Dendrite Spacing Selection during Directional Solidification of Pivalic Acid-Ethanol System

340J. Mater. Sci. Technol., Vol 24 No. 3, 2008Dendrite Spacing Selection during Directional Solidificationof Pivalic Acid-Ethanol SystemMyung-Jin Sukt, Young-Min Park and Youn-Che KimDepartment of Materials and Metallurgical Engineering, Kangwon National University, Samcheok 245-711, KoreaUnidirectional solidification of pivalic acid(PvA)-ethanol(Eth mixture was performed to examine whetheran allowableofdefinitely exists at a given growity and how theis history-dependent. PVA-0 59 wt pct Eth was unidirectionally solidified in the range of growth velocity0.564 um/s at the temperature gradient of 2.3 K/ mm. Sequential change in growth velocity was imposedto determine the upper and lower limits for the allowable range of stable spacing. An allowable range of thesteady state primary spacing was observed at a given growth velocity, and the extent of the range seems tobe dependent on the degree to which step-increase or step-decrease in growth velocity is accomplished. Asthe degree of sequential change in growth velocity increases, the history-dependence of the selection for theprimary dendrite spacing tends to disappearKEY WORDS: Dendrite spacing, History-dependent, Spacing selection, Pivalic acid-ethanol1. Introductionbeen occasionally used as a model substance be-cause their transparency makes it possible to observeIt has long been recognized that primary dendrite in-situ the microstructural evolution during uni-spacing is unique at a given growth condition[l-a, directional solidification. Pivalic acid(PVA)-ethanoland several analytical equations were derived to relate (Eth ) mixture was adopted in the present work, whichthe primary spacing A1 with the growth parameters has an anisotropic interfacial property that might be(growth velocity V and temperature gradient G) 4-6. expected to infuence the dendrite spacing selectionThe equations are commonly expressed as2. ExA∝G-1/2v-1/4As-received PVA(Aldrich, 99% purity) was puHowever, it is now generally accepted that no rified by vacuum distillation followed by zone refinunique primary spacing is stable, but a band of spac- ing with 30 passes through 8 heaters. Eth(Aldriching is allowed at fixed growth condition 7-14). Hunt 99.5%)was used as-received without additional pu-and Lu(9) developed a numerical model that can pre- rification process. The purified PVA and Eth weredict cellular and dendritic spacings, and proposed a melted and mixed in the glove box under the highlower limit of the allowable spacing band where one purity nitrogen atmosphere, the composition be-cell or dendrite is overgrown by the neighboring cell or ing PVA-059 wt pct Eth. The PVA-Eth mixturedendrite. At upper limit tip splitting of cell or branch- was then injected into a thin glass cell (4 mmx02ing of tertiary dendrite arm occurs, restoring the spac. mmx300 mm)by using nitrogen pressure, and sealeding into the allowable range. The average spacing lies with epoxy resin. PVA-Eth mixture was subsequentlythus somewhere between the lower limit and upper subjected to directional solidification in a horizonlimit, and the spacing at a given growth condition tal Bridgman gradient heating stagel16) which wascan be dependent on how the present growth state mounted under the objective of a transmission mi-is attained; that is specimen history-dependent. The croscope. Sequential stepwise variation of the growthhistory-dependent primary spacing was expected by velocity was employed throughout a whole experi-Warren and Langerllsl, and several experimental re- mental run in order to examine the so-called historysults reported so far supported their sono y moduciba velocity the establishment of steady state is criticalnow, the primary spacing in unidirectiontion experiment has shown a reasonable reproducifor the reliable measurement of the dendrite spacingity in a given system, and this may be attributed to It was confirmed from the preliminary experimentthe same experimental situation that growth is always where three sets of dendrite spacing were traced frominitiated from"stop"to the desired growth velocity, the start of growth with a velocity of 8 um/s as showncontinuing with the constant velocity. Depending on in Fig. 1 that the growth should proceed at least 2 cmthe growth condition before the current one the piInn aatahlishment of steady statemary spacing selection may differ within the allow中国煤化工 CCD camera wereable range of the spacing. The present work is under- capttaken to examine the history dependence of primary (4CNMHG中 th of the glass cespacing, giving some insight into primary spacing se- tion was 20 to 40 depending on the size of dendriteslection process. Transparent organic materials have Primary spacing was measured using image analyzingsoftwareby either the shortest distance between thet Prof, Ph. D, to whom correspondence should be addressed, two neighboring dendrites or the width of one denE-mail: panpan@kangwon ac kiJ. Mater. Sci. Technol., Vol 24 No. 3, 20083416810121416182022Fig1 Variation of primary spacing with the growth dis-tance in the initial transient stagooo PvAO, 59 wt pato5min(step-down)Fig 3 Micrographs obtained at v=11.5 um/s which is(a) increased from 7.1 um/ s, and(b)decreasedfrom 17.2 um/sGrowth velocity /(um/sFig 2 Dependence of primary spacing on growth veloc-PVAO. 59 wt pct Ethity at 1.5 times-step variation in growth velocity.Hunt-Lu modeldrite. The temperature gradient was maintained tobe 2.3 K/ mm in the range of growth velocity 0.5-64um/s employed in the present work.△mn( step-up)3. Results and Discussionmin(step●maxFigure 2 shows the result of the experiment inwhich sequential stepwise variation in growth veloc-Growth velocity/(um/s)ity occurs by 1.5 times thegrowth velThere is an allowable range of stable primary spacing Fig 4 Dependence of primary spacing on growth veloc-in the experiments of either step-increasing(step-up)or step-decreasing growth velocity(step-down). Here, the same growth velocity of 11.5 um/s which hasthe stable primary spacing observed. Therefore, the been decreased from 17. 2 pm/s. One can find theactual upper limit of an allowable range of the primary dendrite spacing to be quite different depending onoccurs would be larger than the maximum value, and result on the history-dependent primary spacing isinvolved would be smaller than the minimum value. It 7, 10-14, but there is no theoretical background whichto be noted that the allowable spacing range in the explains the physics of the phenomenacase of step-increasing velocity exists at upper regimeThe adjustment of dendrite spacing after a suddenin this plot than the spacing range of step-decreasing change of growth velocity is accomplished through ei-velocity, an average dendrite spacing of the former ther branching of tertiary arm or elimination of onealways being larger than that of the latter. Thus the dendrite, which in turn would require a critical drivingmaximum value in the step-up experiment and the force. When the stepped increment or decrement inminimum value in the step-down experiment corre- growt中国煤化工 nes-step in Fig2spond to the maximum and the minimum primarythespacing allowed at a given growth velocity, respec-CNMHGuntil the thresh-tively. Figure 3 gives the micrographs showing that old arLy taige is availed. When thethe primary spacing is dependent on the history of stepped change in growth velocity is increased to 2the specimen. Figure 3(a)shows dendrite array at times-step as shown in Fig 4, the situation is some-growth velocity of 11.5 um/s which has been stepwise what different. The average primary spacing in theincreased from 7.7 um/s, while Fig.(b)is obtained at step-up experiment are not always larger than those342J, Mater. Sci. Technol., Vol 24 No. 3, 20082 wt pct salol system(i7 with a nearly isotropic inter-4. Conclusions(1)There is an allowable range of stable primary spacing, and the minimum spacing obtained arin reasonable agreement with the lower limit calcu-lated according to Hunt- Lu model. Average primaryspacing shows specimen history-dependence, giving alarger value at step-increasing growth velocity than atExperimental run No (V-8 um/s)(2)As the degree of the stepped increment inFig5 Ranges of primary spacing at five independent ex. growth velocity increases history-dependence of theof 8 um/sappear. The influence of the previous growth condition on the current one becomes mitigated, and theselection of primary spacing is then equally probablein the step-down one, and the allowable ranges of thewithin the allowable spacing rangestable primary spacing of both step-up and step-downgrowth condition overlap, while the extent of theange slightly shrinks. Almax/AImin is 2.4 at 1.5 times-step, and 2 at 2 times-step. In this case the driving dation Grant funded by the Korean Governmentforce for the change of primary spacing correspond- (MOEHRD)(R05-2004-000-10046The authors areing to the change of growth velocity is sufficiently grateful to Mr. Y MSohn and Mr. w.S. Kim for theirprovided by 2 times-step. If the stepped change in experimental assistancethe growth velocity is even larger than 2 times, therewould be no difference between the allowable rangesREFERENCEof primary spacing in step-up and step-down experi- (RTrivedi and w Kurz: Acta Metall. Mater, 1994Figure 5 shows the primary spacings obtained at (2]HKaya, E. Cadirli, K.Keslioglu and M Marasli: JCryst. Growth, 2005, 276, 583.growth velocity of 8 um/s was employed thioughoutL Makkonen: J Cryst. Growth, 2000, 208, 772a whole experimental run. The average primary spacJJ D Hunt: Solidification and Casting of Metals, Theings are randomly selected within the allowable range,Metals Society, London, 1979, 3.and the individual primary spacing ranges are almost 5 wKurz and D J. Fisher: Acta Metall, 1981, 29, 11R Trivedi: Metall. Trans. A, 1984, A15, 977.probability of any selection for the primary spacing [71 WHuang, X Geng and Y Zhou: J. Cryst. Growthis even within the spacing range allowed at a givengrowth velocity, and the primary spacing selection is [8] S.H. Han and R Trivedi: Acta Metall. Mater., 1994,42,25governed by chance as long as a constant velocity is (91 J.D. Hunt and S.Z. Lu: Metall.Mater.Trans.A,1996employed27A,Hunt and Lull suggested an analytical equation (10)X Lin, W Huang, J. Feng, T Li and YZhou: Actaconcerning a lower limit of the allowable spacing range Mater., 1999, 47, 3271on the basis of numerical analysis. The lower limit ob- [11] H Chen, YSChen, X. Wu and S N Tewari: J. Crysttained according to Hunt-Lu model is drawn in Figs. 2Growth,2003,253,413.and 4 and is in reasonable agreement with the AImin12 D Ma: Metall. Mater. Trans. B, 2002, 33B, 223.In the present work cells were formed at the growth[13 H.J.Diepers, D Ma and LSteinbach: J Cryst. Growth,velocities lower than 1.5 um/s, and this is the reason2002,237-239,149.[14] D Ma: J. Cryst. Growth, 2004, 260, 580why the Hunt-Lu line does not match with the Aimin j15j J.A.Warren and J.S. Langer: Phys. Rev. A, 1990at those growth velocities. The interfacial anisotropic42A,5518property of PVA-Eth system does not seem to afect [16]MJSuk and K. Leonartz: J. Cryst. Growth, 2000,the primary spacing selection in view of that both ex-213,141tent of primary spacing range and features of history-,[17] MJSuk, Y M Park and Y D. Kim: Scripta Materdependence are almost the same as in succinonitrile.2007,57,985中国煤化工CNMHG