Bramfitt关于二维错配度计算

The Effect of Carbide and Nitride Additions on the Heterogeneous Nucleation Behavior of Liquid Iron BRUCE L. BRAMFITT A systematic study of carbide.and nitr ide additions on the heterogeneous nucleation behavior of supercooled liquid iron was undertaken. It was found that t i tanium nitr ide and t i tanium car- bide were very effective in promoting heterogeneous nucleation. These compounds were fol- lowed by si l icon carbide, z i rconium nitr ide, z i rconium carbide, and tungsten carbide in de- creas ing order of effectiveness. The degree of potency of the nucleation catalysts is explained on the basis of the d isregist ry between the lattice parameters of the substrate and the nu- cleating phase. Through the inclusion of planar terms the Turnbul l -Vonnegut " l inear" dis- reg is t ry equation was modified to more accurately describe the crystal lographic relat ionship at the interface during heterogeneous nucleation. THE theoret ical aspects of heterogeneous nucleation h~'ve been discussed in severa l recent review art ic les . 1-4 The interfacial free energy at the nucleating interface is the control l ing factor in heterogeneous nucleation behavior; however, a simple descript ion of the inter - facial energy is not possible since the total interracial free energy of the system is composed of severa l con- t r ibutory factors. Some of these factors are the chem- ical nature of the substrate,5 the topographic features of the substrate surface,8 the electrostat ic potential be- tween the substrate and the nucleated solid, 7 and the lattice strain or d is reg is t ry between the two phases at the interface. 8 The contribution of lattice d isreg ist ry to heterogene- ous nucleation behavior has been emphasized by Turn- bull and Vonnegut 8 who theorized that the effect iveness of a substrate in promoting heterogeneous nucleation depends on the crystal lographic d is reg is t ry between the substrate and the nucleated solid. The d is reg is t ry can be written as 5 = (Aao/ao) where Aao is the dif- ference between the lattice parameter of the substrate and the nucleated solid for a low-index plane, and ao is the lattice parameter for the nucleated phase. For a d is reg is t ry factor up to 0.20, the interface region can be explained by a simple dislocation model that com- pensates for the latt ice stra in in the nucleated phase. The degree of supercool ing of a liquid was postulated to be a parabol ic function of the d isreg ist ry factor. Several invest igators have tr ied to relate hetero- geneous nucleation behavior to crystal lographic dis- reg ist ry . For example, the promotion of heterogene- ous nucleation by the intentional addition of nucleating agents has been studied in a number of pure metals and eutectics. 9- is Bradshaw, Gasper,and Pearson 9 studied the nucleation behavior of gold droplets, 60 to 600 ~ in diam, using a hot-stage microscope. Work- ing with carbides, n i t r ides, and oxides, these invest i - gators found that the least effective as nucleation catalysts were the oxides. They concluded that the d is reg is t ry between the catalyst and the gold was not a significant factor for nucleation behavior since some of the oxides had smal l d is reg is t r ies . BRUCE L. BRAMFITT is Research Engineer, Alloy Development Section, Homer Research Laboratories, Bethlehem Steel Corp., Bethle- hem, Pa. Manuscript submitted December 22, 1969. Using a s imi lar hot-stage technique, Sundquist and Mondolfo 1~ studied the nucleation behavior of sixty bi- nary eutectics. Their main observat ion was that in a eutectic system one phase nucleates the other but not v ice versa . They also studied var ious orientation re- lat ionships in the heterogeneous nucleation of lead droplets by smal l single crysta ls of Ni, Cu, Ag, and Ge 6 and found that for any given nucleating agent the supercool ing was fair ly constant and not dependent on the or ientat ion relat ionships of d is reg is t ry . They postulated that heterogeneous nucleation starts with the formation of an absorbed layer of the nucleated phase on the substrate and that cavit ies in the sub- strate act as sites for heterogeneous nucleation. Reynolds and Tottle n investigated heterogeneous nucleation in Zn, A1, Mg, Sn, Pb, Cu, and Sb castings by applying var ious metal powders to the surface of sand and metal l ic molds. The effectiveness of the powders as nucleating agents was determined by com- paring the grain size at the casting surface exposed to the powders with the grain size at an unexposed sur - face. They found that the metal powders that had a crysta l structure s imi lar to that of the melt mater ia l were effective in promoting nucleation when the lat- tice spacing difference between the powder and the melt mater ia l was less than 10 pct. If the lattice mis - fit was greater than 10 pct, positive results were not obtained. Gl icksman and Childs12 studied the effect of catalytic substrates on the supercooling of l iquid tin. Super- cooling measurements were made in a vacuum-induc- tion furnace s imi lar to the one used in the present investigation. They obtained reproducible supercool ing measurements with and without the presence of the substrate in the melt. Among the substrates tested were carbides, sulf ides, oxides, and individual ele- ments. Working with a single crysta l of yttr ium be- cause its lattice spacing is s imi lar to that of tin, they obtained two character ist ic supercool ing values, de- pending on whether the pr ismat ic or the basal plane was exposed to the melt. Wallace and coworkers ~s- 17 have studied the effect of var ious inoculants on the nucleation behavior of i ron-base al loys. Their work did not involve super- cooling studies but did involve the effectiveness of the foreign mater ia ls on grain ref inement. Most of the additions were selected on the bas is of a good lattice METALLURGICAL TRANSACTIONS VOLUME 1,JULY 1970-1987 reg is t ry between the addition and 6 Fe. They found that the ferroniobium and ferrot i tanium additions as well as titanium carbide and titanium metal were ef- fect ive in producing an equiaxed grain st ructure. Recently, Cros ley, Douglas, and Mofidolfo TM have studied the heterogeneous nucleation behavior of lead using a number of di f ferent substrates. They found that the requ i rements for a good nucleating agent are: a) that the interfacia l energy between the substrate and the liquid be higher than the interracia l energy between the nucleated sol id and the liquid, and b) a good epitaxial fit between low-index planes of the sub- st rate and the nucleated sol id should exist . The present investigation involves a study of the heterogeneous nucleation behavior of supercooled liquid iron with and without the presence of a catalyt ic substrate. The supercool ing resu l ts were evaluated in light of the d i s reg is t ry theory proposed by Turn- bull and Vonnegut. 8 EXPERIMENTAL PROCEDURE The supercool ing measurements were made in a vacuum-induction furnace, see the c ross -sect iona l v iew in Fig. 1. Each charge of pure iron (99.95 pct) was weighed before melt ing in order to maintain a constant weight of 100 • 1 g. The chemical composit ion of the melt ing stock is given in Table I. The crucible SIGHT GLASS ALUMINA THERMOCOUPLE- - SHEATH GRAPHITE SUSCEPTOR ALUMINA INSULATION ALUMINA CATALYST ROD ALUMINA "CRLJCIBLE INDUCTION COIL PYREX TUBE 6"0I). X 3~'LONG ATMOSPHERE , INLET �9 DEFLECTION VACUUM SYSTEM Fig. 1--A cross-sectional view of the vacuum-induction fur- nace in which the supercooling measurements were made. Table I. Analysis of Electrolytic Iron Melting Stock Carbon 0.002" Titanmm Manganese G0.001 (<0.01)* Aluminum Phosphorus 0.001 * Zirconium Sulfur 0.004* Tungsten Sihcon G0.001 Tantalum Chrommm <0.001 Boron Nickel G0.001 Beryllium Molybdenum G0.003 Tm Copper <0.001 Zinc Vanadium <0.001 Oxygen Cobalt G0.001 Nitrogen <0.003 G0.001 <0.005 <0.05 <0.05 <0.0001 G0.0001 <0.001 <0.001 0.0078/0.0083 t 0 0006* *Determined by wet chemical analysis. tDetermined by vacuum fusion analysis. All other elements determined by spectrographic analysis. 120 I00 . 80, o z -I o o sc n,~ LIJ 0.. :3 4C 2O 080 �9 �9 ~ . . . . . . . . . . . . . . . . . o: �9 :* . :o . �9 e l eJ �9 : ~ . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . "_ _ _ _ �9 . . . . . . ~zo ~6o zbo ' z4o 2no 3~o' 36o SUPERHEAT, *F Fig. 2--Effect of superheat on supercooling of liquid iron. containing the charge was placed in a graphite suscep- tor within the melt ing furnace. The cruc ib les used were high-pur i ty aluminum oxide (99.5 pct A1203). After evacuation of the furnace chamber to at least 10-5 to r r , the chamber was backf i l led with zero -grade helium to a pressure of about 400 to r t . Upon melt ing, a thermocouple sheath, 3 mm in diam, was inserted into the melt . Since the sheath cons isted of the same mater ia l s as in the crucib le, the molten iron was ex- posed to only high-purity aluminum oxide. The P t -P t + 10 pct Rh thermocouple was connected to a record - ing potent iometer , which was compensated for room temperature . Visual observat ion of the melt ing opera- tion was made through a sight glass on the water- cooled furnace cover. For the supercool ing studies, the melt was allowed to superheat at least 140~ to insure complete melt ing, and then al lowed to cool at the rate of 175~ per min until f reez ing was complete, during which t ime the amount of supercool ing was recorded. As shown in Fig. 2, init ial tests had establ ished that a superheat below 140~ gives e r ra t i c supercool ing values and would therefore be undesirable as a basis for developing con- s istent supercool ing resul ts . F ig. 2 also indicates the type of data that is generated by exper iments of this nature. It was also establ ished that at least four 1988-VOLUME I,JULY 1970 METALLURGICAL TRANSACTIONS Table II. Carbide and Nitride Powders Used as Potential Nucleating Agents for Liquid Iron Compound Purity, Pct Phases Present Boron Carbide 99.6 B4 C Chromium Carbide 99.0 Cra C2 Hafnium Carbide 99.5 HfC Molybdenum Carbide 99.9 Mo2 C Niobium Carbide 99.8 NbC Silicon Carbide 99,0 aSiC + 13S]C Tantalum Carbide 99.9 TaC Titanium Carbide 99.5 TiC Tungsten Carbide 99,9 WC Vanadium Carbide 98,0 V4 Ca Zirconium Carbide 99,5 ZrC Aluminum Nitride 99,5 A 1N Boron Nitnde 99,9 BN Molybdenum Nitnde 99,5 7Mo N (Approx 20 pct 6MoN) Niobium Nitnde 99.5 NbN Tantalum Nltride 99.5 TaN Titanium Nitride 99,0 TiN Tungsten Nltnde 98.0 WN, W Vanadium Nitride 98.0 VN Zirconium Nitride 99.99 ZrN (Trace of ZnO) The hafnium carbide is typical of the fourteen com- pounds that fai led to promote nucleation. As seen in Fig. 4, the supercool ing of pure iron was not affected by the addition of the hafnium carbide, demonstrat ing that this compound is ineffective in nucleating 5 iron. The reason that hafnium carbide was not effect ive was because it d issolved in molten iron, due to the inherent conditions of the exper imenta l technique, and because nucleation cannot take place unless a surface is avai l - able. Th is situation, typical of the fourteen ineffective compounds, is in contrast to the six compounds which remained solid and thus provided nucleation sites throughout the exper imenta l run. The most effect ive of the group of six compounds were t itanium nitr ide and t itanium carbide, a finding which is in accord with the work of Wallace and co- workers , 1~-17 who demonstrated that t itanium and titanium carbide additions are very effective in pro- ducing grain ref inement in steel ingots and cast ings. According to the theory advanced by Turnbul l and Vonnegut, a nucleating agent wil l be effective in pro- moting nucleation when the latt ice parameters in the melt ' rag-and-freez ing cyc les were requ i red to obtain a consistent value of supercool ing. The next step was the immers ion of a 1-mm diam catalyst rod into the Ior melt . The rod, also of h igh-pur i ty aluminum oxide, contained the nucleating agent. The nucleating agents were the high-purity carbide and nitr ide powders ~ 8r l isted in Table II. Approximately 50 mg of the -325 m mesh powder was bonded to the end of the rod by o6c means of a sodium si l icate binder. With the rod im- o o mersed in the melt at a superheat of 200~ the change in supercool ing, if any, was recorded. The ~ 4c level to which the supercool ing changed was con- s idered to character i ze the nucleation behavior of the part icu lar mater ia l . 2c Each sol idif ied ingot was sect ioned to provide sam- ples for chemical analys is and metal lographic exam- c ination. The chemical analysis consisted of both spec- t rographic and wet analys is . Standard metal lographic technique was employed to study any nonmetal l ic phases that were present , e.g., nit r ides, carb ides, and oxides. Each of the nucleating agents was analyzed by X- ray Izo dif fraction to determine which phase or phases were present. Most of the compounds were found to be pure, as indicated by X - ray diffraction. The phases present Ioo in each of the compounds are given in Table II. 12o " 80 o RESULTS AND DISCUSSION o" z Of the twenty carb ides and nitr ides evaluated, only ~ 60 six proved to be e f fec t ive in promoting nucleation in oo l iquid iron. The character i s t i c supercool ing and re la - t ive ef fect iveness of these six compounds are noted ~ 4o tD in Table III. An example from this group, z i rconium nitr ide, typif ies the change in supercool ing that resu l ts 2o f rom the addition of the compound, Fig. 3. The z i r - conium nitr ide decreased the supercool ing of pure iron to an average value of 12.6~ i .e. , this addition was o moderate ly effective in promoting the heterogeneous nucleation of 6 iron. The average value for a part icu- lar catalyt ic substrate is cal led the character i s t i c supercool ing value ATc for the substrate. 0 .___o . . . . . . o . . . . . . . . ? _ . . . . e o o 0 WITHOUT ADDITION �9 WITH ADDITION e . . . . . . . . . . . . . . . . . . . . . . . . FREEZING CYCLE NUMBER Fig. 3--Supercooling data for the zirconium nitride addition, representative of the effective nucleating agents. e o o . . . . . . . . 0 - - - . . . _e . . . . . -e- . . . . . . . . . . . . . . . . . . o - - - O �9 �9 0 WITHOUT ADDITION �9 WITH ADDITION i i i , i i i | i , = i , i 2 4 6 8 I0 12 14 16 FREEZING CYCLE NUMBER Fig. 4--Supercooling data for the hafnium carbide addition, representative of the compounds that did not promote nuclea- tion. METALLURGICAL TRANSACTIONS VOLUME 1, JULY 1970-1989 l ow- index c rys ta l lograph ic p lanes of both the sub- s t ra fe and the nuc leated so l id a re s imi la r . The de- g ree of mismatch of these parameters , i.e., the d is - reg is t ry , is expressed as 5 = Aao/ao. In Tab le IV, which l i s t s the c rys ta l lograph ic p rop- e r t ies of the ef fect ive compounds , the ao was ca lcu - lated f rom the room temperature value of ao by taking into account the l inear thermal coef f i c ient of expan- s ion of the compound between room temperature and 2800~ 19 The c rys ta l lography of the compounds can be d i - v ided into two bas ic c rys ta l sys tems, namely , cub ic and hexagonal . T i tan ium n i t r ide , t i tan ium carb ide , z i rcon ium n i t r ide , and z i rcon ium carb ide , the com- pounds with the cubic rock -sa l t type of s t ruc ture , have respect ive d i s reg is t r ies of 3.9, 5.9, 11.2, and 14.4 pct, which show a t rend re f lec t ing the re la t ion between d is reg is t ry and supercoo l ing . That is , as the d i s reg is t ry inc reases , the degree of character i s t i c supercoo l ing a lso inc reases . A c lose look at the la t t i ces of 5 i ron and t i tan ium carb ide ind icates the degree of coherency that ex i s ts . The (100) of 5 i ron para l le l to the (100) of t i tan ium carb ide with the [ 100]Fe/ [ 100]TIC is shown in F ig . 5. Fur ther conf i rmat ion is p rov ided by ex is tence of th is type of re la t ionsh ip for both the t i tan ium carb ide and t i tan ium n i t r ide prec ip i ta tes in a i ron. 2~ S i l icon car - bide (ZnS Type B3), with a d i s reg is t ry va lue of 6.0 pct, fa l l s within the t rend of the compounds of the NaC1- type s t ruc ture . The d i s reg is t ry for the NaC1 and ZnS types of s t ruc tures was determined by the d i f fe rence between the ad justed a0 for the compound and the lat - t i ce parameter along the [110] of 5 i ron d iv ided by the parameter a long the [110] of 8 i ron. The parameter a long the [110] of 5 i ron is 4.1457A. The tungsten carb ide prov ides an example of a compound of the hexagona l sys tem. The tungsten a toms f i l l the corner pos i t ions and the carbon a toms f i l l the Table Ill. Summary of Supercooling Data for the Six Compounds Effective in Promoting Nucleation in Liquid Iron Characteristic Relative Compounds Added Supercooling, ATc, ~ Effectiveness Titanium Nitnde 3.1 Very Effective Titanium Carbide 3.3 Very Effective Sdicon Carbide 7.5 Moderately Effective Zirconium Nltride 12.6 Moderately Effective Zirconium Carbide 24.5 Least Effective Tungsten Carbide 29.0 Least Effective . • , 2 1 -~,-~, and ~, -~, -~ pos i t ions of the unit ce l l . As dem- onst ra ted in F ig . 6 by the superpos i t ion of the (111) of 5 i ron on the (0001) of the tungsten carb ide , the con- d i t ions for apply ing the Turnbu l l -Vonnegut equat ion are met in th is case as wel l . The d i s reg is t ry for th is case along the [ 110] of the 5 i ron and the [12]0] of the tungsten carb ide is 29.4 pet, a va lue which imp l ies poor coherency between the two phases . The charac - te r i s t i c supercoo l ing value of tungsten carb ide was found to be 29~ which is c lose to the character i s t i c supercoo l ing va lue of 24.5~ for z i rcon ium n i t r ide with a d i s reg is t ry of only 14.4 pct. Thus , the ca lcu la ted d i s reg is t ry of 29.4 pet for the tungsten carb ide and 8 i ron is much too high for a character i s t i c supercoo l ing va lue of 29~ The above ca lcu lat ions indicate that the Turnbu l l - Vonnegut equat ion p laces a s t r i c t l im i ta t ion on the se - lect ion of a c rys ta l lograph ic re la t ionsh ip , s ince only p lanes of s imi la r a tomic a r rangement a re cons idered . To i l l us t ra te th is point, another c rys ta l lograph ic re - la t ionsh ip between tungsten carb ide and 5 i ron is ,(( ) !t J t j,, T ITANIUM ATOMS - - DASHED C IRCLES CARBON ATOMS - SHADED C IRCLES 8 - IRON ATOMS - SOL ID C IRCLES Fig. 5--The crystallographic relationship at the interface between the (100) of titanium carbide and the (100) of 5 iron. Table IV, Crystallographic Data for the Effective Nucleating Agents = Room Temperature, Crystal Lattice Parameter, A ao Turnbull-Vonnegut Planar Compound System ae Co at 2800~ * Disregistry, Pet Disregistry, Pet TiN Cubic NaC1 (B1) 4.246 - 4.308 3.9 3.9 TiC Cubic NaC1 (B1) 4.3270 - 4.3901 5.9 5.9 SiC Cubic ZnS (B3) 4.35965 - 4.3954 6.0 6.0 ZrN Cubic NaCI (B1) 4.56 - 4.61 11.2 11.2 ZrC Cubic Nacl (B1) 4