Zone Refining of Aluminum and Its Simulation+1

Masayoshi Nakamura1, Mahiko Watanabe1, Kisaburou Tanaka1, Atsushi Kirihata2,+2,Tsunetaka Sumomogi1, Hiroaki Hoshikawa3 and Ichiro Tanaka3

1Faculty of Engineering, Hiroshima Kokusai Gakuin University, Hiroshima 739-0321, Japan2Graduate School of Engineering, Hiroshima Kokusai Gakuin University, Hiroshima 739-0321, Japan3Basic Chemicals Research Laboratory, Sumitomo Chemical Co., Ltd., Niihama 792-8521, Japan

Ultrahigh-purity aluminum with a residual resistivity ratio (RRR) of 60000­65000 was obtained by the ultrahigh-vacuum melting method.However, it was necessary to reduce the concentration of the elements with distribution coefficient k > 1 to further improve the purity ofaluminum. Therefore, we prepared a sample with reduced concentrations of k > 1 elements from an ultrahigh-purity (99.9999%) aluminummaterial by the zone-refining method, and evaluated its purity by electrical resistance measurement and glow discharge mass spectrometry(GDMS). In addition, the zone-refining process was simulated, and the distribution of the solute atoms after approximately 10 passes of zone-refining was predicted. Moreover, the refining conditions were investigated with the aim of achieving higher purity. In experiments, when thezone width was increased from 60 to 80mm at a zone speed of 60mm/h, the concentrations of the elements with k > 1 in the second half of thematerial decreased and RRR improved. When the zone speed was decreased to 30mm/h, a marked effect was observed and RRR increased toabout 85000. The distribution of the solute atoms determined from the simulation was in good agreement with the results of GDMS analysis,thus confirming the usefulness of the simulation. [doi:10.2320/matertrans.M2013419]

(Received November 19, 2013; Accepted January 17, 2014; Published February 28, 2014)

Keywords: zone refining, simulation, ultrahigh purity aluminum, ultrahigh vacuum melting, glow discharge mass spectrometry (GDMS)analysis, residual resistivity ratio

1. Introduction

We already reported that the residual resistivity ratio (RRR)of ultrahigh-vacuum-melted aluminum was greatly improvedfrom RRR = 21000 to RRR = 40000. However, the concen-trations of elements with distribution coefficient k > 1 (Ti, V,Cr, etc.) were hardly reduced by this method.1) Next, weperformed zone melting (zone speed: 60mm/h, zone pass: 10times) employing an RRR = 21000 sample as a startingmaterial and after that, the last-half portion of the refinedsample was melted in ultrahigh vacuum. The experimentalresult showed that the average RRR of the zone-meltedsample was clearly improved (from RRR = 50000­60000 toRRR = 60000­65000) by this procedure. In other words, thereduction in the concentration of k > 1 elements by the zone-refining process is crucial for RRR improvement.

Zone refining of aluminum was firstly reported byBratsberg et al.2) and Revel.3) Kino and coworkers discussedin detail the relationship between zone-refining parameters(e.g., zone speed, molten zone width, pass numbers) andthe purification efficiency from a 5N starting material.4,5)

Hashimoto and coworkers reported superhighly purifiedaluminum (RRR is about 100000) from a 6N starting materialby the cropping method (zone pass: 60 times).6,7) Since then,no beneficial report on superhigh purification for aluminumhas been published.

In general, the zone refining method requires a hugenumber of zone passes. However, the result of purificationdepends on not only the number of passes but also on themolten zone width. Therefore, our aim in this study is to

optimize the molten zone width with the aid of numericalsimulation.

Our numerical simulation model is essentially based on theclassical solidification model8,9) and the molten zone has adiffusion region and a stirring region. In the case of radio-frequency induction heating, the stirring region becomesdominant in the molten region and the width of the diffusionregion ¤ becomes very small. Since the concentrationvariation inside the diffusion region is considered to benegligible, the spatial distribution of the solute atom quantityin ¤ was treated as a constant using the spatially averagedvalue. In addition to this, we introduced a transfer ratio q,which represents the solute quantity transferring from thediffusion region to the stirring region. First, we estimated thediffusion region width ¤ and the transfer ratio q by comparingthe GDMS result of the zone-refined sample with thesimulation result, and then we discussed the optimumcondition for purification.

2. Experimental Procedures

2.1 Zone refining of aluminumThe starting material used in the present work was

99.9999% aluminum (RRR = 21000) produced by SumitomoChemical Co., Ltd. (Mass production of this material is nowbecoming industrially possible.) The sample was a squarepillar (18mm © 18mm © 900mm). To avoid contaminationfrom the material surface, the sample surface was electro-polished in a mixed solution of ethanol and hydrochloricacid, and then it was rinsed with ethanol. Zone refining wascarried out in a cylindrical quartz vacuum chamber (innerdiameter: 50mm, length: 1500mm) equipped with a turbomolecular pump (ULVAC, 150L/min) and the best vacuumachieved was 1 © 10¹7 Pa. The sample was put on the slotof a graphite boat (IBIDEN Inc., slot dimensions: 20mm ©

+1This Paper was Originally Published in Japanese in J. Japan Inst. Metals77 (2013) 44­50. Equation (6) is added to the original paper in J. JapanInst. Metals for providing clearer explanation.

+2Graduate Student, Hiroshima Kokusai Gakuin University

Materials Transactions, Vol. 55, No. 4 (2014) pp. 664 to 670©2014 The Japan Institute of Metals and Materials

20mm © 1000mm) and inserted into the quartz vacuumchamber. The vacuum chamber was surrounded by an axiallymovable output coil (diameter 90mm, 3 turns) connectedwith a radio-frequency power supply (Fuji Denki Inc.,100 kHz, 5 kW). The degree of vacuum was initially1 © 10¹4 Pa order at the first pass and became less than1 © 10¹5 Pa at the last pass (10 times). We carried out thezone refining experiment under the four conditions shown inTable 1. The zone speed was fixed (30 or 60mm/h) and themelting width was adjusted by controlling the output of theRF power supply.

The solidified sample (total length: about 1050mm) afterzone melting was cut into several pieces (60mm length) bywire electric discharge, except the top and tail portionsshown in Fig. 1. We carried out resistance measurement andcomposition analysis with respect to the black points in theFig. 1. The specimen for the electric resistance measurementwas a square pillar of 1.7mm © 1.7mm © 60mm, and thedistance between the voltage terminals was set to be 50mm.RRR was estimated from the electric resistance measured bya 4-terminal method under the following conditions: 5A at4.2K and 1A at 300K. The chemical compositions of soluteatoms were estimated by GDMS measurement (ThermoElectron Corp., VG9000). Before GDMS and RRR measure-ments, surface contamination of the specimens for analysiswas eliminated by electropolishing and rinsing. In addition,specimens for RRR measurement were annealed (180min,773K, 10¹4 Pa) and gradually cooled to remove strain at atemperature gradient of 30K/h.

2.2 Simulation model and calculation algorithmFigure 2 shows a schematic diagram of our simulation

model. The vertical axis C represents the interface betweensolid and liquid (molten zone) and there exist a diffusionregion and a stirring region in the molten zone. For a certainnumber of zone passes, with respect to the solute elementof the distribution coefficient k, the concentration CS of thesolid-phase side and the concentration CL

¤ of the moltenside exhibit the relation CS ¼ kCL

¤ across the solid­liquidinterface. In this solidification, the amount of solute emitted

to the molten zone is n ¼ ð1� kÞCL¤ and the emitted solute

is distributed exponentially as a dashed-dotted line in thediffusion region of width ¤ and the solute transferred to thestirring region is averaged to a concentration of CL.

For RF heating, as in the present experiment, the diffusionregion is considered to be very thin because the majority ofthe molten zone is intensely stirred in the RF electromagneticfield. In this model, it was assumed that the distribution ofthe solute in the diffusion zone would become a rectangleindicated by the solid line in Fig. 2 so that it could easily becalculated. In addition to this, we introduced the transfer ratioq for the amount of solute n that is emitted from the diffusionregion and flows into the stirring region during solidification.Finally, the amount nð1� qÞ was obtained in region ¤,and the transferred amount nq into the stirring region wasaveraged here.

Table 2 shows a schematic diagram of the computation.The melting zone is divided into finite m regions with a widthof a (mm), that is, the length of the melting zone is equal toam (mm). When the first segment is the diffusion region andthe present computation step is (i), the concentration of thediffusion region is

C¤LðiÞ ¼ CLði�1Þ þ ð1� kÞC¤

Lði�1Þ � ð1� qÞ: ð1ÞWhen the melting zone moves to the next step, the backmostregion is solidified with CS:

CS ¼ kC¤LðiÞ

¼ kfCLði�1Þ þ ð1� kÞC¤Lði�1Þ � ð1� qÞg; ð2Þ

where CS is the concentration in solid and k is the distributioncoefficient. Simultaneously, the new stirring region isreconstructed by three components: the distributed quantityfrom the diffusion region, ðm� 2Þ segments with theconcentration CLði�1Þ from the previous stirring region, and

Table 1 Conditions of the zone-refining process.

SampleZone speed,v/mmh¹1

Zone width,w/mm

Number of passes,p/times

ZR-01 60 60 10

ZR-02 60 80 10

ZR-03 60 90 5

ZR-04 30 90 10

Top

100mm 220mm 340mm 820mm 940mm1050mm

Tail

Distancefrom the top

0mm

Fig. 1 Positions used for resistance measurement and compositionanalysis.

x

SC

Melting zone

Stirring region

Diffusion region

( )xC

( )xCS δ

C

C

LCδ

LC

Fig. 2 Schematic diagram of the melting zone.

Table 2 Schematic diagram of the computation model.

Segment 1 2 3 4 m

n(1−q)

CL (i −1) CL (i −1) CL (i −1) CL (i −1) CL(x) C(x)

CLδ

(i ) CL (i ) CL (i ) CL (i ) CL (i ) C(x)

nq

Diffusionregion

Stirring regionRegion

Composition ( i )

Melting zone

Zone Refining of Aluminum and Its Simulation 665

one segment of the new solid region with the concentrationC(x). Therefore, the average concentration in the stirringregion CLðiÞ becomes

CLðiÞ ¼ fð1� kÞC¤Lði�1Þ � qþ CLði�1Þ

� ðm� 2Þ þ CðxÞg=ðm� 1Þ: ð3ÞAs shown in eq. (4), the width of the molten zone includingthe stirring region decreases in a stepwise manner assolidification advances, when the back-end of the moltenzone reaches the tail edge.

CLðiÞ ¼ fð1� kÞC¤Lði�1Þ � qþ CLði� 1Þ

� ðm� jÞ þ CðxÞg=ðm� jÞfor 2 5 j 5 ðm� 10Þ ð4Þ

In the studies by Pfann,8,9) the solute concentration in thesolid as a function of g, the fraction that has solidified, can beexpressed as

CS ¼ k0C0ð1� gÞðk0�1Þ; ð5Þwhere k0 is the equilibrium distribution coefficient, defined asthe ratio of concentration in the solid to that in the liquid atequilibrium, and C0 is the initial solute concentration in theliquid. Thereafter, Burton et al. developed two importantequations10) relevant to solute distribution when a diffusionlayer exists between the solid region and the molten region,which are

CL � CS

C¤L � CS

¼ expð�R¤=DÞ; ð6Þ

kE ¼ k0=fk0 þ ð1� k0Þ expð�R¤=DÞg; ð7Þwhere kE is the effective distribution coefficient when thesolute diffuses through the diffusion region ¤, R is thesolidification speed, and D is the diffusion coefficient of thesolute in the molten region.

Since the exponential factor in eqs. (6) and (7) is identicalto the transfer ratio q,

expð�R¤=DÞ ¼ q: ð8ÞIn this equation, the experimental values of R and D arealready determined, so we can estimate the width of thediffusion region ¤ if the transfer ratio q becomes explicit.

3. Experimental Results and Discussion

3.1 Result of zone refiningTable 3 shows the concentrations and the distribution

coefficients11) of main elements in the raw material used asthe starting materials. In this Table 3, k < 1 elements aredisplayed on the lefthalf, and k > 1 elements are displayedon the righthalf. In zone refining, it is well known thatthe migration direction of the solute is governed by thedistribution coefficient k; the element of the distributioncoefficient k > 1 migrates toward the first (Top) side of thesample, whereas the k < 1 element migrates toward the last(Tail) side. In the case of our starting materials, Ti (k > 1) andSi (k < 1) take the maximum concentration for each categoryof k. Figure 3 shows the variations in the concentrations of Tiand Si estimated by GDMS analysis. Clearly, the concen-tration of Ti decreases gradually from the first point to the lastpoint; in contrast to this, Si increases rapidly beyond 700mmand this behavior is characteristic of zone refining.

Figure 4 shows the variation in RRR, which was estimatedby the correction method for the size effect of resistivity.1)

The maximum RRR value of ZR-02 was approximately70000, which is higher than that of ZR-01. We consider thatthis is due to the difference in the width of the melting zone(ZR-01: 60mm, ZR-02: 80mm), and we will discuss it insection 3.3.2. The RRR of ZR-03 became relatively lowcompared with those of the two other samples because of thedifference in the number of zone passes (ZR-01 and ZR-02:10 times, ZR-03: 5 times).

3.2 Simulation3.2.1 Determination of transfer ratio

Our simulation model requires two unknown factors: thetransfer ratio q and the width of the diffusion region ¤. Asmentioned in section 2.2, the transfer ratio q in our model isequal to the solute emission rate from the diffusion region tothe stirring region.

First, we explored the value of q by parametric fitting forthe GDMS results. Then, we estimated q using the GDMSprofile of Ti (concentration: 0.015 at ppm, k = 2.1) after zonerefining. For this simulation, q was treated as a parameter

Table 3 Concentrations and distribution coefficients of main elements in the raw material.

k < 1 Elements k > 1 Elements

ElementConcentration,

C/at ppm

Distributioncoefficient,

kElement

Concentration,C/at ppm

Distributioncoefficient,

k

Mg 0.11 0.51 Ti 0.015 2.1

Si 0.33 0.14 V 0.014 3.3

Fe 0.043 0.03 Cr 0.014 1.7

Cu 0.059 0.14

Subtotal ofother 25 elements(Li, Be, Mn, Ni,

Co, Ga, Ag, In, Ba,La, Ce, Pb, etc.)

<0.043Subtotal of

other 3 elements(Se, Zr, Mo)

0.011

Totalcomposition,C/at ppm

<0.59 0.054

M. Nakamura et al.666

and the width of a segment was tentatively fixed at 1mm.In addition, we regarded the sample length as 1000mm fornumerical calculation because the aluminum rod lengthchanged from 900mm before refining to about 1050mm afterrefining.

Figure 5 shows the comparison between the simulatedresults and the Ti concentration analyzed by GDMS. Therefining conditions, zone speed v (mm/h), zone width w(mm), and number of zone passes p (times), are as follows:(ZR-01-Ti: v = 60, w = 60, p = 10) and (ZR-03-Ti: v = 60,w = 90, p = 5). The simulated curves were in good agree-ment with the GDMS results, as shown in Fig. 5 when settingq in the range of 0.5 to 0.7. On basis of this result, weadopted q = 0.6 as the transfer ratio at v = 60mm/h.3.2.2 Determination of diffusion region width

Under our experimental conditions (q = 0.6, R =60mm/h = 0.017mm/s, D = 6 © 10¹3mm2/s in molten

aluminum12)), eq. (8) yields the diffusion region width¤ = 0.18mm.

3.3 Simulation and experimental result3.3.1 Effect of zone speed

Figure 6 shows the simulated composition profiles ofSi and Ti. In this simulation, the melting width was fixedat 90mm and the moving speed was changed to 60 and30mm/h. In the case of Si, the both profiles were almost thesame until 800mm and this tendency was also observed inthe cases of Fe and Cu. On the other hand, the profiles of Tiexhibited a difference within the region from 400 to 800mm:the slower moving case was lower in concentration. Thistendency was also observed in the cases of Vand Cr. It can beconsidered that the decrease in the amount of solute is themain reason for the improvement in RRR.3.3.2 Effect of molten zone width

As mentioned in section 3.1, RRR is improved when themolten width increases. Therefore, we simulated the effect ofmolten zone width on the concentration profile and the resultsare displayed in Fig. 7. The difference until 800mm wasalmost zero in the case of Si. However, the profile of Ti wasclearly affected by the molten zone width. In particular, it isinteresting that the concentration decreases with an increasein molten zone width within the region from 400 to 800mm.3.3.3 Comparison between simulation and experimental

resultsWe employed the width of the finite segment of 0.18mm

(the width of the diffusion region) for the simulation, and the

0

10000

20000

30000

40000

50000

60000

70000

80000

0 200 400 600 800 1000Distance, x /mm

Res

idua

l res

istiv

ity r

atio

, RR

R

ZR−01ZR−02ZR−03

Fig. 4 Residual resistivity ratio at each position.

(b) ZR−03−Ti

0.00

0.02

0.04

0.06

0.08

0.10

0 200 400 600 800 1000Distance, x /mm

Con

cent

ratio

n, C

/at−

ppm q=0.5

q=0.6q=0.7GDMS

(a)

Fig. 5 Composition profiles obtained by simulation and analysis for Ti.

(a) Ti

0.00

0.01

0.02

0.03

0.04

0 200 400 600 800 1000Distance, x /mm

Con

cent

ratio

n, C

/at−

ppm ZR−01

ZR−02ZR−03

(b) Si

0.0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000Distance, x /mm

Con

cent

ratio

n, C

/at−

ppm

ZR−01ZR−02ZR−03

Fig. 3 Chemical composition at each position; (a) Result for Ti and(b) result for Si.

Zone Refining of Aluminum and Its Simulation 667

other simulation parameters, such as the zone speed foreach refined sample, are shown in Table 1. Figures 8 and 9show comparisons between the simulated concentration andGDMS data for Ti and V. Figures 8 and 9 represent theresults of ZR-01 and ZR-03, respectively. In this simulation,we used the sets of the distribution coefficient k and theconcentration (at ppm) C shown in Table 3 for each elementas follows, Ti: k = 2.1, C = 0.015 at ppm, V: k = 3.3, C =0.014 at ppm.

As described in sections 3.2.1 and 3.2.2, we estimated themolten zone width ¤ from the GDMS result of Ti andregarded ¤ as a constant. It is clear that our simulation couldproduce accurate fits for both Ti and V by using k and C ofeach element. This finding suggests the above postulationthat ¤ is almost constant under our experimental conditions.

Figure 10 shows the result of the k < 1 elements (a) Si(k = 0.14, C = 0.33 at ppm) and (b) Mg (k = 0.51, C =0.11 at ppm) in sample ZR01. Note that a vertically magnifiedgraph (C < 0.10 at ppm) for Si is drawn in Fig. 10(a).Although the GDMS data of Si varies, the fitting result isin accordance with the GDMS result. On the other hand, theGDMS result of Mg is considerably lower than the simulationresult. We think that Mg evaporated and disappeared in thevacuum atmosphere owing to its high vapor pressure. In thefuture, it will be necessary to simulate the zone-refiningprocess in consideration of the loss due to evaporation.

3.4 Simulation and RRR value at zone speed of 30mm/hUntil now, we have been describing the results obtained

at a zone speed of 60mm/h. We will present the resultsobtained at a lower zone speed, 30mm/h, in the following.

Distance. x /mm

Distance. x /mm

(a) Si

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000

Con

cent

ratio

n, C

/at−

ppm

80mm

120mm

(b) Ti

0.00

0.02

0.04

0.06

0 200 400 600 800 1000

Con

cent

ratio

n, C

/at−

ppm

80mm120mm160mm

Fig. 7 Composition profiles obtained by simulation for zone widths of80­160mm.

(a) ZR−01−Ti

0.00

0.02

0.04

0.06

0.08

0.10

0 200 400 600 800 1000Distance, x /mm

Distance, x /mm

Con

cent

ratio

n, C

/at−

ppm

Con

cent

ratio

n, C

/at−

ppm

SimulationGDMS

(b) ZR−01−V

0.00

0.02

0.04

0.06

0.08

0.10

0 200 400 600 800 1000

SimulationGDMS

Fig. 8 Composition profile and analysis results for ZR-01.

(a) Si

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000

Distance. x /mm

Distance. x /mm

Con

cent

ratio

n, C

/at−

ppm

60mm/h

30mm/h

(b) Ti

0.00

0.02

0.04

0.06

0.08

0.10

0 200 400 600 800 1000

Con

cent

ratio

n, C

/at−

ppm

60mm/h

30mm/h

Fig. 6 Composition profiles obtained by simulation for zone speeds of 60and 30mm/h and a zone width of 90mm.

M. Nakamura et al.668

The starting material is the same as before and its propertiesare shown in Table 3. The estimated width of the diffusionregion ¤ is 0.18mm as mentioned in section 3.2.2.Taking into account the other constants (R ¼ 30mm=h ¼0:0083mm=s, D ¼ 6� 10�3 mm2=s), the transfer ratio qbecomes 0.76 in this case from eq. (8).

Figure 11 shows the comparison between the simulationresults and the GDMS profiles of Ti and V in sample ZR-04.It is obvious that there is good agreement between thesimulation and the experiment. This result indicates theusefulness of our simulation, i.e., it is applicable forpredicting the concentration profile despite the variation inzone speed and/or zone width.

Figure 12 shows a comparison of the RRR measurementresults among three samples. The zone speed was determinedto be 60mm/h for ZR-01 and ZR-02 and 30mm/h for ZR-04. The molten zone width was controlled to 60mm for ZR-01, 80mm for ZR-02, and 90mm for ZR-04. It is clear thatRRR is improved in the order of samples from ZR-01 to ZR-04. In particular, in the case of ZR-04, owing to the decreasein zone speed and the increase in molten zone width, themaximum RRR value was improved to 85000.

Table 4 shows the GDMS results of the ZR-04 samplewith RRR 85000, the portion from 400 to 600mm, before andafter purification. Not only k < 1 elements but also k > 1elements, whose specific resistance contribution coefficientsare large,11) were decreased by this refinement. We think thatfurther purification of this sample is possible by reducing theconcentrations of both k < 1 elements and gaseous compo-nents utilizing our ultrahigh-vacuum melting method.1)

(a) ZR−01−Si

0.0

0.5

1.0

1.5

2.0

0 200 400 600 800 1000Distance, x /mm

Distance, x /mm

Con

cent

ratio

n, C

/at−

ppm

Con

cent

ratio

n, C

/at−

ppm

Simulation

GDMS

0.00

0.05

0.10

0 500 1000

(b) ZR−01−Mg

0.00

0.05

0.10

0.15

0.20

0 200 400 600 800 1000

Simulation

GDMS

Fig. 10 Composition profiles obtained by simulation and analysis for Si (a)and Mg (b).

(a) ZR−04−Ti

0.00

0.02

0.04

0.06

0.08

0.10

0 200 400 600 800 1000Distance. x /mm

Distance. x /mm

Con

cent

raiti

on, C

/at−

ppm

Con

cent

raiti

on, C

/at−

ppm

Simulation

GDMS

(b) ZR−04−V

0.00

0.02

0.04

0.06

0.08

0.10

0 200 400 600 800 1000

Simulation

GDMS

Fig. 11 Composition profile and analysis results for ZR-04.Distance, x /mm

Distance, x /mm

Con

cent

ratio

n, C

/at−

ppm

Con

cent

ratio

n, C

/at−

ppm

(a) ZR−03−Ti

0

0.02

0.04

0.06

0.08

0.1

0 200 400 600 800 1000

SimulationGDMS

(b) ZR−03−V

0

0.02

0.04

0.06

0.08

0.1

0 200 400 600 800 1000

SimulationGDMS

Fig. 9 Composition profile and analysis results for ZR-03.

Zone Refining of Aluminum and Its Simulation 669

4. Conclusions

We carried out zone melting experiments of 6N-grade(99.9999%) ultrahigh-purity aluminum in a vacuum of lessthan 1 © 10¹5 Pa, and the sample after melting was evaluatedby RRR measurement and GDMS analysis. In addition, we

carried out numerical simulation of solute distribution inzone-refined aluminum and compared the results with GDMSresults. The results obtained in this study are as follows.(1) When the molten zone width increased from 60 to

80mm, after 10 zone passes at 60mm/h, RRR reacheda value of about 70000 owing to the decrease in theconcentration of k > 1 elements in the last-half portionof the refined sample.

(2) The effect of molten zone width on the refinementbecame prominent when the zone speed decreased from60 to 30mm/h, and the RRR value was improved toabout 85000 after 10 zone passes.

(3) We think that further purification of this zone-refinedsample is possible by reducing the concentration ofboth k < 1 elements and gaseous components utilizingour ultrahigh-vacuum melting method.

(4) Simulated profiles of Ti, V, and Si were in goodagreement with GDMS results even when the zonespeed and/or zone width varied. This finding indicatesthe usefulness of our simulation method.

Acknowledgements

The authors express their sincere thanks for many valuablesuggestions from Dr. Takao Kino (Emeritus Professor ofHiroshima University, Advisory Board of Hiroshima KokusaiGakuin University) and Dr. Hiroto Osono (EmeritusProfessor of Hiroshima Kokusai Gakuin University).

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(1995) C7-153-157.8) W. G. Pfann: Trans. AIME Journal of Metals 194 (1952) 747­753.9) W. G. Pfann: Zone Melting, Second Edition, (John Wiley & Sons, Inc.,

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Table 4 Concentrations of main elements in the raw material and ZR-04zone-refined specimen.

ElementConcentration, C/at ppm

Raw material ZR-04

k < 1 Elements

Mg 0.11 <0.001

Si 0.33 0.010

Fe 0.043 <0.001

Cu 0.059 0.014

Subtotal ofother 25 elements

(Li, Be, Mn, Ni, Co,Ga, Ag, In, Ba, La,

Ce, Pb, etc.)

<0.043 <0.033

k > 1 Elements

Ti 0.015 0.005

V 0.014 0.007

Cr 0.014 0.011

Subtotal ofother 3 elements(Se, Zr, Mo)

0.011 0.010

Totalcomposition,C/at ppm

<0.64 <0.09

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 200 400 600 800 1000Distance, x /mm

Res

idua

l res

istiv

ity r

atio

, RR

R

ZR−01ZR−02ZR−04

Fig. 12 Residual resistivity ratio at each position.

M. Nakamura et al.670