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higher a peak in a spectrum, the more concentrated the element is in the specimen. Inset in Figure 2.10 shows the analyzed composition of the alloy.
Figure 2.10: A typical EDS spectrum of Ni-Mn-In-Si alloy. Inset shows the results of EDS analysis.
In the present work, the alloy specimen was placed on carbon coated tape and then gold coated to yield an electrically conducting surface for SEM observation.
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The VSM operates on the principle of Faraday's law of induction, which tells us that a changing magnetic flux will produce an electric field [GRIFF95a]. When a sample is placed in a uniform magnetic field, a dipole moment proportional to the product of the sample’s susceptibility and the applied field is induced in the sample. If the sample is vibrated in a sinusoidal manner, an electrical signal can be induced in suitably located stationary pick-up coils (cf. Figure 2.11a). This signal has amplitude proportional to the magnetic moment of the sample, the vibrating amplitude and the vibration frequency. Through the use of lock-in- amplifier and feedback techniques, only that portion of the signal arising from the magnetic moment is picked up and is converted into direct read-out in emu units on a digital panel meter. The VSM consists of the following major parts: 1) water cooled electromagnet and power supply, 2) vibration exciter and sample holder (with angular position indicator), 3) sensing (pick-up) coils, 4) Hall probe, 5) amplifier, 6) control chassis, 7) lock-in amplifier and 8) computer interface.
Figure 2.11: (a) Schematic diagram and (b) photograph of a Lakeshore VSM Model 7410.
The sample is fixed to the lower end of the sample holder after performing the calibration procedure using standard Ni sample. Subsequently, the measurement sequence is
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programmed using the software (IDEASVSM) provided with the instrument. The vibration exciter is then activated and the signal received from the probe and the pick-up coils is converted into the magnetic moment value of the sample. Magnetic field up to 3 T can be applied to the sample using this model of VSM. Normally, magnetic field is automatically increased in steps at a constant temperature (M - H measurements) by setting the program.
These measurements provide Msat value of the sample. Magnetization as a function of temperature at a constant applied field (M - T measurements) is recorded to obtain information of transition temperatures (TC and TM). A sharp decrease in magnetization is observed at the ferromagnetic to paramagnetic phase transition at TC. TC is generally determined from the minimum value of the first derivative of M - T data. The martensitic structural transition in FSMAs is accompanied by an abrupt change in magnetization measured at unsaturated fields. This is due to the change of magnetocryctalline anisotropy of the material during structural phase transitions.
The effective magnetic anisotropy constant Keff of the ferromagnetic alloys can be calculated from the initial magnetization (M–H) curves using the law of approach to saturation [ANDR97a]. Generally, M as a function of applied field can be expressed as
1 2
sat hf
a b c
M M H d H
H H
H
χ
§ ·
= ¨ − − − − ¸+ +
© ¹ (2.9)
where H is applied field, Msat is a saturation magnetization, χhf is high field susceptibility and a, b, c, d are constant coefficients. The coefficients depend on the amount of structural defects and intrinsic fluctuations in the sample. According to Fähnle et al. [FAHN78a], the second term a
H can arise from point-like defects, intrinsic magneto-static fluctuations and
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randomly distributed magnetic anisotropy. c is related to the magneto-crystalline anisotropy.
The constant d arises from the partial suppression of thermally excited spin waves in magnetic field. The paramagnetic term χhfH causes an increase in spontaneous magnetization at high external magnetic fields. The straight forward method for obtaining the coefficients would be to fit the experimental curve with this full expression. But, due to the large amount of coefficients involved, the fitting procedure gives ambiguous results. To overcome this, an alternate expression given below [JINZ98a] containing fewer coefficients is chosen as the fitting equation:
( )
sat1 c
2M H M
H
§ ·
= ¨ − ¸
© ¹
(2.10)When applied field is increased to large values, domain wall movements become relatively unimportant and magnetization of the ferromagnetic sample is primarily controlled by domain rotation. With the assumption that atoms are oriented at random and strain distribution is homogeneous, the above equation is the best fit equation at high fields [WANG95a]. Deciding on the appropriate low field limit is a hurdle in this procedure.
Graham et al. [GRAH93a] discussed this problem and has set the lower field limit for the case of as cast metallic glass at 1 T.
When paramagnetic contribution is comparable to the ferromagnetic contribution, the data obtained from M-H measurement cannot be fit with the above equation. So, data are first fit to the equation,
sat 1 hf
M M b H
H
χ
§ ·
= ¨ − ¸+
© ¹ (2.11)
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and the paramagnetic contribution χhf obtained from the above fit is subtracted from the magnetization data [Msat→ (M - χhfH)] and the subtracted Msat vs H data are then fitted to equation (2.10) to obtain the optimal c value. Once c value is correctly estimated, magneto
crystalline anisotropy constant, Keff can be calculated using the relation [JINZ98a],
1 2 0
15
eff sat
4
K = µ M § ¨ c · ¸
© ¹
(2.12)
VSM provides measured Msat in units of emu/g (≅ Am2kg-1) and so c estimated from the fitting procedure has the unit of (Oe)2.
Magnetization tests have revealed that both the martensitic and the magnetic transitions in FSMAs are accompanied by an abrupt change in magnetization which results in a large MCE. The MCE parameter ∆SM can be calculated from the isothermal M versus H curves. To evaluate ∆SM, the integral in equation (1.23) can be approximately written as [PLAN09a, HUFS00a],
1
0 0
[0 ; ( )] 1 ( ) ( )
H H
M i i
i
S H T i M T dH M T dH
T +
ª º
∆ → = « − »
∆ ¬
³ ³
¼ (2.13)where T(i) = (Ti+1 + Ti)/2, and ∆Ti = Ti+1 – Ti and the integrals are computed numerically using M versus H curves at discrete temperature intervals.