Phase Composition Using a Variable Magnetic Field

Abstract

In the present work the application of the variable magnetic field to investigate the composition of phases present in the alloys is presented. In order to make a study in the variable magnetic field a prototype apparatus was performed. The magnetic leakage of the alloy (k_s) was measured in the reversible range of magnetic field.

Experimental tests were conducted on samples of Fe–Cu alloys have contained the different volume fraction of phases components. Comparison of volume fraction of the solid solution α_Fe determined by weight and magnetic methods was performed. The linear dependence between the magnetic coupling and the volume fraction of phases components was observed. This observation can be used to estimate the quantitative phase composition in a biphase alloys. It has been shown that in the reversible range of the magnetic field, the magnetic leakage of the alloy is equal to the sum of products of volumetric proportions of individual phase components and their magnetic leakage.

In the present work a new method for quantitatively assessing the phase composition using a variable magnetic field is presented which is universal for two-phase alloys if the two phases have different magnetic leakage. This can be particularly useful for assessing the proportion of austenite and retained austenite in heat-treated alloys of iron and carbon.

1. Introduction

The qualitative and quantitative assessment of phase composition is of major importance in specifying and optimising mechanical, physical and usage characteristics of metals and their alloys. This assessment is performed both during research work and in industrial production conditions.

Although a series of methods for determining phase composition exists, none can be considered to be fully universal. In many cases, the results of an examination carried out by one method must be confirmed using other methods. The methods most frequently used to determine phase composition are as follows: the metallographic one, X-ray phase analysis and the chemical isolate (weight) method. However, other methods are also used, namely: the magnetic, dilatometric, ultrasound, calorimetric, neutron diffraction, Mössbauer spectroscopy and electrical resistance methods.^1,2,3)

The traditional magnetic method of quantitatively determining phase composition makes use of a constant magnetic field. This method is based on the linear dependence of the magnetisation or the magnetic induction of examined alloys (determined in magnetic saturation conditions) on the volumetric proportions of particular phase components.^1,2)

In metallographic examinations, a variable magnetic field is used mainly to assess the kinetics of phase transformations, identifying the temperature at which they occur, and also for flaw detection.^4,5) Publications on structural examinations performed using a variable magnetic field describe a qualitative and quantitative influence of the phase composition on the results obtained, but a relationship between these results and the volumetric proportion of phase components is not unambiguously identified.^6,7) The authors⁸⁾ believe that for technical alloys, because of the multitude of variable, interdependent factors, no detailed data on the type of this dependence can be presented.

The purpose of this study is to identify the relationship between the magnetic leakage of the alloy k_s and the volumetric proportion of the phase component with ferromagnetic properties in this alloy. This research was carried out on model samples produced of an alloy of iron and copper. The results of examinations of two-phase alloys containing phase components of different magnetic characteristics carried out in a variable magnetic field can be used for the quantitative assessment of phase composition.

2. Research Methods

Experimental examinations were conducted on model samples made of iron, copper, and alloys of these metals. Iron and copper alloys are two-phase alloys. The components of these alloys are solid solutions α_Fe and α_Cu, in which the solubility of copper and iron, respectively, is close to zero at the ambient temperature.^9,10) These solutions differ in their magnetic properties: α_Fe is ferromagnetic while α_Cu is diamagnetic. The structural components of iron and copper alloys may, depending on the composition, consist of solid solutions of α_Cu and α_Fe as well as the eutectoid mixture α_Cu + α_Fe.

In order to obtain samples with various proportions of phase components, melts were produced in a Balzers VSG-02 vacuum furnace. The charge material comprised technically pure iron (9.97% Fe, 0.1% Mn, 0.05% S, 0.05% P and others) and electrolytic copper (99.9% Cu). After the charge materials were melted and superheated to 1600°C, the alloys were cast into a metal mould previously heated to 500°C. Trial castings in the shape of ϕ 30 × 100 mm cylinders were subjected to stress-relief annealing at the temperature of 650°C for two hours and slowly cooled down with the furnace. After the heat treatment, samples having the shape of ϕ 20 × 20 mm cylinders were taken from the castings for metallographic and magnetic examinations. The symbols of the samples and the weight proportions of the charge prepared for melting are presented in Table 1.

Table 1. Designation and weight fractions of charge.

Sample No.		I	II	III	IV	V	VI
Charge materials, [g]	iron	590.0	532.0	441.0	295.0	149.0	0
	copper	0	66.0	169.0	336.0	503.0	670.0

When ferromagnetic alloys are exposed to an external magnetic field, they are magnetized. The change of the magnetization of the alloy J_S relative to the intensity of the magnetic field H is called the initial magnetization curve. This relationship is a complex function along which five characteristic ranges are distinguished. Examinations by the magnetic method generally applied to quantitatively assess phase composition are carried out with a constant magnetic field in the last (fifth) range of the initial magnetization curve, in which the magnetic moments of all domains are lined up with the direction of the external magnetic field while the alloy magnetization J_S achieves the maximum value. This study makes use of the first range on the initial magnetization curve, which is also referred to as the range of weak magnetic fields in the literature. Ferromagnetics are magnetized in this range by the reversible movement of domain walls, and the process of changing the direction of magnetization of an alloy placed in a variable magnetic field is hysteresis-free in character.⁵⁾

The magnetic leakage of the alloy k_s was determined using a prototype measuring apparatus using the relationship (1). When determining magnetic leakage k_s, the following boundary conditions were assumed: k_s = 0 – no leakage, k_s = 1 – total magnetic leakage.   

$$k_s=1-a\cdot \frac{U_o}{\cdot U_n}$$(1)

where:

U_n– voltage in the transmitting coil [mV];

U_o– voltage in the receiving coil [mV];

a– apparatus constant;

k_s– magnetic leakage.

The measuring apparatus was supplied from a power supply grid with the frequency of f = 50 Hz via an adjustable autotransformer which allowed the voltage fed to the transmitting coil U_n to be changed. The magnetic leakage k_s of samples I–VI was determined in the first, reversible range. The tested samples, shaped like ϕ 20 × 20 mm cylinders, play the role of a magnetic core in the presented diagram (Fig. 1) of the measuring system.

Fig. 1.

Diagram of the experimental; At – autotransformer, V_n i V_o – electromagnetic voltmeters, A – electromagnetic ammeter, R – tested material.

The volumetric proportions of solid solutions α_Fe and α_Cu for samples numbered II–V were determined based on the weight proportions of charge materials, taking into account the micro-porosity measured using the quantitative metallography method. When calculating the volumetric proportion of phase components, it was assumed that in the solid state, iron is completely insoluble in the solution α_Cu and so is copper in the solution α_Fe, based on relationship (2):   

$$V_{\alpha Fe}=\frac{m_{Fe}\cdot {\gamma }_{fe}{\hspace{0.17em}}^{-1}}{(m_{Fe}\cdot {\gamma }_{Fe}{\hspace{0.17em}}^{-1}+m_{Cu}\cdot {\gamma }_{Cu}{\hspace{0.17em}}^{-1})\cdot (1+V_p)}\cdot 100\%$$(2)

where:

V_αFe– the volumetric proportion of the phase component α_Fe in %;

m_Fe– the mass of iron used for the melt [g];

γ_Fe = 7.87– the specific density of iron [g/cm³];

m_Cu– the mass of copper used for the melt [g];

γ_Ce = 8.89– the specific density of copper [g/cm³];

V_p– the volumetric proportion of micro-pores, 0–1.

3. Research Results and Discussion

Metallographic tests were carried out using a Leica optical metallographic microscope bundled with the LeicaQWin application for quantitative image analysis. Images of the microstructure of samples marked IV and V are shown in Fig. 2. The solid solution α_Fe forms a component of the microstructure of sample number I, produced of technically pure iron. The microstructure of samples numbered II–V is made up of the eutectoid α_Fe + α_Cu, (dark areas in the presented microstructure images) and the solid solution α_Cu, (light areas). The only phase component of the sample produced of electrolytic copper, number VI, is the solid solution α_Cu. The volumetric proportions of solid solutions α_Fe and α_Cu for samples number II–V were determined based on the weight proportion of charge materials, taking into account the micropores measured using the quantitative metallography method. Metallographic tests demonstrated that the volumetric proportion of micropores in the trial castings produced was comparable and equal to V_p = 1.5 ± 0.5 %.

Fig. 2.

Selected images of the microstructure of samples marked with symbols; a) – IV and b) – V, Etched with 1% of HNO₃ in ethanol.

Table 2 compiles volumetric proportions of components with ferromagnetic properties V_αFe (solid solution α_Fe) and non-ferromagnetic ones V_n (solid solution α_Cu together with micropores) as well as the magnetic leakage values k_s of the studied samples. Figure 3 shows the change of the magnetic leakage k_s as a function of the volumetric proportion of the phase component with ferromagnetic properties V_αFe for samples numbered I–VI (Table 2).

Table 2. Phase volume fractions of components V_αFe and V_n and values of magnetic leakage k_s, for samples I ÷ VI.

Sample No.	VαFe [%]	Vn [%]	ks
I	100.0	0.0	0.197
II	88.8	11.2	0.267
III	73.6	26.4	0.348
IV	49.2	50.8	0.494
V	24.7	75.3	0.638
VI	0.0	100.0	0.777

Fig. 3.

Magnetic leakage k_s for samples of iron and cooper alloys I ÷ VI as a function of the volume fraction of the phase α_Fe.

The linear dependency of the magnetic leakage k_s on the volumetric proportion of the phase component α_Fe (Fig. 3, correlation coefficient close to 1) supports the conclusion that this parameter can be used to quantitatively assess the phase composition of the examined alloy.

Based on the measured values of magnetic leakage k_s, the volumetric proportion of the phase with ferromagnetic properties V_αFe can be calculated from Eq. (3):   

$$V_{\alpha Fe}=\frac{k_{Cu}-k_s^{}}{k_{Cu}-k_{Fe}}\cdot 100\%$$(3)

where:

k_s– magnetic leakage for a sample made of an iron and copper alloy;

k_Cu– magnetic leakage for a sample containing 100% of the α_Cu phase;

k_Fe– magnetic leakage for a sample containing 100% of the α_Fe phase;

V_αFe– volumetric proportion of the α_Fe phase [%].

Table 3 and Fig. 4 present the volumetric proportion of the solid solution α_Fe for samples II–V determined by the weight method (based on the weight proportions of charge materials) and by the magnetic method with a variable field. The k_Fe and k_Cu symbols found in Eq. (3) represent the values of magnetic leakage determined for samples number I and VI.

Table 3. Volumetric fraction of the solid solution α_Fe determined by the weight method and by the magnetic method with a variable magnetic field.

Sample No.	$V_{{\alpha }_{Fe}}$ , [%] weight method	$V_{{\alpha }_{Fe}}$ , [%] magnetic method
II	88.8	87.9
III	73.6	74.0
IV	49.2	48.8
V	24.7	24.0

Fig. 4.

Comparison of volume fraction of the solid solution α_Fe determined by weight and magnetic methods.

Both the correlation coefficient R² = 0.9998 (Fig. 3), and the high level of consistency in assessing the volumetric share (the absolute error does not exceed 0.9%, Table 3), allow Eq. (3) to be written in the form of Eqs. (4) and (5):   

$$k_S=\mathrm{\Sigma }{V}_{\alpha i}\cdot k_{\alpha i}$$(4)

  

$$\mathrm{\Sigma }{V}_{\alpha i}=1$$(5)

where:

k_s– magnetic leakage of the alloy;

k_αi– magnetic leakage of the i^th phase component;

V_αi– volumetric proportion of the i^th phase.

Relationships (4 and 5) indicate that in the reversible range of the magnetic field, the magnetic leakage of the alloy is equal to the sum of products of volumetric proportions of individual phase components and their magnetic leakage.

The above relationship can be considered to form the basis of a new method for quantitatively assessing the phase composition using a variable magnetic field. This method is universal for two-phase alloys if the two phases have different magnetic leakage. This can be particularly useful for assessing the proportion of austenite and retained austenite in heat-treated alloys of iron and carbon. A microstructure of steels and cast steels after quenching consists of martensite, which is a ferromagnetic material and of retained austenite of paramagnetic properties. A volume fraction of retained austenite is - in this case - one of the criteria of the properly performed heat treatment. An excessive fraction of unstable phase component, such as austenite is the reason of increasing internal stresses and a loss of dimensional stability of quenched parts of machines and devices. Due to a diphase microstructure composition as well as different magnetic properties of both phases the proposed method can be - in such case - specially suitable. For alloys made up of more than two phases, this method used on its own does not allow the volumetric proportions of the phase composition to be unambiguously determined. Yet regardless of the discussed limitations to its use, it has important advantages over other methods, namely: it assesses the proportion with good precision, the measurements are quick and easy and the cost of examinations is low. Because the measurement is quick and easy, it can be used not only in physical metallurgy labs, but also on production lines for the non-destructive control of heat-treated alloys containing phase components of different magnetic properties.¹¹⁾

4. Conclusions

(1) In the reversible range of the magnetic field, the magnetic leakage k_s for an iron and copper alloy is linearly dependent on the volumetric proportions of phase components found in this alloy.

(2) For two-phase alloys of varied magnetic properties, relationships (4) and (5) can be considered to form the basis of a new method for quantitatively assessing the phase composition using a variable magnetic field.

(3) The absolute error in the assessment of volumetric proportions by the proposed method does not exceed 0.9%.

(4) For alloys consisting of more than two phases, the k_s parameter can be used as a supporting method for a separation based on the proportion of two phases.

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