materials
Review Research Status of High-Purity Metals Prepared by Zone Refining
Liang Yu 1,2,3 , Xiaoan Kang 1,2,3, Luona Chen 1,2,3, Kun Luo 4, Yanli Jiang 1,2,3,* and Xiuling Cao 5,*
1 Key Laboratory of New Processing Technology for Nonferrous Metals & Materials, Ministry of Education, Guilin University of Technology, Guilin 541004, China; [email protected] (L.Y.); [email protected] (X.K.); [email protected] (L.C.) 2 Guangxi Scientific Experiment Center of Mining, Metallurgy and Environment, Guilin 541004, China 3 Collaborative Innovation Center for Exploration of Nonferrous Metal Deposits and Efficient Utilization of Resources, Guilin University of Technology, Guilin 541004, China 4 School of Materials Science and Engineering, Changzhou University, Changzhou 213164, China; [email protected] 5 School of Exploration Technology and Engineering, Hebei Geosciences University, Shijiazhuang 050031, China * Correspondence: [email protected] (Y.J.); [email protected] (X.C.); Tel.: +86-135-9163-3992 (Y.J.); +86-135-1331-0032 (X.C.)
Abstract: The zone refining method is a physical method for effectively purifying metals. Increas- ing yield and reducing impurity content have always been the focus of its research. This article systematically summarizes the relevant research on the production of high-purity metals by zone refining, including mechanisms, parameter optimization, zone refining types, analysis methods,
limitations, and future development directions, and it provides relevant theoretical foundations for the production of high-purity metals as well.
Citation: Yu, L.; Kang, X.; Chen, L.; Luo, K.; Jiang, Y.; Cao, X. Research Keywords: zone refining; high-purity metals; purification Status of High-Purity Metals Prepared by Zone Refining. Materials 2021, 14, 2064. https://doi.org/ 10.3390/ma14082064 1. Introduction High-purity metals (99.999% (5N) or higher) are widely used in modern electronic Academic Editor: information, aerospace, defense, and military industries listed in Table1. The development Antonio Sánchez-Coronilla trend of modern science and technology requires high-purity or ultra-high-purity of metals, because some important characteristics of metals are affected by the type and amount of Received: 9 December 2020 impurities in the matrix, and some characteristics are even masked by trace elements [1]. Accepted: 13 April 2021 Metals are often purified by vacuum distillation technology [2], ion exchange tech- Published: 20 April 2021 nology [3], extraction technology [4], electrolytic refining technology [5], zone refining technology [6], and other single or combined technologies. Publisher’s Note: MDPI stays neutral Among them, the zone refining technology has a wide range of applications; in with regard to jurisdictional claims in addition, it is simple and easy to control, has no pollution, has a high product purity, and published maps and institutional affil- iations. is suitable for the final stage of preparing high-purity metals. Since Pfann [7] first used the zone refining technology to purify germanium in 1955, it has been widely used in the purification of high-purity metals and the preparation of high-quality, multi-variety refractory single crystals. Zone refining is a technology of deeply purifying metals. Its essence is to use the difference in solubility of impurity elements in the solid and molten Copyright: © 2021 by the authors. state of the main metal to precipitate the impurities or change the distribution of the Licensee MDPI, Basel, Switzerland. impurity elements. It provides an effective and easy method for preparing high-purity This article is an open access article metals. Theoretically, high-purity metals up to 8N can be obtained. distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
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Table 1. Application of high-purity metals.
Metal Application In [8] ITO targets, CIGS solar cells, liquid crystal displays, etc. Sn [9] Packaging materials, integrated circuits, refractory materials, etc. Ni [10] Stainless steel, alloy steel, high-temperature structural materials, etc. Cu [11] Audio products, integrated circuits, fatigue-resistant cables, etc. Co [12] Magnetic materials, super alloys, electronic component targets, etc. Ti [13] Large-scale integrated circuits, decorative materials, etc. Ga [14] Semiconductor materials, solar cells, catalytic materials, etc. Ge [15] Integrated circuits, photovoltaic cells, infrared optical materials, etc. Te [16] Aerospace, atomic energy, electronics industry, etc. Al [17] Target materials, integrated circuit wiring, optoelectronic storage media, etc.
2. Zone Refining Mechanism 2.1. Basic Principles Zone refining is a technology of deeply purifying metals [18]. The distribution of impurity elements in the solid and liquid phase of the bulk metal melt is determined by the thermodynamic properties of the system. Impurities exist as solid solutions in the main metal. Solid solution is generally due to the presence of metal B atoms in the crystal lattice of metal A, thereby forming a solid solution. Due to the presence of trace impurities, the melting point of the metal may decrease or increase. The extent to which the melting point decreases or increases depends on the content of impurities. Decreasing the melting point causes the solid solution to change from the molten state to the solid state, and the impurities migrate from the solid phase to the liquid phase. When the melting point increases, the opposite is true, and the impurities migrate from the liquid phase to the solid phase. For the binary system composed of A and B (the metal A contains impurities B), there is the following relationship [1,19,20]:
( 0 )2 R T f xB2 ∆T f = xB1 [1 − ]. (1) ∆H f A xB1
In the formula, “1” represents the molten phase, “2” represents the solid solution phase; xA1 and xB1 are the concentrations of metal A and impurity B before the change, while xA2 and xB2 are the concentrations of A and B after the change; ∆H f A is the heat of dissolution when 1 mol A melts into the solution from a solid solution state, and its value 0 is positive. Due to the low impurity content, it can be regarded as a constant; Tf is the melting point of pure A; Tf is the melting point of the solid solution at the mole fraction of 0 xA2; ∆Tf = T f − Tf is the melting point change value; R is the gas constant, and the value is 8.314. Assume xB2 k0 = . (2) xB1
If k0 < 1, that is xB1 > xB2; then, xA1 < xA2, and the concentration of A in the solid phase is greater than the concentration of A in the liquid phase. When ∆Tf > 0, the melting point rises, as shown in Figure1b. If k0 > 1, that is, xB1 < xB2; then, xA1 > xA2, and the concentration of A in the solid phase is smaller than the concentration of A in the liquid phase. When ∆Tf < 0, the melting point drops, as shown in Figure1a. In Figure1, the upper part is the molten liquid zone; the middle is the solid–liquid two-phase equilibrium zone; the lower part is the solid phase zone. MaterialsMaterials 20212021,, 1414,, 2064x FOR PEER REVIEW 33 ofof 2121
FigureFigure 1. 1.Binary Binary system system phase phase diagram; diagram; ( a(a))k k00> > 1;1; ((bb)) kk00 < 1 1..
In the case of k < 1 (see Figure1b), the solid solution containing impurities at the In the case of k00 < 1 (see Figure 1b), the solid solution containing impurities at the phasephase point PP isis heatedheated toto thethe moltenmolten statestate SS andand thenthen cooledcooled toto thethe temperaturetemperature TT;; thethe firstfirst solidsolid phasephase pointpoint toto condensecondense isis QQ,, andand thethe impurityimpurity contentcontent isis reducedreduced comparedcompared toto thethe phase point P.. Then, Then, the the solid solid phase phase at at the the phase phase point point QQ isis heated heated and and melted melted until until it R itreaches reaches the the phase phase point point R, ,afte afterr which which it it is is condensed, condensed, and and the the impurity content inin thethe obtained solid at the phase point E is reduced again, and the heating is repeated with obtained solid at the phase point E is reduced again, and the heating is repeated with condensation, the impurity content in the solid phase is continuously reduced to achieve Materials 2021, 14, x FOR PEER REVIEWcondensation, the impurity content in the solid phase is continuously reduced to achieve4 of 21 the purpose of purifying metals, but the opposite is true for k0 > 1. the purpose of purifying metals, but the opposite is true for k0 > 1. 2.2. Analysis of Changes in Impurities during Zone Refining 2.2. Analysis of Changes in Impurities during Zone Refining TheThe two specific sides process of Formula of zone (3) refining respectively is shown derive in Figurex: 2a. The metal materials to be The specific process of zone refining is shown in Figure 2a. The metal materials to be purified are placed in the tubular furnace; then, install k x a movable heating ring outside the , C0k0(1 k0) o purified are placed in the tubular furnaceC = ; then, installe l > a0 .mo vable heating ring outside (the4) tube (high frequency heating ring canS be used).l tube (high frequency heating ring can be used). Let the initial concentration of an impurity in the metal ingot be C0, which is locally melted into a melting zone; then, slowly move the heating ring to the right. The melting zone also slowly moves from the left end to the right end. The melted metal at the left end gradually solidifies again. At this time, impurities with k0 < 1 are precipitated at the interface between the “reso- lidification zone” and the melting zone, and the concentration of impurities distributed in the liquid phase is greater than that in the solid phase. Therefore, as the melting zone moves to the right, the impurities also move to the right, and finally, they are concentrated at the tail end, and the impurities of k0 > 1 mainly accumulate at the head end of the ingot. So, we repeat the above process many times ; just like a broom sweeping the impurities to the two ends, the impurities are removed from FigureFigure 2. 2. SpecificSpecific process process of of zone zone refining; refining; ( (aa)) Single Single-pass-pass zone refining; refining; ( b) Multi Multi-pass-pass melting zone refining.refining. both ends, purifying the middle of the ingot.
ItLetWhen can the be using initial obtained multi concentration -thatmelting the C zoneS of moving an refining, impurity direction the in advantages the along metal the ingot ofmelting zone be refiningC zone0, which is canan is increas- be locally seen. ingmeltedAs function,shown into in a and Figure melting it can 2b, zone; be a seenseries then, from of slowly closely Equation move spaced (3) the that heaters heating when are ringx/l →used to∞, the thereto right.melt is C into TheS/C0 →multiple melting1, and thezonemelting purification also zones slowly in effect movesthe ingot is not from; afterideal the mu leftat thisltiple end time, tozone the so refining, rightthe value end. the of The impurityx/l melted is not suitableconcentration metal at if the the left widthdistri- end ofgraduallybution the melting reaches solidifies zone a steady again.is fixed, state and or limit thuss thedistribution. ingot should not be made too long. The distri- butionAtImpurities of this impurities time, do impuritiesnot along diffuse thewith in ingot thek0 solid after< 1 arephase, the precipitated molten but the zone mass at passes the transfer interface through rate betweenin the the ingot liquid the is “resolidificationshownphase isin very Figure fast, zone”3. and andthe concentration the melting zone, of impurities and the concentration in the liquid of phase impurities is uniform. distributed After ina zone theFor liquid refining the case phase and of ispurification, k greater0 > 1, the than impu the that distributionrities in the in solidthe of melting phase.impurities zone along are enrichedthe length in of the the solidingot phase.can beTherefore, Sinceexpressed the asimpurities by the Formula melting cannot (3) zone [19,21]: move moves to tothe the right right, with the the impurities melting zone also movein the tosolid the phase,right, andnor finally,can they they migrate are concentrated to the left-side at the solidification tail end, and zone. the impurities It is equivalent of k0 >to 1 distrib- mainly 1 − (1 − ) ∙k0/l utingaccumulate the impurities at the head in endthe oflength theCS ingot.of= C the0 So, rightmost we repeatk0 le (melting the above. zone process width) many of times;the ingot just(3) evenlylike a broom within sweepingthe range theof the impurities length of to the the left two x-l ends,, as shown the impurities in Figure are3b. removed from CS is the impurity concentration at the distance x from the head end, and l is the bothIt ends, can be purifying seen from the the middle combination of the ingot. of Figure 3 that for impurities containing k0 < 1 length of the melting zone. and k0 > 1 in the metal, in order to obtain a better purification effect, the middle part of the bar ingot should be a high-purity metal zone. The ratio of the length of the ingot to the width of the fixed melting zone (L/l) should not be too large, and the number of repetitions of melting has the best value, which is about L/l, and the cut length at both ends should be greater than the length of the melting zone l.
Figure 3. Distribution of impurities along the ingot after the molten zone passes through the ingot; (a) Distribution curve of multiple zone molten impurities along the ingot when k0 < 1; (b) Distribution curve of multiple zone molten impurities when k0 > 1.
3. Influencing Factors and Optimization of Zone Refining Since Pfann [22] published the pioneering work of zone refining, domestic and for- eign scholars have conducted a series of research and discussion on the influencing factors of zone refining from a practical and theoretical perspective. These factors are mainly
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The two sides of Formula (3) respectively derive x:
k x , C0k0(1 k0) o C = e l > 0. (4) S l
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When using multi-melting zone refining, the advantages of zone refining can be seen. As shown in Figure2b, a series of closely spaced heaters are used to melt into multiple melting zones in the ingot; after multiple zone refining, the impurity concentration distribution reaches a steady state or limits distribution. Figure 2. Specific process ofImpurities zone refining; do not(a) Single diffuse-pass in zone the solid refining; phase, (b) Multi but the-pass mass melting transfer zone refining. rate in the liquid phase is very fast, and the concentration of impurities in the liquid phase is uniform. After a zone refining and purification, the distribution of impurities along the length of the ingot It can be obtained that the CS moving direction along the melting zone is an increas- can be expressed by Formula (3) [19,21]: ing function, and it can be seen from Equation (3) that when x/l→∞, there is CS/C0→1, and the purification effect is not ideal at thish time, so the valuei of x/l is not suitable if the width −x·k0/l of the melting zone is fixed, CandS= thusC0 1the− (ingot1 − k 0should)e not. be made too long. The distri- (3) bution of impurities along the ingot after the molten zone passes through the ingot is shownCS inis theFigure impurity 3. concentration at the distance x from the head end, and l is the length of the melting zone. For the case of k0 > 1, the impurities in the melting zone are enriched in the solid The two sides of Formula (3) respectively derive x: phase. Since the impurities cannot move to the right with the melting zone in the solid phase, nor can they migrate to the left-side solidification zone. It is equivalent to distrib- , C0k0(1 − k0) −ko x C = e l > 0. (4) uting the impurities in the lengthS of thel rightmost l (melting zone width) of the ingot evenly within the range of the length of the left x-l, as shown in Figure 3b. ItIt cancan be be obtained seen from that the the combinationCS moving directionof Figure along 3 that the for melting impurities zone containing is an increasing k0 < 1 function,and k0 > 1 and in the it can metal, be seen in order from to Equation obtain a (3) better that purification when x/l→∞ effect,, there the is CmiddleS/C0→ 1,part and ofthe the purificationbar ingot should effect be is nota high ideal-purity at this metal time, zone. so the The value ratio of x/lof isthe not length suitable of the if the ingot width to the of thewidth melting of the zone fixed is melting fixed, and zone thus (L/ thel) should ingot shouldnot be too not large, be made and too the long. number The o distributionf repetitions ofof impuritiesmelting has along the best the ingotvalue, after which the is molten about zoneL/l, and passes the cut through length the at ingotboth isends shown should in Figurebe greater3. than the length of the melting zone l.
FigureFigure 3. 3.Distribution Distribution of of impurities impurities along along the the ingot ingot after after the the molten molten zone zone passes passes through through the the ingot; ingot; (a) ( Distributiona) Distribution curve curve of multipleof multiple zone zone molten molten impurities impurities along along the the ingot ingot when whenk0 k<0 1;< 1 (;b ()b Distribution) Distribution curve curve of of multiple multiple zone zone molten molten impurities impurities whenwhenk k00> > 1.1.
3. InfluencingFor the case Factors of k0 > and 1, the Optimization impurities in theof Zone melting Refining zone are enriched in the solid phase. SinceSince the impurities Pfann [22] cannot published move the to pioneering the right with work the of meltingzone refining, zone in domestic the solid and phase, for- noreign can scholars they migrate have conducted to the left-side a series solidification of research and zone. discussion It is equivalent on the toinfluencing distributing factors the impuritiesof zone refining in the lengthfrom a of practical the rightmost and theoreticall (melting zoneperspective. width) ofThese the ingot factors evenly are withinmainly the range of the length of the left x-l, as shown in Figure3b. It can be seen from the combination of Figure3 that for impurities containing k0 < 1 and k > 1 in the metal, in order to obtain a better purification effect, the middle part of the 0 bar ingot should be a high-purity metal zone. The ratio of the length of the ingot to the width of the fixed melting zone (L/l) should not be too large, and the number of repetitions of melting has the best value, which is about L/l, and the cut length at both ends should be greater than the length of the melting zone l. Materials 2021, 14, x FOR PEER REVIEW 5 of 21
equilibrium distribution coefficient, zone refining rate, melting zone width, diffusion layer thickness, and zone refining times. Materials 2021, 14, 2064 Yang [23] believes that the ingot length/area length ratio (L/l), the type5 and of 21 purity of the container, the composition of the ambient gas, and the degree of vacuum all need to be carefully studied; otherwise, it will become a limitation to achieve the required perfor- 3.mance. Influencing Factors and Optimization of Zone Refining Since Pfann [22] published the pioneering work of zone refining, domestic and foreign scholars3.1. Balanced have conducted Distribution a seriesCoefficient of research and discussion on the influencing factors of zoneThe refining equilibrium from a practicaldistribution and theoreticalcoefficient perspective. k0 of impurities These is factors the key are facto mainlyr that deter- equilibriummines their distribution migration, coefficient, and it runs zone through refining the rate, segregation melting zone purification. width, diffusion By layerobserving the thickness, and zone refining times. degree to which the equilibrium distribution coefficient k0 deviates from 1, it is generally Yang [23] believes that the ingot length/area length ratio (L/l), the type and purity of possible to predict the purification ability of the zone refining process to the correspond- the container, the composition of the ambient gas, and the degree of vacuum all need to be carefullying impurities. studied; otherwise, However, it in will the become actual a limitationoperation to process, achieve theusually required, the performance. impurities have not had time to diffuse, and the temperature has changed greatly, causing the solid/liquid 3.1.interface Balanced to Distribution advance greatly, Coefficient forming a solid phase of new components; that is, non-equi-
libriumThe equilibrium solidification distribution actually occurs, coefficient andk0 impuritiesof impurities are is concentrated the key factor at that the deter- solidification minesinterface their [24]. migration, and it runs through the segregation purification. By observing the degreeTherefore, to which the the equilibrium equilibrium distribution distribution coefficient coefficientk0 deviates k0 is not from fixed, 1, itis so generally the effective dis- possible to predict the purification ability of the zone refining process to the corresponding tribution coefficient (keff) is introduced to improve the zone refining efficiency. The sim- impurities. However, in the actual operation process, usually, the impurities have not had plest method is to optimize keff. The BPS equation is as follows [25,26]: time to diffuse, and the temperature has changed greatly, causing the solid/liquid interface to advance greatly, forming a solid phase of new components; fΔ/D that is, non-equilibrium keff = k0/ k0 + (1 − k0)e . (5) solidification actually occurs, and impurities are concentrated at the solidification inter- facewhere [24]. f is the zone melting rate, D is the impurity diffusion rate, and δ is the thickness of Therefore, the equilibrium distribution coefficient k0 is not fixed, so the effective the boundary layer. As shown in Figure 4, when f ≫ D/δ, the rate of change of keff increases distribution coefficient (keff) is introduced to improve the zone refining efficiency. The rapidly until it approaches 1; when f ≫ D/δ, keff tends to k0, and the melting efficiency at simplest method is to optimize keff. The BPS equation is as follows [25,26]: this time depends on the balance of specific impurities partition coefficient. In terms of h i purification effect, keff is expected to be close to −k0f.∆ /D ke f f = k0/ k0 + (1 − k0)e . (5) It can be clearly seen from Equation (5) that if the δ value is large, the keff is also large, wherewhichf isis thenot zone conducive melting to rate, zoneD isrefining. the impurity diffusion rate, and δ is the thickness of the boundaryTherefore, layer. the δ As value shown must in Figurebe reduced.4, when δf is directlyD/δ, the affected rate of changeby the ofmixingkeff of the increasesmelt. During rapidly the until zone it approachesmelting process, 1; when measuresf D/δ such, keff tends as rotation, to k0, and external the melting magnetic field, efficiencyand oscillation at this time stirring depends are on often the balanceused. If of the specific melt impurities only has partition convection, coefficient. δ is about In 1 mm, terms of purification effect, k is expected to be close to k . which can be reduced to eff0.1 mm by stirring. Stirring0 can be reduced to 0.01 mm [27].
FigureFigure 4. Relationship4. Relationship between betweenkeff and keff fandδ/D. fδ/D.
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It can be clearly seen from Equation (5) that if the δ value is large, the keff is also large, which is not conducive to zone refining. Therefore, the δ value must be reduced. δ is directly affected by the mixing of the melt. During the zone melting process, measures such as rotation, external magnetic field, and oscillation stirring are often used. If the melt only has convection, δ is about 1 mm, which can be reduced to 0.1 mm by stirring. Stirring can be reduced to 0.01 mm [27].
3.2. Zone Refining Rate The selection of the moving speed of the melting zone (that is, the zone refining rate) directly affects the purification efficiency, which is related to the production cost. Therefore, in the purification process, it is necessary to formulate an appropriate rate according to the characteristics of the material itself. When the melting zone movement rate f is very large, the solid phase crystallization rate increases accordingly, making it difficult to remove impurities in the unit cell, and the purification effect is not obvious; when f is small, the component diffusion can be fully carried out, and the impurities inside the crystal can be effectively removed, making the purification efficiency higher [28]. When multiple impurities are involved, the optimal zone melting speed is determined by the impurity with keff closest to the host metal [29]. Prasad [28] optimized its process parameters when purifying tellurium and found that when the zone melting speed was 30 mm/h, it produced better results and obtained 7N pure tellurium material. Zhang [30] found that the melting rate has a significant effect on the zone melting process when purifying metallic tin. When the zone refining rate was reduced from 1.4 to 0.6 mm/min, the metal purity in the ingot increased from 99.99824% to 99.99906% after 10 times of refining. Wan [31] proposed an improved vacuum zone refining process. By modifying the effective distribution coefficient, the axial segregation of impurities was studied. When the zone refining rate was 1 mm/min, the aluminum content was greater than that of the 5N (99.9992%) sample. When preparing single crystal materials, the use of a lower zone refining rate can effectively remove impurity elements inside the crystal and reduce crystal defects, but too low a zone refining rate will cause severe segregation of elements within the crystal and increase the concentration gradient of the component, which is not conducive to the preparation of single crystals; the use of a higher zone refining rate can improve the segregation of impurities and improve production efficiency, but it is not conducive to the elimination of gaseous impurities, which affects the stability of the solid/liquid interface, and it also affects the preparation of single crystals. Therefore, the choice of the optimal refining rate is to strike a balance between the formation of single crystals and the reduction of the degree of segregation [32].
3.3. Length of Melting Zone The length of the melting zone is affected by many factors, such as thermal field, zone refining speed, crucible thermal conductivity, etc. In zone refining, the purity of the product obtained in the narrow melting zone is higher than that in the wider melting zone, but the impurity concentration of the narrow melting zone increases faster, making it difficult to remove impurities in the melting zone, which must be compensated by extending the purification time [33]. Therefore, in order to improve the purification efficiency, the actual production process generally adopts the operation method of using a wide melting zone and a higher zone refining rate at the beginning of purification and then changing to a narrow melting zone and a lower zone refining rate. Jun [34] purified industrial cerium by induction heating and found that the larger zone refining length in the early zone refining and the shorter zone refining length in the later stage can improve the segregation efficiency of solute during the zone refining process, especially for k0 far from the whole solute. During the first zone refining, the impurity concentration of the melting zone will increase for k0 < 1; for k0 > 1, the impurity concentration will decrease. In order to meet the two situations at the same time, to obtain the best separation effect after the first zone Materials 2021, 14, 2064 7 of 21
refining, the melting zone must be as large as possible; that is, the length of the melting zone is the full ingot length. However, when the zone is melted a few times, see Figure5. Materials 2021, 14, x FOR PEER REVIEW 7 of 21 As the length of the melt zone increases, the “limit distribution” curve moves upwards, and the final purity that can be achieved decreases.
Figure 5. Relationship between impurity concentration and number of zone refining refining passes [[35]35]..
Ho [36] [36] obtains the optimal optimal melting zone length length value value for for ten ten passes passes of of zone zone refining. refining. It can can be be seen seen from from Figure 66aa thatthat thethe lengthlength ofof thethe meltingmelting zonezone increasesincreases withwith thethe increaseincrease of the distribution coefficientcoefficient and and decreases decreases with with the the increase increase of of the the number number of of zone zone refining. refin- ing.Following Following this this step step for zonefor zone refining, refining a considerable, a considerable separation separation effect effect can can beobtained. be obtained. As shown in Figure6b, when k < 1, the maximum solute removal rate decreases with As shown in Figure 6b, when k0 < 1, the maximum solute removal rate decreases with the increase of the partition coefficient, and the opposite is true when k > 1. However, the the increase of the partition coefficient, and the opposite is true when k00 > 1. However, the maximum solutesolute removalremoval rate rate increases increases with with the the increase increase of zoneof zone refining refining times. times. Ghosh Ghosh [37] [37]calculated calculated the zone the zone melt melt length length when when meeting meeting the maximum the maximum solute solute removal removal rate according rate ac- cordingto Ho’s numericalto Ho’s numerical model. It model. can be It obtained can be obtained that as the that number as the of number smelting of passessmelting increases, passes the shorter zone melt length can be used to obtain the maximum solute removal rate [38]. increases, the shorter zone melt length can be used to obtain the maximum solute removal Table2 lists the zone refining length when the maximum solute removal rate is obtained rate [38]. Table 2 lists the zone refining length when the maximum solute removal rate is per pass. Table3 lists the purity grade of metal after zone refining. obtained per pass. Table 3 lists the purity grade of metal after zone refining. Table 2. Zone refining length when the maximum solute removal rate is obtained per pass. Table 2. Zone refining length when the maximum solute removal rate is obtained per pass. ≥ ZoneZone Refining Refining Times Times 1 12 23 34 45–8 5–89–19 9–19 ≥2020 NormalizedNormalized melting melting zone zone lengthlength 1 10.35 0.35 0.25 0.250.2 0.20.15 0.150.1 0.1 0.050.05
Table 3. The purity grade of metal after zone refining.
Elements Al As Cd Cu Fe Mg Ni Pb Ga Si Sn Te Zn Ag Purity grade 9N 9N 7N 10N 9N 8N 7N 7N 7N 9N 7N 7N 7N 8N Elements Ge In Ce Purity grade 10N 7N 7N
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Table 3. The purity grade of metal after zone refining.
Elements Al As Cd Cu Fe Mg Ni Pb Ga Si Sn Te Zn Ag Purity grade 9N 9N 7N 10N 9N 8N 7N 7N 7N 9N 7N 7N 7N 8N Elements Ge In Ce MaterialsPurity 2021 grade, 14, x FOR PEER 10N REVIEW 7N 7N 8 of 21
Figure 6. ((a) Optimal zone refiningrefining lengthlength of of 1–10 1–10 passes; passes; ( b(b)) Maximum Maximum solute solute removal removal rate rate during during multi-pass multi-pass zone zone refining. refin- ing. 3.4. Zone Refining Scans 3.4. Zone Refining Scans The zone refining process needs to be repeated many times. As the number of times increases,The zone the purificationrefining process effect needs also increases,to be repeated but aftermany a times. certain As pass the zone number melting, of times the increases,impurity concentration the purification distribution effect also is increases, close to the but “limit after distribution”, a certain pass as shownzone melting, in Figure the5. impurityAt this concentration time, in the distribution process of is drivingclose to the the “ impuritieslimit distribution to both”, as sides, shown impurities in Figure on5. bothAt sides this will time, also in diffusethe process to the of middle.driving Forthe impurities the convenience to both of sides, operation, impurities the empirical on both sidesformula will for also the diffuse number to ofthe zone middle. refining For the times conveniencen can be expressed of operation, as n =thekL empirical/l (where for-k is mulathe empirical for the number constant, of the zone value refining range times is 1 to n 1.5; canL beis theexpressed length ofas then = ingot;kL/l (wherel is the k length is the empiricalof the melting constant, zone); the in value actual range operation, is 1 to the1.5; frequently L is the length used of condition the ingot; is lL is/ lthe=10, length taking of thek = melting 1.5; then, zone);n = 15 in [39 actual]. operation, the frequently used condition is L/l = 10, taking k = 1.5; then, n = 15 [39]. 3.5. Application of Current in Impurity Transmission 3.5. ApplicationApplying of a currentCurrent fieldin Impurity during Transmission the refining process (see Figure7) can improve the segregationApplying of impuritiesa current field at the during solidification the refining interface process through (see electromigration.Figure 7) can improve Dost [the40] segregationconducted a of numerical impurities simulation at the solidification on the process interface of transporting through electromigration. impurities in the cadmiumDost [40] conductedzone refining a numerical system. The simulation results show on the that process the conductivity of transporting of cadmium impurities is higher, in the which cad- miumcan enhance zone refining the migration system. rateThe ofresults impurities show that in cadmium. the conductivity The gas of in cadmium Figure7 is higher, argon, which iscan used enhance to prevent the migration active metals rate fromof impurities reacting within cadmium. other gases. The gas in Figure 7 is argon, which is used to prevent active metals from reacting with other gases.
Figure 7. Schematic diagram of the zone refining system under applied current.
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Figure 6. (a) Optimal zone refining length of 1–10 passes; (b) Maximum solute removal rate during multi-pass zone refin- ing.
3.4. Zone Refining Scans The zone refining process needs to be repeated many times. As the number of times increases, the purification effect also increases, but after a certain pass zone melting, the impurity concentration distribution is close to the “limit distribution”, as shown in Figure 5. At this time, in the process of driving the impurities to both sides, impurities on both sides will also diffuse to the middle. For the convenience of operation, the empirical for- mula for the number of zone refining times n can be expressed as n = kL/l (where k is the empirical constant, the value range is 1 to 1.5; L is the length of the ingot; l is the length of the melting zone); in actual operation, the frequently used condition is L/l = 10, taking k = 1.5; then, n = 15 [39].
3.5. Application of Current in Impurity Transmission Applying a current field during the refining process (see Figure 7) can improve the segregation of impurities at the solidification interface through electromigration. Dost [40] conducted a numerical simulation on the process of transporting impurities in the cad- mium zone refining system. The results show that the conductivity of cadmium is higher, Materials 2021, 14, 2064 9 of 21 which can enhance the migration rate of impurities in cadmium. The gas in Figure 7 is argon, which is used to prevent active metals from reacting with other gases.
Materials 2021, 14, x FOR PEER REVIEW 9 of 21
FigureFigure 7. 7.Schematic Schematic diagram diagram of of the the zone zone refining refining system system under under applied applied current. current. 3.6. Inclination 3.6. Inclination During the refining process in the horizontal area, the longitudinal section of the in- gotDuring will become the refining tapered process due to in the the mass horizontal transfer area, and the even longitudinal cause the sectionmelt to ofoverflow the ingot. To willavoid become this phenomenon, tapered due to the the crucible mass transfer should and be even inclined cause at the an meltangle to θ overflow. relative to To the avoid hori- thiszontal phenomenon, direction, as the shown crucible in Equation should be (6) inclined [41]: at an angle θ relative to the horizontal direction, as shown in Equation (6) [41]: 1 θ = tan × 2h0 (1 − γ/l) (6) −1 θ = tan × 2h0 (1 − γ/l) (6) where h0 is the original height of the ingot and γ is the ratio of solid and liquid metal wheredensity.h0 is the original height of the ingot and γ is the ratio of solid and liquid metal density. MagneticMagnetic field, field, gas gas flow flow rate, rate and, and melt melt stability stability will will also also have have an an important important influence influence onon the the purification purification effect. effect. In In addition, addition, the the phenomenon phenomenon of of backflow backflow in in the the melting melting zone zone willwill also also affect affect the the effect effect of of zone zone refining. refining. This This is is because because the the cooling cooling rate rate of of the the upper upper and and lowerlower ingots ingots differs differs greatly, greatly, and and the the ingot ingot shrinks shrinks unevenly unevenly and and bends bends upwards upwards [42 [42].]. TheThe experimental experimental optimization optimization of theof the above-mentioned above-mentioned zone zone refining refining parameters parameters is not is universalnot universal because because they depend they depend on the on properties the properties of the of specific the specific system, system, such as such equipment as equip- specifications,ment specifications, ingot diameter, ingot diameter, melt viscosity, melt viscosity, and impurity and impurity distribution distribution coefficient. coefficient. 4. Types of Zone Refining 4. Types of Zone Refining Based on the same principle, there are various zone refining technologies. There are Based on the same principle, there are various zone refining technologies. There are two main types, refining in the suspension area and refining in the horizontal area, as two main types, refining in the suspension area and refining in the horizontal area, as shown in Figure8. shown in Figure 8.
FigureFigure 8. 8.(a ()a Horizontal) Horizontal zone zone refining refining technology; technology; (b ()b Suspended) Suspended zone zone refining refining technology. technology.
TheThe emergence emergence of of refining refining in in thethe suspendedsuspended areaarea has greatly promoted promoted the the study study of ofrefractory refractory metals. metals. This This method method can can not not only only effectively effectively remove remove volatile volatile metals metals and and gas gas impurities in refractory metals, as well as avoid secondary pollution of metals in the impurities in refractory metals, as well as avoid secondary pollution of metals in the re- refining process, but also effectively control the metal melt flow [43]. Table4 lists the fining process, but also effectively control the metal melt flow [43]. Table 4 lists the differ- differences between the two methods. ences between the two methods.
Table 4. Differences in zone refining technology [43].
Category Heating Method Advantage Disadvantage Scale The melting zone is supported by Electron beam heating, The ingot does not touch the surface tension, so controlling the Floating zone induction heating, container, so the product purity is Small shape and stability of the melting refining plasma heating, light high, and the equipment occupies batch zone is the key, and the output is heating a small space. low. Simple equipment, continuous purification of multiple melting Horizontal Induction heating, zones, easy loading and Large footprint Batch zone refining resistance heating unloading of materials, easy identification of interfaces, and
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Table 4. Differences in zone refining technology [43].
Category Heating Method Advantage Disadvantage Scale The melting zone is supported by surface Electron beam heating, The ingot does not touch the container, Floating zone tension, so controlling the Small induction heating, plasma so the product purity is high, and the refining shape and stability of the batch heating, light heating equipment occupies a small space. melting zone is the key, and the output is low. Simple equipment, continuous purification of multiple melting zones, easy loading and unloading of Horizontal zone Induction heating, materials, easy identification of Large footprint Batch refining resistance heating interfaces, and the total length of ingots can be increased or decreased as needed
5. High-Purity Metal Analysis Method The purity testing of high-purity metals should be based on the actual application needs as the main standard, which is generally measured by the reduction method. From the development and application of metal purity analysis at home and abroad in recent years, it can be seen that in the determination of trace and ultra-trace metal elements, a basic mode can be attributed to the effective sample decomposition method, efficient separation and enrichment method, and simple, fast, and accurate instrument analysis method [1]. The analysis methods to determine the purity of high-purity metal materials are divided into chemical methods and physical methods, and they mainly consist of chemical analysis methods. Table5 compares various chemical analysis methods. It can be seen that GDMS can be directly analyzed by solid sample injection, with a wide measurement range, a variety of single detection elements, and high detection accu- racy. It has obvious advantages in high-purity detection, but the equipment is expensive. ICP-MS is more popular and has the advantages of speed, economy, and convenience. NAA can be used for precious metal analysis and testing. High-purity metal purity analysis is an important indicator to measure the production level of industrial science and technology. It plays an inestimable role in the develop- ment of high-purity metal production processes and the development of the materials science industry. At the same time, it also follows the progress of science and economic development with increasing improvement, and the analysis of metal purity in the future will develop toward the following aspects [1]: (1) In terms of the number of measured elements, it will develop from single elements to multiple elements simultaneously or continuously. (2) In the analysis method, it will develop from offline/manual operation to online/ automatic mode. (3) In terms of data collection and processing, the application of mathematical methods such as chemo-metrics, pattern recognition, expert systems, artificial intelligence, and neural networks will help to improve the integrity and accuracy of test data. Materials 2021, 14, 2064 11 of 21
Table 5. Comparison of various analysis methods for measuring metallic elements.
Analytical Sampling Method Measuring Range (g/g) Explanation Method The matrix effect is small, the sample processing is simple, it can avoid pretreatment pollution and loss, it is fast and efficient, the detection limit is low, and standard samples can be used, GDMS [44] Solid Constant~10−12 but the price is expensive. The discharge is stable, and the analysis sample can be peeled layer by layer for surface and depth analysis. The self-absorption effect is small. Multiple elements can be determined simultaneously. High resolution and sensitivity, a wide measurement range, a ICP-MS Liquid 10−6~10−12 need to try to eliminate the matrix effect and isotope interference, and the sample processing process is longer. The number of single analysis is small, the analysis range is GF-AAS Solid 10−6~10−9 narrow, and it is not suitable for high melting point metals. Fast speed, high sensitivity, small matrix effect, low detection ICP-AES limit, and serious spectrum interference and matrix interference. Liquid Constant~10−6 [45] Multi-element simultaneous analysis method with the widest range of analysis elements and the largest content span. Fast, simple, and economical non-destructive testing, which can TXRF Solid Constant~10−12 perform multi-element analysis at the same time, but it can only perform surface analysis, and the detection limit is low. High sensitivity, high accuracy and precision, and sensitivity varies from element to element. It can only measure the content NAA Solid, liquid 10−6~10−13 of elements. It requires a small nuclear reactor and has the risk of nuclear radiation. Less sampling, non-destructive analysis. The detection equipment is expensive. It has a lower detection limit than ICP-MS, can be used for NTIMS Liquid 10−10~10−14 isotope age studies, and can accurately measure Re and Os.
6. Numerical Simulation Zone refining experimental research takes a lot of time. Therefore, many numerical models have been developed to effectively predict solute distribution or optimize exper- imental parameters as well as provide guidance for empirical experiments. Reiss [46] assumes that the solute partition coefficient k0 and the melting zone length L remain un- changed, establishes a differential equation between the concentration of each substance, and obtains a mathematical model of zone refining. Lee [47] proposed a model capable of simulating zone refinement and drawing conclusions. This model can pass the repeated pass method even when the zone travel speed and zone length are relatively large and thus cannot be properly purified. Cheung [48] combined a numerical model and genetic algorithm to establish an optimized melting zone length model to achieve maximum pu- rification efficiency. Jun [34] uses induction heating to refine the industrial cerium in a cold crucible and introduces the numerical model of solute redistribution in the process of zone refinement into the genetic algorithm to search for the optimal zone length of different zone channels to improve the solute redistribution efficiency. The experiment and calculation results show that the genetic algorithm is a useful tool to obtain the optimal zone length during the zone refining process, but the stability of the molten zone should be maintained in the cold crucible. Tan Yang [49] reported that the zone refining by combining finite element simulation data and experimental results analysis concluded that the zone refining experiment on the distribution of temperature field around the heat source with ellipsoid, semicircular canals is more suitable than square grooves for the purification of zone refining, as shown in Figure9. The scope of the safety threshold value of indium under a given preheated temperature will greatly boost zone refining efficiency and does not destroy the balance Materials 2021, 14, 2064 12 of 21
of zone refining. In addition, Chen Luona [50] applied the oxidation refining-zone refin- Materials 2021, 14, x FOR PEER REVIEWing joint method to refining indium heat coupling finite element analyses, as shown in12 of 21 Figure 10. Here, argon gas flow in a horizontal transverse turn-back, along the long axis of Materials 2021, 14, x FOR PEER REVIEW the zone refining equipment in the opposite direction from exports, presents12 of 21 “up” in the
zone refining equipment, forming annular flow. The model more accurately reflects the oxidation refining and zone refining temperature field as well as flow field distribution.
Figure 9. Temperature cross-section: (a) SiC thermal conductor, (b) graphite electrothermal assem- bly. FigureFigure 9. Tempe 9. Temperaturerature cross cross-section:-section: ( (aa)) SiC SiC thermalthermal conductor, conductor, (b )(b graphite) graphite electrothermal electrothermal assembly. assem- bly.
FigureFigure 10. 10. FlowFlow diagram diagram of of argon gasgas flow flow in in the the zone zone refining refining equipment. equipment . Figure 10. Flow diagram of argon gas flow in the zone refining equipment. 6.1.6.1. Iterative Iterative Modeling Modeling of of Constant K K 6.1. Iterative ModelingFor ofFor Constant different different K distribution coefficients coefficients and and melting melting zone zone lengths, lengths, Bochegov Bochegov [51] consid- [51] con- sidered the limit distribution of impurities after purification by zone refining technology For different ereddistribution the limit distributioncoefficients of and impurities melting after zone purification lengths, byBochegov zone refining [51] con- technology and and proposed analytical solutions. It divides the ingot into three regions in the length di- sidered the limit distribution of impurities after purification by zone refining technology rection, and the impurity distribution function is shown in Equation (7). and proposed analytical solutions. It divides the ingot into three regions in the length di- rection, and the impurity distribution functionAe Bxis, shown 0 in ≤ xEquation ≤ L − 2l (7). ⎧ ( 2 ) ( 2 ) k(L l k) AeB L l AeB L l k-1 Bx ⎪ l Ae , 0 ≤ x ≤1 L S−(x2)l + 1 l e C ( ) = S(L 2l) + lk ek S(L-2l) + lk ek , L − 2l < x ≤ L – l (7) ⎧ B(L 2l)S x B(L 2l) k(L l k) ⎪ Ae ⎨ (Ae ) k-1 ( ) + AeB L 2l l k 1 k S x⎪ k 1 k l e k 1 CS(x) = S(L 2l) + l e S(L-2l) +1 l (Le − x) , , L L−−l2 Materials 2021, 14, 2064 13 of 21 proposed analytical solutions. It divides the ingot into three regions in the length direction, and the impurity distribution function is shown in Equation (7). AeBx, 0 ≤ x ≤ L − 2l k(L−l−k) AeB(L−2l) AeB(L−2l) − S(x) + lk 1e l , L − 2l < x ≤ L – l CS(x) = S(L−2l)+lk−1ek S(L−2l)+lk−1ek (7) B(L−2l) − Ae (L − x)k 1, L − l < x ≤ L S(L−2l)+lk−1ek Materials 2021, 14, x FOR PEER REVIEW 13 of 21 A and B are constants, and B is derived from known conditions: k B = eBl − 1 . (8) l k B = ( − 1). (8) A is determined according to non-normalizedl conditions: A is determined according to non-normalized conditions: Z L−2l Z L−l Z L = ( ) + ( ) + ( ) Cs0L L C2sl1 x dx lCs2 x dx L Cs3 x dx. (9) 0 ( ) L−2l ( ) L−l ( ) Cs0L = ∫0 Cs1 x dx + ∫L 2l Cs2 x dx+ ∫L l Cs3 x dx. (9) x is the coordinate of the crystallization front relative to the starting point of the ingot, and x is the coordinate of the crystallization front relative to the starting point of the ingot, and cs(x) is the impurity concentration function on the coordinate x on the solid phase, where Cs0 cs(x) is the impurity concentration function on the coordinate x on the solid phase, where is the initial impurity concentration. S is determined according to the following expression: Cs0 is the initial impurity concentration. S is determined according to the following expres- sion: n k+n k ∞ k (l − x − l) S(x) = − ∑ 0 (10) l k l k(k +n 1)(k(l+ x2 )l)···k+n (k + n) S(x)n==−0 ∑∞ 0 (10) l n = 0 k(k + 1)(k + 2)⋯(k + n) where n is the number of zone refining. where n is the number of zone refining. The vertical axis corresponds to the ratio C/Cs0 of the impurity concentration to its The vertical axis corresponds to the ratio C/Cs0 of the impurity concentration to its initial concentration, and the horizontal axis corresponds to the coordinate relative to the initial concentration, and the horizontal axis corresponds to the coordinate relative to the origin of the ingot. Thinner lines correspond to the distribution with a finite amount of origin of the ingot. Thinner lines correspond to the distribution with a finite amount of passages with their numbers increasing as the lines approach the limiting distribution, as passages with their numbers increasing as the lines approach the limiting distribution, as shown in Figure 11. shown in Figure 11. Figure 11. Limiting distributiondistribution for for the the case case of of molten molten zone zone size sizel = 0.2l = 0 and.2 and impurity impurity distribution distribution factor factor (a) k = (a 2) andk = 2 (b and) k = (b 0.5.) k = 0.5. 6.2. Iterative Modeling of Variable K 6.2. IterativeSpim [52 Modeling] proposed of Variable a new iterativeK model that can be used to study the effect of zone meltSpim length [52] and proposed distribution a new coefficient iterative onmodel refining that efficiency,can be used including to study the the final effect impurity of zone meltconcentration length and distribution distribution and coefficient the minimum on refining zone passefficiency, required including to reach the the final final impurity state. In concentration distribution and the minimum zone pass required to reach the final state. In this model, by considering four different regions along the sample, the solute concen- tration distribution in each subzone of the melting zone is quantified. The formula is as follows: dx k ∑M 1 Cn 1 , X = 0 ⎧ i Z q = 0 S q dx ⎪ n kidx n 1 n ⎪CS(X dx)+⋯ + CS(X + Z dx) − CS(X dx) , 0 < X ≤ 1 − Z n Z CS(X) = C dx . (11) ⎨ 0 − ∑M 1 Cn , 1 − Z < X < 1 Z Z q = 0 S q dx ⎪ M 1 n ⎪ ∑q = 0 C C − S q dx , X = 1 ⎩ 0 M Materials 2021, 14, 2064 14 of 21 this model, by considering four different regions along the sample, the solute concentration distribution in each subzone of the melting zone is quantified. The formula is as follows: ! M−1 k dx Cn−1 X = i Z ∑ S(q dx) , 0 q=0 h i n + ··· + kidx n−1 − n < ≤ − CS(X −dx) Z CS(X+Z−dx) CS(X−dx) , 0 X 1 Z Cn = ! . (11) S(X) M−1 Materials 2021, 14, x FOR PEER REVIEW C dx n 14 of 21 0 − ∑ C , 1 − Z < X < 1 Z Z S(q dx) q=0 M−1 Cn ∑q=0 S(q dx) C0 − M , X = 1 Cheung [53] established a database containing the changes in solids concentration (CS) andCheung liquid [53 concentration] established a(C databaseL) to obtain containing the variable the changesk, so during in solids the simulation concentration pro- (cess,CS) and for liquideach C concentrationL in any melting (C Lzone,) to obtain k can thebe easily variable accessedk, so during from the simulationdatabase. Compar- process, foring eachthe twoCL in model any melting simulations zone, withk can constant be easily k accessedand variable from k thefor database.aluminum Comparing refining, it thecan twobe concluded model simulations that using with variable constant k ink theand simu variablelationk isfor closer aluminum to the refining,experimental it can im- be concludedpurity distribution that using curve variable than kconsideringin the simulation constant is k closer. The toresults the experimental show that the impurity variable distributionsolute distribution curve thanmethod considering is used to constant simulatek. Thethe impurity results show distribution that the variablein the refining solute distributionprocess in different method isregions, used to which simulate is closer the impurity to the experimental distribution in result the refining k than processthe usual in differentmethod. regions, which is closer to the experimental result k than the usual method. CheungCheung [[48]48] interactedinteracted with the numericalnumerical model through the AI (artificial(artificial intelli-intelli- gence,gence, AI)AI) searchsearch methodmethod toto quantitativelyquantitatively determinedetermine thethe influenceinfluence ofof thethe variablevariable solutesolute distributiondistribution coefficientcoefficientk kon on the the distribution distribution of impuritiesof impurities in multi-pass in multi-pass purification purification by zone by refining.zone refining. The results The results show show that thethat interaction the interaction between between the numericalthe numerical model model and and the the AI searchAI search technology technology can can provide provide the bestthe best set ofset melting of melting zone zone lengths lengths to achieve to achieve maximum maxi- purificationmum purificatio efficiency.n efficiency. As shown As shown in Figure in Figure12, each 12, node each represents node represents the length the oflength a fusion of a zonefusion and zone is and linked is linked to subsequent to subsequent nodes nodes of possible of possible solutions, solutions, resulting resulting in an in explosive an explo- combinationsive combination of expansion. of expansion. ZhangZhang [[54]54] carriedcarried outout aa zonezone meltingmelting processprocess toto purifypurify SbSb underunder thethe conditionsconditions ofof inertinert gasgas protectionprotection andand heaterheater movementmovement ratesrates ofof 2,2, 1,1, andand 0.50.5 mm/min,mm/min, respectively. ByBy fittingfitting the the impurity impurity concentration concentration curve curve obtained obtained from from the experiment the experiment with the with Spim the model, Spim the k values of Pb, As, and Fe impurities at each moving rate are retrieved. This helps to model,eff the keff values of Pb, As, and Fe impurities at each moving rate are retrieved. This morehelps accuratelyto more accurately predict the predict time required the time for required zone refining for zone and refining achieve and the achieve efficiency the of effi- Sb zone refining. ciency of Sb zone refining. Figure 12.Figure Representative 12. Representative tree of possibilities tree of possibilities.. 6.3. Iterative Modeling Considering Diffusion Area Nakamura et al. [55] proposed a numerical simulation model that divides the melting into two independent regions, namely the diffusion region and the stirring region, as shown in Figure 13a, and the vertical axis C represents the solid and liquid. There is an interface between them, and there are diffusion regions and stirring regions in the molten region. This numerical model introduces a transfer ratio q to illustrate the amount of so- lute transferred from the diffusion zone to the stirring zone during the diffusion process. Figure 13b is a schematic diagram of the model calculation; the length of the melting zone is equal to am (mm). When the first segment is the diffusion area, the concentration is as shown in Equation (12): Materials 2021, 14, x FOR PEER REVIEW 15 of 21 δ δ CL(i) = CL(i 1) + (1 − k)CL(i 1) × 1 − q . (12) The new mixing zone consists of three parts: the distribution of the diffusion zone, the (m−j) segment with the concentration of CL(i−1) in the previous agitating zone, and one segment of the new solid zone with the concentration of C(x). Therefore, the average con- centration in the stirring area CL(i−1) becomes δ ( k)CL(i 1) × q + CL(i 1) × m j + C(x) C ( )= , 2 ≤ j ≤ m − 10. (13) L i m-j Burton [26] established two important equations related to the distribution of solutes Materials 2021, 14, 2064 when there is a diffusion layer between the solid zone and the molten zone. 15 of 21 CL CS δ = exp −fδ/D (14) CL CS 6.3. IterativeAssume Modeling that the Consideringexponential Diffusionfactor in Equation Area (14) is the transmission ratio q. Nakamura et al. [55] proposed a numerical simulation model that divides the melting into two independent regions, namelyexp the −f diffusionδ/D = q region and the stirring region,(15) as shown in Figure 13a, and the vertical axis C represents the solid and liquid. There is an The experimental values of f and D have been determined, and if the transfer ratio q interface between them, and there are diffusion regions and stirring regions in the molten is clear, the width of the diffusion region δ can be estimated. The advantage of this model region. This numerical model introduces a transfer ratio q to illustrate the amount of solute is that when the δ of one impurity is determined by parameter fitting, the same δ value transferred from the diffusion zone to the stirring zone during the diffusion process. can be used to derive the distribution curve of other impurities. Figure 13. (a) Schematic diagram of the melting zone; (b) Schematic diagram of the computation model. Figure 13. (a) Schematic diagram of the melting zone; (b) Schematic diagram of the computation model. Figure 13b is a schematic diagram of the model calculation; the length of the melting zone is equal to am (mm). When the first segment is the diffusion area, the concentration is as shown in Equation (12): δ δ CL(i)= CL(i−1) + (1 − k)CL(i−1) × (1 − q). (12) The new mixing zone consists of three parts: the distribution of the diffusion zone, the (m−j) segment with the concentration of CL(i−1) in the previous agitating zone, and one segment of the new solid zone with the concentration of C(x). Therefore, the average concentration in the stirring area CL(i−1) becomes ( − ) δ × + × ( − )+ ( ) 1 k CL(i−1) q CL(i−1) m j C x C = , 2 ≤ j ≤ m − 10. (13) L(i) (m − j) Materials 2021, 14, 2064 16 of 21 Burton [26] established two important equations related to the distribution of solutes when there is a diffusion layer between the solid zone and the molten zone. C − C L S = (− ) δ exp f δ/D (14) CL − CS Assume that the exponential factor in Equation (14) is the transmission ratio q. exp(− f δ/D)= q (15) The experimental values of f and D have been determined, and if the transfer ratio q Materials 2021, 14, x FOR PEER REVIEWis clear, the width of the diffusion region δ can be estimated. The advantage of this16model of 21 is that when the δ of one impurity is determined by parameter fitting, the same δ value can be used to derive the distribution curve of other impurities. 6.4.6.4. Evaluation Evaluation ModelingModeling and Experiment Since there are various experimental parameter combinations in the process of im- Since there are various experimental parameter combinations in the process of im- proving zone refining efficiency, it is very time-consuming and even unfeasible to study proving zone refining efficiency, it is very time-consuming and even unfeasible to study only through experiments. only through experiments. In addition, refining systems in different regions have the best experimental param- In addition, refining systems in different regions have the best experimental param- eters. Therefore, the application of the numerical model as described above is a good as- eters. Therefore, the application of the numerical model as described above is a good sistant to guide the experimental performance. In this way, the influence of each parame- assistant to guide the experimental performance. In this way, the influence of each pa- ter on the refining result can be predicted, and the theoretically optimal parameter com- rameter on the refining result can be predicted, and the theoretically optimal parameter bination can be obtained in a short time and at low cost. combination can be obtained in a short time and at low cost. Therefore, experimental research is necessary to prove the accuracy of simulation Therefore, experimental research is necessary to prove the accuracy of simulation prediction or to correct the model itself. It is recommended to combine simulation and prediction or to correct the model itself. It is recommended to combine simulation and experiment to study the refinement of metal regions. experimentIn order to studyto carry the out refinement zone refining of metal and regions. prepare high-purity metal indium, corre- spondingIn order process to carry improvement out zone refining and equipment and prepare research high-purity and development metal indium, are correspond-required. ingFor process this reason, improvement our team andLi Qing equipment [56], Tan research Yang [49] and, developmentand Li Yicheng are [57] required. designed For the this reason,vacuum our zone team refining Li Qing system [56], for Tan a multi Yang- [refining49], and zone, Li Yicheng whose structure [57] designed is shown the vacuumin Fig- zoneure 1 refining4. system for a multi-refining zone, whose structure is shown in Figure 14. FigureFigure 14. 14.Schematic Schematic diagram diagram of vacuumof vacuum refining-electromigration refining-electromigration high-purity high-puri indiumty indium refining refining plant plant in multi-refining in multi-refining zone. zone. The vacuum zone refining/electromigration refining device is composed of stepping motor numerical control equipment, a high-purity argon gas purifier, a high-frequency power supply, an induction heating coil, an electromagnetic shielding device, a quartz furnace tube, and a vacuum pump. The quartz furnace tube is equipped with a cooling jacket, and a quartz boat is placed inside to carry indium. In the process of zone refining, the width of the melting zone is controlled by the output of high-frequency power, while the moving speed of the melting zone is precisely controlled by the numerical control table of the stepping motor. The general speed is 3–30 mm/hour. An electromagnetic shielding device is used to prevent electromagnetic interference between the melting zones. The Materials 2021, 14, 2064 17 of 21 The vacuum zone refining/electromigration refining device is composed of stepping motor numerical control equipment, a high-purity argon gas purifier, a high-frequency power supply, an induction heating coil, an electromagnetic shielding device, a quartz furnace tube, and a vacuum pump. The quartz furnace tube is equipped with a cooling jacket, and a quartz boat is placed inside to carry indium. In the process of zone refining, the width of the melting zone is controlled by the output of high-frequency power, while Materials 2021, 14, x FOR PEER REVIEW 17 of 21 the moving speed of the melting zone is precisely controlled by the numerical control table of the stepping motor. The general speed is 3–30 mm/hour. An electromagnetic shielding device is used to prevent electromagnetic interference between the melting zones. The atmosphereatmosphere during during the the refining refining process process is is controlled controlled jointly jointly by by the the diaphragm diaphragm vacuum vacuum pumppump and and the the high-purity high-purity argon argon gas gas purifier. purifier. First,First, the the diaphragm diaphragm vacuumvacuum pumppump pumpspumps the vacuum vacuum up up to to about about 0.06 0.06 MPa MPa for for 20 20min. min. Then, Then, the the air air valve valve of of the the vacuum vacuum pump pump path is closed,closed, andand thethe airair valve valve leading leading to to ultra-high-purityultra-high-purity argon argon gas gas is is opened opened for for argon argon gas gas (the (the pressure pressure of of argon argon gas gas is is always always slightlyslightly higher higher than than 1 atmospheric1 atmospheric pressure). pressure). The The above above operation operation was was repeated repeated 3 times 3 times to completeto complete the airthe exchange air exchange process, process, and theand high-purity the high-purity indium indium was prepared was prepared in the in area the melting/electromigrationarea melting/electromigration process process under under the protection the protection of ultra-high-purity of ultra-high-purity argon argon gas. The gas. vacuumThe vacuum zone refining/electromigrationzone refining/electromigration joint joint method method for high-purity for high-purity indium indium extraction extrac- cantion be can used be withoutused without high vacuum high vacuum under theunder condition the condition of the preparationof the preparation of high-purity of high- 6Npurity indium, 6N indium, and it can and significantly it can significantly reduce reduce the technical the technical threshold threshold and gas and raw gas material raw ma- costs,terial indicating costs, indicating that the that technology the technology has obvious has obvious industrial industrial application application prospects. prospects. InIn order order to to solve solve the the problem problem of of small small processing processing capacity capacity of of metal metal indium indium in in the the zonezone refining refining process, process, Li Li Yicheng Yicheng et et al. al. [57 [57]] adopted adopted the the method method of of simultaneous simultaneous heating heating ofof multiple multiple furnacefurnace tubes,tubes, which which doubled doubled the the processing processing capacity capacity of ofthe the zone zone refining refining pro- process.cess. Figure Figure 15 15shows shows the the working working picture picture of the of thevacuum vacuum refining refining/electromigration/electromigration high- high-puritypurity indium indium refining refining plant plant in the in thesingle single refining refining zone zone of 4 of furnace 4 furnace tubes. tubes. At Atpresent, present, the thesmall small unit unit of the of thelaboratory laboratory has hasbeen been able ableto complete to complete the continuous the continuous treatment treatment of 100 of kg 100indium kg indium per year. per year.The whole The whole process process has a has high a high energy energy utilization utilization rate, rate, with with no nowaste waste wa- water,ter, waste waste gas, gas, waste waste residue residue discharge discharge,, and environmental friendliness,friendliness, and and 6N 6N indium indium cancan be be obtained. obtained. Figure 15. Vacuum zone refining/electromigration high-purity indium refining device designed Figure 15. Vacuum zone refining/electromigration high-purity indium refining device designed with multiple furnace tubes. with multiple furnace tubes. LiLi Qing Qing [56 [56]] and and Chen Chen Luona Luona [50 ][50] designed designed a new a new vacuum vacuum zone zone refining/electromigration refining/electromi- high-puritygration high indium-purity refining indium device refining designed device bydesigned Tan Yang by [Tan49] withYang multiple [49] with furnace multiple tubes. fur- nace tubes. The heat of an alumina ceramic heating sheet was introduced into the graphite sheet as a constant temperature heat source, as shown in Figure 16. Materials 2021, 14, 2064 18 of 21 Materials 2021, 14, x FOR PEER REVIEW 18 of 21 The heat of an alumina ceramic heating sheet was introduced into the graphite sheet as a constant temperature heat source, as shown in Figure 16. FigureFigure 16. 16.Zone Zone refiningrefining equipmentequipment diagram. 7.7. Existing Existing Problems Problems andand ProspectsProspects AfterAfter nearly nearly 70 70 yearsyears ofof development,development, the zone refining refining technology technology has has made made great great progressprogress in in both both process process research research and and application application field field expansion. expansion. The The process process isis becoming becom- moreing more mature, mature, but there but there are still are problemsstill problems in the in followingthe following aspects aspects [1,27 [1,27]:]: (1)(1) TheThe requirementsrequirements for for raw raw materials materials are are high. high. The Thepurity purity of the of raw the material raw material rod must rod mustmeet meetcertain certain requirements, requirements, and the and gap the impurities gap impurities C, H, O C,, etc. H, O,contained etc. contained in it must in it mustbe controlled be controlled within within a certain a certain range, range, so as to so avoid as to avoidthe power the power and temperature and temperature fluc- fluctuationstuations caused caused by gas by impurities gas impurities in the in zone the refining zone refining process, process, which whichaffects the affects qual- the qualityity of the of material. the material. (2)(2) ForFor impuritiesimpurities withwith aa balancedbalanced distribution coefficient coefficient close close to to 1, 1, the the content content of of the the raw material rods must be strictly controlled so as not to affect the final performance raw material rods must be strictly controlled so as not to affect the final performance of the materials: for example, magnesium, calcium, iron, and antimony in bismuth; of the materials: for example, magnesium, calcium, iron, and antimony in bismuth; lead, magnesium, silicon, and aluminum in indium. lead, magnesium, silicon, and aluminum in indium. (3) The influence of side effects. Side effects include the evaporation of high vapor pres- (3) The influence of side effects. Side effects include the evaporation of high vapor sure impurities in the melting zone caused by agitation, temperature increase, or low pressure impurities in the melting zone caused by agitation, temperature increase, pressure inert gas flow through the melting zone, due to chemical reactions between or low pressure inert gas flow through the melting zone, due to chemical reactions impurities (such as between carbon and sulfur, hydrogen, or oxygen), and the slag- between impurities (such as between carbon and sulfur, hydrogen, or oxygen), and ging process often brings complex problems that are difficult to predict. Sometimes, the slagging process often brings complex problems that are difficult to predict. in order to remove an impurity, it is necessary to add a second reaction element to Sometimes, in order to remove an impurity, it is necessary to add a second reaction complete, and the latter is selected to generate a compound with the former. During element to complete, and the latter is selected to generate a compound with the former. zone refining, it is easier than removing certain impurities alone. (4) DuringThe bar zone size refining,is limited. it The is easier emergence than removing of refining certain in the impuritiessuspension alone. zone solves the (4) Thecrucible bar size pollution is limited. existing The in emergence the conventional of refining zone in refining, the suspension making the zone zone solves refin- the crucibleing technology pollution develop existing rapidly. in the However, conventional due zone to gravity, refining, the makingtechnique the requires zone refining that technologythe size of the develop raw material rapidly. rod However, must be controlled due to gravity, within the a certain technique range requires to obtain that a thestable size refining of the raw zone. material rod must be controlled within a certain range to obtain a (5) stableLow production refining zone. efficiency and high cost. The low speed and multiple refining re- (5) Lowquired production by the zone efficiency refining greatly and high extend cost. the The production low speed time and and multiple reduce the refining pro- requiredduction efficiency; by the zone after refining each zone greatly refining, extend the thefirst productionand last ends time of the and bar reduce need to the productionbe removed, efficiency; which reduces after each the zoneutilizati refining,on rate the of firstraw andmaterials last ends and ofincreases the bar needthe toproduction be removed, cost. which reduces the utilization rate of raw materials and increases the (6) productionThe development cost. speed of product testing and analysis technology lags behind. With (6) Thethe developmentimprovement speedof purification of product technology, testing and a analysisvariety of technology highly sensitive lags behind. impurity With theanalysis improvement methods came of purification into being, technology, but these methods a variety have of certain highly limitations, sensitive impurity which restrict the development of zone refining technology. Materials 2021, 14, 2064 19 of 21 analysis methods came into being, but these methods have certain limitations, which restrict the development of zone refining technology. (7) The large-scale application of advanced zone refining technology is limited. The research on zone refining technology has made great progress, and it has been used in industrial production in certain fields, but some of the deficiencies have hindered its large-scale application: the suspension zone refining technology equipment in- vestment is expensive, and raw material storage container selection is more difficult. Moreover, it is susceptible to secondary pollution during operation, and the optimal production process parameters are easily changed with the material. In recent years, the market demand for high-purity metals has continued to expand, and zone refining has become the preferred method for preparing such materials, with broad application prospects. In view of the current market demand, the focus of research on zone refining at this stage should be shifted to the following aspects [27,54]. (1) Combining zone refining technology with other purification technologies, developing an ideal purification method combining multiple technologies, such as electromi- gration/zone refining, vacuum degassing-zone refining, to effectively remove gas impurities and ensure the stability of subsequent zone refining proceed to obtain higher purity materials. (2) Upgrade the zone refining equipment, increase the degree of automation and improve the zone refining technology to obtain a stable and simple operation process, improve production efficiency, and reduce production costs. (3) Improve trace element analysis technology to make simultaneous or continuous de- termination of trace and ultra-trace multi-elements. In addition, the industrialization of zone refining technology is also the main development direction in the future. With the deepening of research, zone refining technology will definitely develop toward the industrialization of low cost, practicality, high efficiency, high reliability, and high complexity. Author Contributions: Conceptualization, Y.J. and L.Y.; software, X.K. and L.C.; writing—original draft preparation, Y.J. and L.C.; writing—review and editing, L.Y., X.K. and L.C.; supervision, X.C. and K.L.; project administration, X.C. and L.Y.; funding acquisition, X.C., L.Y. and K.L. All authors have read and agreed to the published version of the manuscript. Funding: The work was supported by the National Natural Science Foundation of China (51465014), Guangxi Innovation Driven Development Project (Grant No. AA17204021), the foundation of Guangxi Key Laboratory of Optical and Electronic Materials and Devices (No. 20KF-4) and Founda- tion of introduction of senior talents in Hebei Province (H192003015). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data sharing is not applicable for this article. Conflicts of Interest: The authors declare no conflict of interest. References 1. Guo, X.Y.; Tian, Q.H. High Purity Metal. Materials; Metallurgical Industry Press: Beijing, China, 2010. 2. Guo, X.; Zhou, Y.; Zha, G. A novel method for extracting metal Ag and Cu from high value-added secondary resources by vacuum distillation. Sep. Purif. Technol. 2020, 242, 116787. [CrossRef] 3. 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