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Purification is a primary application of zone melting, in which the improvement of efficiency, production yield and minimum achievable impurity level are always the research focus due to the increasing demand for high purity metals. This paper has systematically outlined the whole development of related research on zone refining of metals including basic theories, variants of zone refining, parametric optimization, numerical models, and high purity analytical methods. The collection of this information could be of good value to improve the refining efficiency and the production of high purity metals by zone refining.

High purity (99.999% (5N) or more) metals play a key role in current high-tech industrial field, such as special electronics, integrate circuits, photovoltaic systems, optical elements, chemical applications, etc., as in these areas even low concentrations of impurities could completely deactivate the desirable function.

Metal | Application | Metal | Application |
---|---|---|---|

Al [ | Integrated circuits, semiconductor, LCD screen, catalyst market, optical products, and electronic ceramics | Ga [ | Ga based III-V semiconductor used in electronic and optoelectronic industries, such as GaAs |

Ge [ | Radiation detector, infrared devices, fiber optic, infrared device, semiconductors, Catalyst | In [ | In based III-V semiconductor used in electronic and optoelectronic industry, such as InP |

Sb [ | Semi-conductor devices for crystal doping, photocell cathodes | Te [ | compounds Semiconductor employed in electronic and optical device, such as CdTe |

Cd [ | Infrared detector, solders for semi-conductor processing | Se [ | II-VI compounds semiconductor |

44 tons in 2002 to 165 tons in 2014, respectively, as seen in

In general, to fulfill the need of high purity or electronics-grade materials, a number of methodologies have been investigated including precipitation, crystallization, electrolysis, vacuum distillation, solvent extraction and zone melting, etc. [

Zone refining is used extensively to produce high purity final materials since the early 1950s [

Zone melting refining has essentially the same mechanism as for the purification via unidirectional solidification/segregation. The solution of the impurities in one metal is mostly different in liquid or solid state. The ratio of impurities concentration in solid (C_{S}) to that in liquid (C_{L}) is defined as equilibrium distribution coefficient k (see

To analyze the impurities distribution in zone melting in a simple way, following variables are defined.

L = 1 ; Z = z / L < 1 ; X = x / L ≤ 1

where L is the length of the sample; z is the zone length; Z is the normalized zone length; x is the movement distance of the molten zone; X is the normalized movement distance of the molten zone.

The critical important parameters in zone refining are the equilibrium distribution coefficient k as well as the effective distribution coefficient k_{eff}. k_{eff} is defined as the experimental C_{S}/C_{L}. However, due to the difficulty in getting the experimental C_{L}, it can be calculated with the following―so called Burton-Prim- Slichter (BPS)―model and equation:

k e f f = k k + ( 1 − k ) exp ( − V δ / D ) (1)

where D is the impurity diffusion coefficient in the melt, δ the thickness of the diffusion boundary layer at the solid/liquid interface and V is the molten zone movement velocity. The molten zone movement velocity and diffusion layer thickness are two important parameters which can be altered to affect the k_{eff}. In addition, the thickness of the diffusion layer depends on the convection inside the melt and the melt property itself, such as viscosity, diffusivity of the solute. If diffusion is the only concentration compensation process in the melt, the diffusion layer would be too thick and hence worsen the refinement efficiency. If convection currents are available, δ is about some millimeters and can be reduced to 0.1 mm by moderate stirring and to 0.01 mm by intense stirring [_{eff} if k < 1 and a higher k_{eff} if k > 1. Regarding that the higher movement velocity would allow more passes of molten zone per unit of time, nevertheless, it should be limited by the constitutional supercooling factor as following [

V ≤ G D k m C s ( 1 − k ) (2)

where G is the temperature gradient in the liquid, C_{S} is the impurity concentration in solid at the freezing interface, and m is the slope of the liquidus line in

In the case of unidirectional solidification of a melt with a planar liquid/solid interface and considering a simple binary system with liquidus and solidus approximating to straight lines as well as assuming the solute diffusion in solid as neglected but in liquid as completed, the solute distribution along the bar was presented by Scheil [

C s C o = k ( 1 − X ) k − 1 (3)

By comparison, making following assumptions in zone refining process:

・ the distribution coefficient k is constant, independent of temperature

・ the zone length and travel rate are constant in each pass

・ the densities of liquid and solid are the same

・ the model regards to one-dimensional analysis

・ diffusion of the solute in the solid is negligible and diffusion of solute in the melt is complete

After one pass of a molten zone, Pfann [

C s C 0 = 1 − ( 1 − k ) exp ( − k X Z ) for 0 ≤ X ≤ 1 − Z (4)

For the last zone length, where the normal freezing takes place, the solute distribution is derived by using of equation (3) as following:

C s C 0 = { 1 − ( 1 − k ) exp ( − k 1 − Z Z ) } × { 1 − [ X − ( 1 − Z ) Z ] } k − 1 for 1 − Z ≤ X ≤ 1 (5)

When the bar is refined through many zone passes, a steady state or ultimate impurity concentration distribution will be attained, at which segregation flux of impurities at freezing interface is always compensated by an equal backward flux at the melting interface throughout the bar. This phenomenon can be illustrated easily by simulation with Spim model, as seen in

However, the concentration distribution profile will be stable when the number of zone passes exceeds nine, i.e. the ultimate impurity concentration distribution is achieved. Besides, the ultimate concentration distribution can be represented with a function as following [

c ( X ) = A e B X (6)

where A and B are constants and derived from

k = B L e B L − 1 (7)

A = C 0 B L e B L − 1 (8)

The efficiency of zone refining is affected by a variety of experimental factors, which can be altered to optimize the process. These factors include [

1) Effective distribution coefficient (k_{eff}), representing the experimental ratio of C_{S} to C_{L}. This factor itself (as seen in chapter 2.1) is dependent on the diffusion layer thickness between liquid/solid, movement velocity of the zone, diffusion coefficient of each impurity as well as the heating power.

2) Zone movement velocity, which should be normally kept slow enough to increase the refining efficiency (decrease k_{eff} for k < 1 and increase k_{eff} for k > 1) but at the same time too low velocities increase the time consumption for each pass tremendously. The term refining efficiency refers here to the maximum impurity removal a zone refining process can achieve.

3) Zone length that is the length of the molten zone, affecting both the ultimate distribution of the elements as well as the rate, at which it is achieved. This length is affected by many factors, such as heating power, zone movement velocity, thermal conductivity of crucible and charge, etc.

4) The temperature gradient at the solid/liquid interface, influencing the microsegregation of impurities at that area. This is also controlled by heating power, zone movement velocity, thermal conductivity of crucible and charges, etc.

5) The number of zone passes. Less passes can’t attain a product with high purity; however, more passes consume more time.

The experimental optimization of the above mentioned zone refining parameters are not of general use, as they are dependent on the properties of particular systems, such as equipment specifications, specimen diameter, melt viscosity, and the diffusion and distribution coefficients of impurities [

Various zone refining technologies exist based on the same principle. According to the geometry or the way of charging, they could be categorized in four types, e.g. horizontal-, vertical-, floating- as well as continuous zone refining (as presented in

Variants of zone refining | Characteristics | Advantages | Disadvantages | Application |
---|---|---|---|---|

Horizontal zone refining | Crucible is positioned horizontally; Heating elements move horizontally | Easy to load and unload materials; easily distinguish the interface | Bulk transport phenomenon; equipment occupies more spaces | Most metals, except for some reactive materials |

Vertical zone refining | Crucible is positioned vertically and heating elements move vertically | Less place occupation | Not easy to load and unload materials; more risk on cracking crucible | Most metals, except for some reactive materials |

Floating zone refining | Without crucible; The material is positioned vertically; The molten zone is held by liquid surface tension | Less contamination resources; less place occupation; good heat transfer | Limited charging material with high surface tension; Less production due to small size of material | Reactive metals, such as silicon, tungsten, zirconium, iron, etc. |

Continuous zone refining | Having feeding inlet and product and waste outlet; Feed Materials and get product and waste continuously | High production; High refining efficiency | Complicated design; High cost; Difficulty in operation | Theoretically most metals, but the development is in the experimental stage; no practical results or commercial use at present |

In addition, to obtain a certain zone length, the zone melting equipment should be provided with a proper heating field. In general an ideal zone refining apparatus should allow the control of short zones with short spacings and consume electrical power economically to heat the materials up to the melting point. Due to consideration of costs, materials properties as well as controlling of desirable zone length, the available heating techniques can include resistance heating, induction heating, electrical discharge or radiation heating. Amongst them resistance heating is most popularly used in zone refining of metals with low melting point, such as Cadmium [

Zone refining is generally engaged in one or more heating elements moving through the charge with a very low velocity. To attain a high purity metal, multiple numbers of passes must be performed. If only one heater is applied (single-

Heating methodology | Advantages | Disadvantages | Application |
---|---|---|---|

Resistance heating | Simple, practical, cheap | Difficult in control of zone length; more risk on contamination from container | Most common heating element; more suitable for small charges with modest melting point (less than 500˚C) |

Induction heating | Providing higher power; Shorter zone can be established; providing stirring degree; less possibility of contamination from container | Occupy more floor space; expensive; power probably changing sharply as the variation of position, conductivity, and thickness of the charge | Semiconductors and most metals |

Electrical discharge | Melt the refractory metal | Demand on vacuum system; expensive | Refractory metals |

Radiation heating | More feasible to get short zone length; less possibility of contamination from container; possible to melt refractory metals | Need one pair of spherical concave mirror; Occupy more floor space; precise radiation path and focus | Most Metals |

zone refining,

Optimization of the process parameters in a zone refining process is done with

the aim to improve refining efficiency and to reduce the time it takes to attain ultimate concentration distribution. Generally, the main parameters to be optimized are movement velocity of heating element, zone length, and the number of passes. Zone length is not an independent factor but a consequence of power, movement velocity of heating element, type of cooling system and the thermal conductivity of charge and crucible. Lowest zone movement velocity strongly extends the whole process time and hence should be maintained to an appropriate value in balance with the refining efficiency. The optimization of zone length and the number of passes is more complicated than optimization of velocity because they can affect each other as well as they both depend on the property of treated materials.

When researching on parameters optimization of zone refining of aluminium with a constant zone length, Kino, et al [

In multi-pass zone refining, it is well known that the best refining efficiency in the first zone pass is achieved by normal freezing, i.e. the zone length is equal to the length of the bar [

In conventional procedures of zone refining, the refining effectiveness per zone pass decreases while the number of passes increases until the impurities cannot be removed any more. In this case the ultimate impurity concentration distribution profile is achieved (as shown in

In addition, most of zone refining theories, such as Pfann equations (Equation (4) and (5)) make the assumption that the impurity diffusion in the solid is negligible. This assumption is though only allowed if high-quality crystals are grown. In reality, the crystal quality of substance produced by zone refining is often very poor, with the result that the impurities have less activation energy, leading to higher diffusivity [^{−10} m^{2}/sec at the melting point [

It is a popular phenomenon that the shape of the bar becomes wedged when it was refined in an opened horizontal boat [

θ c = arctan ( 2 h 0 ( 1 − α ) l ) (9)

where, h_{0} is the initial height of the bar, α is the ratio of density in solid state to that of liquid and l is the zone length. It has been numerically demonstrated that the zone refining process is not affected by this modest inclination of the bar from the heat transfer point of view [

In order to reduce the impurities with a distribution coefficient close to unity (which are difficult to be removed via common ways), an electric current field is helpful to be applied as an additional heating concept during zone refining (see

As mentioned above, the known optimization regimes for experimental parameters are of limited general use, as they are strongly dependent on individual

system characteristics. Consequently, numerous numerical models have been developed to predict the solute distribution or to optimize experimental parameters as well as to give guidance for empirical trials.

For single pass zone refining, the impurity distribution profile after one pass refinement can be predicted with Equations ((4) and (5)). Regarding to handling the multi-pass zone refining, a basic differential equation, derived independently by Lord [

Z k d C S ( X ) n = ( C S ( X + Z ) n − 1 − C S ( X ) n ) d x for 0 ≤ X ≤ 1 − Z (10)

and

d C S ( X ) n = 1 − k L − X C S ( X ) n d x for 1 − Z ≤ X ≤ 1 (11)

Lord and Reiss have derived an exact expression of the impurity concentration distribution as a function of distance X respectively. However the Lord model is valid only with the assumption of semi-infinite ingots and the Reiss model is accurate only for k in the range of 0.9 to 1.1, which confines the application of them. Therefore some new models are put forward―as explained briefly in the following―to provide a more accurate simulation of global impurity concentration distribution profile.

Based on the typical assumptions and equations stated in section 2 and the above differential Equations ((10), (11)), Spim, et al [

Generally speaking, the equilibrium distribution coefficients are calculated from the solute concentrations of liquid and solid phases at a particular temperature (e.g. eutectic temperature) in the equilibrium diagram, and are used for simulation

purposes as a constant value along the whole zone refining process, as seen in chapter 5.1. However, using the same simulation model, Cheung, et al. [_{L} refers to a corresponding C_{S}, and resulting in a specific k. Therefore during simulation processing, for each C_{L} at any melting zone, the k could readily be accessed from the database to provide more accurate input values of k for the model simulation (see in

A new numerical simulation model has been proposed by Nakamura, et al [

emitted from diffusion region to that dissolves into the stirring region during solidification (as seen in

C L − C S C L δ − C S = exp ( − R δ / D ) (12)

From the definition of transfer ratio q, it is known that the exponential factor in the two above equations is identical to the transfer ratio q,

exp ( − R δ / D ) = q (13)

In this equation, δ and q can be calculated when each one is explicit, as the R and D are already determined for a specific refining event. Therefore before using this model, δ and q must be estimated by comparison the results of experiment with the results of simulation with setting of different δ and q for one impurity. The advantage of this model is that when δ is determined by parametric fitting for one impurity, the distribution profile of other impurities can be derived by using the same value of δ.

As a large variety of experimental parameter combinations (presented in section 2) exist during the course of optimizing the zone refining process and improving the refining efficiency, investigation through experiments alone is very time- consuming and is even not practicable. Besides, the optimum experimental parameters differ from individual zone refining systems. Therefore, the application of numerical model as stated above is a good assistant to guide the experiment performance. That can predict the influence of each parameter on the refining results and get the theoretical optimum parameters combination with short time and low cost. In some cases, to get a clear insight in the variation of zone length, zone temperature distribution, zone shape, etc., the overall heat transfer in the system should be simulated as well [

After accomplishment a high purity metal refining through zone melting, a challenging task is to analyze the impurity concentration in the product. Currently a variety of available methodologies are existed to fulfill this task, each based on different mechanism with individual detection limit and accuracy.

・ Residual resistivity ratio (RRR)

According to the Matthiessen’s rule ρ = ρ i ( T ) + ρ 0 , the electrical resistivity of metals contains the ideal resistivity ρ_{i}(T), a temperature-dependent function of lattices vibrations as well as ρ_{0}, the temperature-independent sum of all kinds of lattice defects. Impurity elements occupy the lattice or are located in the lattice as interstitial atoms, resulting in the appearance of defects, such as dislocation, stacking faults, etc. [_{0} when temperature decreases nearly 0 K especially. Based on this, residual resistivity ratio (RRR = (R(300K))/(R(4K)) is used to measure the qualitative level of purity of metals [

・ Glow-discharge mass spectrometry (GDMS)

GDMS is a versatile and important tool to analyze the trace elements with remarkable high sensitivity. Its principle is to measure the ion beam intensity, i.e. the numbers of ions arriving at detector after ionization of the material with plasma, which is proportional to the number of the elements in the sample. Its sensitivity could be up to 1 ppb for most of the elements, and up to 1 ppm for the light and non-metallic elements, such as Carbon, Nitrogen, Oxygen [

・ Inductively coupled plasma-mass spectrometry/optical emission spectrometry (ICP-MS/ICP-OES)

ICP-MS and ICP-OES can also be used to determine the compositions of different materials with very low detection limit. They both use the inductively coupled plasma as the ion source, while differs from each other in the type of detecting signals. The sample system between ICP-MS and ICP-OES is similar, but the detection limit of ICP-OES is typically 100 - 1000 times poorer than that of ICP-MS, with most elements in the range of 1 - 10 ppb [

In addition, there are also some other analytical methodologies, such as Atomic absorption spectrometry with graphite furnace (AASGF) with the limit of detection limit range between 10 - 400 ppb [

Zone refining is a validated and effective process to produce high purity metals. The parametric optimization and numerical models for zone refining of various materials aiming to improve the refining efficiency have been researched extensively in the last decades. However, the efficiency and the yield have always been the issues of zone refining. Therefore, further researches on zone refining of metals could be done with the center of following aspects: first, using current simulation model to optimize the experimental parameters for any given system

Detection limit | Precision | Quant-analysis | Sample phase | Operating cost | Capital cost | |
---|---|---|---|---|---|---|

RRR | N.A. | N.A. | No | Solid | Medium | Medium/low |

GDMS | Excellent for most elemetns | High | Yes | Solid | High | Very high |

ICP-MS | Excellent for most elments | 1% - 3% | Yes | Solution | High | Very high |

ICP-OES | Very good for most elements | 0.3% - 1% | Yes | Solution | High | High |

AASGF | Excellent for some elements | 1% - 5% | Yes | Solid/Solution | Medium | Medium/high |

SSMS | Good | 3% - 7% | Yes | Solid | Medium/low | Medium/low |

XRF | Good | High | Yes | Solid | Medium/low | Very high |

Van der Pauw Hall effect | N.A. | N.A. | No | Solid | Low | Low |

as a guidance for experiments, meanwhile reversely applying experimental results to further correction of the numerical model; second, upgrading the common zone refining equipment, such as using multi-zones scheme, installation of external temperature detectors for a better control of the molten zone length, improving the automatization, etc. is also a good view to meet the target; third, focusing on some individual details, such as the variation of molten zone shape (changed by power, velocity, physical properties of the material), effects of temperature gradient on refinement, the interaction activity of different impurities, etc.; fourth, comparison research on zone refining potential or efficiency of different metals, or comparison/cooperation research on zone refining with other refining methodologies, such as cooled finger crystallization [

The Authors would like to thank the China Scholarship Council (CSC) for the financial support of the scholarship holder X. Zhang.

Zhang, X.X., Friedrich, S. and Friedrich, B. (2018) Production of High Purity Metals: A Review on Zone Refining Process. Journal of Crystallization Process and Technology, 8, 33- 55. https://doi.org/10.4236/jcpt.2018.81003