EP2152918B1 - Novel additive comprising lead and/or a lead alloy intended to treat baths of liquid steel - Google Patents

Abstract

The present invention relates to an additive in the form of flux-cored wire for treating baths of liquid steel with a view to obtaining steels having a high lead content. The additive comprising metallic lead and/or one or more lead alloys according to the invention for treating baths of liquid steel, and is in the form of flex-cored wire composed of a metal sheath and a finely divided filling material, the latter being composed of a powder of metallic lead and/or of lead alloy and of a powder containing a material capable of releasing a gas, which is inert with respect to the liquid steel, at the temperature of the liquid steel bath. Characteristically, said powder of metallic lead and/or of lead alloy comprises a particle size fraction GR between 200 μm and 500 μm and said particle size fraction GR has the following characteristics: - through a 200 μm sieve: GR < 5%; - through a 300 μm sieve: 90% ³ GR ³ 10%; - through a 400 μm sieve: 40% £ GR < 100%; - through a 500 μm sieve: 100% ³ GR ³ 90%.

Description

The present invention relates to an additive in the form of cored wire for the treatment of liquid steel baths to obtain steels with a high content of lead.

Lead is well known for improving the machinability of steels because, insoluble in steel, it forms exogenous inclusions of lead (nodules) which act as a lubricant and promote the division of chips during the machining of rolled steels. However, it has significant disadvantages of use, given its toxicity, its high density (higher than that of liquid steel) and its low melting point. It is introduced into liquid steel baths by injection of balls or shots through a submerged lance or in the form of cored wire, the latter technique being known to be generally more flexible and more reliable.

The addition efficiencies obtained today with the conventional flux cored wires do not make it possible to make significant additions of lead, under penalty of generating large quantities of harmful fumes and as a result considerable inconveniences vis-à-vis the hygiene and personal safety.

The document EP 0 316 921 describes a lead-containing additive for steel baths, in the form of a cored wire composed of a metallic sheath and a finely divided filling material, the latter containing metallic lead and / or lead alloys and a material containing lime and releasing carbon dioxide (CO ₂ ) at the temperature of the liquid steel bath. The release of CO ₂ in the steel bath produces, around the cored wire, an intense turbulence which has the effect of emulsifying the lead particles in the molten steel and driving them in motion inside the bath, thus improving their distribution in the liquid steel bath. Moreover, the use of this additive has made it possible to limit the emissions of harmful fumes and to better control the addition process, while increasing the addition efficiency compared with those previously known.

However, it has been found that the use of this type of additive does not allow to have, in the liquid steel ladle, a uniform distribution of lead inclusions throughout the casting. Furthermore, the final steel product obtained through the use of this additive does not have a homogeneous distribution of lead inclusions. In addition, the yield of the addition of lead in the molten steel bath always remains below 70%.

The present invention aims to overcome these disadvantages by proposing a new additive comprising a lead and / or lead alloy powder whose size and particle size distribution are very specific, said powder being associated with a compound capable of ensure a homogeneous distribution of lead in the liquid steel bath.

• au tamis de 200µm : G_R ≤ 5% ;
• au tamis de 300µm : 90% ≥ G_R ≥ 10% ;
• au tamis de 400µm : 40% ≤ G_R ≤ 100% ;
• au tamis de 500µm : 100% ≥ G_R ≥ 90%.

For this purpose, the invention relates, according to a first aspect, to an additive comprising metallic lead and / or lead alloy (s) intended to treat liquid steel baths, said additive being in the form of compound flux-cored wire. a metallic sheath and a finely divided filling material, the latter consisting of a metallic lead powder and / or lead alloy and a powder of a compound capable of releasing a gas, inert with respect to the liquid steel, at the temperature of the liquid steel bath, said additive being characterized in that said metallic lead powder and / or lead alloy powder consists of a particle size fraction G _R of between 200 μm and 500 μm and in that said particle size fraction G _R has the following characteristics:

• with a sieve of 200 μm: G _R ≤ 5%;
• 300μm sieve: 90% ≥ G _R ≥ 10%;
• with a 400 μm screen: 40% ≤ G _R ≤ 100%;
• 500μm sieve: 100% ≥ G _R ≥ 90%.

• au tamis de 200µm : G_R ≤ 5% ;
• au tamis de 300µm : 90% ≥ G_R ≥ 10% ;
• au tamis de 400µm : 40% ≤ G_R ≤ 100% ;
• au tamis de 500µm : 100% ≥ G_R ≥ 90%.

According to a second aspect, the invention relates to a process for treating liquid steel baths with an additive comprising metallic lead and / or lead alloy (s), comprising a step of adding to said baths of an additive in the form of a cored wire composed of a metallic sheath and a finely divided filling material, the latter consisting of a metallic lead powder and / or lead alloy and a powder of a gas-releasable compound, inert with respect to the liquid steel, at the temperature of the liquid steel bath, said metallic lead powder and / or lead alloy powder consisting of a G _R size fraction which is between 200 μm and 500 μm and which has the following characteristics:

• with a sieve of 200 μm: G _R ≤ 5%;
• 300μm sieve: 90% ≥ G _R ≥ 10%;
• with a 400 μm screen: 40% ≤ G _R ≤ 100%;
• 500μm sieve: 100% ≥ G _R ≥ 90%.

According to a third aspect, the subject of the invention is the use of the additive comprising metallic lead and / or one or more lead alloys, described above, for treating liquid steel baths.

The invention also relates, according to a fourth aspect, to a rolled product made of steel with a high lead content obtained by the aforementioned process, characterized in that the lead nodules are less than 100 μm in size and, for the most part, up to at least 80%, distributed in the rolled steel according to a type of random distribution as shown in figure 3a . This distribution gives the rolled steel optimum machinability characteristics.

The use of this new additive makes it possible to very significantly improve the lead addition efficiencies and therefore the possibility of making greater additions under satisfactory hygiene and safety conditions. It also makes it possible to obtain a better distribution of the nodules of lead in final in the solid steel while decreasing the phenomena of remanence and contamination of the refractories of the pockets used for the treatment of these steels. The production costs of these steels are thus improved.

• la figure 1 représente les caractéristiques de tailles et de répartitions granulométriques de la fraction granulométrique G_R ;
• la figure 2 présente la variation du rendement en plomb en fonction de la quantité d'additif ajouté au bain d'acier exprimée en longueur de fil fourré ajoutée par tonne d'acier liquide ;
• la figure 3 représente de manière schématique les différents types de répartitions des nodules de plomb dans le produit final en acier solide ;
• la figure 4 représente un diagramme permettant le calcul de la distance minimale avec le nodule de plomb le plus proche.

Other features and advantages of the invention will appear on reading the detailed description and the following exemplary embodiments, as well as the appended figures in which:

• the figure 1 represents the characteristics of sizes and particle size distributions of the grain size fraction G _R ;
• the figure 2 shows the variation in lead yield as a function of the amount of additive added to the steel bath expressed as the length of flux-cored wire added per tonne of liquid steel;
• the figure 3 schematically represents the different types of distribution of lead nodules in the final solid steel product;
• the figure 4 represents a diagram allowing the calculation of the minimum distance with the nearest lead nodule.

The present invention relates to a novel additive comprising metallic lead and / or lead alloy (s) intended for the treatment of liquid steel baths with a view to obtaining steels with a high lead content. In known manner, this additive is in the form of cored wire composed of a metal sheath and a finely divided filling material, the latter consisting of a metallic lead powder and / or lead alloy and a powder of a compound capable of releasing a gas, inert with respect to the liquid steel, at the temperature of the liquid steel bath.

Advantageously, said metallic lead powder and / or lead alloy powder consists of a particle size fraction G _R of between 200 μm and 500 μm. This granulometric fraction is preferably in the form of small granules or very fine beads.

• au tamis de 200µm : G_R ≤ 5% ;
• au tamis de 300µm : 90% ≥ G_R ≥ 10% ;
• au tamis de 400µm : 40% ≤ G_R ≤ 100% ;
• au tamis de 500µm : 100% ≥ G_R ≥ 90%.

Characteristically, said granulometric fraction G _R has the following characteristics:

• with a sieve of 200 μm: G _R ≤ 5%;
• 300μm sieve: 90% ≥ G _R ≥ 10%;
• with a 400 μm screen: 40% ≤ G _R ≤ 100%;
• 500μm sieve: 100% ≥ G _R ≥ 90%.

These granulometric characteristics are schematically represented in the figure 1 attached.

This granulometric distribution (contained in the area materialized at the figure 1 ) gives the cored wire optimum filling properties leading to an efficient metallurgical treatment of liquid steel baths. The choice of such a particle size distribution ensures a level of residual porosity much lower than those observed in cored wires made from a conventional lead powder. The porosity is thus between 5% and 20% maximum while for a conventional yarn, the value is generally between 15 and 40%.

The metallic sheath surrounding the additive is formed of a material capable of dissolving in the steel bath with a speed sufficiently high to allow the release of said additive and without introducing unwanted components therein. Preferably, the metal sheath is unalloyed mild steel. Its thickness is between 0.1 and 1 mm, preferably between 0.2 and 0.6 mm.

Furthermore, the diameter of the cored wire according to the invention is between 5 and 20 mm, preferably between 9 and 15 mm.

The additive according to the invention is in the form of cored wire containing from 100 to 1000 g of lead per meter of wire.

With regard to the powder of compound able to spontaneously release a gas, inert with respect to the liquid steel, at the temperature of the liquid steel bath (between about 1550 and 1650 ° C.), this is also present in finely divided form, with a particle size of less than 1 mm, preferably less than 0.5 mm.

Advantageously, the release of the gas bubbles in the liquid steel bath creates an updraft which leads to a very random distribution of the lead inclusions formed from the particle size fraction according to the invention, thereby standardizing their distribution in the dye bath. liquid steel.

In a particular embodiment, the compound capable of spontaneously liberating a gas, inert with respect to the liquid steel, is a mineral compound such as limestone (calcium carbonate) or uncured dolomite, and said inert gas by compared to liquid steel is carbon dioxide. In this case, the inorganic compound is used in an amount of 3 to 30% by weight relative to the weight of the lead metal and / or lead alloy or alloys used (s).

According to a second aspect, the invention relates to a process for treating liquid steel baths with an additive comprising metallic lead and / or lead alloy (s), comprising a step of adding to said baths an additive in the form of the cored wire described above.

A cored wire containing such a powder makes it possible to obtain a lead yield in the liquid steel greater than that obtained with a conventional wire or with that described in the document EP 0 316 921 .

The figure 2 presents industrial results concerning the lead yield as a function of the quantities added (the variation of the lead yield as a function of the quantity of additive added to the steel bath expressed as the length of cored wire per tonne of steel).

Dans cette équation:

• C_I est la teneur initiale en plomb dans la poche d'acier liquide ;
• C_F est la teneur finale en plomb obtenue dans la poche d'acier liquide ;
• C_A est la teneur visée en plomb dans la poche d'acier liquide ;
• Y_Pb est le rendement de l'addition de plomb.

The lead yield is defined by the following equation: $${\mathrm{Y}}_{\mathrm{Pb}}\mathrm{=}\left({\mathrm{VS}}_{\mathrm{F}}\mathrm{-}{\mathrm{VS}}_{\mathrm{I}}\right)\mathrm{/}{\mathrm{VS}}_{\mathrm{AT}}$$

In this equation:

• C _I is the initial lead content in the liquid steel ladle;
• C _F is the final lead content obtained in the liquid steel ladle;
• C _A is the target lead content in the liquid steel ladle;
• Y _Pb is the yield of the addition of lead.

The cored wire containing the lead powder and / or a lead alloy whose particle size respects the specificities described in this invention makes it possible to obtain a higher lead yield than with a conventional powder. It also makes it possible to obtain very regular and constant yields regardless of the length of yarn injected into the liquid steel bath. Thus, the smaller dispersion makes it possible to very substantially increase the chances of success in obtaining the lead shot in the final steel.

Thanks to a higher efficiency, the hygiene and safety conditions during the treatment of the liquid steel bags are also substantially improved. There is less release of harmful fumes over the pocket. The phenomena of sedimentation of lead in the bottom of the pocket and pollution of the refractory pockets walls are also greatly reduced.

The addition of the additive according to the invention in the liquid steel ladle takes place before the casting. Depending on the desired final lead content, an amount of from 0.1 to 10 kg of additive in the form of cored wire per ton of liquid steel to be treated is introduced. The cored wire is discharged into the steel bath at a speed of 50 to 200 m / min, preferably 100 to 150 m / min.

The following two examples illustrate the high values of lead yield obtained through the use of the new additive according to the invention.

Example 1

• 13.6 mm outer diameter cored wire
• Thickness of strip between 0.35 and 0.40 mm
• Amount of calcium carbonate in the mixture: 6.3% by weight
• Metric weight of the thread: 970 g / m
• Injection speed: 120 m / min
• Liquid steel weight in pocket: 95 t
• Targeted lead content: 0,260%
• Lead content obtained after treatment: 0, 248%
• The yield of the addition of lead to cored wire obtained is: 71.8%

Example 2

• 13.6 mm outer diameter cored wire
• Thickness of strip between 0.35 and 0.40 mm
• Amount of calcium carbonate in the mixture: 5.8% by weight
• Thread length injected: 334 m
• Thread injection speed: 150 m / min
• Liquid steel weight in pocket: 115 t
• Targeted lead content: 0.200%
• Initial lead content in the liquid steel bath: 0.009%
• Lead content obtained after treatment: 0.191%
• The yield of the addition of lead in cored wire obtained is: 72.0%.

Because the particle size of the lead particles contained in the flux-cored wire has been chosen within a very small range of 200 to 500 μm, the lead inclusions, insoluble in the liquid steel, are distributed evenly throughout the pocket.

Advantageously, the reduced size of the lead inclusions makes it possible to greatly reduce their sedimentation in the bottom of the pocket. This leads to a constant lead content in the liquid steel bath from the beginning of the emptying of the pocket until the end of the casting. The solidified product is therefore more homogeneous in lead content irrespective of the quantity of liquid steel remaining to flow. This is illustrated in the following example.

Example 3

• 13.6 mm outer diameter cored wire
• Thickness of strip between 0.35 and 0.40 mm
• Amount of calcium carbonate in the mixture: 6.5% by weight
• Quantity of powder injected by cored wire: 297 kg
• Thread injection speed: 120 m / min
• Pocket weight: 95 t
• Targeted lead content: 0,260%
• Lead content obtained on the first cast blooms: 0.252%
• Lead content obtained on blooms in the middle of the pocket: 0.245%
• Lead content obtained on blooms at the end of emptying pocket: 0.249%.

The term "bloom" refers to a solidified steel unit (round, rectangular, or polygonal steel ingot).

Furthermore, the use of the cored wire containing a finely divided lead powder according to the invention makes it possible to reduce the washing operations of the bags used for the preparation of liquid steels with a high lead content. Pocket refractories are less polluted by heavy lead infiltration. The steelmaker notes fewer lead residues in the opening / closing systems of the taphole as well as in the joints between the refractory bricks.

The scrap rate of rolled products (bars) of high lead steels is greatly reduced by the use of the additive containing a lead powder and / or lead alloy whose particle size is described herein. invention. The bars are discarded if the size and distribution of the lead nodules do not meet the specifications imposed by the client of the steelmaker. With the additive according to the invention, 100% of the bars are compliant while the use of a cored wire containing a conventional lead powder can cause up to 30% of scrap.

In addition to smaller sizes, the lead nodules are more suitably distributed in the rolled product thus promoting the machinability properties. There are no standard or international methods for characterizing the distribution of lead nodules in laminates; that's why we have specifically developed a criterion for qualifying the distribution of the population of lead nodules in rolled products.

Therefore, the Applicant has specifically developed a criterion for qualifying the distribution of the population of lead nodules in rolled products. It has therefore defined distribution indices and the associated criteria and finally the conditions for experimental measurements.

Où :

• I_R : indice de répartition
• D : diagonale de la zone d'analyse
• d_i : distance minimale entre les nodules de plomb (les plus proches voisins - Fig. 4)
• NI : nombre de nodules de plomb avec une distance minimale associée.

Thanks to an in-depth study by numerical simulation modeling the different distributions envisaged figure 3 , the plaintiff has identified relevant indices to qualify these distributions. It also determined the thresholds associated with each of these indices. In this way, it has been shown that a distribution index I _R greater than 1.4% makes it possible to differentiate with a tolerance interval of 99% a random distribution of the other types of distribution.
The index I _R is defined as follows: $$I_R=\left(100/D\right)*\left({\displaystyle \underset{i=1}{\overset{\mathit{OR}}{\Sigma }}}\left(d_i\right)/\mathit{OR}\right)$$

Or :

• I _R : distribution index
• D : diagonal of the analysis area
• d _i : minimum distance between lead nodules (nearest neighbors - Fig. 4 )
• NI: number of lead nodules with a minimal distance associated.

The lead nodules are distributed randomly (thus favoring machinability) when I _R is greater than 1.4%.

This index I _R is relevant only if a large number of lead nodules are taken into account. This number has been fixed at 500. A specific method of analysis has thus been developed.

The characterization of the lead nodules is carried out on the surface of a sample taken at mid-radius from a rolled steel bar with a larger diameter at 40 mm, and observed in the rolling direction. The surface of the sample taken is polished to 1 μm sheet.

Lead nodules are identified and characterized by observation of the sample surface with a scanning electron microscope equipped with a backscattered electron detector (SEM-FEG) coupled to an image analyzer. With this mode of observation and thanks to the chemical contrast, lead nodules appear with a significantly higher average gray level than the steel matrix and inclusions of other types (such as sulphides, oxides, nitrides). .) which makes it possible to distinguish them and isolate them easily.

The measurement method consists in observing an area of at least 25 mm ² , in a square-shaped area centered at mid-radius of the bar. All lead nodules with a small ferret diameter greater than 2 microns are taken into account and measured. More than 500 lead nodules must be taken into account. For each of these nodules, the position parameters (X and Y coordinates in the reference of the zone examined) and the main morphological parameters (surface of the nodule, diameter of Feret ...) are saved in a file of results.

The distribution parameters are then calculated to highlight the distribution of lead nodules to optimize the machinability properties of the product. Several types of distributions, represented in the figure 3 annexed, are taken into account: random ( Fig. 3a ), in clusters ( Fig. 3b ), in strips ( Fig. 3c ) or in a network ( Fig. 3d ). In order to guarantee a sufficient difference in processability with respect to that known for high-lead-rolled steels treated with conventional flux-cored wires, it has been determined that the proportion of nodules distributed according to the random type should be maximum. and preferably at least 80%.

The use of an additive in the form of a cored wire containing a lead powder whose particle size is as defined in figure 1 allows to obtain a homogeneous rolled steel product containing lead nodules of very small size, less than 100 microns, and distributed in a very predominantly random distribution. This distribution gives the steel properties improved machinability compared to those obtained on steels treated with conventional cored wires or those described in document EP 0 316 921 .

• l'amélioration du rendement de l'addition de plomb dans le bain d'acier liquide;
• l'amélioration des conditions d'élaboration et de traitement des aciers à haute teneur en plomb : en effet l'accroissement du rendement d'addition permet de réduire l'émission des fumées nocives et donc une amélioration des conditions d'hygiène et de sécurité pour le personnel d'aciérie;
• une forte amélioration de la distribution et de la finesse des inclusions de plomb dans l'acier liquide qui permet de maintenir constante la teneur en plomb de l'acier du début de la coulée jusqu'à la vidange complète de la poche;
• une forte diminution de la sédimentation du plomb en fond de poche et ainsi une quasi disparition des résidus de plomb dans les systèmes d'ouverture/fermeture des trous de coulée ainsi que dans les joints des briques réfractaires;
• l'amélioration des propriétés finales d'usinabilité des produits en acier laminé grâce à une meilleure distribution des nodules de plomb dans l'acier laminé selon une répartition très majoritairement de type aléatoire, caractérisée par une méthode innovante développée spécialement pour palier à l'absence de méthode standard internationale;
• la forte réduction des taux de rebuts des produits laminés pour défauts internes liés à la présence de nodules de plomb de grande taille non désirables et/ou mal répartis dans les produits en acier laminés.

The use of the novel additive comprising metallic lead and / or a lead alloy, according to the invention, for treating the liquid steel bags with a view to obtaining steels with a high lead content has many advantages and leads in particular to at :

• improving the efficiency of the addition of lead in the liquid steel bath;
• the improvement of the conditions of elaboration and treatment of steels with a high lead content: indeed, the increase in the addition yield makes it possible to reduce the emission of harmful fumes and thus an improvement of the health and safety conditions for steelworks personnel;
• a strong improvement in the distribution and fineness of the lead inclusions in the liquid steel which makes it possible to keep the lead content of the steel constant from the beginning of the casting until the complete emptying of the pocket;
• a strong decrease in the sedimentation of lead in the bottom of the pocket and thus a virtual disappearance of the lead residues in the opening / closing systems of the tapholes as well as in the joints of the refractory bricks;
• the improvement of the final machinability properties of rolled steel products thanks to a better distribution of lead nodules in rolled steel in a predominantly random distribution, characterized by an innovative method specially developed to overcome the absence international standard method;
• the strong reduction in the rejection rates of rolled products for internal defects related to the presence of large lead nodules that are undesirable and / or poorly distributed in rolled steel products.

Claims (13)

1. Additive comprising metallic lead and/or one or more lead alloys, for treating baths of liquid steel, said additive being in the form of flux-cored wire composed of a metal sheath and a finely-divided filling material, the latter being formed of a metallic lead powder and/or lead alloy powder and of a powder containing a material able to release a gas, which is inert with respect to the liquid steel, at the temperature of the bath of liquid steel, said additive being characterised in that said metallic lead powder and/or lead alloy powder consists of a particle size fraction G_R between 200 µm and 500 µm, and in that said particle size fraction G_R has the following characteristics:

   - through a 200 µm sieve: G_R ≤ 5 %;

   - through a 300 µm sieve: 90 % ≥ G_R ≥ 10 %;

   - through a 400 µm sieve: 40 % ≤ G_R ≤ 100 %;

   - through a 500 µm sieve: 100 %≥ G_R ≥ 90 %.
2. Additive according to claim 1, wherein the metal sheath is made of unalloyed mild steel.
3. Additive according to either claim 1 or claim 2, wherein the metal sheath is from 0.1 to 1 mm thick, preferably from 0.2 to 0.5 mm thick.
4. Additive according to any one of claims 1 to 3, wherein the flux-cored wire has a diameter from 5 to 20 mm, preferably from 9 to 15 mm.
5. Additive according to any one of claims 1 to 4, wherein the filling material has a particle size which does not exceed 1 mm.
6. Additive according to any one of claims 1 to 5, wherein the flux-cored wire contains from 100 to 1000 g of lead per metre.
7. Additive according to any one of claims 1 to 6, wherein the material able to release a gas, which is inert with respect to the liquid steel, is a mineral compound formed of limestone (calcium carbonate) or non-calcined dolomite, the gas released thus being carbon dioxide.
8. Additive according to claim 7, wherein the mineral material is present in an amount of 3 to 30 % by weight based on the weight of lead or lead alloy (or alloys) used.
9. Method for treating baths of liquid steel using an additive comprising metallic lead and/or one or more lead alloys, the method comprising a step of adding to said bath an additive in the form of a flux-cored wire composed of a metal sheath and a finely-divided filing material, the latter being formed of a metallic lead powder and/or lead alloy powder and of a powder of a material able to release a gas, which is inert with respect to the liquid steel, at the temperature of the bath of liquid steel, said metallic lead powder and/or lead alloy powder consisting of a particle size fraction G_R between 200 µm and 500 µm and having the following characteristics:

   - through a 200 µm sieve: G_R ≤ 5 %;

   - through a 300 µm sieve: 90 % ≥ G_R ≥ 10 %;

   - through a 400 µm sieve: 40 % s G_R ≤ 100 %;

   - thorough a 500 µm sieve: 100 % ≥ G_R ≥ 90 %.
10. Method according to claim 9, wherein 0.1 to 10 kg of flux-cored wire is added per tonne of liquid steel to be treated.
11. Method according to either claim 10 or claim 11, wherein the flux-cored wire is added to the bath of liquid steel at a speed of 50 to 200 m/min, preferably of 100 to 150 m/min.
12. Use of an additive comprising metallic lead and/or one or more lead alloys according to any one of claims 1 to 8, for treating baths of liquid steel.
13. Rolled steel product having a high lead content and containing lead nodules smaller than 100 µm, obtained by the method according to any one of claims 9 to 11, characterised in that, when the distribution of the nodules is defined corresponding to the following formula: $$I_R=\left(100/D\right)*\left({\displaystyle \sum _{i=1}^{\mathit{NI}}}\left(d_i\right)/\mathit{NI}\right)$$

    

    
    where:

    I_R : distribution index

    D: diagonal of the analysis zone

    D_I : minimum distance between the closest lead nodules

    NI: number of lead nodules with an associated minimum distance,

    I_R is greater than 1.4%.

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