research article mathematical analysis of the effect of...

Research ArticleMathematical Analysis of the Effect of Iron and Silica on theReduction Performance of Manganese Ores

S Ghali1 and E A Mousa2

1Steel and Ferroalloys Department Central Metallurgical Research and Development Institute (CMRDI) PO Box 87El-Felezzat Street 1 El-Tebbin Helwan Cairo 11422 Egypt2Pyrometallurgy Department Central Metallurgical Research and Development Institute (CMRDI) PO Box 87El-Felezzat Street 1 El-Tebbin Helwan Cairo 11422 Egypt

Correspondence should be addressed to E A Mousa mousa71yahoocom

Received 30 September 2014 Revised 17 December 2014 Accepted 18 December 2014

Academic Editor Sunghak Lee

Copyright copy 2015 S Ghali and E A Mousa This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In the current study a factorial design is used to investigate the effect of total iron and silica on the metallurgical performance ofdifferent grades of manganese ores The derived mathematical formulations are applied to estimate the reduction disintegrationindex (RDI

+63 RDI

+315 and RDI

minus05) reduction index (total reduction index (RIT) manganese reduction index (RIM) and iron

reduction index (RIF)) and softening-melting property (start of softening (1198791198781) end of softening (119879

1198782) start of melting (119879

1198981)

and end of melting (1198791198982)) of manganese ores The RDI

+63and RDI

+315are increased with the individual effect of SiO

2and the

interaction effect of iron with silica while they are decreased as the total iron increased The high-Fe high-SiO2manganese ore

showed the highest RIT and RIFThe RIMwas almost identical in all manganese oresThe presence of high content of SiO2resulted

in a narrow softening range (62ndash83∘C) while the high-Fe high-SiO2manganese ore exhibited a wider softening range (135ndash140∘C)

The melting range was very small in high-Fe low-SiO2(3ndash16∘C) and high-Fe high-SiO

2(6ndash8∘C) manganese ores while the low-Fe

low-SiO2manganese ore showed wider melting range (72ndash74∘C) The derived mathematical models are in a good agreement with

the experimental results The calculations are carried out using Matlab program

1 Introduction

Manganese is considered to be one of the most importantalloying elements in different grades of steel and cast ironManganese improves the tensile strength machinabilitytoughness hardness and abrasion resistance of steel Inaddition manganese has favourable influence on forgingwelding and grain refining properties in steel casting Man-ganese can be used for production of less expensive austeniticsteel grades by replacing the expensive alloying elements suchas nickel [1ndash4] Moreover manganese is important to controlthe sulfur content control in steel and it is commonly usedas oxidizers of molten steels [5] Manganese is usually addedin the form of ferromanganese (FeMn) to steel during itstreatment in the ladle furnace About 90ndash95 of manganeseproduction is used in steelmaking in the form of alloyssuch as ferromanganese and silicomanganese while sim30

of manganese production is used for desulfurization anddeoxidation of steel while the other 70 ofmanganese is usedpurely as alloying element in steel [6] Ferromanganese alloyis relatively expensive because it is produced by carbothermicreduction of manganese ores in the submerged electric arcfurnace (SAF) which is highly energy consuming [7 8]Energy input to SAF for production of high carbon ferro-manganese (HC FeMn) is 18400ndash24000MJton including300ndash360 kg of fixed carbon and 2400ndash3400 kWh electricalpower [9] In addition fluxing materials (eg limestone anddolomite) are usually added in amount of 200ndash450 kgtonHCFeMn to adjust the basicity of slag [10] Smelting reductionprocesses require relatively high temperature (sim1500∘C) forproduction of HC FeMn and higher temperature (above1600∘C) is required for silicomanganese (SiMn) productionManganese ores are commonly contaminated with manyimpurities (eg Fe

2O3 SiO2 CaO Al

2O3 P etc) which are

Hindawi Publishing CorporationJournal of MetallurgyVolume 2015 Article ID 679306 10 pageshttpdxdoiorg1011552015679306

2 Journal of Metallurgy

Table 1 Chemical composition of different grades of manganese ores

Ore description T Fe T Mn SiO2 Al2O3 CaO MgO P LOIHigh Fe-low Si 2348 3473 675 056 038 016 0051 829Low Fe-low Si 39 478 793 435 026 018 0063 967Low Fe-high Si 272 3666 2726 249 197 026 0062 888High Fe-high Si 3324 1367 1632 132 02 006 012 1003

normally present in the form of complexminerals (eg Pyro-lusite bixbyite braunite manganite hausmannite tephroiteand rhodonite) [9] Manganese ores can be classified accord-ing to their contents of manganese into different categoriesThe ores containing at least 35 manganese are defined asmanganese ores while the ores having 10ndash35Mn are knownas ferruginous manganese ores [9] The ores containing 5ndash10 manganese are defined as manganiferous ores while theores containing less than 5 manganese with the balanceof iron are classified as iron ores The manganese ores areoften found contaminated with iron and silica which affectthe reduction process the energy consumption and the oper-ation stability Intensive work has been carried out to identifythe reduction kinetics of manganese ores and the influenceof different impurities on the high temperature metallurgicalproperties The influence of iron and silica on the metallur-gical properties of four different grades of manganese oresis discussed [11] The ores are classified as high-iron high-silica low-iron low-silica high-iron low-silica and low-ironhigh-silica ores It was reported that the high-iron low-silicaone exhibited a good reducibility and narrow melting rangewhich is required for FeMn alloy and manganese-rich slagproduction The low iron-low silica manganese ores showedthat the highest melting temperature makes it suitable forSiMn alloy production The low iron-high silica manganeseores exhibited low melting temperatures therefore it couldbe used for manganese-rich slag production The high iron-high silica manganese ore showed good reducibility withlow melting temperature which makes it suitable for theproduction of manganese-rich slagThe investigation carriedout on the reduction of siliceous manganese ore by graphiteindicated that the manganese oxide is firstly dissolved intothe molten MnO-SiO

2-Al2O3-CaO-MgO slag and then it is

reduced from the slag [12 13] The reduction of manganeseoxide in slag is strongly retarded by silica The carbothermalreduction of manganese oxides was studied in presenceof hydrogen helium and argon at different temperatures[14 15] It was found that the carbothermal reduction ofMnO at constant temperature was the fastest in hydrogenfollowed by helium and the slowest in argonThis magnitudeeffect of the surrounding atmospheres on the reduction ratewas decreased as the temperature increased from 1275∘C to1400∘C The manganese oxides were reduced to 120572-Mn andMn23C6and Mn

7C3depending on the carbon to ore ratio A

reduction retardationwas accompaniedwith the reduction ofmanganese ores which are contaminated with iron oxides [1617] The reduction of Fe

2O3-MnO

2-SiO2mixed oxides with

CO gas is investigated [18] It was found that the formationof hard reducible fayalite-manganoan [(FeMn)

2SiO4] phase

resulted in a retardation of the reduction process [15] Theutilization of composite briquettes consisting of manganese

ore coke fines and organic binder improved the thermalstability softening property and reducibility of manganeseore in smelting arc furnace [19]

The previous survey indicates that in order to main-tain a stable operation of ferromanganese production withlowest energy consumption it is important to keep themetallurgical properties of the applied manganese ores at theoptimum conditions Although many experimental studieswere carried out to estimate the effect of different parameterson the smelting reduction of manganese ores few studiestried to estimate the magnitudersquos effect of the individualand interaction parameters on the overall reduction processThe factorial design provides a novel approach to preciselyestimate the effect of different parameters either individuallyor collectively on the process [20ndash23]The current study aimsto investigate the effect of total iron and silica on the metal-lurgical properties of manganese ores using factorial designapproach Regressionmodels are derived based on the exper-imental results of different manganese ores grades which arecontaminatedwith unequal proportions of iron and silica [11]The magnitude effects of the individual and combinationsparameters on the low-temperature reduction disintegrationreduction index and softening-melting range are evaluated

2 Materials and Methods

21 Source and Analysis of Manganese Ores A 22 factorialdesign is used to determine the main effect of total ironand silica and their interactions on the low-temperaturereduction disintegration index (RDI) reduction index (RI)and softening-melting property (SMP) of different gradesof manganese ores The testing methods of the reducedmanganese ores including RDI RI and SMP are reportedby Zhang et al elsewhere [11] The RDI is classified intoRDI+63

(the ratio of reduced manganese ores with size largerthan 63mm after tumbling test ) RDI

+315(the ratio

of reduced manganese ores with size larger than 315mmafter tumbling test ) and RDI

minus05(the ratio of reduced

manganese ores with size smaller than 05mm after tumblingtest ) The reduction index (RI) is classified into RIT(reduction index of total Fe-Mn oxides) RIM (reductionindex of only manganese oxide) and RIF (reduction indexof only iron oxide) The softening-melting property (SMP) isclassified into 119879

1198781(start of softening) 119879

1198782(end of softening)

1198791198981

(start ofmelting) and1198791198982

(end ofmelting)The chemicalcomposition of the manganese ores is given in Table 1 [11]

22 Statistical Design By convention the total iron in man-ganese ores is denoted by ldquo119860rdquo The average of iron contentin the low iron-manganese ores is equal to 331 and the

Journal of Metallurgy 3

Table 2 Effect of total iron (119860) silica (119861) and their interaction (119860119861) on on RDI+63

Source of variance The average effect Sum of square(SS)

Mean square (MS)(MS = SSdegree of freedom)

Magnitude effect119865119900(MSVarianceMS

119864)

119860 minus11518 2653286 2653286 9096124119861 54581 5958171 5958171 2042609119860119861 minus964705 1861311 1861311 6381037Error 1166777 0291694Total 2495329

Table 3 Effect of total iron (119860) silica (119861) and their interaction (119860119861) on RDI+315




119864)

119860 1765325 6232745 6232745 1763527119861 4867275 4738073 4738073 1340617119860119861 minus647918 8395942 8395942 2375594Error 14137 0353425Total 1389866

average of iron content in the high iron-manganese ores isequal to 2836 Similarly the silica will be denoted by ldquo119861rdquoThe average of silica content in the low silicon-manganeseores is equal to 734 and the average of silica content in thehigh silica-manganese ores is equal to 2179

Based on this concept the effect of a factor is donatedby a capital Latin letter Thus ldquo119860rdquo refers to the effect of totaliron ldquo119861rdquo refers to the effect of SiO

2 and ldquo119860119861rdquo refers to the

interaction combination effect of total Fe and SiO2 The low

and high level of ldquo119860rdquo and ldquo119861rdquo are denoted by ldquominusrdquo and ldquo+rdquorespectively The four treatment combinations in the designare usually represented by lowercase letters where the highlevel of any factor in the treatment combination is denotedby the corresponding lowercase letter and the low level of afactor in the treatment combination is denoted by the absenceof the corresponding letterThus ldquo119886rdquo represents the treatmentcombination of Fe ldquo119860rdquo at high level and SiO

2ldquo119861rdquo at low level

ldquo119887rdquo represents ldquo119860rdquo at low level and ldquo119861rdquo at high level and ldquo119886119887rdquorepresents both factors Fe and SiO

2(119860 and 119861) at the high

levels while ldquo(1)rdquo is used to denote both factors at low levels

3 Results and Discussions

31 Mathematical Formulations Mathematical formulationsare driven to estimate the effect of Fe SiO

2 and their interac-

tion (Fe-SiO2) on the metallurgical properties of manganese

oresThe effect of ldquo119860rdquo at low level of119861 is [119886minus(1)] and the effectof ldquo119860rdquo at high level of 119861 is [119886119887 minus 119887] The main effect of ldquo119860rdquo isthe average of its effect at low and high level of 119861 as given in

119860 =1

2[119886119887 minus 119887] + [119886 minus (1)] =

1

2[119886119887 + 119886 minus 119887 minus (1)] (1)

The average effect of ldquo119861rdquo can be calculated from the effect ofldquo119861rdquo at low level of ldquo119860rdquo ([119887 minus (1)]) and at the high level of ldquo119860rdquo(ie [119886119887 minus 119886]) as given in

119861 =1

2[119886119887 minus 119886] + [119887 minus (1)] =

1

2[119886119887 + 119887 minus 119886 minus (1)] (2)

The interaction effect ldquo119860119861rdquo is defined as the average differ-ence between the effect of ldquo119860rdquo at the high level of ldquo119861rdquo and theeffect of ldquo119860rdquo at the low level of ldquo119861rdquo as given in

119860119861 =1

2[119886119887 minus 119887] minus [119886 minus (1)] =

1

2[119886119887 + (1) minus 119886 minus 119887] (3)

The sum of squares (SS) of 119860 119861 and 119860119861 can be calculated asgiven in (4)ndash(6) respectively Consider

SS119860=[119886119887 + 119886 minus 119887 minus (1)]

2

4 (4)

SS119861=[119886119887 + 119887 minus 119886 minus (1)]

4

2

(5)

SS119860119861=[119886119887 + (1) minus 119886 minus 119887]

4

2

(6)

The total sum of squares (SS119879) and sum of squares (SS

119864) can

be calculated using (7) and (8) respectively Consider

SS119879=

2

sum

119894=1

2

sum

119895=1

119899

sum

119896=1

1199102

119894119895119896minus1199102

4 (7)

SS119864= SS119879minus SS119860minus SS119861minus SS119860119861 (8)

32 Application of Factorial Design

321 Reduction Disintegration Index (RDI) The completeanalyses of the effect of Fe (119860) andor SiO

2(119861) on reduction

disintegration index (RDI) of manganese ores can be calcu-lated using (1)ndash(8) The effects of Fe andor SiO

2on RDI

+63

RDI+315

and RDIminus05

are given in Tables 2ndash4 respectivelyIn Table 2 it can be seen that the highest negative effect

on RDI+63

is exhibited by the interaction of iron and silicafollowed by the individual effect of iron On the other handsilica exhibited a positive effect on RDI

+63of the reduced

manganese ores The results in Table 3 indicate that both of


Table 4 Effect of total iron (119860) silica (119861) and their interaction (119860119861) on RDIminus05




119864)

119860 0185425 0068765 0068765 3704831119861 0893125 1595345 1595345 8595207119860119861 2370475 112383 112383 6054839Error 0007424 0001856Total 1290984

Table 5 Regression coefficient values for RDI+63 RDI+315 andRDIminus05

119884 1205730

1205731

1205732

12057312

120576

RDI+63 7618 minus05759 2729 minus482353 plusmn0419RDI+315 8396099 0882662 2433638 minus323959 plusmn0441RDIminus05

595688 0092713 0446563 1185238 plusmn00386

iron and silica have an individual positive effect on RDI+315

while the interaction coefficient of iron and silica affects neg-atively the RDI

+315of the reduced manganese ores Table 4

indicates that the individual and collective parameters havepositive effects on RDI

minus05with relatively higher magnitude

for the interaction coefficient parameter of iron with silicaThe experimental results can be generally expressed in

terms of regression model as given in (9) for RDI+63

RDI+315

and RDIminus05

respectively Consider

119884 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (9)

where 119884 refers to RDI+63

RDI315

or RDIminus05

1199091is a coded

variable representing the total iron 1199092is a coded variable

representing the SiO2 1205731015840119904is regression coefficient and 120576 is the

residual (the difference between observed and fitted point ofthe design) 120573

0is the intercept which is the grand average of

all observations the regression coefficients 12057311205732and 120573

12are

one-half the corresponding factor while 120576 is the residual Thevalues of 120573

0 1205731 1205732 and 120576 are given in Table 5 In all cases the

residuals are very small and can be neglectedThe relation between the natural variables and the coded

variable is given as follow the coded variable is equal to[(natural variable minus 12(variable at high level + variable atlow level))12(variable at high level minus variable at low level)]Consequently the RDI

+63 RDI

+315 and RDI

minus05can be

predicted as a function of total iron and SiO2as given in (10)ndash

(12) respectively Consider

RDI+63= 5911397 minus 00533 [TotalFe]

+ 0730374 [SiO2] + 1221772 [TotalFe] [SiO

2]

(10)


+ 0591889 [SiO2] + 0903718 [TotalFe] [SiO

2]

(11)

0

20

40

60

80

100

(1) a b ab

Variables

Experimental resultsCoded variablesActual variables

RDI +

63

Figure 1 The experimental and predicted RDI+63

by using codedand actual variables

RDIminus05= 7960216 minus 0013098 [TotalFe]

minus 018336 [SiO2] minus 014559 [TotalFe] [SiO

2]

(12)

The RDI+63

RDI+315

and RDIminus05

for the differentgrades of manganese ores (low-Fe low-Si high-Fe low-Silow-Fe high-Si and high-Fe high-Si manganese ores) arecalculated based on (10)ndash(12) The calculated values of RDIare compared to the experimental results as can be seen inFigures 1 2 and 3The given notations summarized the gradeof ores as follows refers to low-Fe low-Si ore 119886 refers tohigh-Fe low-Si ore 119887 refers to low-Fe high-Si ore 119886119887 refersto high-Fe high-Si ore It can be seen that in all cases thecoded and actual variables are in good agreement with thoseof the experimental results The RDI

+63and RDI

+315are the

highest in low-Fe high-Si ores and the lowest in low-Fe low-Si oresThis indicates that silica has the ability to improve thestrength of manganese ore during the reduction at 500∘C [11]In the iron-manganese oxides manganese ferrite (Fe

2MnO4)

is formed in vicinity of large pores as a result of solid solutionreaction between MnO and Fe

2O3 On the other hand the

presence of silica in iron-manganese ore is able to diminishthe formation ofmanganese ferrite (MnFe

2O4) consequently

decreasing the porosity and improving the strength of theore [18 24] The iron content has a significant effect on


Table 6 Effect of total iron (119860) silica (119861) and their interaction (119860119861) on the RIT




119864)

119860 19687 7751559 7751559 3994748119861 63685 8111558 8111558 4180273119860119861 6268 7857565 7857565 4049378Error 0776175 0194044Total 9356233

Table 7 Effect of total iron (119860) silica (119861) and their interaction (119860119861) on the RIM




119864)

119860 minus23 1058 1058 2116119861 minus03 018 018 36119860119861 minus14 392 392 784Error 002 0005Total 147

0

20

40

60

80

100

(1) a b ab

Variables


RDI +

315



the reduction disintegration index The ore disintegrationincreases with iron due to the crystal distortion which isaccompanied by the transformation of hematite tomagnetiteSuch disintegration is caused on one hand by lattice trans-formations and on the other hand by an anisotropic reactionrate [25] Hematite crystallizes in hexagonal rhombohedrallattice while magnetite has an inverse spinel lattice structureDuring the transformation from hematite to magnetite alayer of close magnetite grows on the surface of the poroushematite and results in cracks and disintegrations The unitcell volume ofmagnetite is equal to 59207 A3 which it is equalto 30272 A3 for hematite This results in a disintegration ofthe ore during reduction In addition the transformation ofMnO2into Mn

2O3is accompanied by sharp increase in the

cell volume from 5564 to 83456 [11] Therefore the indexof reduction disintegration is decreased as the iron andormanganese content in the ore increased

0

2

4

6

8

10

(1) a b ab

Variables


RDI minus

05

Figure 3 The experimental and predicted RDIminus05


322 Reduction Index (RI) The effect of total Fe andor silicaon the reduction index is calculated based on the total Fe-Mnoxides (RIT) Mn oxide (RIM) and Fe oxide (RIF) as givenin Tables 6ndash8 Table 6 indicates that total Fe has the highestpositive effect on the total reduction RIT Both of the silicaand the interaction of total Fe with silica have almost equalpositive effect which is lower than the individual effect of FeTable 7 shows that all parameters have negative effect on thereduction ofmanganese (RIM)with relatively higher negativeeffect of total Fe Table 8 indicates that the total iron has arelatively high positive effect on the reduction of iron oxide(RIF) On the other hand the interaction coefficient betweenFe and silica exhibited a negative effect on the reduction ofiron oxides

The results of experiments can be expressed in terms ofregression models of RIT RIM and RIF as given in (13) The


Table 8 Effect of total iron (119860) silica (119861) and their interaction (119860119861) on the RIF




119864)


Table 9 Regression coefficient values for RIT RIM and RIF

119885 1205730

1205731

1205732

12057312

120576

RIT 6124925 98435 318425 3134 plusmn0389RIM 9815 minus115 minus015 minus07 plusmn005RIF 8439425 107277 03065 minus13015 plusmn0483

values of 1205730 1205731 1205732 and 120576 are given in Table 9 In all cases the

residuals are very small and can be neglected Consider

119885 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (13)

where 119885 refers to RIT RIM or RIFThe RIT RIM RIF can be predicted as a function of

total iron and SiO2as given in (14)ndash(16) respectively The

calculated values of RIT RIM and RIF are compared to theexperimetal results as can be seen in Figures 4ndash6 It can beseen that in all cases the coded and actual variables are in agood agreement with the experimental data Consider

RI = 5037273 + 0034632 [TotalFe]

+ 0281486 [SiO2] minus 010768 [TotalFe] [SiO

2]

(14)

RIM = 9812223 minus 000774 [TotalFe]

+ 002085 [SiO2] + 0101729 [TotalFe] [SiO

2]

(15)

RIF = 6689649 minus 001438 [TotalFe]

+ 1065985 [SiO2] + 0270166 [TotalFe] [SiO

2]

(16)

It can be seen in Figure 4 that high-Fe high-Si and high-Fe low-Si manganese ores exhibited the highest reductionindex On the other hand the lowest reduction index wasexhibited in low-Fe low-Si and low-Fe high-Si ones Thisindicates that the reduction index ofmanganese ore increasesas iron oxide content increasesThe reduction index based onmanganese oxide (RIM) is almost identical for the differentgrades of manganese ores as shown in Figure 5 This canbe attributed to the simple reduction of MnO

2to MnO

The reduction index based on iron oxide (RIF) is high inthe ores rich with iron and low in the ore poor in ironoxides as shown in Figure 6 This is attributed to the higherreducibility of iron oxides compared to that of manganeseoxides Although the reduction of wustite (Fe

119909O) to metallic

iron required relatively high potential of reducing gas (120578CO asymp30 120578H2 asymp 30) the reduction of MnO toMnmetal is more

0

20

40

60

80

100

(1) a b ab

RIT

Variables


Figure 4 The experimental and predicted RIT by using coded andactual variables

complicated and can be only proceeded by solid carbon atvery high temperature (asymp1423∘C) Therefore the reductionindex decreased as manganese content increased

323 Softening-Melting Property (SMP) A mathematicalregression model is derived to estimate the effect of total ironandor silica on the softening-melting property ofmanganeseores during reductionThe softening ranges can be estimatedbased on the determination of temperature at which thereduced ores start to soften (119879

1198781 starting of softening) and

the temperature at which the softening finsihed (1198791198782 end of

softening) The melting range can be determined based onthe identification of the start of melting (119879

1198981) and the end

of melting (1198791198982) The effects of total iron andor silica on

the softening property of reduced manganese ores are givenin Tables 10 and 11 respectively It can be seen that the ironand silica affect negatively the start and the end softeningtemperature

The effect of iron andor silica content on the meltingproperty of manganese ores including 119879

1198981and 119879

1198982is given

in Tables 12 and 13 respectively As can be seen in Table 12the iron and the iron with silica affect positively the starttemperature of melting while silica exhibited a negative effecton the start temperature of melting Both of iron and silicadecreased the end temperature of melting of manganese ore


Table 10 Effect of total iron (119860) silica (119861) and their interaction (119860119861) on 1198791198781




119864)






119864)


0

20

40

60

80

100

120

(1) a b ab

RIM

Variables


Figure 5 The experimental and predicted RIM by using coded andactual variables

while the interaction of iron and silica has positive effect onthe end of melting as given in Table 13

The relation between the natural variables and the codedvariable for 119879

1198781 1198791198782 1198791198981 and 119879

1198982can be summarized in (17)

The values of 1205730 1205731 1205732 and 120576 are given in Table 14 Consider

119867 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (17)

where119867 refers to 1198791198781 1198791198782 1198791198981 or 1198791198982

The 1198791198781 1198791198782 1198791198981 and 119879

1198982can be predicted as a function

of total iron and SiO2as given in (18)ndash(21) respectively The

calculated values of 1198791198781 1198791198782 1198791198981 and 119879

1198982are compared to

the experimental results as can be seen in Figures 7ndash10 It canbe seen that in all cases the coded and actual variables are ina good agreement with the experimental results Consider

1198791198781= 1135617 minus 023482 [TotalFe]

+ 2242574 [SiO2] + 0431248 [TotalFe] [SiO

2]

(18)

0

20

40

60

80

100

(1) a b ab

RIF

Variables


Figure 6 The experimental and predicted RIF by using coded andactual variables

1198791198782= 1297323 minus 005525 [TotalFe]


2]

(19)

1198791198981= 130935 + 0121556 [TotalFe]


2]

(20)

1198791198982= 1399393 + 0165758 [TotalFe]


2]

(21)

Figures 7 and 10 showed that the lowest start temperatureof softening (119879

1198781) and melting (119879

1198981) is exhibited in high-Fe

high-Si manganese ore which is equal to 1062ndash1089∘C and11995ndash1225∘C respectively Figures 8 and 11 clarify that thehighest end of softening (119879

1198782) and melting (119879

1198982) is exhibited

in high-Fe low-Si manganese ore which is equal to 1152ndash1154∘C and 1273ndash1276∘C respectively This indicates that the






119864)

119860 44 3872 3872 1936119861 minus79 12482 12482 6241119860119861 22 968 968 484Error 8 2Total 17330





119864)

119860 minus19 722 722 361119861 minus82 13448 13448 6724119860119861 30 1800 1800 900Error 8 2Total 15978

Table 14 Values of regression coefficient for 1198791198781 1198791198782 1198791198981 and 119879

1198982

1205730

1205731

1205732

12057312

120576

1198791198781

112325 minus1475 minus2375 minus2125 plusmn151198791198782

12405 minus40 minus320 minus50 plusmn25Δ119879119878

1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982

12665 minus95 minus410 150 plusmn10Δ119879119898

3666 minus321825 minus20175 351 plusmn037

0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)

Figure 7 The experimental and predicted 1198791198781by using coded and

actual variables

presence of relatively high percentage of silica resulted in adecrease of the start softening andmelting temperaturesThiscan be attributed to the formation of relatively low meltingrhodonite phase (MnSiO

3 mp 1242∘C) as a result of the

reaction between SiO2and MnO [26] The formation of low

melting rhodonite phase resulted in a narrow softening range(119879Δ119878) in low-Fe high-SiO

2manganese ore as can be seen in

0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables

Figure 9 The high-Fe low-si and high-Fe high-si manganeseores showed a narrow melting range as can be seen inFigure 12 This can be attributed to the formation Fe-Mnolivine in the presence of relatively high concentration of iron[11]

Based on the previous findings it can be concluded thatthe factorial design is very useful approach to predict andprecisely estimate the effect of different impurities such asFe andor Si which commonly contaminate the manganeseores and affect negatively the smelting reduction processThederived mathematical regression models are able to predictthe reduction disintegration index reduction index and thesoftening-melting property of manganese ores as a functionof the content of total iron and silica

4 Conclusions

In the current study a factorial design is built on the exper-imental data of four grades of manganese ores containing


0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)

Figure 9 The softening range (119879Δ119878) for experimental coded and

actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)

Figure 10 The experimental and predicted 1198791198981

by using coded andactual variables

different percentages of iron and silica (low-Fe high-Si high-Fe low-Si low-Fe high-Si and high-Fe high-Si manganeseores) The main findings can be summarized as follow

(1) Regression formulations are derived to estimate theeffect of total Fe andor SiO

2on the reduction disin-

tegration indexes (RDI+63

RDI+315

and RDIminus05

) ofmanganese ores The RDI

+63and RDI

+315increased

with the individual effect of SiO2and the interaction

effect of Fe-SiO2while they decreased as the total

Fe increased The RDIminus05

increased with Fe anddecreased with individual effect of silica and theinteraction effect of Fe-SiO

2in the manganese ores

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)

Figure 12 The melting range (119879Δ119898

) for experimental coded andactual variables

(2) The effect of total Fe andor SiO2on the reduction

indexes (total reduction ofmanganese and iron oxides(RIT) manganese oxides reduction (RIM) and ironoxides reduction (RIF)) is developed The RIT andRIF increased as the iron oxide content in manganeseore increased The RIM was almost identical due tothe simple conversion of MnO

2to MnO

(3) The effect of total iron and SiO2on the softening-

melting property (start of softening (1198791198781) and end of

softening (1198791198782) start of melting (119879

1198981) and end of

melting (1198791198982)) is mathematically derived The devel-

oped formulations could be used to precisely predictthe effect of total Fe and silica on the softening-melting property of manganese ores


(4) The validation of regressions formulations was foundto be in a good agreement with the experimental datawhich indicates the efficiency of the factorial designto predict the metallurgical properties of manganeseores under the influence of different impurities

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] S-M Jung C-H Rhee and D-J Min ldquoThermodynamicproperties of manganese oxide in BOF slagsrdquo ISIJ Internationalvol 42 no 1 pp 63ndash70 2002

[2] A Ahmed S N Ghali M Eissa and S A El Badry ldquoInfluenceof partial replacement of nickel by nitrogen on microstructureand mechanical properties of austenitic stainless steelrdquo Journalof Metallurgy vol 2011 Article ID 639283 6 pages 2011

[3] S N Ghali ldquoLow carbon high nitrogen low nickel stainlesssteelrdquo Steel Research International vol 84 no 5 pp 450ndash4562013

[4] S N Ghali A AhmedM Eissa H El-FaramawyMMishrekyand T Mattar ldquoProduction and application of advanced highnitrogen steelrdquo in International Conference on Science andTechnology of Ironmaking and Steelmaking Jamshedpur IndiaDecember 2013

[5] E T Turkdogan Fundamental of Steelmaking The Institute ofMaterials London UK 1996

[6] B K Sedumedi and X Pan ldquoBenchmarking techniques inferromanganse productionrdquo in Proceedings of the InternationalConference on Mining Mineral Processing and MetallurgicalEngineering (ICMMME rsquo13) pp 158ndash163 Johannesburg SouthAfrica April 2013

[7] S-M Jung S-H Kim C-H Rhee and D-J Min ldquoTher-modynamic study on MnO behavior in MgO-saturated slagcontaining FeOrdquo ISIJ International vol 33 no 10 pp 1049ndash1054 1993

[8] R Sen ldquoProduction of ferro manganese through blast furnacerouterdquo in Proceedings of the National Workshop on Ferro AlloyIndustries in the Liberalised Economy pp 83ndash91NML Jamshed-pur India 1997

[9] R Kononov O Ostrovski and S Ganguly ldquoCarbothermalsolid state reduction of manganese ores 1 Manganese orecharacterisationrdquo ISIJ International vol 49 no 8 pp 1099ndash11062009

[10] M Eissa H El-Faramawy A Ahmed S Nabil and H HalfaldquoParameters affecting the production of high carbon ferroman-ganese in closed submerged arc furnacerdquo Journal of Mineralsand Materials Characterization and Engineering vol 11 no 1pp 1ndash20 2012

[11] Y Zhang Y Zhang Z You Y Zhao G Li and T Jiang ldquoStudyon themetallurgical performance of typical manganese oresrdquo in5th International Symposium onHigh TemperatureMetallurgicalProcessing pp 345ndash352 TMS John Wiley amp Sons San DiegoCalif USA 2014

[12] O I Ostrovski and T J M Webb ldquoReduction of siliceousmanganese ore by graphiterdquo ISIJ International vol 35 no 11pp 1331ndash1339 1995

[13] M Yastreboff O Ostrovski and S Ganguly ldquoCarbothermicreduction of manganese from manganese ore and ferroman-ganese slagrdquo in Proceedings of the 8th International FerroalloysCongress pp 263ndash270 Beijing China June 1998

[14] R Kononov O Ostrovski and S Ganguly ldquoCarbothermalsolid state reduction of manganese ores 2 Non-isothermaland isothermal reduction in different gas atmospheresrdquo ISIJInternational vol 49 no 8 pp 1107ndash1114 2009

[15] R Kononov O Ostrovski and S Ganguly ldquoCarbothermal solidstate reduction of manganese ores 3 Phase developmentrdquo ISIJInternational vol 49 no 8 pp 1115ndash1122 2009

[16] M S Fahim H El Faramawy A M Ahmed S N Ghali andA T Kandil ldquoCharacterization of Egyptian manganese ores forproduction of high carbon ferromanganeserdquo Journal ofMineralsandMaterials Characterization and Engineering vol 1 no 2 pp68ndash74 2013

[17] A A El-Geassy M I Nasr A A Omar and E A MousaldquoIsothermal reduction behaviour of MnO

2doped Fe

2O3com-

pacts with H2at 1073ndash1373 Krdquo Ironmaking and Steelmaking vol

35 no 7 pp 531ndash538 2008[18] A-H A El-Geassy M I Nasr A A Omar and E-S A Mousa

ldquoInfluence of SiO2andor MnO

2on the reduction behaviour

and structure changes of Fe2O3compacts with CO gasrdquo ISIJ

International vol 48 no 10 pp 1359ndash1367 2008[19] Y Huaming and Q Guanzhou ldquoFabrication and industrial

application of ferromanganese composite briquetterdquo Journal ofCentral South University of Technology vol 5 no 1 pp 7ndash101998

[20] Y Gao M Olivas-Martinez H Y Sohn H G Kim and CW Kim ldquoUpgrading of low-grade manganese ore by selectivereduction of iron oxide and magnetic separationrdquoMetallurgicaland Materials Transactions B Process Metallurgy and MaterialsProcessing Science vol 43 no 6 pp 1465ndash1475 2012

[21] S Ghali M Eissa and H El-Faramawy ldquoSimulation ofaustenitic stainless steel oxidation containing nitrogen at tem-perature range 500∘Cndash800∘Crdquo International Journal of Statisticsand Mathematics vol 1 no 3 pp 24ndash32 2014

[22] S Ghali and E A Mousa ldquoAnalysis of the reduction yield ofsynthetic iron oxide sinter reduced by H

2at 900ndash1100∘C using

factorial design approachrdquo Steel Grips August 2014[23] E AMousa and S Ghali ldquoFactorial design analysis of reduction

of simulated iron ore sinter reduced with CO gas at 1000ndash1100∘Crdquo Ironmaking amp Steelmaking 2014

[24] A A El-Geassy M I Nasr and E A Mousa ldquoInfluence ofmanganese oxide and silica on the morphological structure ofhematite compactsrdquo Steel Research International vol 81 no 3pp 178ndash185 2010

[25] H W Gudenau D Senk A Babich et al ldquoSustainable devel-opment in iron- and steel research CO

2and wastesrdquo ISIJ

International vol 44 no 9 pp 1469ndash1479 2004[26] I-H Jung Y-B Kang S A Decterov and A D Pelton ldquoTher-

modynamic evaluation and optimization of the MnO-Al2O3

and MnO-Al2O3-SiO2systems and applications to inclusion

engineeringrdquo Metallurgical and Materials Transactions B vol35 no 2 pp 259ndash268 2004

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Table 1 Chemical composition of different grades of manganese ores

Ore description T Fe T Mn SiO2 Al2O3 CaO MgO P LOIHigh Fe-low Si 2348 3473 675 056 038 016 0051 829Low Fe-low Si 39 478 793 435 026 018 0063 967Low Fe-high Si 272 3666 2726 249 197 026 0062 888High Fe-high Si 3324 1367 1632 132 02 006 012 1003

normally present in the form of complexminerals (eg Pyro-lusite bixbyite braunite manganite hausmannite tephroiteand rhodonite) [9] Manganese ores can be classified accord-ing to their contents of manganese into different categoriesThe ores containing at least 35 manganese are defined asmanganese ores while the ores having 10ndash35Mn are knownas ferruginous manganese ores [9] The ores containing 5ndash10 manganese are defined as manganiferous ores while theores containing less than 5 manganese with the balanceof iron are classified as iron ores The manganese ores areoften found contaminated with iron and silica which affectthe reduction process the energy consumption and the oper-ation stability Intensive work has been carried out to identifythe reduction kinetics of manganese ores and the influenceof different impurities on the high temperature metallurgicalproperties The influence of iron and silica on the metallur-gical properties of four different grades of manganese oresis discussed [11] The ores are classified as high-iron high-silica low-iron low-silica high-iron low-silica and low-ironhigh-silica ores It was reported that the high-iron low-silicaone exhibited a good reducibility and narrow melting rangewhich is required for FeMn alloy and manganese-rich slagproduction The low iron-low silica manganese ores showedthat the highest melting temperature makes it suitable forSiMn alloy production The low iron-high silica manganeseores exhibited low melting temperatures therefore it couldbe used for manganese-rich slag production The high iron-high silica manganese ore showed good reducibility withlow melting temperature which makes it suitable for theproduction of manganese-rich slagThe investigation carriedout on the reduction of siliceous manganese ore by graphiteindicated that the manganese oxide is firstly dissolved intothe molten MnO-SiO

2-Al2O3-CaO-MgO slag and then it is

reduced from the slag [12 13] The reduction of manganeseoxide in slag is strongly retarded by silica The carbothermalreduction of manganese oxides was studied in presenceof hydrogen helium and argon at different temperatures[14 15] It was found that the carbothermal reduction ofMnO at constant temperature was the fastest in hydrogenfollowed by helium and the slowest in argonThis magnitudeeffect of the surrounding atmospheres on the reduction ratewas decreased as the temperature increased from 1275∘C to1400∘C The manganese oxides were reduced to 120572-Mn andMn23C6and Mn

7C3depending on the carbon to ore ratio A

reduction retardationwas accompaniedwith the reduction ofmanganese ores which are contaminated with iron oxides [1617] The reduction of Fe

2O3-MnO

2-SiO2mixed oxides with

CO gas is investigated [18] It was found that the formationof hard reducible fayalite-manganoan [(FeMn)

2SiO4] phase

resulted in a retardation of the reduction process [15] Theutilization of composite briquettes consisting of manganese

ore coke fines and organic binder improved the thermalstability softening property and reducibility of manganeseore in smelting arc furnace [19]

The previous survey indicates that in order to main-tain a stable operation of ferromanganese production withlowest energy consumption it is important to keep themetallurgical properties of the applied manganese ores at theoptimum conditions Although many experimental studieswere carried out to estimate the effect of different parameterson the smelting reduction of manganese ores few studiestried to estimate the magnitudersquos effect of the individualand interaction parameters on the overall reduction processThe factorial design provides a novel approach to preciselyestimate the effect of different parameters either individuallyor collectively on the process [20ndash23]The current study aimsto investigate the effect of total iron and silica on the metal-lurgical properties of manganese ores using factorial designapproach Regressionmodels are derived based on the exper-imental results of different manganese ores grades which arecontaminatedwith unequal proportions of iron and silica [11]The magnitude effects of the individual and combinationsparameters on the low-temperature reduction disintegrationreduction index and softening-melting range are evaluated

2 Materials and Methods

21 Source and Analysis of Manganese Ores A 22 factorialdesign is used to determine the main effect of total ironand silica and their interactions on the low-temperaturereduction disintegration index (RDI) reduction index (RI)and softening-melting property (SMP) of different gradesof manganese ores The testing methods of the reducedmanganese ores including RDI RI and SMP are reportedby Zhang et al elsewhere [11] The RDI is classified intoRDI+63

(the ratio of reduced manganese ores with size largerthan 63mm after tumbling test ) RDI

+315(the ratio

of reduced manganese ores with size larger than 315mmafter tumbling test ) and RDI

minus05(the ratio of reduced

manganese ores with size smaller than 05mm after tumblingtest ) The reduction index (RI) is classified into RIT(reduction index of total Fe-Mn oxides) RIM (reductionindex of only manganese oxide) and RIF (reduction indexof only iron oxide) The softening-melting property (SMP) isclassified into 119879

1198781(start of softening) 119879

1198782(end of softening)

1198791198981

(start ofmelting) and1198791198982

(end ofmelting)The chemicalcomposition of the manganese ores is given in Table 1 [11]

22 Statistical Design By convention the total iron in man-ganese ores is denoted by ldquo119860rdquo The average of iron contentin the low iron-manganese ores is equal to 331 and the






119864)






119864)









2(119860 and 119861) at the high







119860 =1

2[119886119887 minus 119887] + [119886 minus (1)] =

1

2[119886119887 + 119886 minus 119887 minus (1)] (1)


119861 =1

2[119886119887 minus 119886] + [119887 minus (1)] =

1

2[119886119887 + 119887 minus 119886 minus (1)] (2)


119860119861 =1


1

2[119886119887 + (1) minus 119886 minus 119887] (3)


SS119860=[119886119887 + 119886 minus 119887 minus (1)]

2

4 (4)

SS119861=[119886119887 + 119887 minus 119886 minus (1)]

4

2

(5)

SS119860119861=[119886119887 + (1) minus 119886 minus 119887]

4

2

(6)


119864) can


SS119879=

2

sum

119894=1

2

sum

119895=1

119899

sum

119896=1

1199102

119894119895119896minus1199102

4 (7)






2on RDI

+63

RDI+315

and RDIminus05


on RDI+63


+63of the reduced







119864)

119860 0185425 0068765 0068765 3704831119861 0893125 1595345 1595345 8595207119860119861 2370475 112383 112383 6054839Error 0007424 0001856Total 1290984


119884 1205730

1205731

1205732

12057312

120576


595688 0092713 0446563 1185238 plusmn00386








RDI+315

and RDIminus05


119884 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (9)


RDI315

or RDIminus05

1199091is a coded






12are





+63 RDI

+315 and RDI

minus05can be




+ 0730374 [SiO2] + 1221772 [TotalFe] [SiO

2]

(10)


+ 0591889 [SiO2] + 0903718 [TotalFe] [SiO

2]

(11)

0

20

40

60

80

100

(1) a b ab

Variables


RDI +

63





2]

(12)

The RDI+63

RDI+315

and RDIminus05


+63and RDI

+315are the


2MnO4)




2O4) consequently







119864)

119860 19687 7751559 7751559 3994748119861 63685 8111558 8111558 4180273119860119861 6268 7857565 7857565 4049378Error 0776175 0194044Total 9356233





119864)


0

20

40

60

80

100

(1) a b ab

Variables


RDI +

315






0

2

4

6

8

10

(1) a b ab

Variables


RDI minus

05










119864)



119885 1205730

1205731

1205732

12057312

120576




119885 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (13)




RI = 5037273 + 0034632 [TotalFe]


2]

(14)


+ 002085 [SiO2] + 0101729 [TotalFe] [SiO

2]

(15)


+ 1065985 [SiO2] + 0270166 [TotalFe] [SiO

2]

(16)


2to MnO




0

20

40

60

80

100

(1) a b ab

RIT

Variables












1198981and 119879

1198982is given







119864)






119864)


0

20

40

60

80

100

120

(1) a b ab

RIM

Variables





1198781 1198791198782 1198791198981 and 119879



119867 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (17)


The 1198791198781 1198791198782 1198791198981 and 119879






1198791198781= 1135617 minus 023482 [TotalFe]

+ 2242574 [SiO2] + 0431248 [TotalFe] [SiO

2]

(18)

0

20

40

60

80

100

(1) a b ab

RIF

Variables



1198791198782= 1297323 minus 005525 [TotalFe]


2]

(19)

1198791198981= 130935 + 0121556 [TotalFe]


2]

(20)

1198791198982= 1399393 + 0165758 [TotalFe]


2]

(21)


1198781) and melting (119879



1198782) and melting (119879








119864)






119864)



1198982

1205730

1205731

1205732

12057312

120576

1198791198781



1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982



0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)


actual variables






0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables



4 Conclusions



0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








119864)






119864)









2(119860 and 119861) at the high







119860 =1

2[119886119887 minus 119887] + [119886 minus (1)] =

1

2[119886119887 + 119886 minus 119887 minus (1)] (1)


119861 =1

2[119886119887 minus 119886] + [119887 minus (1)] =

1

2[119886119887 + 119887 minus 119886 minus (1)] (2)


119860119861 =1


1

2[119886119887 + (1) minus 119886 minus 119887] (3)


SS119860=[119886119887 + 119886 minus 119887 minus (1)]

2

4 (4)

SS119861=[119886119887 + 119887 minus 119886 minus (1)]

4

2

(5)

SS119860119861=[119886119887 + (1) minus 119886 minus 119887]

4

2

(6)


119864) can


SS119879=

2

sum

119894=1

2

sum

119895=1

119899

sum

119896=1

1199102

119894119895119896minus1199102

4 (7)






2on RDI

+63

RDI+315

and RDIminus05


on RDI+63


+63of the reduced







119864)

119860 0185425 0068765 0068765 3704831119861 0893125 1595345 1595345 8595207119860119861 2370475 112383 112383 6054839Error 0007424 0001856Total 1290984


119884 1205730

1205731

1205732

12057312

120576


595688 0092713 0446563 1185238 plusmn00386








RDI+315

and RDIminus05


119884 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (9)


RDI315

or RDIminus05

1199091is a coded






12are





+63 RDI

+315 and RDI

minus05can be




+ 0730374 [SiO2] + 1221772 [TotalFe] [SiO

2]

(10)


+ 0591889 [SiO2] + 0903718 [TotalFe] [SiO

2]

(11)

0

20

40

60

80

100

(1) a b ab

Variables


RDI +

63





2]

(12)

The RDI+63

RDI+315

and RDIminus05


+63and RDI

+315are the


2MnO4)




2O4) consequently







119864)

119860 19687 7751559 7751559 3994748119861 63685 8111558 8111558 4180273119860119861 6268 7857565 7857565 4049378Error 0776175 0194044Total 9356233





119864)


0

20

40

60

80

100

(1) a b ab

Variables


RDI +

315






0

2

4

6

8

10

(1) a b ab

Variables


RDI minus

05










119864)



119885 1205730

1205731

1205732

12057312

120576




119885 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (13)




RI = 5037273 + 0034632 [TotalFe]


2]

(14)


+ 002085 [SiO2] + 0101729 [TotalFe] [SiO

2]

(15)


+ 1065985 [SiO2] + 0270166 [TotalFe] [SiO

2]

(16)


2to MnO




0

20

40

60

80

100

(1) a b ab

RIT

Variables












1198981and 119879

1198982is given







119864)






119864)


0

20

40

60

80

100

120

(1) a b ab

RIM

Variables





1198781 1198791198782 1198791198981 and 119879



119867 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (17)


The 1198791198781 1198791198782 1198791198981 and 119879






1198791198781= 1135617 minus 023482 [TotalFe]

+ 2242574 [SiO2] + 0431248 [TotalFe] [SiO

2]

(18)

0

20

40

60

80

100

(1) a b ab

RIF

Variables



1198791198782= 1297323 minus 005525 [TotalFe]


2]

(19)

1198791198981= 130935 + 0121556 [TotalFe]


2]

(20)

1198791198982= 1399393 + 0165758 [TotalFe]


2]

(21)


1198781) and melting (119879



1198782) and melting (119879








119864)






119864)



1198982

1205730

1205731

1205732

12057312

120576

1198791198781



1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982



0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)


actual variables






0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables



4 Conclusions



0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








119864)

119860 0185425 0068765 0068765 3704831119861 0893125 1595345 1595345 8595207119860119861 2370475 112383 112383 6054839Error 0007424 0001856Total 1290984


119884 1205730

1205731

1205732

12057312

120576


595688 0092713 0446563 1185238 plusmn00386








RDI+315

and RDIminus05


119884 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (9)


RDI315

or RDIminus05

1199091is a coded






12are





+63 RDI

+315 and RDI

minus05can be




+ 0730374 [SiO2] + 1221772 [TotalFe] [SiO

2]

(10)


+ 0591889 [SiO2] + 0903718 [TotalFe] [SiO

2]

(11)

0

20

40

60

80

100

(1) a b ab

Variables


RDI +

63





2]

(12)

The RDI+63

RDI+315

and RDIminus05


+63and RDI

+315are the


2MnO4)




2O4) consequently







119864)

119860 19687 7751559 7751559 3994748119861 63685 8111558 8111558 4180273119860119861 6268 7857565 7857565 4049378Error 0776175 0194044Total 9356233





119864)


0

20

40

60

80

100

(1) a b ab

Variables


RDI +

315






0

2

4

6

8

10

(1) a b ab

Variables


RDI minus

05










119864)



119885 1205730

1205731

1205732

12057312

120576




119885 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (13)




RI = 5037273 + 0034632 [TotalFe]


2]

(14)


+ 002085 [SiO2] + 0101729 [TotalFe] [SiO

2]

(15)


+ 1065985 [SiO2] + 0270166 [TotalFe] [SiO

2]

(16)


2to MnO




0

20

40

60

80

100

(1) a b ab

RIT

Variables












1198981and 119879

1198982is given







119864)






119864)


0

20

40

60

80

100

120

(1) a b ab

RIM

Variables





1198781 1198791198782 1198791198981 and 119879



119867 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (17)


The 1198791198781 1198791198782 1198791198981 and 119879






1198791198781= 1135617 minus 023482 [TotalFe]

+ 2242574 [SiO2] + 0431248 [TotalFe] [SiO

2]

(18)

0

20

40

60

80

100

(1) a b ab

RIF

Variables



1198791198782= 1297323 minus 005525 [TotalFe]


2]

(19)

1198791198981= 130935 + 0121556 [TotalFe]


2]

(20)

1198791198982= 1399393 + 0165758 [TotalFe]


2]

(21)


1198781) and melting (119879



1198782) and melting (119879








119864)






119864)



1198982

1205730

1205731

1205732

12057312

120576

1198791198781



1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982



0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)


actual variables






0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables



4 Conclusions



0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








119864)

119860 19687 7751559 7751559 3994748119861 63685 8111558 8111558 4180273119860119861 6268 7857565 7857565 4049378Error 0776175 0194044Total 9356233





119864)


0

20

40

60

80

100

(1) a b ab

Variables


RDI +

315






0

2

4

6

8

10

(1) a b ab

Variables


RDI minus

05










119864)



119885 1205730

1205731

1205732

12057312

120576




119885 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (13)




RI = 5037273 + 0034632 [TotalFe]


2]

(14)


+ 002085 [SiO2] + 0101729 [TotalFe] [SiO

2]

(15)


+ 1065985 [SiO2] + 0270166 [TotalFe] [SiO

2]

(16)


2to MnO




0

20

40

60

80

100

(1) a b ab

RIT

Variables












1198981and 119879

1198982is given







119864)






119864)


0

20

40

60

80

100

120

(1) a b ab

RIM

Variables





1198781 1198791198782 1198791198981 and 119879



119867 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (17)


The 1198791198781 1198791198782 1198791198981 and 119879






1198791198781= 1135617 minus 023482 [TotalFe]

+ 2242574 [SiO2] + 0431248 [TotalFe] [SiO

2]

(18)

0

20

40

60

80

100

(1) a b ab

RIF

Variables



1198791198782= 1297323 minus 005525 [TotalFe]


2]

(19)

1198791198981= 130935 + 0121556 [TotalFe]


2]

(20)

1198791198982= 1399393 + 0165758 [TotalFe]


2]

(21)


1198781) and melting (119879



1198782) and melting (119879








119864)






119864)



1198982

1205730

1205731

1205732

12057312

120576

1198791198781



1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982



0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)


actual variables






0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables



4 Conclusions



0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








119864)



119885 1205730

1205731

1205732

12057312

120576




119885 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (13)




RI = 5037273 + 0034632 [TotalFe]


2]

(14)


+ 002085 [SiO2] + 0101729 [TotalFe] [SiO

2]

(15)


+ 1065985 [SiO2] + 0270166 [TotalFe] [SiO

2]

(16)


2to MnO




0

20

40

60

80

100

(1) a b ab

RIT

Variables












1198981and 119879

1198982is given







119864)






119864)


0

20

40

60

80

100

120

(1) a b ab

RIM

Variables





1198781 1198791198782 1198791198981 and 119879



119867 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (17)


The 1198791198781 1198791198782 1198791198981 and 119879






1198791198781= 1135617 minus 023482 [TotalFe]

+ 2242574 [SiO2] + 0431248 [TotalFe] [SiO

2]

(18)

0

20

40

60

80

100

(1) a b ab

RIF

Variables



1198791198782= 1297323 minus 005525 [TotalFe]


2]

(19)

1198791198981= 130935 + 0121556 [TotalFe]


2]

(20)

1198791198982= 1399393 + 0165758 [TotalFe]


2]

(21)


1198781) and melting (119879



1198782) and melting (119879








119864)






119864)



1198982

1205730

1205731

1205732

12057312

120576

1198791198781



1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982



0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)


actual variables






0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables



4 Conclusions



0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








119864)






119864)


0

20

40

60

80

100

120

(1) a b ab

RIM

Variables





1198781 1198791198782 1198791198981 and 119879



119867 = 1205730+ 12057311199091+ 12057321199092+ 1205731211990911199092+ 120576 (17)


The 1198791198781 1198791198782 1198791198981 and 119879






1198791198781= 1135617 minus 023482 [TotalFe]

+ 2242574 [SiO2] + 0431248 [TotalFe] [SiO

2]

(18)

0

20

40

60

80

100

(1) a b ab

RIF

Variables



1198791198782= 1297323 minus 005525 [TotalFe]


2]

(19)

1198791198981= 130935 + 0121556 [TotalFe]


2]

(20)

1198791198982= 1399393 + 0165758 [TotalFe]


2]

(21)


1198781) and melting (119879



1198782) and melting (119879








119864)






119864)



1198982

1205730

1205731

1205732

12057312

120576

1198791198781



1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982



0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)


actual variables






0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables



4 Conclusions



0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








119864)






119864)



1198982

1205730

1205731

1205732

12057312

120576

1198791198781



1196888 1165125 minus833125 1629125 plusmn071198791198981

12295 220 minus395 110 plusmn101198791198982



0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS1

(∘C)


actual variables






0

200

400

600

800

1000

1200

1400

(1) a b ab

Variables


TS2

(∘C)


actual variables



4 Conclusions



0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

20

40

60

80

100

120

140

160

180

(1) a b ab

Variables


TΔS

(∘C)


actual variables

0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm1

(∘C)







RDI+315

and RDIminus05


+63and RDI

+315increased






0

200

400

600

800

1000

1200

1400

1600

(1) a b ab

Variables


Tm2

(∘C)



0

20

40

60

80

100

(1) a b ab

Variables


TΔm

(∘C)





2to MnO




1198981) and end of







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







References


















2doped Fe

2O3com-




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



research article mathematical analysis of the effect of...

Documents