The diffusion of carbon into tungsten Item Type text; Thesis-Reproduction (electronic) Authors Withop, Arthur, 1940- Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 25/09/2021 09:44:03 Link to Item http://hdl.handle.net/10150/347554 THE DIFFUSION OF CARBON INTO TUNGSTEN by Arthur Withop A Thesis Submitted to the Faculty of the DEPARTMENT OF METALLURGICAL ENGINEERING In Partial Fulfillment of the Requirements .For the Degree of MASTER OF SCIENCE In the Graduate College THE UNIVERSITY OF ARIZONA 1966 STATEMENT BY AUTHOR This thesis has been submitted in partial ful­ fillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library,, Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permis­ sion for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: / r / r ~ t / r t e //Date Professor of Metallurgical.Engineering ACKNOWLEDGMENTS I wish to express my appreciation to my advisor, Dr0 K 0 L 0 Keating, for his valuable guidance and advice with this project, to Mr, A, W, Stephens for his assist­ ance with the equipment, and to all the graduate students in the Department of Metallurgical Engineering for their encouragement and confidence. Finally, I am grateful to my wife, Toni, for her sacrifices and patience during my academic years. TABLE OF CONTENTS Page LIST OF ILLUSTRATIONSooooeooooo o O deoooeoooeoooooooooe vi LIST OF TABLES,0„OOOOOOO-OOOOOOOOOOOOOOOOOOOOOQOOOOOOO vii ABSTRACT0 .0 „o.oeo OOOOOOOOOOftOOOOOOOOOOOOOOOOOOOOOOOOO viii lo INTRODUCTIONOOOOOOOOOOOOOOOOOOOOOOOOOO.O 1 II. THEORY. 00000000000000006000000000 00 0.0 o O o 4 2.1 * S Laws oooooooooooooooooooaoooo 4 2.1.1 Steady-State-Diffusion..= 4 2.1.2 Non-Steady State DiPPxisaon.......oo.oo o. 5 2.2 Solution to Flck's Law............. 5 2.3 Diffusion Lengch.ooooooo.ooooooo.oo 8 2.4 Arrhenius Relation.......oo.oo....o 9 2.5 Meohanisms....ooooooooooooooooooooo • 9 2.5.1 Interstitial Diffusion... 10 2.5.2 Meaning of D^............ 10 2.6 van1t Hoff Equation... ...........I. 12 III. EXPERIMENTAL PROCEDURE.. ’ 15 3 o l Diffusion Couple.. .........ooooo.o. 15 3o2 F U m a G e OO.O.O.OOOOOO.OOOOOOOOOOOOO* 16 3.3 S e C t l O m n g o OQ.OOO.OOOOOOOOOOO.OOOOO 20 3.4 X —Ray Diffraction..ooo.ooo.oooooooo 23 4 ir V TABLE OF CONTENTS— Continued Page IV, EXPERIMENTAL RESULTS,,,,,,,,,,,,,,,,,,,, 30 V o DISCUSSION OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO '35 5.1 Comparison of''Results' with.... Literature, o,,,,-,,,,000,0,00000000 35 5.2 Equilibrium Analysiso,,,,*,,,,,,,,, 37 VI , CONCLUSIONS ,,00000 <>00000000,,0000000,,og 35 REFERENCES o,,,,o,,,,,,,,,,00,0,00,0000000,0,0o,,,,,,, LIST OF ILLUSTRATIONS Figure Page 2-1 Tungsten-Carbon Diffusion Couple 0 „ „ 0«= <,»<,«o = = 7 2-2 Interstitial Mechanism,,, 0 »=,,, »6,,, o = = 11 3-1. Tungsten Microstructure , 18 3-2 Vycor Tube Furnace0000000000,00000,00000,0000 15 3-3 Induction Piirnace 0,0,0000000,000,00000 0,00000 21 3-4 Diamond Grinding Unit,„,,«,,o,,, =,, =,,,,o«, =, 24 3-5 X —Ray Diffractometer000,000,oooooooooooooo,,, 25 ' 3-6' Tungsten Carbide Microstrueture,,,„,,„„0,,=0, 27 4-1 Loge K vs'Dlffuslon-Anneal'Temperature at'... 6 h o u r s OOOOOOOOOOO OOOOOO, 00000 00000,0009000 32 5-1 Loge D vs Diffusion-Anneal Temperature- Curves From Literature0,000000000000ooooo,, 3 6 vi LIST OF TABLES Table Page 1 Results of Literature Survey0 =>«, <> = <>» <> = „. <,00000 2 2 Chemical Analysis' of Diffusion' Couple'"' "... - MatenalS 00000 ooooeooooooo*oo<>ooo»QOO 00 0000 17 3 Dl f fu s 1 on - Annea 1 Data. 00 000=. 00 000000 = 00 000000 22 4 Surface Reactlon-Rate Data. = = o o 0 = = = o = = = = = = = =» 31 vll ABSTRACT This investigation was concerned with the kinetics of the tungsten carbide reaction of cylindrical specimens of graphite and tungsten in the temperature interval 979° - 1382° C 0 The kinetics of the carbide formation were studied in relation to Pick's Laws of diffusion and the van't Hoff relation for reaction-rate constants0 Analysis of the surface reaction and penetration was determined by x-ray diffraction techniques0 The results showed that in the temperature range studied, diffusion was not controlling but rather the chemical reaction rate.of carbide formation determined the amount of tungsten carbide. The activation energy for the reaction, W -f C = WC, was- found to be -10,090 + 1200 cal/mole. viii- Io INTRODUCTION During the past decade there has been considerable energy expended in an effort to study solid state diffusion in body-centered cubic metals (Thomas and Leak, 195^5 Ranthenau, 1958; Adda and Kiriananko, 1959J Smith, 19621 Federer and Lundy, 19635 Murdock, Lundy, and Stansbury, 1964)o This is due in part to the formation of inter- metallic compounds in this lattice system, and currently is of interest as new materials for high temperature structural applications* Because these compounds exhibit various crystal structures, lattice imperfections, and bonding types, knowledge of their diffusion mechanisms and activation energies is of basic valuee Concerning the diffusion of carbon into tungsten there is wide disagreement among previous investigators (Pirani and Sandor, 19475 Kottrel, 19565 Aleksandrov, i9605 Becker, Becker, and Brandes, I96I5 Aleksandrov, 1962) on the experimental values of the frequency factor, D^, and the activation energy, Q, in the Arrhenius relation* Their results appear in Table 1* Values of D0 vary by many orders of magnitude and the values of Q differ by JO Kcal/ mole* 1 TABLE 1 Results of Literature Survey 2 Temperature Investigator D , cm /sec Q, Kcal/mole Range, °C PIrani and Sandor, 1947 0.31 59 ± 5 1535-1805 Kottrel, 1956 2.54 x 10 -112 + 3 above 1400 6 Aleksandrov, i960 1.80 x 101 39o5 + 13.4 above 1400 Becker, Becker, and Brandes, -6 . 1961 . 1.60 x 10 50.34 1400-2400 Aleksandrov, 1962 0.31 - 61«5 + lo5 900 ...... 3 These discrepancies suggested that a study of the kinetics of the reaction forming tungsten carbide was neededo It was felt that a study of diffusion, in terms of Pick's Laws, for the tungsten-carbon system would resolve this problem* However, in the temperature inter­ val studied, 980° - 1380° C, no measurable diffusion was observed. Examination of the carbide concentration at the diffusion couple interface, in relation to the van't Hoff equation, showed that in the temperature range investigated a diffusion mechanism was not controlling the reaction. It was found that the reaction kinetics were controlled by the ability of carbon and tungsten to react to form tungsten carbide. II. THEORY 2,1 Pick's Laws It was proposed.by Pick in 1855 that the mass flow of solute through an isotropic solvent material could be expressed mathematically„ Based upon the heat- flow equations derived by Pourier (Birchenall, 1959)^ Pick proposed two laws to describe this diffusion,, Pick's two laws are based upon the equilibrium conditions of the system, i.e., steady-state or non-steady-state diffusion, 2,1.1 Steady-State Diffusion, Pick's first law states that the atomic flux, J, across a given plane of area. A, will be proportional to the atomic concentra­ tion gradient, d c/ d x, across that plane, i,e,, J (2|S S ) = -D( £ ) £f (SSgg£g). 2-1( - ll t - - where D, the proportionality constant, is called the diffusion coefficient. The negative sign indicates that if a concentration gradient exists in a system, matter will flow in such a manner as to decrease the gradient. As the material becomes homogeneous the flux approaches zero, which satisfies Eq» (2-1). 20lo2 Non-Steady-State Diffusion0 If the concentration at some point, x, is a function of time, Eqe (2-1) is not a convenient form to use. To obtain Pick's second law it is necessary to use Eq„ (2-l) and a material balance to find another differential equation (Shewmon, 1963)0 The resulting relation then is 8c/81 = 8/8 x (D 8 c/8x) „ (2-2) It is desirable in diffusion studies to describe the concentration of solute as a function of position and time, c(x,t)0 That is, in a given diffusion couple composed of materials A and 33, it is of value to know the depth of penetration of A into B 0 2,2 Solution to Pick's Law If the diffusion distance is short relative to the length of the solvent material, c(x,t) can be ex­ pressed in terms of error functions. When the diffusion couple approaches homogeneity an infinite trigonometric series can describe e(x,t) (Crank, 1956), The present study will be concerned with non-steady-state diffusion; therefore, it shall deal with error functions. Solution of Eq, (2-2) in terms of c(x,t) requires a knowledge of the boundary conditions of the system. The geometry of the diffusion couple will be discussed in Section 3.1; however, it is necessary to know that the couple has an extended, or semi-infinite, solute source, as shown in Pig.