-A), (6-A), and (7-A) into equation

(b-A) resu lts in ,

t AiPi k kiS ^ Ei - * 1 ■ ^ (8-a)

Combining constants gives the relation desired,

I± » _ £kJH. (9-A) where,

, AV k i . k^ Ei k ± ». 1 1 1 ------r:------(io-A) ilit 11*7

This constant, k[, is assumed to be independent of temperature and pressure since the terms on the right hand side of equation (10-A) are independent of temperature and pressure for low pressures.

The relation between the vapor composition and the ion intensities was given by equation (15) a s,

. I l / g~lAi

1 L where

NT ■ Pi - "i ^ P i t I Substituting equation (9-A) into equation (12) results in,

T 1i A '

N i ' ( U - A ) u 1 I f equation (10-A) i s examined i t is found that only the isotopic abundance, A^, the instrument constant, k.^, and the multiplier efficien­ cy, E^, are functions of the component type. All other constants are the same for each component, therefore, equation (11-A) reduces to ,

KfV „ i/A i ki Ei Ni "<=T------(12-A) L It was stated before that the instrument constant, k.p is a function of the ionization cross-section, <57’ the geometry of the ionization source, and the electron current. The last two factors are the same for each 11*8 component. Thus (12-A) reduces again to,

v ui/AiCnEi Ni - ~ (13-A) E ^ / A ^ E .

Inghram, Hayden, and Hess (1*3) discuss the efficiency of electron multi­ pliers. They find in general the efficiency of the electron multiplier for a given ion is determined by the number of secondary electrons pro­

duced by the first collision of the ion with the target. The number of

secondary electrons produced by this first collision depends on:

1) the energy of the incident ion;

2) the mass of the incident ionj

3) the electronic configuration <£ the ion;

U) the charge on the ion;

5) the chemical and physical composition of the target surface;

6) and the angle with which the incident ion strikes the target surface .

The energy and charge of the ion is the same for all ions studied in

this research. The target surface and angle of incidence is the same

also for each ion. Therefore, the only difference is in the mass of Hie

ion and the electronic configuration of the ion. Iron, chromium, and

nickel are each transition elements with unfilled 3-d electron shells

but their outermost electronic configuration is very similar. Bie main

difference in multiplier efficiency is therefore felt to be due to the 11*9 differences in the masses of the iron, chromium, and nickel isotopes studied in this research.

Inghram, Hayden, and Hess (1*3), using sin g ly charged ions and a silver-magnesium target, found that at a constant ion energy, the number of secondary electrons produced per ion c o llisio n was inversely pro­ portional to the mass of the ion. Prom their data, for an ion energy of 3000 volts, the number of secondary electrons produced by the mass

52 isotope of chromium would be approximately 2 percent greater than the mass 58 isotope of n ick el. However, the target material i s different in the mass spectrometer used in this investigation. This same mass ef­ fect in the electron multiplier should also affect the studies made in th is research on the isotopic abundances of iron , chromium, and nickel listed previously in Table 1. But, the experimental values agree well

with the accepted values. Therefore the ion mass effect was neglected in this research and equation (13-A) reduces to the equation used in this thesis,

(ll*-A)

L APPENDIX B

Derivation and Discussion of Equation (26) presented in the Text.

For a 3 component liquid system, equation (25) has the form,

'(2) (2) '(2) a (2> In 1 Ini n T(2) 1 N^dlnNT4 N^dlnNg N^dlnN* (1-B) J i T N- (1) (1) (1) Using the relations,

dN dlnN (2-B)

(3-B)

dNY - -d # -dNY (U-B) 1 2 3 and substituting equations (2-B) and (U-B) into equation (1-B) results in ,

'(2 ) (2) a<2> , n v(2) In 1 In ai C!l _2_)dNg + N3 )dN^ rv(l) ,(D N. n ; n ; N? I f 3

(i) (1) (5-B) which i s the form used in a ll ternary a c tiv ity calculations in th is thesis. Ihere is an equation of the same form used to calculate the a c tiv itie s for the other two components of the ternary alloy .

150 1 5 1

For a binary liquid system the most useful form of equation (25) i s ,

f ( 2 ) (6-B)

1 J(D

The integration path from state 1 to state 2 is of no consequence since only exact integrals are involved. However, there are certain in te ­ gration paths in the ternary alloys that are more convenient and more accurate to employ. A ll integrations must be performed graphically by plo versus N. and determining the area under the

The experimental vapor compositions w ill have experimental errors present and the resultant graphical integrations w ill reflect these errors. Also the process of construction and deter­ mination of the area under the curves can introduce small errors into the values of the integraticns and subsequent activity calculations.

It should be noted that the above equations for determining activities involves only graphical integrations and does not involve both graphical integrations and graphical d ifferen tiation s as Darkens (19) method, which is used for the calculation of the a c tiv itie s of components 2 and 3 from a knowledge of the variation of the a c tiv ity o f component 1 with composition in the ternary alloy. In general graphical integrations can be performed more accurately than graphical differentiations. APPENDIX C

Interaction Effects on Thermodynamic Activities

Wagner (140 has shown that the activity coefficient, of a solute

in a multicomponent alloy can be expressed as,

Id y2(N2,N3,»!,,•••) - ln^l ♦ " j W ; ♦ B3 ^ * . . . (1-C) ^ k3 where ^ 2 is the activity coefficient at infinite dilution of component

2 in the 1-2 binary. Hie partial derivatives are taken as the concen­

trations of a ll solutes approach zero. This equation i s s tr ic tly valid

only when the concentrations of a ll solutes approach zero and the higher

order terms in the Taylor expansion can be neglected. However the

equation is often quite satisfactory for more concentrated solutions.

The p a rtia l derivatives are represented by the symbols et c .,

defined as:

and equation (1-C) becomes,

^ y 2(*>2>N3>1V" > ■ 2 ♦ N2iE i 2) * B3£ P ♦ ♦ ••• (2- 0)

To discuss the effects of impurities on the activity of say, chromium,

in a basic iron-chromium alloy let us designate ^ as the activity co-

efficient of chromium, and let the important impurities be nitrogen, 153 silicon, carbon, oxygen, and sulfur which are the important impurities in the chromium used in this research to produce the alloys. Equation

(2-C) becomes,

^ + NCr E% + + NSi £1r * No ^Cr + No £°r +

«S £ L (3-°)

Unless oxygen and nitrogen is picked up by the alloy during melting under vacuum the values of N.T, Nn, N , N , and N_ should not exceed 0 U Ol s

0.001. Therefore, in order for a given impurity to change by

1 percent'the interaction parameter, £ ^ , must be 10 or greater, if

equals approximately 1. The only experimental data available at l600°C is for iron base liquid alloys. The values of E or> £ ? > ani

are given in a summary paper by Ohanti and Goken (1|5). I t has been shown by Wagner (Uii) that at infinite dilution of all solutes that

®lere^ore in the absence of data we can approximately say that ^ q1* “ etc. From the data summarized by Ohanti and Goken

(U5),

£'& ’« -8.8 and -13.7

E f ' - -It-3

E x' * -9-9 For Nickel

£ Ni - i.fc 0

E n1 ■ i - 2 Hie maximum interaction parameter is on the order of 10. This would

require a mole fraction of .001 to change the activity of chromium or nickel by 1 percent. It is felt that the experimental accuracy of the activities of iron, chromium, and nickel determined in this research is on the order of 10 percent. Therefore it is reasoned from the preceeding discussion that the impurity levels encountered in the alloys will have negligible effect on the accuracies of the activities. APHSNDIX D

Chemical analysis procedures for the ternary iron-chromium-nickel condensates

I. For condensates with less than Uo percent chromium

A. Iron Analysis:

1. Dissolve the condensate off the pyrex plate in 100 ml of 1:10

Sulfuric acid under a protective carbon dioxide atmosphere to retain all Fe in the +2 ferrous state.

2. Dilute the solution to 250 ml with distilled water which has recent­ ly been boiled to remove a ll dissolved oxygen.

3. Titrate the ferrous iron to the ferric state with .01 or .02

Normal potassium permanganate employing a .025 Molar ortho-phenanthroline

indicator.

B. Chromium Analysis:

li. Boil the solution from 3 and add silver nitrate (1 mg A NO-, for o ^ each mg of Cr).

5. While boiling add 2.5 to 3*5 grams ammonium persulfate to oxidize

all Cr to the hexavalent state, boil for 15 minutes.

6. Destroy any permanganate ion formed by adding 5 ml of 1:1* hydro­

chloric acid.

7. Cool and titrate the hexavalent Cr with .02 Normal ferrous ammoniun

sulfate with a .025 Molar ortho-phenanthroline indicator.

1 5 5 8. Evaporate the solution down to 200 ml and let cool and stand overnight.

C. Nickel Analysis:

9. Filter the silver chloride, formed from steps it and 6, on a filter paper designed for fine precipitates.

10. Add 30 ml of 1:1 hydrochloric acid and $ ml of nitric acid and boil to oxidize to the ferric state.

11. While cooling add ammonium hydroxide until ferric hydroxide begins to precipitate.

12. A^d 60 ml of 20 percent tartaric acid solution plus $ ml of Uo percent ammonium chloride solution to complex the iron and chromium.

13. Add ammonium hydroxide until solution is slightly basic and filter the solution. lit. Add a little acetic acid and bring to a temperature of 60°C.

15. Add an alcoholic solution of dimetyl-glyoxime to precipitate the Ni as nickel dimethyl-glyoxime (NiC H O N ) of which 20.33 percent is Ni. o lit 1 a 16. Filter the precipitate on a weighed glass fritted disc using slight suction. 17. Dry at 120°C, cool in a dessicator and re-weigh.

I I . For condensates with more than 1*0 percent Cr, which w ill not d is­ solve in sulfuric acid 1. Dissolve in 20 ml of 1:1 hydrochloric acid plus 100 ml distilled water.

2. Dilute to 500 ml in a volumetric flask.

3. Pipette two 100 ml aliquots for the Fe analysis and save the remain­ ing 300 ml for the Cr and Ni analyses.

A. Iron Analysis: h. Add 25 ml of 1:1 hydrochloric acid and bring to a boil.

5. Add stannous chloride to reduce all Fe to the ferrous state.

6. Immediately cool in ice to 30°C, then add 10-15 ml of a 5 percent +2 mercuric chloride solution to destroy excess Sn reductant, then cool to 15°C. 7. Add 50 ml of a sulfuric-phosphoric acid mixture.

8. Titrate ferrous Fe to ferric Fe by .01 or .02 Normal potassium dichromate with a .01 Molar diphenylamine sulfonate indicator.

B. Chromium Analysis:

9. Add 10 ml of 98 percent sulfuric acid to the remaining 300 ml aliquot from 3. Evaporate the solution down until all hydrochloric acid has been driven off, this must be done very carefully to avoid the formation of insoluble chromium oxides.

10. Test to see if all hydrochloric acid is removed by adding 2 drops of silver nitrate.

11. From the solution free of chloride ion proceed from step U of the analysis procedure for condensates with less than UO percent Cr. APPENDIX E

Correction of the analyzed vapor composition to the equilibrium vapor composition in the Knudsen-cell

The equation relating the vapor pressure to the molar flux of component i from the Knudsen-cell Is,

where p^ is the partial pressure of component i in the vapor phase of

A the Knudsen-cell, is the molar flux of component i in moles/ cm sec, k1 is the Clausing correction factor for a finite length orifice, T is the absolute temperature of the Knudsen-cell, and is the molecular weight of component i in the vapor phase.

The experimental vapor composition measured by the chemical analysis of the condensate is given by,

V * *^■4 Mi ' (2-B) ^ L where Nv is the mole fraction of component i in the condensate. The equilibrium vapor composition in the Knudsen-cell is given from the ideal gas law as,

wv Pi Ni ■ (3- e ) 2 pi L

158 159

Substituting equation (l-E) into (3-E) results in,

N l ' (U_E)

Substituting equation (2-E) into (i*-E) for «L results in,

T . n | \ | mT 1 t \ r — (5-B) \J5T) L which is the equation used to correct the condensate vapor composition to the equilibrium Knudsen-cell composition, n T. APPENDIX F

Discussion of the calculation of the activities in the ternary iron-chromium-nickel alloys from the vapor composition equations

The equations used to determine the activities of Cr, Ni, and Fe are,

(2) v(2) WL mL ,tL L In aCrCr __ « In Nflr + + I / (-CL. Cr . -I®_)dNv Fe x MtV *+ ,(_H NCr------%SL.)A i I z y r Nv Nv ) Fe v Nv aCr NCr \ NCr “Fe wCr “Ni (1) (1-F)

, '(2) a(2) NV^ 1 N^ N^1 v aTTT' " “^ t i r * I )dNCr+ Ni Ni \ wNi Cr % i Fe (1) (2-F)

. '(2) ( (2) wv(2) I L L m1 mL In^Fe . ln %e „ + \ (JW_ _ JSL W +

1 N?e NCr ^ NL *Ni ^ KD 1(1) ^ O F ) Hie integrals must be evaluated from reference state 1, where the

activity is known from the mass spectrometer determinations, to reference

state 2. The integrals are evaluated graphically in all cases. The

graphs to evaluate the above integrals for the integration path along

160 NQr * .20 is shown in Figures 27 through 32. These graphs are plotted from the reference (20Cr-20Ni-60Fe) alloy to the binary (20Cr-80Ni) alloy for each integral but the iron activity integrals. The curves are fairly smooth and easy to construct in all graphs but Figure 31 L which i s the graph of ( Fe/N^e - N ^ ^ v ^ versus N^r used to calculate the activity of iron. In this graph straight lines were constructed between each experimental data point, because of the uncertainty of the curve. This introduces only a small error because the value of this integral is quite small due to the small value of the ordinate and small variation of NQr.V Note that all curves whose absissa is N^r V r e fle c t the maximum in Nqj. that exists in Figure 19. This maximum

causes a change in sign of the in tegrals in Figure 29 and Figure 31.

The construction of the curve near the maximum is somewhat arbitrary ow­

ing to the lack of stifficient data points in the region of the maximum.

Calculation of the activities of iron and nickel in the ternary alloys using the iron-nickel binary as the reference state

The calculation of the activities of nickel and iron from the iron-

nickel binary still employs equations (2-F) and (3-F). The integration

paths from state 1 in the iron-nickel binary to state 2 in the ternary

was along a constant nickel concentration line for the iron-rich alloys

and along a constant iron concentration line for nickel-rich alloys. 162

The extrapolation of the ratio Nq^ ^ v into the iron-nickel binary was discussed in the main text. The graphs used to evaluate the integrals / x L of equation (2-F) along an integration path of NNi ■ .10 is shown in

Figures 33 and 3h. The extrapolation of the (N^1. , v - Ncr/Nv ) Wl/% i Cr ordinate to 0 percent chromium is shown in Figure 33. •»-i o > o > •»-i o IUE 7 VRAIN F H VAPOR VARIATION THE OF COMPOSITION FUNCTION 27. FIGURE WITH W W 60 , FOR ALLOYS C, 1600 WITH CONSTANT A CHROMIUM CONTENT ATOMIC 20 OF PERCENT U. >

o . Vopor Composition Function 0>

- l 6 . 0 - 0.8 0.4 tm rcin e n pr Np apor, V in Fe Fraction Atom . 0.3 0.2 eeec Al loy Reference 0.4 n AT !

3 6 1 0.5 -Jo FIGURE VARIATION 28. OF THE VAPOR COMPOSITION AT FUNCTION WITH 60 , FOR C, ALLOYS 1600 WITH CONSTANT A CHROMIUM CONTENT ATOMIC OF 20 PERCENT o i N o ^ >o Vapor Composition Function z > k. -6 4 - 3 - aaac Alloy Rafaranca tm rcin i n ao, NN- Vapor, in Ni Fraction Atom 0.2 . 0.4 0.3 v k 6 1 0.5 FIGURE VARIATION 29. OF THE VAPOR COMPOSITION FUNCTION WITH 60 , FOR ALLOYS C, 1600 WITH CONSTANT A CHROMIUM CONTENT ATOMIC 20 OF PERCENT

Vcpor Composition Function .5 :6 5 05 05 06 06 06 06 06 0.65 0.64 0.63 0.62 0.61 0.60 0.59 0.58 7 .5 0 0:56 0.55 6 I ------eeec Alloy Reference tm rcin r n apor, V in Cr Fraction Atom ------til Cr AT ------I U E 0 VARIATIONFIGURE 30. OF THE VAPOR COMPOSITION FUNCTION WITH 60 , FOR ALLOYS C, 1600 WITH CONSTANT A CHROMIUM CONTENT ATOMIC 20 OF PERCENT

Vapor Composition Function z > > Li. tm ato F i Vpr P N Vapor in Fe raction F Atom 0.2 eeec Alloy A Reference . 0.4 0.3 v n AT X re 166 0.5 1 6 7

Reference Alloy

-i o > o

,a>

0.9

o

0.8

0.7 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 Atom Fraction Cr in Vopor,NQr

FIGURE 31. VARIATION OF THE VAPOR COMPOSITION FUNCTION WITH nY' AT , o 1600 C, FOR ALLOYS WITH A CONSTANT CHROMIUM CONTENT OF 20 ATOMIC PERCENT 168

-5

Reference Alloy

- 4

- J Z > 2 z z

-JI ®lli_ > 1° u. z z - 3

o c3 li. c o -2 o a . oE O

o OQ. >

0 0.2 0.3 0.5 A tom F ractio n Nilin V apor, N Ni

FIGURE 32. VARIATION OF THE VAPOR COMPOSITION FUNCTION WITH N„. AT o Nx 1600 C, FOR ALLOYS WITH A CONSTANT CHROMIUM CONTENT OF 20 ATOMIC PERCENT IU E 3 VARIATIONFIGURE 33. OF THE VAPOR COMPOSITION FUNCTION AT WITH Njy 60C FOR ALLOYS 1600°C, WITH CONSTANT A NICKEL CONTENT ATOMIC 10 OF PERCENT

Vapor Composition Function I i taoae Vle n e i Binary - Ni Fe in Value xtrapolated E 0.2 0.3 tm aton C i Vapor,N in Cr n ractio F Atom . 0.5 0.4 0.6 . v 0.7 0.8 0.9 16? 170

,0 ) > U.

z

Reference Fe-Ni Alloy

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Atom Fraction Iron in Vapor , N v

FIGURE 34. VARIATION OF THE VAPOR COMPOSITION FUNCTION WITH N AT , o Fe 1600 C, FOR ALLOYS WITH A CONSTANT NICKEL CONTENT OF 10 ATOMIC PERCENT BIBLIOGRAPHY

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