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BORROWING LIBRARY

DATE

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1/

3/17/65

-

APPLICATION OF THE ELECTRON CONCENTRATION CONCEPT TO GROUP IV-B AND V-B ELEMENT INTERSTITIAL COMPOUNDS

A THESIS Presented to The Faculty of the Graduate Division by William Henry Elliott, Jr.

In Partial Fulfillment of the Requirements for the Degree Master of Science in Metallurgy

Georgia Institute of Technology February, 1966

APPLICATION OF THE ELECTRON CONCENTRATION CONCEPT TO GROUP IV-B AND V-B ELEMENT INTERSTITIAL COMPOUNDS

Approved:

Chairman

/

/

I Date approved by Chairman:

- 196c

11

ACKNOWLEDGMENTS The author wishes to express his complete and sincere appreciation to his thesis advisor, Dr. N. N. Engel, who suggested this project. Without his teaching, consultation, and experience this work would not have been possible. A great deal of appreciation is also extended to Dr. Stephen Spooner for his help and advice on the preparation of the manuscript, and to Dr. R. F. Hochman for his invaluable teaching and review of the background material. To Dr. E. A. Starke, Jr. are also extended thanks for his help and encouragement. In addition, gratitude is expressed to the entire staff of the Georgia Tech library for their contributions of time and effort in obtaining the literature which was important to this work. Finally, the author would like to give special thanks to his wife, Pat, for her love, encouragement, and understanding.

iii

TABLE OF CONTENTS

ACKNOWLEDGMENTS LIST OF TABLES

Page ii iv

LIST OF FIGURES SUMMARY

viii

Chapter I. SURVEY OF PREVIOUS WORK AND THEORIES Earliest Work Interstitial Solid Solutions High Temperature Phase Studies The Latest Theories Summary of Previous Work and Theories II. PROCEDURE III. RESULTS Phase Distribution and Electron Concentration Postulates Binary Phase Diagrams Brewer Type Diagrams Physical Properties Postulates Thermal Properties Elastic Properties Electric Properties IV. CONCLUSIONS AND RECOMMENDATIONS Recommendations for Further Work

1 1

5 10 11 14 16 18 18 18 19 21 31 31 36 56

59 69 70

APPENDIX

71

BIBLIOGRAPHY

96

iv

LIST OF TABLES Page

Table 1.

Classification of Normal Interstitial Structures

9

2.

Theoretical Bonding Configurations of Pure Metals and Equi-atomic Compounds

33

Ratio of the Radii of some Atoms of Nonmetals and Metals

34

3.

4.

Ionization Potentials of the Nonmetal Interstitials

5.

Melting Point Trends

40

6.

Melting Points

41

7.

Boiling Points of the Mono-carbides

51

8.

Thermal Conductivities

53

9.

Modulus of Elasticity

57

10.

Hardness of the Borides, Carbides, and Nitrides

60

11.

Electrical Properties of the Borides, Carbides, and Nitrides

64

Thermal Coefficient of Electrical Resistance

68

12.

• • •

35

v

LIST OF FIGURES Figure

Page

1. Determination of the Limits of Electron-Concentration Phases

4

2. Stability Ranges of Electron-Concentration Phases

6

3. The Electronic Quantum States in Atoms

7

4. Electron Distribution over the Fifth Period Elements

8

5. Brewer Type Diagrams for Titanium

23

6. Brewer Type Diagrams for Zirconium

21l

7. Brewer Type Diagrams for Hafnium

25

8. Brewer Type Diagrams for Vanadium

27

9. Brewer Type Diagrams for Niobium

28

10. Brewer Type Diagrams for Tantalum

29

11. Theoretical Bonding Configuration and Melting Points of Column III through VI Equi-atomic Compounds

37

12. Theoretical Bonding Configuration and Comparison of Average Actual and Theoretical Melting Points of Column III through VI Equi-atomic Compounds

38

13. Melting Points versus Period

43

14. Theoretical Bonding Configuration and Comparison of Actual and Theoretical Melting Points of Column III Equi-atomic Compounds

44

15. Theoretical Bonding Configuration and Comparison of Actual and Theoretical Melting Points of Column IV Equi-atomic Compounds

45

16. Theoretical Bonding Configuration and Comparison of Actual and Theoretical Melting Points of Column V Equi-atomic Compounds

46

17. Boiling Points of the Mono-carbides

52

vi

LIST OF FIGURES (Continued) Page

Figure 18.

Thermal Conductivities versus Period

55

19.

Modulus of Elasticity

58

20.

Rockwell Hardness Values of the Carbides

61

21.

Rockwell Hardness Values of the Borides and Nitrides .

22.

Specific Resistance versus Period

66

A-1.

The Titanium-Beryllium System

72

A-2.

The Titanium-Boron System

73

A-3.

The Titanium-Carbon System

71+

A-4.

The Titanium-Nitrogen System

75

A-5.

The Titanium-Oxygen System

76

A-6.

The Zirconium-Beryllium System

77

A-7.

The Zirconium-Boron System

78

A-8.

The Zirconium-Carbon System

79

A-9.

The Zirconium-Nitrogen System

8o

• • •

62

A-10. The Zirconium-Oxygen System

81

A-11. The Hafnium-Boron System

82

A-12. The Hafnium-Carbon System

83

A-13. The Hf-N System

84

A-14. The Hafnium-Oxygen System

85

A-15. The Vanadium-Boron System

86

A-16. The Vanadium-Carbon System

87

A-17. The V-N System

88

A-18. The Vanadium-Oxygen System

89

vii

LIST OF FIGURES (Continued) Figure

Page

A-19. The Niobium-Boron System

90

A-20. The Niobium-Carbon System

91

A-21. The Niobium-Nitrogen System

92

A-22. The Tantalum-Borum System

93

A-23. The Tantalum-Carbon System

94

A-24. The Tantalum-Nitrogen System

95

viii

SUMMARY

Because of the ever increasing industrial need for materials which are capable of withstanding high temperatures and will retain their physical and mechanical properties at these temperatures, the "metal-like" class of compounds which includes the transition metal interstitial alloys has come under much investigation. This work was undertaken to determine the applicability of the electron concentration concept to the interstitial compounds and diagrams of the early transition elements. The method of attack was to gather as much of the data on the physical properties and diagrams as was available in the literature and to examine the trends in this data using the rules of the electron concentration concept. In general, the results can be broken down into two sections, the first concerning the distribution of phases in the diagrams, and the second concerning the physical and mechanical properties. The distribution of phases in the diagrams was determined by using Brewer type diagrams which were constructed from the available binary diagrams. It was found that the one, two, and three-electron phases predicted by the electron concentration concept apply well to the transition metal interstitial alloys, and also that no fractional electron phases appeared. The physical and mechanical properties were studied by plotting the data versus the period of the metallic constituent. It was found that the following factors are important in the determination of these physical properties: (1) total number of outer bonding electrons in the metal atom; (2) total

ix

number of inner bonding electrons in the metal atom; (3) principal quantum number of the incomplete inner subshell in the metal atom;

(4)

relative sizes of the transition metal and alloy atoms; and (5) the ionization potentials of the alloy atoms. These factors are given in order of decreasing importance. It was also determined that a ratio of 0.61 rather than 0.59 between the transition metal and alloy atoms might be more appropriate for determining the formation of interstitials.

1

CHAPTER I

SURVEY OF PREVIOUS WORK AND THEORIES Earliest Work It has always been one of man's great desires to be able to make predictions about the properties of various metals and alloys. Metallurgists, in particular, have always been in need of some method whereby they might gain an insight into such properties as melting points, boiling points, cohesive energies, crystal lattices, and even more complex properties such as magnetic effects. Some of the earliest work of importance was done by such noted 2 scientists as Mott and. Jones , Pauling 3 , and Seitz 4 . Generally speaking, the work of these scientists was based mainly on an effort to obtain a mathematical model that would fit the experimental data, and in a great number of cases the physical interpretation of the mathematics was left undecided. In fact, there were a great number of early publications that were based on such advanced mathematics that even the specialists could not solve the related equations. One of the first scientists to try what might be called the "systematic approach" was Hume-Rothery 5 in 1930. One of his rules was to the effect that the elements of the periodic chart will crystallize in lattices such that the number of nearest neighbors is (18-N), where N is the column number of the long periodic chart. If it is remembered that this is only an approximate rule, it can be said that the rule fits

2

well to the elements in columns 14, 15, 16, and 17 where there are 4, 3, 2, and 1 nearest neighbors respectively. The lattices of cadmium and

zinc, which are in column 12, also seem to fit the rule, as does the diamond lattice and the sodium thallide lattice. A major problem is encountered with Hume-Rothery's (18-N) rule; it fails for all elements with column numbers less than 12 (54 elements), and also for mercury, thalium, oxygen, nitrogen, sulfur, indium, and lead. Hume-Rothery not only worked with the (18-N) rule but with the conditions for formation of stable phases in metals and alloys as well. This work was also very important in that it led to the formation of another rule in which he postulated that the stability of the beta, gamma, and epsilon phases in the CuZn binary alloys depends upon the electron concentration or the ratio between the electrons and the atoms. He found that the beta brass phase is stable when the ratio of electrons to atoms is 3:2, which can be called an electron concentration of 1.5. Further study showed that the ratio of electrons to atoms in the gamma phase is about 21:13 and in the epsilon phase is about 7:4. These three phases with electron to atom ratios of 21:14, 21:13, and 21:12 have come to be known as the Hume-Rothery phases. They will appear in alloys of copper, silver, gold, nickel, paladium, cobalt, and iron as the copper representative and elements from columns 12 through 16 in the periodic table as the zinc representative. Approximately the same ratios between electrons and atoms will occur for these alloy phases as occurred for the CuZn alloy phases In 1949, Engel

6

pointed out that by altering Hume-Rothery's (18-N)

rule to some extent, it could be applied to metals as well as the rest

3

of the elements. He began by making a close study of the metals, and found that if the (18-N) rule lattices are considered as electron concentration phases in which the crystal structure is controlled by the number of outer bonding or valence electrons per atom, he could assign

7, 6, 5, 4, and 2 outer electrons per atom to the elements in columns 17, 16, 15, 14, and 12 respectively. His next step was to extend the systematics of the rule to include the metallic elements, such that the three metallic lattices would be controlled by 3, 2, and 1 outer bonding electrons per atom. Engel therefore postulated that the body centered cubic lattice which predominates the column 1 metals was a one-electronper-atom phase, that the hexagonal close packed lattice which can be found in columns 2 and 12 was a two-electron-per-atom phase, and that the face centered cubic lattice was a three-electron-per-atom phase In other work, Engel

1,7

.

has demonstrated such matters as the

stability of these electron concentration phases (he has used them to account for the distribution of lattices in the periodic chart), and has made several particular applications to demonstrate the general utility of his theory. Because so much of this study is based on the application of Engel's theory, a full explanation of its application will be reserved for full coverage later;only certain results of some of his work will be presented here. Figure 1 illustrates the method used by Engel to determine the limits of stability of his electron concentration phases. It should be noticed that the binary phase diagrams which were picked for use are those where the atomic sizes of the components are as nearly equal as possible. This is important because of the well known rule that the

600

600

400

200

70

I

1,0

20

1,2

40

1

1:4

'

60

60

e6

ell

20 1 210

20

212

E/ ektronkoncenf ratio n

1400

f40

1200

f20 ...-...'

f000

10

,-' ,...'

800

40

60

60

2'4 2,8 2,6 Elektronkoncenfration

100%AI 1

.3!0

„.. . . . . . . ---„_,

800

■

600

600

a 400

400

200

40

20

40

60

80

/0

200

0 100•40o Co 0

0 20

40

60

80

Figure 1. Determination of the Limits of Electron Concentration Phases. —

100% Ni

5

solubility depends on the ratio between the atomic sizes of the alloyed atoms. The actual limits of stability are presented in Figure 2, and are the highest possible values under ideal circumstances. Such factors as the size factor, the competition with other kinds of bonds, and the occurrence of intermetallic phases are pointed out by Engel

8

as having

an influence on the real limits in alloys, decreasing the spread of electron concentrations in which the phases are stable. Figures 3 and 4 contain information about the electronic quantum states and the electron distribution in pure solid state elements 7 . Interstitial Solid Solutions Because of the wide range of interstitial structures that are formed between the early transition metals and the second period metalloids, it should be of value to consider here the conditions necessary for their formation. In 1929, Hagg 9 published the first systematic study of the structure and formation of interstitials. He stated that, if the size of the nonmetal atom is less than 0.59 that of the metal atom, interstitial structures are formed, whereas complex structures are formed for higher ratios. Hagg has also suggested a classification of metal-interstitial structures based on (1) the nature of the metal lattice, and (2) the coordination number of the nonmetal atoms. Table 1 shows this classification where the radius ratio of R

x

to R

m

is given for the appear-

ance of each type of structure. Here, R x refers to the radius of the nonmetal atoms and R

m

to the radius of the metal atom.

These interstitial structures have the following characteristics: (1) the nonmetal atoms are situated in the interstices between the metal

c.b.c.

h.c.p.

1

2

diamond

c.f.c.

3

4

5b lattice

5

electrons pr atom

Figure 2. Stability Ranges of Electron-Concentration Phases.

rn

7

Period

2. 6 10 14

s p ci f

744,

The energy Levels of

6

suantized

5 th

electrons.

4th

3d

1st

i

Figure 3. The Electronic Quantum States in Atoms.

8

1610L. 4A

•K

20

\ .

% •

...

lb■

r.;

A ...

%

1

4

' f i

2000

. %%

IA

%

11:

Ell NG POINT

i ‘• ./ /i

/

s'

ATOMIC DISTANCE

f /

t

1

/

I

I

'

A I;. \

•

,,

%

,

I

I.

• LTP61• POINT %

% %1" .

Mo

Y

1 1 11111 '1 / 1111111

Rh

% 1111L 2

0.

I

1.9 2.1

-

Sb

In

11111 1

U.

■ 10 17 16 IS PAIRED ELECTRONS

14

13 12

0 —

ELECTRON DISTRIBUTION IN 1311STALLINE PHASE. — ELECTRON DISTRIBUTION IN GAS PHASE. ----ELECTRON DISTRIBUTION \* IN CRYSTALLINE PHAS WITH 7 ORBITS.

9

AO All #Arr IIII

Aar Ar APP' 41 r , 4_

A

--t---

i

1

uNpAIRED d ELECTRONS

All,

7 6 5 4

irill

3 2

I1 maim

Kr Rb Sr 7 Zr Nb Mo Mo Ru Rh Pd A6 Cd In

1

0 Sn SD To I x

FIFTH PERIOD

Figure 4. Electron Distribution over the Fifth Period Elements.

Classification of Normal Interstitial Structures (10)

Table 1.

Coordination Type of Metal Lattice and Coordinates of No. (C.N.) Metal Atoms of Metal 12

Possible Coordinates Condition for C.N. of Occurrence, Nonmetal of Nonmetal Atoms R /R Atoms x m

Face-centered cubic

6

12

8

Hexagonal close packed 000, 1/3 2/3

Body-centered cubic 000,

8

11

Simple Hexagonal c/a = 1 000

NaC1 structure Fluorite and zincblende structure Wurtzite structure

0 12 oo 111. 0, 2 2 2 0, 00

000, 0 1 1 1 1 0 2, 2 2 0

1

>0.41

4

f * 4, f * 3/4 3/4, ** ± 3/4 * 3/4, ± 3/4 3/4

> o.23

6

2/3 1/3 *, 2/3 1/3 3/4

> 0.41

4

00 3/8, 1/3 2/3 7/8, *** 00 5/8, 1/3 2/3 1/8

> 0.23

4

±ol 47 ± 1 0, 1 4 ± 1-.1 1 0 4 013 ± yi T, ± IT 7 0 0

> 0.29

6

1/3 2/3 1

> 0. 5 3

10

atoms in such a way that the largest spaces are occupied so that maximum contact is maintained and maximum coordination is achieved, (2) the metal atoms are in contact, and the structure is usually the same or similar to the metal structure, and (3) a wide range of composition is possible within each phase

10

.

Further studies of the structure and formation of interstitials 12 11 have been carried out by Kiessling in 1950 and, by Samsonov in 1963. High Temperature Phase Studies In July, 1963 Brewer 13 published the first of his works dealing with high temperature phase studies of the transition elements. His main interest was with the transition elements because of their general utility as high temperature alloys and also because, with the exception of the column III elements, their atomic sizes are nearly equal, thus assuring few size effects. By making use of a plot of the various phases found between the transition elements, Brewer was able to show that the three normal metallic lattices progress through the ternary diagrams in a systematic manner. Brewer has constructed these plots for nearly all combinations of about thirty of the transition metals. A comparison between the phase boundaries as found using Brewer's plots and the calculated values based on the electron concentration concept shows that with only a very few exceptions the same values occur. For example, in the binary diagram of a three-electron face centered cubic metal with a one-electron body centered cubic metal, the electron concentration concept predicts that the face centered cubic phase will exist for an electron concentration down to about 2.25. At this point

11

there will be a slight gap; the hexagonal close packed phase then begins and continues down to about 1.9 electrons per atom, at which point there should be another slight gap to 1.75 electrons per atom where the cubic body centered phase begins. The formation of phases between the ferromagnetic elements iron, cobalt, and nickel, is not immediately explainable by the electron concentration concept. These phases appear to be stabilized over rather narrow ranges of electron concentration and appear as narrow vertical bands in Brewer's plots. One possible explanation for their occurrence 1 in this fashion has been offered by Engel . Another interesting phenomenon found in Brewer's

14

plots is the

formation of phases between the three normal electron concentration phases at fractional values of electron concentration. The A 15 and sigma phases are good examples of this formation. These phases appear in many respects to be quite similar to the well known Hume-Rothery phases which also occur at fractional values of electron concentration. Up to this time, no one has found a reason for their formation. The Latest Theories One of the foremost authorities in the field of refractory metals and their compounds is G. V. Samsonov

12 15 16 of the Institute of Metal' '

loceramics and Special Alloys in the Soviet Union. Samsonov has been very active in this field for the past fifteen years, during which time he has contributed many valuable works to the available literature. Of particular interest are his theories concerning the structure and properties of the so-called "metal-like" class of compounds which consist

12

mainly of the transition metal interstitials. These theories have been presented, in various degrees of completeness, in several places in the recent literature. According to Samsonov

12

, the chief factors determining the nature

of the crystalline structure and physical properties of these compounds are: (1) the relative sizes of the atoms of the metal and the nonmetal, (2) their electronegativity, (3) the ionization potentials of the atoms of the nonmetals, and

(4)

the accentuating capacity and degree of fill

of the incomplete electron shells of the atoms of the transition metals. In explanation of his theories, Samsonov

15

states that it may be

assumed as a first approximation that the bonding between the cores of atoms of transition metals and nonmetals in the crystal lattices of refractory chemical compounds is provided by an electron cloud in which delectrons of the transition metals and outer electrons of the metal and nonmetal participate. This is to say that the degree of nonfilling of the d and f electron shells of transition metal atoms strongly influences the character of the bonding. As a qualitative estimate of this degree of nonfilling, Samsonov proposed the expression 1/Nn, which he called the "repulsive" or "acceptor" ability of a transition metal atom. In this expression, n denotes the number of electrons in the unfilled d level, and N is the principal quantum number of the d level. His main arguments in proposing this expression were as follows: In the motion of an electron in the field of the core of a transition metal atom, i.e., an atom lacking s electrons, the probability of perturbation of the electron path---which has as its limiting case the statistical filling of one of the vacant sites of the d shell by

an electron---is the greater, the lower the filling of the d shell and the lower its energy - level. The latter is, of course, described by the principal quantum number. In other words, in the statistical distribution. of electrons whose paths might have been perturbed during passage in the field of the core of an atom with n electrons in the d. level (whose principal. quantum number is N), the position probability of such electrons is the probability of the simultaneous occurrence of two events. This probability is equal to the product of the probabilities of such events, 1/N and 1/n, i.e., 1/Nn— . As a physical interpretation of these theories, Samsonov

proposes

that an increase in the repulsive or acceptor ability. of the + ras ItIor metal atom will cause a displacement of the relative maximum of the electron concentration in the direction of the metal atom for constant values of the ionization potential. When the value of 1/En is held constant and the ionization potential is increased, a displacem.nt will be caused in the direction of the nonmetal atom with a correspondTng change in the character of the bonding, that is, from metallic. to ionic bonding. Samsonov has used as an example of the practical application of his theories the analysis of data on the superconductivity transition temperatures of a number of refractory. compounds. An examination. of this data shows that for the borides, carbides, and nitrides of the column IV, V, and VI transition metals, the superconductivity transition temperatures increase sharply as the value of 1 /Nn decreases from 0.1.670.100 for Ti, Zr, V, and hf, and from 0.67-0.50 for Ta, Nb, W, and Mo. This is explained as the formation of a maximum concentration of weakly bound electrons for specific values of the acceptor ability and the ionization potential, which also provides the highest transition tempera-

tures. Thus, for carbides and nitrides of column IV and V metals, the transition temperatures increase with an increase in the content of the nonmetal. For example, for Nb 2N, Tk = 9.5 ° K; for NbN---15 °K; for Mo 2C--o 2.9 K; and for MoC---8 °K. Furthermore, an increase in the content of the nonmetal in these phases causes replacement of a portion of the more stable and rigid metal-metal bonds by less rigid metal-nonmetal bonds, or, in other words, it causes the appearance of an additional number of weakly bound electrons. Following this logic, Samsonov states that in order to increase the transition temperature in the Nb-N system as an example, one should either increase the acceptor ability of the metallic component by adding a small amount of a strong acceptor such as hafnium or slightly increase the donor ability of the nonmetallic component by adding a certain amount of oxygen. The correctness of this argument seems to have been shown by the first experiments of this sort. Samsonov has also stated that the application of these concepts to the understanding of the changes in bonding by varying the metal and nonmetal representatives in the refractory compounds has given satisfactory results. He does not, however, offer any examples of his results in the available literature. Summary of Previous Work and Theories There have been numerous attempts to develop a set of satisfactory rules for predicting the physical properties of metals and alloys. Of the presently available theories nearly all have some shortcomings; they either fail to give a good physical explanation or they fail to satisfy our present knowledge mathematically.

15

Due to its general utility and application to nearly all areas of metallurgical endeavor, the electron concentration concept as proposed by Engel

6

was chosen for application to the groups III-B through VI-B

element interstitial compounds to determine its applicability.

16

CHAPTER II

PROCEDURE Since few of the important physical properties of the early transition metal interstitial compounds are readily available, it was necessary to make a thorough search of the literature and compile these data. Almost all of the physical properties have been taken from the work of Samsonov

12,16

with the exception of the oxides which

were taken from the work of Shaffer and Hausner

18

. Pearson's Handbook

concerning lattice spacings and structures was particularly important in the determination of the structures of the phases involved. As many of the binary phase diagrams as possible were also collected. The main contributions were from the works of Lustman and Kerze Hansen

20

, Rostoker

21

, and. Rudy and Stecher

22

10

, Samsonov

16

•

Since all of the physical properties were not available in one work, and when available the data was often outdated or incomplete, it was necessary to edit the available data and condense it for optimum usage. Both graphs and tables were used where it was felt they would be beneficial. The first attempts to systematize the physical properties were by the mathematical method, i.e., both qualitatively and quantitatively. It was found, however, that there were too many factors to consider if one was to obtain good quantitative results. For this reason it was decided that the best method of attack was the graphical method, or in

,

17

other words, an examination of the trends. When approached from the electron concentration concept, these trends were, in general, explainable as to their direction, and in some cases it was possible to explain exceptions. The greatest majority of the background material was from the work of Engel to some extent.

1678 .

The work of Samsonov

12 15 ' was also used

18

CHAPTER III RESULTS Phase Distribution and Electron Concentration Because of the importance of phase diagrams in working with the physical properties of the transition metal interstitials, the question naturally arises as to whether or not the electron concentration concept is of any use in working with these phase distributions. The electron concentration theories can definitely be used to account for the phase distribution in these diagrams, the most important and interesting part of the periodic chart being the transition metal region. Postulates It was mentioned in a previous chapter that in 1949 Engel6 proposed what is the foundation of the electron concentration concept, that only the outer bonding electrons are important in controlling the lattice. In particular, it was shown that the body centered cubic lattice is a one-electron-per-atom phase, that the hexagonal close packed lattice is a two-electron-per-atom phase, and that the face centered cubic lattice is a three-electron-per-atom phase. When combined with the limits of stability as shown in Figure 2 and a sufficient knowledge of the size factor and its related effects, this seemingly minute amount of information is all that is necessary to make far reaching predictions.

19

Binary Phase Diagrams Rather than examining each of the phase diagrams of interest, it is felt that by systematically covering the diagrams of only one transition metal it will be possible to demonstrate the applicability of the theory. Thus, the remainder of the diagrams can be examined from the same point of view by the reader without an extended excursion from the development. As an example of a random set of diagrams, zirconium alloyed with some of the second period elements may be taken. The electron distribution of zirconium in the low temperature hexagonal close packed lattice 2 6 2 6 d10 . 2 is ls 2s p 3s p d

2 6d2 1 1 4s p d 5s P, and in the high temp erature

cubic body centered lattice, ls

2

2 6 2s p

2 6 10 3s p d

2 6 3 4s p d

1 5s .

When small atoms are added into interstitial solution, the electron concentration of the zirconium atoms will increase, and a good way to look at this is that it is due to almost complete ionization of the interstitial atoms. The electrons which have been added to the metal atoms will distribute themselves between the d-level positions and the outer bonding positions. This will stabilize the hexagonal two-electron phase relative to the one-electron phase and increase the overall bonding strength. This increase in bonding strength will result in increased melting points, also increased hardness. An explanation of the physical and mechanical properties of these interstitial compounds will be given in a later section. As the interstitial atoms are added up to the equiatomic composition, the electron to atom ratio will increase, and for carbon will raise up to eight at the equi-atomic composition where the NaCl phase will be formed. This phase is equivalent to a face centered

20

cubic three-electron-per-atom phase of metal atoms with second period atoms as interstitials. In contrast, when the alloy atoms are comparable to zirconium atoms in size, substitutional solid solutions and phases are formed and d-electron bonds are broken. The stability range of the one and twoelectron phases becomes depressed to lower temperatures and the melting point of the NaC1 type phase is low, as is the case in the BerylliumZirconium diagram. If the nonmetal atoms are small enough to be taken up interstitially, then essentially all the electrons will be ascribeable to the zirconium rather than being shared as in the substitutional alloys. Boron, which is just small enough to form interstitial solid solutions, does not contribute sufficient electrons to essentially stabilize the one and two-electron phases of the pure metal (see Figure 6). It can also be seen in the phase diagram that the strongest bonding will form at about ZrB 2 . There are at least three different possible causes for a maximum to occur at ZrB 2, among which are that an ionic compound is formed, that the boron atoms form a network which is not interacting with the zirconium atoms, and that the boron atoms form a network which interacts in some sort of a bonding situation with the zirconium atoms. Based on the work of Samsonov

12

and Kaufman

26

it is felt that the boron

atoms form a network within the interstices of the zirconium atoms. The formation of this network would require the pairing or similar removal of a certain number of the electrons from each boron atom leaving a more favorable number of electrons to participate in d-bonding. Carbon and the following elements are small enough to form inter-

21

stitial solid solutions. Carbon contributes sufficient electrons to stabilize the one and two-electron phases slightly and has just the right number of electrons to develop the strongest possible bonding pattern at the equi-atomic composition. Nitrogen contributes sufficient electrons to stabilize the one and two-electron phases markedly, but adds so many electrons to the equi-atomic NaC1 type phase that the d-shell starts to become oversaturated and bonding strength decreases. By saturated it is meant that five electrons are in the d-shell, since more than five d-electrons will result in internal pairing with its inherent loss in bonding. Oxygen added into solid solution contributes so many electrons to the d-shell in zirconium metal that a maximum in d-bonding is obtained in the two-electron phase. Extensive over saturation occurs in the delectron shell in the equi-atomic NaC1 type phase which causes it to melt at a rather low temperature and also causes it to be metastable. Further addition of oxygen results in the formation of

Zr02'

with ionic type bond-

ing and a higher melting point. The binary phase diagrams of the column III, IV, V, and VI transition metals with second period elements are presented in Appendix A for reference. The phase diagrams for Hf-N and V-N are constructed by interpolation. Brewer Type Diagrams Because of their general utility in allowing the observation of the effect of electron concentration on the distribution of phases over the diagrams in question, Brewer type diagrams were constructed from the binary diagrams of the transition metals with the second period inter-

22

stitial elements. It should be remembered from previous discussions that 13 the diagrams published by Brewer in 1963 were very instrumental in substantiating the usefulness of the electron concentration concept when dealing with the transition metals. The Brewer-type diagrams for the column IV metals are shown in Figures 5, 6, and 7, and it is immediately obvious that they are quite similar. This is to be expected, of course, if the distribution of phases is due only to the outer bonding electrons. Two diagrams are presented for each of the transition elements, one at a high temperature and one at a moderate temperature. This allows a more complete picture of the effects. It can again be seen, as in the binary diagrams, that the one and two-electron phases are stabilized by the addition of electrons. The equi-atomic NaCl type phase is stabilized by the addition of electrons to the point where the d-shell becomes saturated, which occurs for carbon in the zirconium and hafnium diagrams but not in the titanium diagram. As can be seen in Figure 5, the Brewer-type diagrams for titanium, the greatest stabilization of the three-electron phase

,

appears to be for nitrogen and is as yet not explainable by the theory. Extensive electronic over saturation occurs for oxygen thereby breaking up the d-bonding pattern. Figures 8, 9, and 10 show the Brewer-type diagrams for the column V metals. Again, two diagrams are presented for each of the transition metals. The similarity between these diagrams is not quite as marked as it was for the diagrams of the column IV metals, but there is still much to be seen. The stabilization of the three-electron phase appears to go strictly according to theory for these three metals. It is also interest-

23

TEMPERATURE = 500°C

Ti

0

10

20

30

40

50

ATOMIC PER CENT

TEMPERATURE = 1500°C B

—

C

Ti III N I

II

I

I 0

10

I 20

I 30

0 40

ATOMIC PER CENT

Figure 5. Brewer Type Diagrams for Titanium.

50

24

TEMPERATURE = 500 °C

C

III

—N

I 10

I 20

I 30

40

50

40

50

ATOMIC PER CENT

TEMPERATURE = 1500°C

Zr

0

10

20

30

ATOMIC PER CENT

Figure 6. Brewer Type Diagrams for Zirconium.

25

TEMPERATURE = 500°C

— C

1 Hf

III \

\

\ \ \

\ \ ∎N

0

1 10

—N

\\ \

\\

20

1 30

1 40

0 50

ATOMIC PER CENT

TEMPERATURE = 2000°C

III

—

C

Hf

■ N

0

10

1 20

r30

40

ATOMIC PER CENT

Figure 7.

Brewer Type Diagrams for Hafnium.

50

0

26

ing to note that the maximum melting points for the NbC and TaC threeelectron phases occurs at a composition of about 55 atomic percent of the metallic constituent instead of 50 atomic percent. This can be seen in Figures A-18 and A-21. The melting points are highest at this composition because the bonding configurations of the three-electron phases are more nearly 5 d-electrons and 3 outer electrons. By actual calculation there should be 8.3 electrons per transition metal atom if the carbon atoms are assumed to be completely ionized, compared to 9.0 electrons per transition metal atom at the equi-atomic composition under the same assumptions. The stabilization of the hexagonal two-electron phase with an increase of electrons occurs over a wider range for the column V metals than for the column IV metals, thus conforming more to the theory. Of even greater interest though is the comparison of the range of stability of these two-electron phases to the perfect two-electron composition. This perfect two-electron composition is shown in the diagrams of Figures 8, 9, and 10, and it can be seen that the fit is quite good. The actual range of stability of the two-electron phase for vanadium extends to the left of the line indicating perfect composition, whereas for niobium and tantalum the range of stability moves towards the right of the diagrams, such that for tantalum the range of stability is extending to the right of the line of perfect composition. To further illustrate the applicability of the theory, one may calculate the number of d-electrons by assuming that there are exactly two outer electrons and that the interstitial atoms are completely ionized. Such calculations indicate that there are from 2.4-4.5, 2.5-4.5, 2.4-3.5, 4.3-5.0, 5.0-6.0, 4.5-5.5 d-

27

TEMPERATURE = 500°C

C

/

■

b

\ \

// de

/

0

I 10

/

/

/

—

II

N

)4/// 1

I 20

I 30

I 40

0 50

ATOMIC PER CENT TEMPERATURE = 1500°C B

N

10

20

30

40

ATOMIC PER CENT

Figure 8. Brewer Type Diagrams for Vanadium.

50

28

TEMPERATURE = 500°C B

C

Nb N

to 0

10

20 30 ATOMIC PER CENT

40

50

TEMPERATURE = 1500°C B

C

Nb N

0

I 10

I 20

30

1 40

ATOMIC PER CENT Figure 9. Brewer Type Diagrams for Niobium.

(

50

0

29

TEMPERATURE = 500 °C B

C

Ta

N

0

I 10

I 20

0 30

40

50

TEMPERATURE = 2000 °C B

C

Ta

N

0 0

10

20

30

40

ATOMIC PER CENT

Figure 10. Brewer Type Diagrams for Tantalum.

50

30

electrons for each atom of titanium, zirconium, hafnium, vanadium, niobium, and tantalum respectively. The unusual behavior of the one-electron phase for the tantalum alloys, as shown in Figure 10, is as yet not explainable by the concept; however, little is known about the tantalum-nitrogen system and what is available is not very sure. It can be seen now that the one, two, and three-electron phases which were shown to be applicable to the diagrams between transition metals by Brewer

13 are indeed applicable to the transition metal inter-

stitial alloys. This can be seen most graphically in the excellent fit of the two-electron phase region of the Brewer-type diagrams of the column V metals with the line indicating perfect two-electron concentration. It is also demonstrated by the fact that in all of the Brewer-type diagrams there is a transition from one to three-electron regions when moving from left to right across the diagrams. The only exception to the predictions of the concept appears to be the greatest stabilization of the three-electron phase at nitrogen in the Brewer-type diagrams for titanium. There are two reasons for this exception under consideration; that the three-electron phase is stabilized at nitrogen because of extended vacancies, or that the titanium-nitrogen binary diagrams are in error such that the three-electron range has been shown too wide. A natural extension of the electron concentration concept arises when the stability of interstitial compounds is considered. Since there are an increasing number of d-electrons in the transition metals with increasing column number, there is less ability to take up added electrons. This means that the stable carbides, for example, can take

31

up less and less electrons per metal atom; whereby the carbides change from MeC to Me2C

, Me3C'

and Me4C' and the last transition elements do

not exhibit stable carbides at all. Physical Properties Examination of the data on the physical properties of the compounds in question has allowed the explanation of the trends on the basis of the electronic structure and crystal structure. Postulates It is proposed that the following factors are important in determining the physical properties and the crystal structures of this class of compounds: (1) total number of outer bonding electrons in the metal atom; (2) total number of inner bonding electrons in the metal atom; (3) principal quantum number of the incomplete inner subshell in the metal atom; (4) relative sizes of the transition metal and alloy atoms; and, (5) the ionization potentials of the alloy atoms. These factors are given in order of decreasing importance, the first, second, and fourth of which having been previously substantiated and the remainder to be substantiated in the following sections. It should also be mentioned at this point that factors (1) and (2) are controlled by the crystal structure and the degree of ionization of the interstitial atoms. These factors are almost the same as those considered by Samsonov

12,

except for factor (1), and it should be pointed out that the major differences between theories occur because of the application of these factors to the explanation of the physical properties of the transition metal interstitial compounds.

It should also be pointed out that a great deal of this work is dependent on the work of Lewis ? .o That is, the idea of the formation of electron pairs is important in understanding the contribution to bonding energy from the inner bonding electrons. In order to fully understand the application of the electron concentration concept to the explanation of the physical properties of transition metal interstitials, it is best to begin with the ideal case, which will occur when there are three electrons in the s and p shells and five electrons in the d shell. This particular configuration yields the maximum bonding energy and hence the highest expected melting point, modulus of elasticity, hardness, and other physical properties. As an example of this ideal case, let us begin with a transition metal such as zirconium. In the low temperature hexagonal phase, zirconium will have two electrons in the 4d level, one in the 5s level, and one in the 5p level. If carbon is added interstitially to the zirconium, the number of electrons which can be ascribed to each zirconium atom increases up to eight at the composition 50 atomic percent zirconium and 50 atomic percent carbon. The structure of the compound ZrC at this composition is the NaC1 type which has been described previously. The added electrons from the ionized carbon atoms will distribute themselves between the outer bonding and d-level positions in the zirconium atoms. Since the NaC1 type structure can be considered as two interpenetrating face centered cubic lattices, and since the electron concentration concept ascribes three electrons to the face centered cubic lattice, this phase may be considered as a face centered cubic three-electron-per-atom metallic phase of zirconium atoms with carbon atom ions as interstitials.

33

Table 2. Theoretical Bonding Configurations of Pure Metals and Equi-atomic Compounds

Columns Electrons III

IV

V

VI

VII

VIII

IX

X

.ETA]

I 2

2

1

1

2

2

3

3

d

1

2

4

5

5

6

6

7

paired d

0

0

0

0

0

2

2

4

effective d

1

2

4

5

5

2+

4

3

s-p

3

3

3

3

d

3

4

5

6

paired d

0

0

0

2

effective d

3

4

5

4

s-p

3

3

3

3

d

4

5

6

7

paired d

0

0

2

4

effective d

4

5

4

3

s-p

3

3

3

3

d

5

6

7

8

paired d

0

2

4

6

effective d

5

4

3

2

IDES

IDES

_____

NITRIDES

r

s-p

31+

Table 3.

Ratio of the Radii of some Atoms of Nonmetals and Metals (16)

Metalloid (x) Radius of Metal

Be

C

N

0

0 Radius of Metalloid Atom 11_, A x

Metal Atom Rme , A

B

1.13

0.97

0.77

0.71

0.60

Rx/RMe

Ti

1.47

0.77

0.66

0.52

0.48

0.41

Zr

1.60

0.71

0.61

0.48

0.44

0.38

Hf

1.59

0.71

0.61

0.48

0.45

0.38

v

1.35

0.83

0.71

0.57

0.52

0.44

Nb

1.47

0.77

0.66

0.52

0.48

0.41

Ta

1.47

0.77

0.66

0.52

0.48

0.41

Hagg suggests a limit of 0.59 for the formation of interstitials. This work suggests that interstitials form to the right of the double line.

35

Table 4.

Ionization Potentials of the Nonmetal Interstitials (16)

Ionization Potentials of Subsequent Electrons (ev) Atoms 1st

2nd

3rd

4th

Be

9.30

18.12

153.1

216.6

B

8.28

24.99

37.70 258.0

C

11.24

24.28

47.55

64.10 390.1

N

14.51

29.41

47.36

77.00

0

13.57

34.75

54.80

77.50 113.3

5th

6th

7th

8th

338.5

97.30

487.4 549

663

137.3

735

867

36

This leaves five electrons to go into the d-level positions of the zirconium atoms. On top of this very strong electronic bonding, the maximum number of d-electron bonds plus three outer electron bonds, is added the ionic bond between the negatively charged zirconium atoms and the positive carbon ions. In Table 2 the theoretical bonding configurations are shown for the column III through X pure metals and the column III, IV, V, and VI equi-atomic borides, carbides, nitrides, and oxides. The theoretical bonding configurations are also shown graphically in Figure 11; however, in Figure 11 is shown additionally the theoretical melting points based on the maximum theoretical bonding configuration. Table 3 shows the ratio of the radii of some atoms of nonmetals and metals as well as the limit for the formation of interstitials. Table 4 shows the ionization potentials of the nonmetal interstititals. Thermal Properties When this work was begun, it was felt that the deviations from the ideal case would be small enough so that it would be relatively simple to fit such things as the electronic contribution to the melting point to a mathematical formula. The easiest way to do this is shown in Figure 11, and it can be seen in Figure 12, a comparison with the accepted values, that there are other factors to consider. In other words, it can be seen that the contribution to the melting point from the d-electrons and from the outer-electrons is not a constant, but changes from column to column and also within each column. It is possible to obtain a result for this electronic contribution by working with one transition element at a time but the result seems to

▪

▪

O

► -•

rj

TOTAL ELECTRONS PER METAL ATOM ID rn

NJ

O

N3

1

• d

P3

rt O

tD 0

n

M rt

•

H

d

n CD

d

tp:, O o 0, 0

d

pi

+P

........ .

P

0

.t.

Cl) CL • 1.-1 •

eq

d

O

0 rh 1-1• cria

d

0

rr

r.

O

0 0

0

f-P

\ \ \ \ \ \

d

SINI Od11/31132103H1

0

S

11, N

P

d

:::;A;;;; Ma . t .

H. CIO

d

a ..UM1

0 H.

:•,:•••:\\;\

d

rt

O i-h

O

\ \ \ \ \ \ `‘. \ \ \ \ \ \ \ \ \ \ \

1-1

\

\

0 H H H

d

rt

S + P

\\ \ \ \\\\\\\.\ ■ \\\\ \ \X

Pi

0 0

1 1.-.

H 5.0 0

LE

CD 0 7C

1--, CI 0 CD 0 0

PO CD 0 CD 0 7C

0 0 0 CD 0 0 0 0 7C 7C

01 CD CD 0 0

01 CD CD CD 0 7C

CD D CD 0 CD 0 0 0 7C X CD

0 CD CD 0 7C

0 0

.4 1-.

N.)

0

O

O 0 0 O 0 0 0 0 0 7C 7C 7C

•

rml

TOTAL ELECTRONS PER METAL ATOM

0

s•-+

fD

O

Cr)

o

1—•

'V

r

o—)

t.0

CO

1%3 •

EgWil„. 4

m

fD rt. 0

03

O 70

• M OQ cl•

0 CA

ttl O gu

• ed 0) 0 o r1, ly 0 C3 00 0 I-. 0 O 0 0 0 0 1-ri H. H 00 H H H

70

CO

0

00

r-

0" a

1-1

1V31 13H03 H1

rr rt 0" H. 14 0 0 0

l \\\\\

\ \ \ \ \ \\ \ \

\ \ \ \ \ \

1,1

1 11

\

\\

\

\ \\

'

'

'

''

•

70

0

O 03

H I HO on rt 0 O 0 El 1-4 0

...... \\.„\

\ \ \\ \

O rn CI

.

O 4

\w"• \

• H 0 0 0Q

\ \\ \

\\\ \ \

a n •

. . . .... - . S +

. • . • .... ....

\ \\ \ \\ \\ \\ \\ \\\

\ \

O

O

P-1 (.1

(-) rr

...\

a

\ " \

0 1`..\\., \`‘ \\\\\.\\-..\\••••

dr I

1-3

► ■

0 rt

8£

0

O 0

0 0 0 7C

I r.)

0

1

I

Lo

0

EL

EL

7C

7K

I

I

4. 0

c7, 0

tri 0

01

0 0 EL 0 7C

7K

I

1 s4 0

0 0 0

CO 0

7C

AVERAGE MELTING POINTS

0 0 7C

i kl, 0

0 0 0

1 1—. 0 0

0 7C

I I—. I—,

0 0 0 0 7C

I I--.

N3 0 0 0 0 7C

39

be contradictory to previous work done by Engel. In effect, all that is accomplished by such an approach is to force the values to fit the mathematics involved, i.e., one is able to satisfy the mathematics but the results obtained do not lend themselves to a reasonable physical interpretation. For example, a change in the temperature scale from centigrade to kelvin will force the ratio of the contributions from outer-electrons to d-electrons to change in such a manner that they become unreasonable. For this reason it was decided to examine the trends involved in the data and to explain these trends physically rather than mathematically. The information presented in Figure 12 has been taken substantially from Table 5, which contains the melting point trends of the column III through VI pure metals as well as some of the interstitial compounds. Table 5 has in turn been derived from the data contained in Table 6 and Figure 13. Table 6 shows the melting points of as many of the borides, carbides, nitrides, and oxides as are available along with the year in which these values were made available. Figure 13 shows the same melting points plotted against the period of the metallic constituent; this allows a readily obtainable idea of how the melting points change from period to period. Figures 14, 15, and 16 show the theoretical bonding configuration and a comparison of the actual and theoretical melting points of the column III, IV, and V equi-atomic compounds respectively. These figures show the trends which occur within columns, whereas the trends from column to column are shown primarily in Figure 12. Referring to Table 2 and Figure 11, it can be seen that the ideal,

Table 5. Melting Point Trends (°K)

Sc

Y

Avg.

Ti

Zr

Hf

Avg.

V

Nb

Ta

Avg.

Mo

2741

3202

2705

2893

Metal

1670

1773

1721

1883

2124

2503

2170

2173

MeB Me

----

----

----

450

1139

830

806

350

MeB

----

----

----

2333

3263

3333

2976

2523

2553

2703

2593

503

450

476

1537

1679

1660

1625

910

1012

951

2173

2223

2197

3420

3803

4 163

3795

3083

3753

MeN Me

1253

1177

1215

1340

1129

752

1074

460

MeC MeN

-

727

—739

197

550

908

552

MeN

2923

2950

2936

3223

3253

3225

3245

Me

----

910

910

310

829

560

566

or

----

2683

2683

2193

2963

3063

2739

-

MeC Me -

MeC

-

-

Me0 Me0

2

-

2 Me 0 2 5

750

-

D = Decomposes

Avg.

W 3673

3283

1000

-

2623

2673

2648

958

80

-680

-300

4153

3663

2973

2993

2983

-168

158

150

----

----

----

450

1180

793

808

----

----

----

2633

2573

3360

2855

1044

-797

---- -1270

2158

1908

----

-

360

1813

-

-

212

988

1753

-

-

500

-

121

-

270

-

635

D

2403

-

1270 2403

Table 6. BORIDES

Melting Points

CARBIDES

NITRIDES

OXIDES

.... Metal

Phase

Ti

TiB 2 Ti 2B

Zr

ZrB

V

Nb

Year

Phase

3253

1954

TiC

2473

1954

Melting Point ( oK) Year 3420

1952

Phase TiN

Melting Point ( oK) Year 3478

1958

Phase Ti203 TiO 2 TiO

Melting Point ( oK)

Year

2403

1951

2193

1958

2033

1958

ZrC

3803

1950

ZrN

3253

1958

Zr02

2963

1958

HfC

4163

1954

HfN

3255

1951

Hf0

3063

1958

1959

VC

3083

1958

VN

2633

1958

V2 0 3

2253

1951

2623

1959

V C 2

2438

1962

V0 2

1813

1951

2523

1958

V3 B 2

2343

1959

1bB 2

3273

1959

3753

1960

Nb B 3 4 NbB

3173

3373

1960

3313

1953

3263

1952

2953

1953

HfB 2 HfB

3523

1953

3333

1951

VB 2 V 3B 4 VB

2673

ZrB ZrB Hf

Melting Point ( oK)

2 12

Nb 3B 2

NbC 1959 1'tb 2 0

2553

1959

2223

1959

Nb N 2 NbN

2

2693

1961 Nb203

2053

1951

2573

1950

1753

1951

(continued)

Nb205

Table 6.

BORIDES

Metal Ta

Melting Point o Year ( K)

CARBIDES

NITRIDES

OXIDES

Year

Phase

Melting Point o ( K)

Melting Point ( o K)

1943

TaN

3360

1954

1943

Ta2N

2323

1961

3373

1931

TaC

Melting Point o ( K) 4153

2923

1931

Ta2C

3673

TaB

2703

1931

Ta 3 B 2

2393

1931

Phase

TaB 2 Ta 3 B 4

Phase

(Continued)

Year

Phase

Ta 20 5

Year 1958

43

CARBIDES

BORIDES 50

5000 45

^\\^

4500

40

Of B 2

Amm Pw-Aim

4000

35

Ta 82..... 2 r B2 Ti dz N b B2

LdA

Ta

LaLa 30

3500 ..........T2&. No

V8

Tab

NOB

V3 Bi

3000

25

VB T.3112

4312 V

'Pl

463B2 Zr

2500

20 T

2000

15 4

5

6

° IC

OXIDIS3

NITRIDES

5000

4000

4500

3500

4000

2.1.02

Till

',....-

6

Period

PERIOD

.

3000 Taft ZrN

Ta 0

a

3500

2500

V 0,

lb

TiO2

vN 2000

3000

Hf

, •1; ,TiO

, 86

.■••

VO2

Ta

2

Zr 1500

2500 Ti

1 000

2000 4

5

6

Period

Figure 13. Melting Points versus Period.

Period

Ta 2

5

44

BORI DES Sc

Y

CARBIDES La

Sc

NITRIDES Sc

La

Y

OXIDES Sc

La

Y

La

12

12000° K

11 _

11000° K

10 _

1000 0° K 900 0° K

TOTAL ELE CTRONS PE RMETALATOM

9 8_

8000° K

"7.7

72

o_ • 7_

7000° K

747'

6

Col

■—• 6000°K 0—

.01111M

/ /

I

5_

5000 ° K /

.(r)

///

/

4_

///

4000°K

•1".1

3_

3 000° K

2_

2000 ° K 1 0 00° K —0

-0

—0

—0

—0

0°K

0 MINNIM 4111■1 .O■1111.

THEORETICAL ACTUAL

Figure 14. Theoretical Bonding Configuration and Comparison of Actual and Theoretical Melting Points of Column III Equi-atomic Compounds.

LiJ

45

TOTALELECTRONSPER METAL ATOM

12 -

Ti

Zr

CARBIDES Hf

Ti

Zr

NITRIDES Hf

Ti

Zr

OXIDES Hf

Ti

Zr

Hf

_ 12000° K

11 -

_ 11000° K

10 -

_ 10000°K

9-

9000° K

8-

_ 8000° K

7-

7000° K

6-

6000° K 5000°K

54-

4000° K

3-

_ 3 0 00°K

2-

_

2000° K

_ 1000 °K 0° K

0 • • • THEORETICAL ACTUAL

Figure 15. Theoretical Bonding Configuration and Comparison of Actual and Theoretical Melting Points of Column IV Equi-atomic Compounds.

MELTING POINT ( °K)

BORI DES

▪

▪

O

1••■•

-

TOTAL ELECTRONS PER METAL ATOM CJ1

C.)

CO

IJ

1„

CYR 4

,

l0

N.)

s+P

.......

O

O rn

H

Ol

.§ . NMI

1V0I 13d03H1

CI

1-4

rn

■•■ \\

\ \ \ \\ \ —4

\ \ \ \

.:.:.:.:.:.:.:. .....

\\\\

.

.....

rri 0

LA

.

.

... ..13111

\

. .

1

0 0 7C

1---. 0 0 0 0 7C

IV 0 0 0 0 7C

Ca 0 0 0 0 7C

1

i

(re

01

■.1

0 0 0

0 0 0

7C

7C

I

I 4=.

e 0 0

o

7C

0

0

I

CO 0 0 0 0 0 0 0 0 7C 7C

MELTING POINTS ( ° K)

I

I

I

I

I—,

1—.

I—.

l0 0 0 0

0 0 0 0

7c

7c

o

o

1-. 0 0

o

n

N3 0 0

o

n

1+7

or maximum, bonding situation should occur in three types of compounds; column V borides, column IV carbides, and column III nitrides. As explained previously, this is because in these compounds there are three outer bonding electrons and five d-electrons which is the maximum. The average melting points of the three types of compounds which should exhibit the ideal type of bonding are shown in Table 5, and, as a first approximation, should be indicative of whether or not the ideal bonding situation has actually been achieved. As can be seen, the average melting points of these three types of compounds are not the same, as would be expected. Instead, the melting points of the column IV carbides are a great deal higher than those of the column V borides and the column III nitrides, the average values being 3795 K, 2593 K, and 2936 o K respectively. There is little doubt as to the cause of the lower average melting points of the borides. It has been pointed out by Hagg 9 , Samsonov12, and others that the equi-atomic borides of the transition metals contain chains of boron atoms running through the interstices of the crystal lattice. It is felt that the formation of these chains requires the pairing of electrons, thus reducing the number available to go into the d-shell of the metal atoms. Both the carbides and the borides should exhibit the NaCl type lattice; however, the borides do not. The borides exhibit instead, a rather complex orthorhombic type of structure which may be caused by any of several factors such as the formation of these chains of boron atoms or the ratio of the atomic radii of the metal and alloy atoms. The net result of all this is that there will be less delectron bonds formed in the borides than in the carbides. Furthermore, there will be fewer electrons ionized off of the boron atoms, causing

48

smaller coulomb forces and a smaller contribution from the ionic bond. This reduction in the number of d-bonds and lowering of the ionic bond strength results in about 1200 °K difference in the melting points of the column V borides and the column IV carbides. An explanation of the cause of the lower average melting points of the nitrides is not so easily afforded. It is simple enough to propose a reason for the lower melting points, but there is not nearly so much data available to support the suggestion. Based on the available data, it is assumed that the primary cause for the lower melting points is the incomplete ionization of the nitrogen atoms. For example, a certain number of the nitrogen atoms may ionize off only the three plevel electrons, leaving the two s-level electrons internally paired on the nitrogen atoms. The ionization potentials, as presented in Table

4,

show a slight tendency toward this occurrence. Since it is not necessary for the number of d-electrons per transition metal atom to be an integral number, it is felt that just about any reasonable reduction in melting point can be caused by this mechanism. The only problem with a theory such as this is that the factor causing the incomplete ionization would have to remain an unknown for the present. By analogy with other compounds of this type, it is reasonable to expect that sufficient data on the modulus of elasticity would substantiate this explanation. There remain now only two main groups of compounds which deviate from the theoretical expectations and have not been explained. These two groups are the column III carbides and the column V carbides, the deviations of which can be seen in Figures 14 and 16 respectively. The column III carbides appear to be too low by a constant amount, namely

4-9

about 1000 oK. It is felt that an explanation very similar in nature to that proposed for the column III nitrides should also satisfy the deviation of this group. The differences would be that rather than removing three p-electrons from the nitrogen atoms, only two p-electrons would be removed from the same random number of carbon atoms.

This would again

lower the number of d-electron bonds and the contribution from the ionic bond, and a good check would be the difference in the amount of the lowering of the melting points of these two groups. It turns out that the column III nitrides are about 900 °K lower than would be expected whereas the column III carbides are about 1000 o K lower as was stated above. This should be a good check on the partial ionization of the carbon atoms; the modulus of elasticity should also be a good indication. The column V carbides, rather than being low by a constant amount, appear to be quite a bit like the column IV carbides, varying greatly within the column. Here again is an effect of incomplete ionization. To verify this fact one needs only to look at the curves of the modulus of elasticity and the hardness of the column IV and column V carbides. For example, tantalum shows a modulus of elasticity which is lower than expected, indicating a more metallic bond than expected and hence less ionization of the carbon atoms than for vanadium and niobium. To understand this effect, however, one must realize that it is only a part of the overall effect. This overall effect is brought about by two distinct factors: (1) the natural increase in the contribution to bonding due to the increase in the principal quantum number, and (2) the decrease in bonding brought about by incomplete ionization. An explanation of the relationship between the bonding configuration and the elastic properties will be given

50

in the next section. As a resume, it may be pointed out that the third column metal compounds all exhibit melting points about 1000 °K below expectations, Figure 14, that fourth column metal compounds fit fairly well when allowance is made for the influence of period or principal quantum number, Figure 15, and that the fifth column compounds also follow expectations with allowance made for principal quantum number with exception of the borides. The fifth column melting points are on the high side. In Table 7 and Figure 17 is shown the available data on the boiling points of the interstitial compounds. As can be seen, all that is encompassed is the column IV and column V mono-carbides. It is interesting to note that the boiling point of TaC is given as 100 °K higher than that of HfC, HfC having the higher melting point. Because of the extremely high temperatures, the accuracy of this data is doubtful. However, the general behavior of tantalum is similar with respect to melting points.and boiling points. It should be pointed out that the boiling points of HfC and NbC have been calculated rather than measured experimentally. Table 8 contains the available data on the thermal conductivities of the borides, carbides, and nitrides of the column IV and V transition metals respectively. The year in which they were determined is also given. In Figure 18 this data is shown plotted against the period of the transition metal. It is unfortunate that more data is not available as it might be possible to get a better physical interpretation of the conduction process. As it is, there is only sufficient data available

51

Table 7.

Boiling Points of the Mono-Carbides (16)

Boiling Point Phase

°C

TiC

o

K

Year

4300

4573

1951

ZrC

5100

5373

1956

HfC

5400

5673

1961

vc

3900

4173

1956

NbC

4500

4773

1961

TaC

5500

5773

1957

52

0

K

6500

6000 TaC HfC 5500 ZrC ;-1

5000

NbC 4500

TiC

4000

VC

3 5 00

4

5

6

Period Figure 17. Boiling Points of the Mono-carbides.

53

Table

Phase TiB

2

TiB

2

ZrB

2

ZrB ZrB

NbB TaB TaB

2

Thermal Conductivity (cal/cm-deg-sec)

Temperature ( °C)

Year

0.058

23

1950

0.063

200

1950

0.010

1500

1961

0.058

23

1950

0.060

200

1950

*

0.029

12

NbB

Thermal Conductivities

*

2

TiB

8.

2 2

1952

0.040

23

1950

0.047

200

1950 1950

0.026

2

0.033

2

0.0869

TiC

200

1950

20

1961 1961

TiC

--mg

TiC

P'., 0.095

TiC

0.098

600 800 966

TiC

0.10

1200

1961

TiC

0.102

1400

1961

TiC

0.108

1600

1961

TiC

0.11

1800

1961

TiC

0.112

2000

1961

ZrC

0.10

ZrC

0.0750

ZrC

0.104

HfC

0.070

0

1961

VC

0.094

0

1961

NbC

0.044 0.053

0

1961

TaC

*

* Porosity = 15 percent Porosity = 5 percent

0

1961 1961

1961

530

1962**

2100

1962**

1959

Table 8.

Phase

(Continued)

Thermal Conductivity (cal/cm-deg-sec)

Temperature ( oc)

TiN

0.046

20

TiN

0.070

100

1954

TiN

0.019

600

1954

TiN

0.014

950

1954

ZrN

0.049

20

ZrN

0.033

200

1954

ZrN

0.018

490

1954

ZrN

0.013

800

1954

VN

0.0270

20

1961 xxx

Nb N 2 NbN 0.75 NbN

0.0200

20

1961 xxx

0.0191

20

1961***

0.009

20

1961

0.0240

20

1961

0.0205

20

1961

Ta N 2 TaN xxx

Porosity = 0

Year

1961***

1961 xxx

BORIDE5

CARBIDES

MMDE5

9.920

UMW

0.070

TIC(180011C.....-

0.110

T111(100° C)

0.070 TIC(160 4

T1B (200°C)

2re(2090°C) ZrC(0°C)

DAN TIB (23°C)

•

TiC(1400)

ZrB2(200°C) 0.060

0 060

iTiii;:(51.1

2r112(23°C)

TiC( IMO) VC

0.050

0. 913

9002 (206°C)

E 0.050

Tie

MN

8

TIC

ZrN(20°C)

NbB,(23°C) 0.040

0.0130

0.040

74132 (200°C) 0.030

• Z r 12

0.020

Zre(600°C)

ZrN(200 °C)

8.070

0.030

TaB2 (23°C)

VN

0.050

e." TaN(20 %-...)—

0.020 Z10°C)

2rN(490°C) ZrN(1100 °C)

TIN( 50°C)

T4C(^0°C) 0.010

0.000

0.050

T1B 2 (1500°C)

0.010

NbN

.. —.. 4

4 PERIOD

PERIOD

Figure 18. Thermal Conductivities versus Period.

PERIOD

56

to show the metallic nature of the bond in the transition metal interstitial compounds. Elastic Properties Many of the industrial applications of the transition metal interstitial compounds are based on the high elastic properties of this class of compounds, especially the retention of these properties at elevated temperatures. If for no other reasons than these, it is important to determine the factors which influence the elastic properties. To explain the trends in the elastic properties, one must begin by realizing that there is a dualistic nature in the bonding of these interstitial compounds. It has been explained previously that there is both electronic bonding and ionic bonding making up the total bonding picture, i.e., each of the transition metal interstitials will have a certain proportion of the total bonding made up of an electronic component and a certain proportion of an ionic component. If this is accepted, then it seems to be only logical that each of the physical properties will be influenced to a different extent by each component of the bonding. For example, the electronic component may be more important in determining the melting point of a particular interstitial compound, whereas the ionic component may be more important in determining the hardness. In Table 9 the modulus of elasticity is presented for as many of the borides, carbides, and nitrides of the column IV and V transition metals as is available. Also presented is the temperature at which, and the year in which these values were determined. Figure 19 shows this same data plotted against the period of the metallic constituent,

57

Table 9.

Phase

Modulus of Elasticity (16), (25)

Modulus of Elasticity (kg/mm2)

Temperature (oc)

Year

54000

20

35000 27300 26200

20 20

1961* 1958 1960 1961

TiC

46000

20

ZrC HfC

35500 35900

20 20

VC NbC TaC

43000 34500

20

29100

20 20

TiN

25600

20

TiB 2 ZrB 2 VB 2 TaB 2

20

1961* 1958 1961 1961* 1948 1953

1958

Determined on specimens of the following composition: TiC

00% Ti, 20.4° C tot., 0.4% C free)

VC

(81.7% V, 18.0% C tot., 0.3% C free)

TiB 2

(69.06% Ti, 30.2% B, 0.3% C)

58

70,000

60,000

TiB2

MODULUSOF ELASTICITY ( KG/MM2)

50,000

TiC VC 40,000

\ NbC

•

ZrC ZrB2

HfC

30,000

TaC

VB2

TaB2

TiN 20,000

Hf Ti 10,000

Zr

0 5 PERIOD Figure 19. Modulus of Elasticity.

6

59

giving an idea of how the values change within each column. In order to test the theory the column V carbides may be taken as an example. Based on the information presented in the previous section, it is already expected that the carbon atoms in the compound TaC are not ionized as much as those of VC or NbC as examples. If it is now assumed that the carbon atoms in VC are ionized more fully than those in NbC, those in TaC being least ionized, then the decrease in the modulus of elasticity from VC to TaC as shown in Figure 19 can be accounted for. Following the same line of thought, one would now expect the trends in the hardness values to be in the same direction. In Table 10 as many of the Rockwell A hardness values for the borides, carbides, and nitrides of the column IV and V transition metal interstitials are presented as are available. Also presented are the years in which these values were determined. It should be mentioned that the porosities of these materials is not stated. Figures 20 and 21 show this data plotted against the period of the metallic constituent. Although here is no data available on the hardness of VC, the change in hardness from NbC to TaC is in the expected direction. This explanation can be extended to cover the other types of compounds also. Electric Properties The metallic nature of the transition metal interstitial compounds is important in their industrial uses. It is at first immediately obvious that the conductivities of these materials is of the same order of magnitude as the pure metals themselves. The positive thermal coefficients of electrical resistance also show the metal-like nature of this class of compounds.

Table 10. Hardness of the Borides, Carbides, and Nitrides*(16)

Hardness Phase

Rockwell A

Year

TiB

86 84

1960 1960

69-72

1953

92-92.5

1952

83

1960

2 ZrB 2 ZrB ZrB 12 VB 2 TiC

92.5-93.5

1952 1960

ZrC HfC NbC TaC

87

TiN ZrN NbN

75

1960

84

1960

86

1960

84

83 82

1960 1960 1960

The porosities of these materials were not stated.

61

CARBIDES 100

95 TiC

90

ZrC 85

•••I•I••

HfC NbC

rad

Ta 8o

75

70

65

4

5 Period

6

Figure 20. Rockwell A Hardness Values of the Carbides.

62

BORIDES AND NITRIDES

100

95

• ZrB

12

90

TiB

2

• NbN

85 ZrB 2 • VB

75

70

65

ZrN

2

TiN

•

ZrB

5 Period

Figure 21. Rockwell A Hardness Values of the Borides and Nitrides.

63

In Table 11 is presented the specific resistance and conductivities of as many of the borides, carbides, and nitrides of the column IV and V transition metals as are available. Also shown are the temperatures at which these values are applicable and the years in which they were obtained. Figure 22 shows this data plotted against the period of the metallic constituent. Since the column V carbides have been used as examples in the previous sections, it seems only fitting to continue the practice. Figure 22 shows the specific resistance changes for the column V carbides, and it can be seen that the specific resistance of the compound VC is higher than that of NbC which is itself higher than that of TaC. This trend in the data indicates that these materials are becoming more metallic in nature with increasing principal quantum number. Another way of looking at it would be to say that the bonding in VC is more ionic than the bonding in TaC. At any rate, the only way to accomplish this is to have the carbon atoms in VC more ionized than those in TaC which is the same bonding situation that was proposed in the previous sections. Applying this proposed mechanism in an analagous manner, one is able to satisfactorily explain the trends in the remaining types of compounds. It is interesting to compare the electrical conductivities of the column IV metal compounds with the metals themselves. As examples, MeB 2 andMeNrbtcondurshateml,ndMCisamotgd. The column V metals are better conductors than the column IV metals; nevertheless, their compounds generally exhibit more resistance than the column IV compounds. This is especially pronounced for the mono-borides and the semi-nitrides, i.e., for the lower electron concentrations.

64

Table 11. Electrical Properties of the Borides, Carbides, and Nitrides

Phase

TiB TiB 2 ZrB 2 ZrB 12 HfB 2 VB VB 2 VB 2

Specific Resistance (microohm.cm)

Temp. co

Conductivity ity -1 (ohm. ' cm. -1) 25000 69500 62500

60

20 20 20 22

16670

1952 1960 1960 1952

8.8

20

113600

1959

35-40

20

28600-250000

1952 1931

4o

14.4 16.6

Year

-14o

286000

19

20

52600

NbB NbB 2

64.5 34.0

20 20

15500 29400

TaB TaB

100 37.4

20 20

10000 26800

TiC

52.5

ZrC

50.0

20 20

19100 20000

HfC VC NbC TaC

45.0 65 51.1 42.1

20

22250

1960 1960

20 20 20

15400 19600 23750

1960 1960 1960

TiN TiN 0.765 ZrN ZrN 0.879 HfN V N 3 VN

25 50.6

20 20

40000

21.1

1960 1963 1960 1963

2

3.5

1960 1956 1960 1952 1960 1960

33.0 123.0

20 20 20 20

19700 74400 25100 30400 8140

1961 1961

85.0

20

11700

1960

37

(continued)

65

Table 11.

(Continued)

Specific Resistance (microohm.cm)

Temp. ( oc)

Conductivity -1 . -1 (ohm. cm. )

Nb N 2 NbN

142.0

20

7042

1961

78.0

'20

12820

1961

Ta N 2 TaN

263.0

20

3802

1961

128.0

20

7812

1961

Phase

Year

66

I _ITL

--

6L

DI8,1R)

.

,

52:011qm 59L ,MTI

MA

11

1

oaa Dal

xz ty

2

.vax..ds

2

0.0E 4. (•mo-mitooawm) aztre4uTsag .TJT.edS

A

a 00 0Z Te (•mo-untooaDTK) aoireviTsag ouTDGels

Figure 22.

0.0Z 4. (•..0-m,( 00 J.TW) aoue y9Teafl

Specific Res is tance versus Period.

0

67

The thermal coefficient of electrical resistance of the borides, carbides, and nitrides of the column IV and V transition metals is presented in Table 12. Also included is the temperature range over which the values are applicable and the year in which they were determined. The main usefulness of this data is in providing a better estimate of metallic nature of these compounds, and at present the trends can only be evaluated on the basis of the conductivities at a given temperature.

68

Table 12.

Phase

Thermal Coefficient of Electrical Resistance (16)

Thermal Coefficient of Electrical Resistance (deg.

TiB

-1

3

• 10 )

Temperature Interval

Year

( cc)

2

2.78

300-2000

1961

2

1.76

300-1800

1961

1.62

- 79- + 64

1952

1 fB2

3.6

20-2630

1931

VB

3.16

100-1100

1958

2

1.39

100-1100

1958

2

1.48

100-1100

1958

TiC

1.16

300-2000

1961

ZrC

0.95

300-2000

1961

HfC

1.42

300-2000

1961

NbC

0.86

300-2300

1961

TaC

1.07

400-2000

1961

TiN

2.48

100-1100

1958

ZrN

4.3

20-2560

1931

VN

0.7

TaN

0.03

ZrB Zr3

2 NbB TaB

12

1956 20-1410

1931

69

CHAPTER IV CONCLUSIONS AND RECOMMENDATIONS From this investigation it was concluded that: 1. The one, two, and three electron phases predicted by the electron concentration concept apply well to the transition metal interstitial alloys as shown by the excellent fit of the two-electron-phase region of the Brewer type diagrams of the column V metals. The line indicates perfect two-electron compositions and the appearance of the one, two, and three-electron phases in all cases where they were predicted. The metallic nature of these phases is demonstrated by their good electrical conductivity. 2. No fractional electron phases appear in the diagrams of the transition metal interstitial alloys. r 2 3. The 5d6sp bonding configuration is the strongest possible type for the transition metal interstitial alloys, being stronger 5 than the 5d 6s of tungsten and the 5d Osp of rhenium. -

4. The postulates which were proposed as controlling the physical properties, i.e., (a) total number of outer bonding electrons in the metal atom, (b) total number of inner bonding electrons in the metal atom, (c) principal quantum number of the incomplete, bonding, inner subshell in the metal atom, (d) relative sizes of the transition metal and alloy atoms, and (e) the ionization potentials of the alloy atoms, are valid.

70

5.

A ratio of 0.61 rather than 0.59 between the transition

metal and alloy atoms, as determined emperically from the binary diagrams, although not a large variation, is more appropriate for determining the formation of interstitials. Recommendations for Further Work It is recommended that: 1. This work be extended to cover the rest of the transition metals. 2. Further work be undertaken to extend the number of available phase diagrams for the transition metals with the second period interstitial elements and to confirm those already in existance. 3. When complete phase diagrams are available, Brewer type diagrams be constructed and evaluated. 4•

Further work be undertaken to extend and confirm the phys-

ical properties of the transition metal interstitial alloys. 5.

A systematic set of experiments be formulated and carried

out to determine the quantitative effects of the factors important in determining the physical properties of the transition metal interstitial alloys. 6. A study be made to determine the exact degree of ionization of the interstitial atoms and the exact electronic configuration of the transition metal interstitial alloys.

71

APPENDIX On the following pages appear the available phase diagrams for the column IV and column V transition metals with the second period interstitials.

72

wt %Be

Composition

5

0

20

10

30

40 50 60 80 100 I

1600 .t 1\ - I\ 1‘ \ 1400 1 1 \\ - 1 \ I 1200 i

I

I

I

_

‘

g-

\ ILiq E 0 1+./3‘ ‘ H 1000 )4 .1.., _ 800

Liq + TiBe 12

U2400 ° 0

Liq

2000 E I-

--Liq +- -^I. Ti Be (Ti 4Be ) 1 ITi Be -- 1

-

!,< a÷ g p i. Ti Be (Ti 4 Be 3 ) W - -I- ___i__— - i1T7Be 4 3

600 11 0

I "."1"

0

- 2800

a + Ti Be (Ti Be 3 ) I I4 30 20 40 50 60 10 Composition

Ti Be 10 T Be e

1600 Ti Be 12 Ti Be /

70

80

/ 1200 90

100 at %Be

Figure A-1. The Titanium-Berylliun System.

iu

73

3000

0

5

Composition 20 30 I I

10 I

i

wt %B 40 50 60 70 80 100 I I 1 1 iiA

\

....."

\.

/

2600

/

/

/

/ / Liq + TiB 2

2200

k i(

' P /

1

I 1

2200 ±50° C

, I B + TiB 1 "- 1800. 0 C 1 I

I I TiB

f3 + T i B

886 ±4° C

10

1 20

30

40

0)

-

TiB (42 1

-

II

I I

—

I

I I

I

I Ti 1i 2B5 I I IIII I

I

I 1

I I I I I

1 1 1 I

I I

I 1

70

80

90

0

0. a)E

-

-

I

50 60 Composition

--

I

I

I II

-

1,

I

4400

-

J

TiB

1

a + TiB

I

I

I I I

_

— 3600 1.1-

14TiB2 + Ti2B 1 51 1 I I 1

iB + TiB 2

D

1

j

1000

600

-

' ' ,I

1. 1 2 B

16

1400

1

I I

1 -, 20600 c 2

+ Liq _ L.41 I LTC

. 1800 0

I

I

.,

1

-

Ti 2 B + I TiET 1

I.2 ,.. - T' ,Ti 2 B.......

0

1

I I

I I I

I I 1 1

I

/

- 5200

I ......ij I I / 1 / I i I i 1

-

2800

2000

-

—

_

1200

101 at. %B

Figure A 2. The Titanium Boron System. -

—

I

74

Composition 0

3200

2

5 I

i

wt %C

10 I

15 I

20

3000 / 2800

i /

Liq

/

2600

/

/

2400

/ /

_ 4400

Ill

Liq + TiC

0

/1

I/

ie

2200

- 4800

/ ,

/

//

4000 -

2000

I-

LL.

0

- 3600 E

Liq

0

a.

- 5200 -

/

aEi

5600

// //

-

1800

E

1750 ±20° C

3200 TiC

1600 2800 1400

0

- 2400

+ TiC

1200 2000 1000

a

+ f3

_

920 t3 ° C

_ 1800 800 a

+ TiC

- 1200

600 0

10

20 30 Composition

40

50 at. %C

Figure A 3. The Titanium Carbon System. -

-

75

0

5

3000

wt %N

Composition 10

I

20 I

I

---...••• ......•• ...."

2800

"'-

/

Liq

/

/

4800

/

2600

5200

/ / Liq + / !I / / TIN i

2400 /

4400

/ I / 2350 ±25°C

/ / /Liq +a

2200

4000

/

Liq 2020 ±25°C 2000

3600 tL

g

U

0

a)

0 a) 42

e

1800 p

a)

o_ E a) I— 1600

3200 a E

, + TiN

F-

TiN 2800

1400 2400

a 1200

2000 1000 1600

a+ c 800 e+ TiN

600

1200

D

10

20

30

Composition

40

50 at %N

Figure A-4. The Titanium—Nitrogen System.

76

Composition

0

5

2000

w t %0

10

20

30

Liq

- L i ci

3600

77 +

Liq + a .'