ScienceDirect. Measuring solid liquid interfacial energy by grain boundary groove profile method (GBG)

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1 Available online at ScienceDiect Mateials Today: Poceedings 2S (215 ) S36 S313 Joint 3d UK-China Steel Reseach Foum & 15th CMA-UK Confeence on Mateials Science and Engineeing Measuing solid liquid intefacial enegy by gain bounday goove pofile method (GBG) S. Son*, H. Dong a Depatment of Engineeing, Univesity of Leiceste, Univesity Road, Leiceste, LE1 7RH, UK Abstact The solid liquid intefacial enegy plays impotant ole in the liquid solid tansfomation, thus it is vey impotant to have quantitative values of the intefacial enegy as this will help gain moe knowledge into the stuctual natue of the inteface. It will assist in gaining fundamental knowledge into the physics of intefaces and also in impoving the technology in the cystal gowth and foundy. Gündüz designed a adial heat flow appaatus in applied tempeatue gadient to poduce gain bounday goove pofile in 1984[2]. Based on the design by Gündüz, a novel adial heat flow appaatus is designed. To obtain the solid liquid intefacial enegy, Gibbs Thomson coefficient value is equied. To obtain accuate values of Gibbs Thomson coefficient, the inteface goove pofile, tempeatue gadient in solid and themal conductivity values fo the solid and liquid must be known. 214 The Authos. Published by Elsevie Ltd. 215 The Authos. Published by Elsevie Ltd. This is an open access aticle unde the CC BY-NC-ND license Selection ( and Pee-eview unde esponsibility of the Chinese Mateials Association in the UK (CMA-UK). This is an open access Selection aticle and Pee-eview unde the unde CC BY-NC-ND esponsibility of license the Chinese ( Mateials Association in the UK (CMA-UK). Keywods: Gain bounday goove method; Themal conductivity; Suface enegy; Radial heat flow appaatus; Gibbs Thomson coefficient 1. Intoduction The solid liquid intefacial enegy is the evesible wok, at constant tempeatue, chemical potential and volume, equied in extending o foming a unit aea of inteface between solid and liquid [1]. The solid liquid intefacial enegy plays an impotant ole in all pocesses that involves nucleation and gowth of solids fom its liquid state. One of the oles of intefacial enegy includes dictating the tempeatues at which solids nucleate fom its liquids. If the gowth of the solid occus at steps in the inteface, then the intefacial enegy affects the tansfomation ate. * Coesponding autho. Tel.: addess: ss397@le.ac.uk The Authos. Published by Elsevie Ltd. This is an open access aticle unde the CC BY-NC-ND license ( Selection and Pee-eview unde esponsibility of the Chinese Mateials Association in the UK (CMA-UK). doi:1.116/j.matp

2 S. Son and H. Dong / Mateials Today: Poceedings 2S ( 215 ) S36 S Solid liquid intefacial enegy also plays impotant ole in detemining the gowth mophology which may lead to solidification occuing in the pefeed cystallogaphic diections. The solid liquid intefacial enegy is also impotant in the phenomena such as coasening of dendites, sinteing, wetting and phase tansfomation. [3] Nomenclatue ΔT d diffusion undecooling ΔT k kinetic undecooling ΔT cuvatue undecooling adius of the inteface cuvatue Gibbs Thomson coefficient G tempeatue gadient SL solid liquid intefacial enegy * S entopy of fusion pe unit volume 1.1. Theoy Duing measuement, liquid is held at a tempeatue T I, below melting tempeatue T m. The liquid is then undecooled by ΔT= T m -T I. This value of T I depends on the composition of the liquid, the enegy baie fo atoms going fom liquid to solid and the inteface cuvatue. The undecooling is ΔT= ΔT d +ΔT k +ΔT but at equilibium, the diffusion and kinetic undecooling becomes zeo as thee ae no tansfe of atoms and the composition gadient at the inteface is zeo. Thus ΔT = ΔT. LIQUID PHASE Flat inteface Cuved inteface Gain A SOLID PHASE Gain B Fig. 1. Schematic of equilibated gain bounday goove pofile. When the solid liquid intefacial enegy is isotopic, this means when it is not a function of cystallogaphic aangements, T S SL f Fo plana solid liquid inteface intesecting plana gain bounday, the Gibbs Thomson coefficient is given in the fom of cuvatue undecooling and the adius of the cuvatue, (1)

3 38 S. Son and H. Dong / Mateials Today: Poceedings 2S ( 215 ) S36 S313 T S SL f And by integating both sides of the equation in y diection, y T dy y 1 dy (2) (3) If the themal conductivities ae equal, the tempeatue depends on the tempeatue gadient and the distance. Thus the left hand side of the equation becomes, T Gy When the themal conductivities of the solid and liquid ae not equal, the left hand side of the equation can be calculated by integating numeically calculated ΔT values[2]. And the ight hand side becomes, (4) 1 cosd 1 sin 2 And thus the equation to solve becomes, (5) 1 2 Gy 2 1 sin (6) The themodynamic definition of Gibbs Thomson coefficient can be used to obtain the solid liquid intefacial enegy which is given as, S SL * T Gy 2. Design of the novel adial heat appaatus Due to the impotance of the liquid to solid tansfomation pocess, thee have been many effots and methods in tying to measue the solid liquid intefacial enegy. A pape by Jones [3], have listed the techniques that wee used in the ealy yeas of the eseach towads measuing the solid liquid intefacial enegy. Howeve, fom the eseaches that wee caied out ove the last decade, it can be seen that the most common expeimental method that wee used to obtain the intefacial enegy is the gain bounday goove pofile method. And by diect application of the Gibbs Thomson equation, the value of intefacial enegy can be obtained. This method is convenient as it can be used to detemine the intefacial enegy fo both pue and multi component systems as well as fo tanspaent and opaque mateials. By eviewing the papes that wee published ove the last decade into gain bounday goove pofile method, thee ae thee main appaatus that has been used in obtaining the goove pofile, which ae Bidgman type appaatus [7-1], hoizontal tempeatue gadient appaatus [5,6] and adial heat flow appaatus [2]. (7)

4 S. Son and H. Dong / Mateials Today: Poceedings 2S ( 215 ) S36 S a) b) Fig. 2. (a) Schematic of Hoizontal tempeatue gadient appaatus [5,6]; (b) Schematic of Bidgman type appaatus [4]. Fo the novel appaatus, the design was based on the adial heat flow appaatus as it was the set up mainly used when applying gain bounday goove pofile method. The adial heat flow appaatus povides highe tempeatue application and also povides adially symmetic cucible which is impotant in maintaining the tempeatue gadient and also enables the measuement of themal conductivity of solid Set up The cucible consists of thee pats which ae the main body of the cucible and the top and bottom lids. The cucible body was machined fom machinable alumina with inne diamete of 35mm, oute diamete of 45mm and height 1mm. The two lids wee machined also fom machinable alumina, to fit tightly onto both ends of the cucible body. The bottom cucible lid has holes dilled to fix alumina tubes fo both the heating element and the themocouples. The heating element was made of Kanthal A1 of diamete 1.2mm and was wound into a coil of 14mm to cove the entie length of the cucible including the lids. This was inseted into the cente alumina tube. The thee measuement themocouples wee inseted in though the alumina tubes placed in the bottom cucible lid, with one that is vetically moveable, and the othe two placed at diffeent distance fom the cente tube. The vetically moveable themocouple was inseted to the whole length of the cucible, and the othe measuement themocouple and the contol themocouple was inseted to the half the length of the cucible. The schematic of the bottom cucible lid can be seen as in fig.3.

5 31 S. Son and H. Dong / Mateials Today: Poceedings 2S ( 215 ) S36 S313 Fig. 3. Bottom cucible lid. To povide the tempeatue gadient, the alumina cucible is placed inside a wate cooling jacket with a cental boe, made of stainless steel. This povides the tempeatue gadient hoizontally. To pevent the tempeatue gadient fom occuing vetically, two heates ae placed to fit onto eithe side of the cucible. Top and bottom heates ae made of machinable alumina and each holds a coil of Kanthal A1. The heates ae designed to fit onto the cucible lids. Fig. 4. Schematic of the novel adial heat flow appaatus.

6 S. Son and H. Dong / Mateials Today: Poceedings 2S ( 215 ) S36 S The funace chambe is made of aluminum with two lids. The bottom lid has inlet fo wate jacket and holes fo cuent leads and themocouples. The top lid has holes fo outlet of wate jacket and holes fo cuent lead and agon inlet and outlet. All the fitting and holes ae sealed with O ing and ubbe bungs. The chambe is filled with Agon. The schematic of the expeimental set up is shown in fig. 5. The contol and the ecoding will be done by LabView softwae. Fig. 5. Schematic of the expeimental set up. 3. Themal conductivity of solid To be able to calculate Gibbs Thomson coefficient, the themal conductivity atio is equied and the adial heat flow appaatus is an ideal set up to measue the themal conductivity of the solid phase. The sample in the cylindical cucible is placed in the adial heat flow funace in a stable tempeatue gadient. The sample is held at a stable tempeatue gadient fo a peiod to each steady state condition. The tempeatue gadient in the cylindical sample at the steady state condition can be epesented by Fouie s Law G S dt d Q 2lK S (8) The Fouie s Law equation above whee Q is the total input powe, l is the heating element length, is the distance of the solid liquid inteface to the cente of the sample and K S is the themal conductivity of the solid phase. This equation (8) can be integated to give K S Hee, a a Q T T 1 2 ln( 2 / 1 ) / 2l (9) (1)

7 312 S. Son and H. Dong / Mateials Today: Poceedings 2S ( 215 ) S36 S313 Whee a is an expeimental constant, 1 and 2 ae distances fom the cental axis of the sample and T 1 and T 2 ae the tempeatues at 1 and 2. To calculate the themal conductivity of solid phase, the cylindical sample was placed inside the adial heat flow appaatus. It was necessay to achieve a lage tempeatue gadient in ode to obtain a eliable themal conductivity measuement. The sample was positioned so that it was placed inside a wate cooling jacket, which was held at 293K using efigeating ciculation bath. The tempeatue gadient was achieved by heating the sample fom the cente using Kanthal A1 heating element wie. The sample was heated up in steps of 5K up to 1K below the melting point of the sample and was held at each set tempeatue fo moe than 2 hous to achieve steady state. The contol and measuements wee caied out using LabView softwae and the measuements wee saved. Once the measuement pocedue was completed, the sample was emoved and cut tansvesely to obseve the values fo 1 and 2. Measuement themocouple tube Cental alumina tube R 2 R 1 Measuement themocouple tube Contol themocouple alumina tube Fig. 6. Tansvesely cut sample of A21 alloy to obtain the distance values 1 and 2 The themal conductivity value of the solid phase of aluminum alloy A21 was obtained by the method descibed above and it was compaed with the values fom a liteatue by Ovefelt [11], and it is shown in figue 7. The esults show that the adial heat flow funace set up is eliable and can be futhe impoved to be used in futue expeiments. Table 1. A21 chemical composition (Supplied by SAG via Holset Engineeing Co. Ltd) Alloy (wt%) Al Si Fe Cu Mn Mg Zn Ti Ag A21 Bal

8 S. Son and H. Dong / Mateials Today: Poceedings 2S ( 215 ) S36 S Themal conductivity (W /cm C) Tempeatue ( C) A21 [11] Expeimental data Fig. 7. The themal conductivity of solid phase of A21 aluminum alloy in compaison with the expeimental esult 4. Conclusion and futue woks The solid liquid intefacial enegy is an impotant physical paamete in eseach into solidification and mateial pocessing whee solid and liquid coexist such as casting and cystal gowth. It also is useful themo physical paamete fo eseaches who compae expeimental solidification mophology to the esults that ae obtained fom theoetical models. Thus it is vey impotant to obtain the intefacial enegy value. It was found that to expeimentally measue the solid liquid intefacial enegy, the diect application of Gibbs Thomson equation to the gain bounday goove pofile was the most poweful method pesent. In ode to obtain gain bounday goove shape to apply Gibbs Thomson equation, a novel adial heat flow appaatus was designed. This appaatus povides stable tempeatue gadient and stable tempeatue contol to obtain the equilibated solid liquid inteface with a gain bounday. The futue plans include caying out an expeiment on aluminum alloys such as A21 and LM5. Refeences [1] D.P. Wooduff, The Solid Liquid Inteface, vol. 36, Cambidge Univesity Pess, Cambidge, 1973, p. 1. [2] M. Gündüz, D. Phil. Thesis, Univesity of Oxfod, [3] D R H Jones, Jounal of Mateials Science 9 (1974) [4] S. Engin, U. Böyük, N. Maaşlı, Jounal of Alloys and Compounds 488, no. 1 (Novembe 29) [5] B. Bayende, Maaşlı, M.Gündüz, J. Cyst.Gowth 194 (1998) 119. [6] U.Böyük, K. Keşlioǧlu, N. Maaşlı, Themochimica Acta 463 (27) [7] U. Böyük, S. Engin, N. Maaşlı, Jounal of Alloys and Compounds, 476(1-2), (29) [8] U. Böyük, N. Maa slı, H. Kaya, E. Cadılı, K. Ke slio glu, Appl Phys A (29) 95: [9] S. Engin, U. Böyük, N. Maaşlı, Jounal of Alloys and Compounds, 488(1), (29) [1] S. Engin, U. Böyük, N. Maaşlı, Cuent Applied Physics, 11(4), (211) [11] R. A. Ovefelt, R. E. Taylo, S. I. Bakhtiyaov, D. Wang, AFS Tansactions (22)