Furnaces: Improvement of Low Cement Castables by Non-WettingAdditives

Saied AFSHAR and Claude ALLAIRE

CIREP-CRNFDepartment of Engineering Physics & Materials Engineering,

Ecole Polytechnique of Montreal (CRIQ campus),8475 Christophe Colomb Street,

Montreal Quebec H2M 2N9Canada

Abstract:

Aluminosilicate castables are widely used in the aluminum transformation furnaces.

Commercial additives such as BaSO4, CaF2 and AlF 3 are generally added in such castables to

prevent the chemical reactions occurring between molten aluminum and the furnace refractory

lining. This work presents and analyses the effect of various amounts of the above additives

as well as the influence of pre-firing temperatures on the corrosion behavior of an

aluminosilicate low cement castable matrix in contact with liquid Al – 5% Mg alloy. The

results of the present study may help choose the type and the appropriate quantity of the non-

wetting agents according to the operating temperature of the aluminum furnaces.

Introduction:

Some specific additives, so called “non-wetting” agents, are generally employed by refractory

producers in order to enhance the corrosion resistance of aluminosilicate castables. Among

these additives, BaSO 4, CaF 2 and AlF 3 are the most common ones. Although, more than a

decade, the non-wetting agents are used in the aluminosilicate refractories, their beneficial

effect is not yet totally approved.

Recently, a particular attempt has been made to characterize the proper role of barium sulfate

in the protection mechanism of refractories [1-3]. It has been pointed out that barite, by

reacting with alumina and silica among the fine particles of the refractories, forms hexa-

celsian and or celsian in the firing temperature ranging between 900 to 1200 oC [1,2,4]. Such

transformations reduce the amount of free silica within the matrix and should consequently

improve the corrosion resistance of the refractory. However, the protective effect of barium

sulfate appeared to be significantly reduced for the cases that firing temperatures exceeded

1050 oC [1,2].

Compared to barium sulfate, the effect of AlF 3 and CaF 2 has been less studied. The

experiences carried out on the aluminosilicate ceramics, having a mullite-like composition,

have not been conclusive to show the efficiency of the fluoride additives [3,5]. However,

based on the mineralogical analysis results reported, it has been postulated that the fluoride

additives act as mineralizers, favoring the mullite formation during high temperature firing of

aluminosilicate materials [6].

The purpose of this study was to analyze and to compare the efficiency of the three mentioned

commercial additives used to protect a low cement castable against aluminum attack. In order

to establish their appropriate quantity, various amounts of additives as well as some

combinations of them have been used. The effect of firing temperature, which limits the

performance of such additives, has been also studied.

Experimental procedures:

Materials: An aluminosilicate low cement castable (see Table I for chemical composition),

which did not contain originally any non-wetting additive, was used in this study. Since the

beneficial effect of non-wetting agents concerns mainly the fine particles of refractories

[1,2,7,8], the aggregates of the above castable, having a size greater than 500 µm, were

removed from the refractory using a sieve. The remaining fine powders, referred here to as

“refractory matrix”, were then used as the basic testing material for sample preparation. The

weight ratio of refractory matrix to the castable was about 50%. The chemical composition of

the refractory matrix is also given in Table I.

Table I: Chemical composition of materials in weight percent

Sample Al2O3 SiO2 Fe2O3 TiO2 CaO Alkalis

Low cement castable 67.0 29.5 0.8 1.4 1.1 0.2Refractory matrix 73.1 21.4 0.16 0.67 2.41 0.2

Sample preparation: The refractory powders (matrix) were dry-mixed, based on the weight

fractions given in Table II, with three commercial non-wetting additives (powders) to prepare

five series of samples: A (aluminum fluoride), B (barium sulfate), C (calcium fluoride), AB

(aluminum fluoride + barium sulfate) and BC (barium sulfate + calcium fluoride). Various

amounts of water were added to the samples, according to the composition of the mixes. For

the samples containing both sulfate and fluoride additives, the portions of water, required to

provide a relative good fluidity of the mixes, were higher than those containing only one kind

of additive. The casting information is summarized in Table II. After five to ten minutes of

mixing with water, the mixes were cast in the cylindrical molds ( φ=28mm, L=20mm), on a

vibrating table for a few minutes. All samples were dried for at least 24 hours in air, before

removing from the molds and cured for 24 hours at 110 oC in an oven. Since the corrosion

resistance of aluminosilicate refractories are generally changed for the cases that the firing

temperature is higher than 1000 oC [1,2,9,10], four firing temperatures around this critical

value were selected: 900, 1000, 1100 and 1200 oC. Samples were then fired at these

temperatures for five hours, with a heating rate of 2 oC per minute.

Table II: Samples prepared from refractory matrix and non-wetting additives

Sample AlF3(wt%)

BaSO4(wt%)

CaF2(wt%)

Water(wt%)

Firingtemperatures (oC)

Withoutadditive

0 0 0 10* 900

1 10 9003.5 10 900 and 1100Series A7

0 010 900, 1000 and

11001 10 900

3.5 10 900 and 1100Series B 07

010 900, 1000 and

11001 10 900

3.5 10 900 and 1100Series C 0 07 10 900, 1000 and

1100Series AB 7 7 0 14 900, 1100 and

1200Series BC 0 7 7 15 900, 1100 and

1200* This value was twice higher than that required for the castable.

Corrosion immersion test: The corrosion resistance of the samples to aluminum attack was

evaluated via an immersion test procedure. Based on the CIREP corrosion immersion test

(originally developed by Alcan International Ltd. [11]), 2 identical samples were charged with

2 kg of aluminum in a crucible and heated to 850 oC. To obtain an Al-5 wt.% Mg, 100 g of

Mg were added to molten aluminum in the temperature range of 700 to 800 oC. The corrosion

tests were performed for a four-day period. To maintain the composition of alloy, 40 g of

magnesium were daily added to the molten metal.

Upon the completion of the tests, samples were taken out of the liquid aluminum, cooled to

room temperature, and cut across a central plane parallel to the cylindrical axis, in order to

observe the extent of the corrosion and the penetration depth of aluminum.

Results and discussion :

General aspect of corrosion: Corrosion aspect of aluminosilicate refractories is often

recognizable, by naked eyes, from its black appearance. Through microscopic observations,

the “corroded zones” of refractory by molten aluminum can be described as a composite

material constituted of fine grains of corundum surrounded by an interconnected metallic

network (Figure 1). In such a case, most of the time an electric resistance measurement may

rapidly reveal the presence of aluminum within the refractory, without the need of

microscopic examination.

Figure 1: Aspect of “corroded zone” in an aluminosilicate material.

Usually, in front of the “corroded zones”, a dark layer is also visible in the refractory samples.

Within this region, there is neither significant change in the microstructure of the refractory

nor trace of metal penetration. Only the color of the original texture of the refractory appears

darker in this layer (Figure 2). The term “discolored layer” is then employed here to

distinguish this layer from the corroded zones. However, even in the absence of corrosion

(metal penetration) in a sample, the presence of discolored layer should be considered as a

sign of weakness of the refractory against aluminum attack because discoloration precedes

generally metal infiltration.

The thickness of the discolored layer may vary from a few microns to more than several

centimeters, depending on open porosity content of the samples. In the case of the materials

showing a poor corrosion resistance to aluminum attack, it has been frequently observed that

the wide discolored layers appear when samples are highly porous [5]. Thus, the cause of

discoloration can be attributed to the metallic vapors, for instance Mg, coming from the metal

bath and diffusing through porosity network. The metallic vapors should then superficially

react with some reducible refractory compounds leading to the color change of the refractory.

Corrodedarea

500××

Al

Al2O3

However, such discoloration may be disappeared after a heating at about 1000 oC, in air, for a

few hours.

Figure 2: Discolored layer observed in front of corrosion in thematrix of an aluminosilicate castable.

Corrosion resistance of the castable and its matrix without any additive: Without adding non-

wetting agent, the aluminosilicate low cement castable showed a very poor corrosion

resistance to aluminum attack. Samples of 1 ×1×2 inches made of this material, and pre-fired

at 900 oC, have been totally corroded and impregnated by the aluminum alloy after the

corrosion immersion test (Figure 3-a). By contrast, samples made from the fine particles of

this refractory exhibited a better resistance to aluminum attack. The corroded layer was

limited to 2 or 3 mm thick at the metal/refractory interface (Figure 3-b). Considering the

chemical composition of the castable and its matrix (Table I), it can be suggested that the

lower silica content in the fine particles may have played an important role in the corrosion

resistance of the samples.

Corroded zoneDiscolored layer

Unaffectedrefractory

200××

Aggregate

Figure 3: Corrosion aspect of the castable (a) and its “matrix” (b), without non-wetting agent.

Effect of aluminum fluoride – Series A: The central cross section of the samples containing

various amounts of aluminum fluoride, and pre-fired at different temperatures, are presented

in Figure 4 after the immersion test. Compared to the sample without additive (Figure 3-b),

the addition of 1 wt% of aluminum fluoride (Figure 4-a) apparently had no beneficial effect.

By contrast, the increase of AlF 3 content from 1 to 7 wt% has obviously improved the

corrosion resistance of the refractory matrix samples in the firing temperatures ranged from

900 to1100 oC.

Figure 4: Series A samples - % in AlF 3 content (firing temperature).

Best results are obtained for the samples containing 7 wt% of fluoride. Even for the firing

temperature higher than 1000 oC, at which a significant reduction in corrosion resistance of

aluminosilicate castables are generally observed [1,2,9,10], only some discolored zones of

about 1 mm thick were visible at the upper corner of the samples (Figure 4-f). However, it

should be noted that an empty brittle dome has been observed on the top of these samples,

after firing at 1100 oC (Figure 5). The X-ray analysis revealed that the dome was mainly

a b

a : 1% (900oC) b : 3.5% (900oC) c : 7% (900oC)

d : 7% (1000oC) e : 3.5% (1100oC) f : 7% (1100oC)

composed of cristobalite. This may imply that a segregation of fine silica particles to the

upper surface has been occurred during sample casting. Then, during firing, the formation of a

superficial thin glassy layer followed by some gas-forming reactions in the volume might

have led to dome formation. The dome was broken during handling the samples, and then

removed before the corrosion test. In fact, the presence of free silica phases is not desirable in

terms of corrosion resistance. The cause of discoloration observed at the upper corners of the

samples, pre-fired at 1100 oC (Figure 4-f), may be related to some remaining part of the dome.

Figure 5: Empty dome observe d on the top of the samples, containing7 wt% AlF 3, pre-fired at 1100 oC.

Based on the thermodynamic calculations and experiments [12-14], it is expected that AlF 3

converts a mixture of alumina and silica to mullite via fluorotopaz (Al 2F2SiO4) according to

the following reactions:

2 AlF 3 + 2 SiO 2 = Al2F2SiO4 + SiF 4 (PSiF4 = 1 atm at 600 oC) (1)

2 Al2O3 + SiO 2 + SiF 4 = 2 Al2F2SiO4 (2)

2 Al2F2SiO4 = 2Al2O3⋅ SiO 2 + SiF 4 (PSiF4 = 1 atm at 1100 oC) (3)

In the previous works [6], it has also been concluded that the addition of aluminum fluoride to

aluminosilicate-based ceramics favors the mullite formation during sintering. In accordance

with equation (2), the phase analysis carried out on the samples of Series A revealed the

presence of fluorotopaz in the samples containing 7 wt% AlF 3, pre-fired at 900 oC (Figure 6).

The absence of fluorotopaz in the same samples after firing at 1100 oC, may indicate that this

phase has been totally decomposed accordingly to equation (3). On the other hand, the

presence of the dome observed on these samples (Figure 5) should be attributed to some SiF 4

coming from decomposition of fluorotopaz (equation (3)).

Dome

Figure 6: X-ray diffraction spectrums of the Series A samples for various amount (%) of AlF 3

and two different firing temperatures. C: corundum, M: mullite, S: silica, A: anorthite, CF:

calcium fluoride, FT: fluorotopaz.

Figure 7: Variation of peak intensities of some crystalline pha ses, detected

by X-ray diffraction, according to AlF 3 content of samples.

In general, the decrease in corrosion resistance of castables, after firing at more than 1000 oC,

may be attributed to the decomposition of some aluminosilicate compounds, for instance

meta-kaoline, releasing free silica [9,10]. The mullite formation, to the detriment of silica, at

1100 oC (see above equations) should counterbalance the silica-forming reactions and

consequently preserves the corrosion resistance of samples. Although, some increase in peak

intensity of mullite were observed with raising firing temperature from 900 to 1100 oC,

unfortunately, the present data are not conclusive in terms of mullite formation versus

aluminum fluoride content (Figure 7). In fact, due to the heterogeneous nature of castables

0

5

10

15

20

25

AlF3 content - Firing temperature

Rel

ativ

e p

eak

inte

nsi

ty in

%

MulliteAnorthiteCaF2Al2SiO4F2

0%-900oC 1%-900 oC 3.5%-900oC 7%-900oC 7%-1100oC

CC

CC

CC

MM M MS

A

CF

FT FT

0%

1%

3.5%

7%

7%

900oC

900oC

900oC

1100oC

900oC

and the presence of numerous aluminum based compounds in the starting material, it was not

possible to follow precisely all the phase transformation resulting from AlF 3 addition.

The other major differences, revealed by X-ray analysis, between the series A samples and the

basic material were the presence of some CaF 2 and anorthite in the fired samples containing

AlF3. As already postulated [6], aluminum fluoride should partly react with calcium oxide of

the refractory to form calcium fluoride, according to thermodynamic equilibrium calculations.

Theoretically [15], even at room temperature, the following reaction may take place:

2 AlF 3 + CaO = 3 CaF2 + Al2O3 ∆Go (25 oC) = - 430 kJ

The effect of CaF2 on the corrosion resistance of samples is discussed in a next section.

Effect of barium sulfate – Series B : Figure 8 shows cross sections of Series B samples after

the corrosion test. Similar to Series A, any beneficial effect was observed for 1 wt% additive

(Figure 8-a). The improvement in corrosion resistance of samples was realized, especially for

the firing temperatures ≤ 1000 oC, when 7 wt% barium sulfate was employed (Figures 8-c and

d). In case of 3.5 wt% BaSO 4, the overall aspect of sample shows a better resistance to metal

attack compared to the corresponding sample from Series A (Figures 8-b and 4-b). By

contrast, as it was expected [1-2], the performance of barite decreased after firing at 1100 oC.

The large discolored stripes of 3 mm thick were visible at the periphery of samples (Figures

8-e and f). Similar to its corresponding sample in Series A, some corroded zones of 1 mm

thick were also detected in the sample containing 3.5 wt% barite, pre-fired at 1100 oC

(Figures 8-e and 4-e).

Figure 8: Series B samples - % in BaSO 4 content (firing temperature).

a : 1% (900oC) b : 3.5% (900oC) c : 7% (900oC)

d : 7% (1000oC) e : 3.5% (1100oC) f : 7% (1100oC)

The role of barium sulfate in protection mechanism of aluminosilicate castables has been

already studied and attributed to some barium aluminum silicates forming during firing [1,2].

In the present work, the X-ray analysis performed on the Series B samples confirmed the

presence of BaAl2Si2O8, whose peak intensity increased with barite content (Figure 9 and 10).

On the other hand, an increase in silica content of samples, after firing at 1100 oC, was also

observed, which may explain the lower corrosion resistance of those samples.

Figure 9: X-ray diffraction spectrums of the Series B samples for various amount (%) of

BaSO4 and two different firing temperatures. C: corundum, M: mullite, S: silica, B: barium

aluminum silicates, A: anorthite.

Figure 10: Variation of peak intensities of some crystalline phases, detected

by X-ray diffraction, according to BaSO 4 content of samples.

0

5

10

15

20

25

BaSO 4 content - Firing temperature

Rel

ativ

e in

tens

ity p

eak

in %

Barium aluminosilicateSiO2Mullite

0%-900o C 1%-900 oC 3.5%-900oC 7%-900 oC 7%-1100oC

S

CC

CC

CC

M M M

B7%

7%

3.5%

1%

0%

1100oC

900oC

900oC

900oC

900oC

M

BAB

Effect of calcium fluoride – Series C: The overall aspects of the tested samples from Series C

are shown in Figure11. For the firing temperature below 1000 oC (Figures 11-a, b and c), the

efficiency of CaF2 seems to be lower in the protection of the castable samples, in comparison

with AlF 3 and BaSO 4. Even, in some cases, the corrosion resistance of the basic material

appeared to be considerably decreased. The use of 3.5 wt% calcium fluoride has visibly

provoked the formation of large cracks which facilitated the metal penetration and contributed

to the sever corrosion observed in the samples (Figures 11-b and e). By contrast, at 7 wt%

content of the additive, an improvement in corrosion resistance of samples was observed,

similar to the other additives. Curiously, for this amount of CaF 2, the resistance to aluminum

attack appears to be gradually increased with firing temperature raising from 900 to 1100 oC

(Figures 11-c, d and f). Among all the pre-fired samples at 1100 oC, the best corrosion result

was obtained for the samples containing 7 wt% calcium fluoride (see Figures 4-f, 8-f and 11-

f).

Figure 11: Series C samples - % in CaF2 content (firing temperature).

The role of calcium fluoride, as mineralizer, in aluminosilicate based materials has been

studied in the previous works [6]. Compared to AlF 3, it was concluded that CaF 2 is less

effective in terms of mullitization. While, increasing calcium fluoride to 7 wt% considerably

increased the amount of anorthite. The phases analysis performed on Series C samples also

confirmed a significant effect of CaF 2 in anorthite formation. The presence of both higher

calcium fluoride content and firing temperature obviously favored the formation of a larger

quantity of anorthite (Figures 12 and 13). On the other hand, the presence of the non

negligible amounts of anorthite observed in Series A samples, especially those pre-fired at

900 oC and containing 7 wt% aluminum fluoride, may be attributed to their content in calcium

a : 1% (900 oC) b : 3.5% (900 oC) c : 7% (900 oC)

d : 7% (1000 oC) e : 3.5% (1100 oC) f : 7% (1100 oC)

C

fluoride (Figures 6 and 7). The good performance of samples containing 7 wt% CaF 2, after

firing at 1100 oC, suggests that anorthite may play a beneficial role in the corrosion

mechanism.

Figure 12: X-ray diffraction spectrums of the Series C samples for various amount (%) of

CaF2 and two different firing temperatures. C: corundum, M: mullite, S: silica, A: anorthite,

CF: calcium fluoride.

Figure 13: Variation of peak intensities of some crystalline phases, detected

by X-ray diffraction, according to CaF2 content of samples.

However, based on the present analysis (Figure 13), no beneficial effect of calcium fluoride

on mullitization is observed. Even, similar to the cases with BaSO 4 (Figure 10), it seems that

0

5

10

15

20

25

CaF2 content - Firing temperature

Rel

ativ

e pe

ak in

tens

ity in

%

AnorthiteCaF2Mullite

0%-900oC 1%-900oC 3.5%-900oC 7%-900oC 7%-1100oC

S A

CF

C C

CC

MM M

M

A A

0%

1%

3.5%

7%

7%

900oC

900oC

900oC

900oC

1100oC

CC

the amount of mullite decreased with increasing CaF 2. The X-ray analysis also indicated that

some unreacted calcium fluoride may remain in the samples even after firing at 1100 oC.

Effect of additive mixes – Series AB and BC: The above results showed that the effect of non-

wetting-additives may vary with firing temperature. For instance, barium sulfate is effective

for firing temperatures up to 1000 oC, while the performance of CaF 2 appears after firing at

higher temperatures. In order to obtain a good corrosion resistance in a large firing

temperature range, the mixes of the fluoride additives with barium sulfate were used. The

results of the corrosion tests are presented in Figure 14.

Figure 14: Series AB (7 wt% AlF 3 + 7 wt% BaSO4) and BC (7 wt%BaSO4 + 7 wt% CaF2) samples - (firing temperature).

Except in the case of Series AB samples, pre-fired at 1100 oC (Figure 14-b), which their

corrosion aspect is comparable with that of Series A (Figure 4-f), the combination of the

additives apparently reduced the proper effect of individual non-wetting agent. This should be

partly due to the higher amount of water required to cast the samples of these series (see Table

II), which obviously resulted in higher porosity (Table III).

Table III: Apparent porosity measured in the samples after firing at 1100 oC

Samples Withoutadditive

SeriesA

SeriesB

SeriesC

SeriesAB

SeriesBC

ApparentPorosity 27.5 % 27 % 26.5 % 27 % 32 % 32.5 %

a : AB (900 oC) b : AB (1100 oC) c : AB (1200 oC)

d : BC (900 oC) e : BC (1100 oC) f : BC (1200 oC)

Conclusion:

The results of the study on the effects of the non-wetting agents indicated that:

- At 7 wt% content, the additives improved the corrosion resistance of the fine portion of

the aluminiosilicate castable.

- Firing temperature influenced differently the protective effect of the additives: with AlF 3

and BaSO 4, increasing firing temperature reduced the corrosion resistance, while with

CaF2, an improvement was observed.

- The beneficial effect of BaSO 4 was attributed to the formation of some barium

aluminosilcate compounds, whose quantity appeared to be proportional to barite content.

- It seems that the improvement induced by the addition of AlF 3 is due to its action in

converting silica to mullite via fluorotopaz formation.

- Adding CaF 2 favored the anorthite formation. Parallel to corrosion resistance

improvement, the amount of anorthite appeared to be increased with firing temperature.

- In terms of corrosion resistance improvement, no practical interest was found when the

mixes of the additives were used.

From the present work, it can be postulated that the efficiency of non-wetting additives, to

protect the castables, is in their potential role in converting silica to some aluminosilcates

based crystalline phases that are more resistant to aluminum attack.

References:

1 - Afshar, S. and Allaire, C., “The Corrosion of Refractories by Molten Aluminum”, JOM,pp. 23-27, May 1996.

2 – Afshar, S., Allaire, C., Quesnel, S. and Allahverdi, M., “Corrosion des RéfractairesAluminosiliceux au Contact de l’Aluminium Liquide”, Centre Québecois de Recherche et deDéveloppement de l’Aluminium, le Journal Al-13, Vol. 2, No. 2, pp. 21-36, 1996.

3 – Allahverdi, M., Afshar, S. and Allaire, C., “Corrosion Resistance of AluminosilicateCeramics to Molten Al-5% Mg Alloy”, in Proceedings of International Symposium onAdvances in Refractories for Metallurgical Industries II, 35 th Annual Meeting of Metallurgistsof CIM, Montreal (Canada), pp. 295-303, 1996.

4 – Schmutzler, H.J. and Sandhage, K.H., “Transformation of Ba-Al-Si Precursors to Celsianby High-Temperature Oxidation and Annealing”, Met. Mater. Trans. B, 26B, pp. 135-148,1995.

5 - Allahverdi, M., Afshar, S. and Allaire, C., “Additives and the Corrosion Resistance ofAluminosilicate Refractories in Molten Al-5% Mg”, JOM, pp. 30-34, February 1998.

6 - Allahverdi, M., Allaire, C., and Afshar, S., “Effect of BaSO 4, CaF 2 and AlF 3 as well asNa2O on the Aluminosilicates Having a Mullite-like Composition”, Canadian Ceram. Soc.,Vol. 66, No. 3, pp. 223-230, August 1997.

7 – Richter, T., Vezza, T., Allaire, C. and Afshar, S., “Castable with Improved CorrosionResistance Against Aluminum”, Eurogress Aachen (Germany), pp. 86-90, 1998.

8 - Afshar, S. and Allaire, C., “The Corrosion of Refractory Aggregates by MoltenAluminum”, JOM, pp. 43-46, May 2000.

9 – McDonald, H.A., Dore, J.E. and Peterson, W.S., “How Molten Aluminum Affects PlasticRefractories”, J. Metals, pp. 35-37, 1958.

10 – Isselbächer, E. et al., “ Comportement des Matériaux Réfractaires vis-à-vis des Bainsd’Aluminium du Point de Vue de la Formation d’Inclusions Dures”, Aluminium (6), pp. 375-379, June 1971.

11 – Allaire, C., “Refractories for the Lining of Holding and Melting Furnaces”, Advanced inProduction and Fabrication of Light Metals and Metal Matrix Composites, ed. M.M.Avedesian et al. (Montreal) Canada: CIM, pp. 163-174, 1992.

12 – Moyer, J.R. and Rudolf P.R., “ Stoichiometry of Fluorotopaz and Mullite Made fromFluorotopaz”, J. Am. Ceram. Soc., 77 (4), pp. 1087-1089, 1994.

13 – Moyer, J.R., “Phase Diagram for the SiF 4 Join in the System SiO 2-Al2O3-SiF4”, J. Am.Ceram. Soc., 79 (11), pp. 2965-2968, 1996.

14 - Moyer, J.R., “Phase Diagram for Mullite-SiF 4”, J. Am. Ceram. Soc., 78 (12), pp. 3253-3258, 1995.

15 – Bale, C.w., Pelton, A.D. and Thompson, W.T., “F*A*C*T* 2.1 – User Manual”, EcolePolytechnique of Montreal / Royal Military College, Canada, ( http://www.crct.polymtl.ca),July 1996.