INTRODUCTION
Magnetic materials underwent a great development in the 20th century (Coey, 2001). Practical progress of magnetism largely depends on relevant advancement in coercivity control resulting from combined control of magneto crystalline an isotropy and microstructure (Coey, 2001).
Amorphous materials can be used as alternative materials for magnetic material applications. These are obtained by a rapid quenching of metal from liquid to solid state with a cooling speed of about 106 K sec^{–1}. They are characterized by long distance order absence of atomic arrangement and consequently they exhibit interesting mechanical, chemical and magnetic properties (Luborsky, 1983).
However, industrial applications related to these amorphous alloys have been restricted because of difficulties related to bulk material production. Thermal spray can resolve this problem by considering rapid solidification of powder particles under high feed rates. In this study, we have used highvelocity oxyfuel (HVOF) thermal spray technique. This process is adequate for spraying low and intermediate melting temperature materials (e.g., polymers and metals). It permits to obtain high particle velocities needed for amorphization compared to other spray techniques. In this study, FeNb alloy was chosen as feedstock material for its good aptitude to amorphization (Cherigui et al., 2003; 2004a, b). Literature is very poor on the use of such material as a feedstock for thermal spraying. It is well known that microstructure, especially grain size, determine the hysteresis loop of a ferromagnetic material. Accordingly, magnetic softening should occur when structural correlation length or grain size becomes smaller than the ferromagnetic exchange length (Alben et al., 1978). However, other factors can be associated to the magnetic softening when using thermal spray technology. These are mainly related to an isotropy of the layered structure, porosity level and phase content modification by evaporation.
In order to resolve the posed problem concerning the law connecting the phenomenon to the considered variables, an experimentation process is necessary. Naturally, during experimentation, various values will be given to the variables planned in order to know the influence of these variations on the phenomenon.
In the same time and in order to quantify the role of the porosity of coating on the magnetic properties of FeNb, a model of data processing is considered based on the statistical methods of experiments planning. Such a methodology is an adequate tool for the study of complex processes with parameter interdependencies. In this context, mathematics formulas are used to relate HVOF process parameters to both porosity and magnetic properties of FeNb coatings. The predicted magnetic properties are then correlated to the porosity level for each material, taking into account the interdependency revealed by the optimized network structure.
MATERIALS AND METHODS
Coating manufacturing: Thermal spraying of Fe_{50}Nb_{50} (+044) powders was carried out using a commercial Sulzer Metco CDS HVOF spray
system on copper substrates. Two substrate shapes were used: Tubes (Ø22x1
mm) and sheets (70x25x1 mm). A gas mixture of oxygen and methane was used to
produce the flame. The subsequent combustion of oxygen and methane produced
a nominal flame temperature of 2500 K with a hypersonic velocity of about 2000
m sec^{–1}. Experiments were carried out by varying two process parameters,
namely spray distance X_{1} (distance separating the gun tip from the
substrate plan) and methane fuel flow rate, X_{2}. In addition, the
cooling system was selected from either water or air system and thus represented
the third variable, X_{3}. The other parameters were kept to a reference
condition as shown in Table 1. After spraying, annealing treatment
at 800°C was carried out on samples in order to improve their magnetic properties.
Table 1: 
HVOF spray parameters 


Fig. 1: 
Morphology of FeNb coatings 
Coating characterization: After metallographic preparation, crosssections of FeNb coatings were analyzed using an optical microscope. The microstructure revealed porosity features presence (Fig. 1).
The percentage of this feature in the microstructure was calculated by image analysis using NIH image free software.
Six images were used to assess mean and standard deviation associated to porosity rate. Magnetic measurements were realized using a hysteresismeter Bull M2000 SIIS, which enabled to draw the hysteresis loop of the considered samples. It permitted also to calculate magnetic properties, namely coercivity Hc and saturation magnetization Ms.
SIMULATION MODEL
The statistical methods of experiments planning used to recognize the correlations between the parameters of a given problem and its responses. The correlations are recognized considering large but simple mathematical operations processed. This technique permits to analyse the processing experimental data; it is effective for the study of the process comprising much independent variable.
The experimentation takes place according to a plan of type 3^{1}.2^{2
} experiences represented on the Table 2 and 3,
while varying parameters judged influential.
Table 2: 
Varied parameters judged influential 

Table 3: 
Plan of type 3^{1}.2^{2} experiences taken 

() inferior value, (0) average value, (+) superior value 
Because of the diversity of parameter units, these are coded according to the
relation (1):
X_{i} 
: 
Input variables 
x_{i} 
: 
Real values of input variables 
x_{i0} 
: 
Basic values of input variables 
Δx_{i} 
: 
Interval of variation 
RESULTS AND DISCUSSION
Porosity: The confidence interval of the coefficients (Scheffler, 1986):
Δβ_{i} = S(β_{i}).t_{α,
fy} = 0.085 for α = 0.05 and f_{1} = N(m1) = 24,
with: t (0.05, 24) = 1.711 and S(β_{i})
= 0.05
Δβ_{i} 
: 
Significant value of regression coefficients 
β_{i} 
: 
Regression coefficients 
S{β_{i}} 
: 
Dispersion of regression coefficients 
t_{α, fy } 
: 
Student test 
α 
: 
Confidence degree (α = 0.05); 
f_{1} 
: 
Freedom degrees number 
Considering solely the meaningful regression coefficients, the model will have the shape:
After transformation (X_{1}^{*} = X_{1}^{2} – 2/3), the model becomes:
The tentative value of the Fischer criteria (Nalimov et al., 1965) is
F_{exp.} = 2.44 (F_{th.} = 2.62); the model is therefore inadequate.
P 
: 
Porosity 
F_{exp} 
: 
Experimental value of the Fischer test 
F_{th} 
: 
Theoretical value of the Fischer test 
If the spray distance are kept constant for average values (X_{1 }= 300 mm), the model becomes:
The effect of the fuel flow and the cooling type on the porosity is represented
in Fig. 2a.
For the variation interval of fuel flow [157.65, 145] l min^{–1}, the porosity increases nonlinearly in using the air cooling system and decreases in using the water cooling. For a fuel flow variation from 161.5 to 200, the porosity rate increases nonlinearly for the air cooling mode and decreases for the second.
This evolution is due to the reduction of the flame temperature with increasing fuel flow rate (Marple et al., 2001). This reduction favours the presence of the unmolten particles in the coating. In addition, for those particles that do melt their viscosity is increased such that they are unable to impact and adhere to the substrate. Generally, for low fuel flow rates, the particle velocity and temperature are associated with low spray efficiency. For high fuel flow rates, increase of particle velocity and evaporation could be related to the lowering of magnetic property values. These effects are associated with a high porosity level.
If the fuel flow is kept constant for average values (X_{2 }= 172.5 min^{–1}), the model takes the form:
The effect of spray distance and the cooling type on porosity is represented
in Fig. 2b.
For a spray distance variation from 200 to 250 mm, the porosity increases linearly and remains stable for a spray distance varying from 250 to 400 mm in using the water cooling system.
This dependence can be explained by considering particle temperature variation
with respect to spray distance. For short spray distances, particle residence
time is short in the flame. Consequently, they are less heated when they strike
the substrate and thus cannot flatten adequately. This leads to a high porosity
level in the coating (Sobolev and Giuilemany, 1994; Zhao and Lugscheider, 2004).
In contrast, for large spray distances, particles leave the flame and begin
to solidify before they impinge on the substrate. The porosity level increases
consequently for the same conditions.
Coercivity: The confidence interval of the coefficients (Scheffler, 1986) is equal to 0.24.
Considering the meaningful regression coefficients solely, the model will have the shape:
The tentative value of the Fischer criteria (Nalimov and Tschemova, 1965) is F_{exp.} = 2.20 (F_{th.} = 2.62); the model (6) is therefore inadequate.

Fig. 2a: 
Effect of the fuel flow and the cooling type of the porosity 

Fig. 2b: 
Effect of spray distance and cooling type on the porosity 
If the spray distance are kept constant for average values (X_{1 }= 300 mm), the model becomes:
The effect of the fuel flow and the cooling mode on the coercivity is given
in Fig. 3a.
From Fig. 3b, we can note that for a spray distance of 300
mm, the fuel flow influences on the coercivity.
When the fuel flow increases, the coercivity shows a clear variation. To explain such a correlation, one has to consider the effect of the coating porosity level as intermediate variable between the process parameters and the magnetic properties.

Fig. 3a: 
Effect of fuel flow and cooling type of the coercivity 

Fig. 3b: 
Effect of spray distance and cooling type on coercivity 
The linear increase of coercivity is explained by the fact that the porosity acts against the continuity of magnetic properties through the coating structure. These are considered as defects anchoring Bloch walls and involving consequently an increase of coercivity (Nacken and Heller, 1961). One can conclude that an improvement in coercivity can be related to low porosity content and this is obtained when spray distance is around 300 mm.
If the fuel flow is kept constant for average values (X_{2 }= 172.5 min^{–1}), the model takes the form:

Fig. 4a: 
Effect of fuel flow and cooling type on the saturation magnetisation 

Fig. 4b: 
Effect of spray distance and cooling type on saturation magnetisation 
The effect of spray distance and the cooling type on coercivity is represented
in Fig. 3b.
For a fuel flow equal 172.5 l min^{–1}, the coercivity decreases rapidly with the spray distance varying from 200 to 250 mm and slowly from 250 to 280 mm. It increases slowly with the spray distance varying from 310 to 400 mm.
Saturation magnetisation: The confidence interval of the coefficients (Scheffler, 1986) is equal to 0.102.
Considering the meaningful regression coefficients solely, the model will have the shape:
The tentative value of the Fischer criteria (Nalimov and Tschernova, 1965) is F_{exp.} = 2.51 (F_{th.} = 2.62); the model (9) is therefore inadequate.
If the spray distance are kept constant for average values (X_{1 }= 300 mm), the model becomes:
The effect of the fuel flow and the cooling type of the saturation magnetisation
is represented in Fig. 4a.
The Fig. 4a shows that for a spray distance of 300 mm, the
saturation magnetisation decreases linearly under the effect of the cooling
type. In this case the fuel flow does not have any influence.
If the fuel flow is kept constant for average values (X_{2 }= 172.5 min^{–1}), the model takes the form:
The effect of spray distance and the cooling type on saturation magnetisation
is represented in Fig. 4b.
For a constant value of the fuel flow, the saturation magnetization increases slowly with the spray distance increase. It shows a feeble increase in using the air cooling compared the using of water cooling system.
Generally, in magnetism studies, the decrease of this parameter is related to coercivity increase (Bozorth and William, 1945).
CONCLUSIONS
The research studied the effect of HVOF thermal spraying parameters on the porosity and magnetic properties of coatings using a model of data processing based on the statistical methods of experiments planning:
• 
The preliminary results showed that FeNb coatings have nonmagnetic
structure. After crystallization by heat treatment at a temperature of about
800°C, the magnetic properties of the FeNb were weakly improved. 
• 
Predicted results show that spray distance and fuel flow modified
the deposit porosity. A decrease resulted in improvement of coercivity and
saturation magnetization. 