Second-order Magnetic Phase Transition Research Articles

Magnetic, magnetocaloric properties and phenomenological model in amorphous Fe60Ru20B20 alloy

Magnetic, magnetocaloric properties and phenomenological model of amorphous Fe60Ru20B20 alloy are investigated in detail. The amorphous alloy has been synthesized using melt spinning method. The magnetic transition nature undergoes a second-order magnetic phase transition from ferromagnetic to paramagnetic states with a Curie temperature of 254 K. Basis on the thermodynamic Maxwell׳s relation, magnetic entropy change (−ΔSM) is calculated. Further, we also report a theoretical investigation of the magnetocaloric effect using a phenomenological model. The best model parameters and their variation with temperature and the magnetic field were determined. The theoretical predictions are found to agree closely with experimental measurements.

Magnetic and magnetocaloric properties in Ba-doped La0.7Ca0.3MnO3 nanoparticles

La0.7Ca0.3−xBaxMnO3 nanoparticles with the crystalline size d = 38 and 39 nm for x = 0.025, and 0.05, respectively, were synthesized by utilizing the solid-state reaction and mechanical ball milling methods. We have used the Banerjee's criteria, the mean-field, and the thermodynamic theories, and isothermal magnetization, M(H), data around Curie temperature (TC) to investigate the magnetic phase transformation and the temperature (T) and magnetic field (H) dependences of magnetic entropy change, ΔSm(T, H), for nanoparticles. These exhibit the samples undergoing a second-order magnetic phase transition with an existence of the short-range ferromagnetic order in the samples. Under an applied magnetic field change ΔH = 30 kOe, the maximum value of ΔSm (denoted as |ΔSmax|) are obtained about 4.4 J kg−1 K−1 corresponding to a relative cooling power (RCP) value about 140 J kg−1. Field dependences of |ΔSmax| and RCP can be expressed by the power laws, |ΔSmax| = a × Hn and RCP = b × HN, where a and b are coefficients, n and N are the field exponents, respectively. Interestingly, all the ΔSm(T, H) curves measured at different applied fields are collapsed onto a universal curve, ΔSm(T, H)/ΔSmax versus θ = (T − TC)/(Tr − TC), where Tr is the reference temperature.

Theoretical investigation of the magnetocaloric effect of La0.7(Ba, sr)0.3MnO3 compound at room temperature with a second-order magnetic phase transition

In this paper, the prediction of magnetic and magnetocaloric properties of La0.7(Sr,Ba)0.3MnO3 (LSBMO) compound have been conducted using a phenomenological model. Indeed, the investigation of magnetic properties has revealed that the sample exhibits a paramagnetic to ferromagnetic phase transition. Interestingly, the Curie temperature (TC) was found to decrease from 322 to 300K with the decrease of magnetic fields. Moreover, the magnetocaloric data displays a large value of the magnetic entropy change, 1.5Jkg−1K−1 under an applied magnetic field change of 20kOe, which increases with the increase of the applied magnetic field, making it a promising compound for ecologically-friendly magnetic refrigeration at room temperature. Finally, the construction of the universal curve of the magnetic entropy change proves that the studied manganite undergoes a second order magnetic phase transition.

Simple Set-Up for Adiabatic Measurements of Magnetocaloric Effect

We present a cost-effective and robust set-up designed to measure directly the magnetic field-induced adiabatic temperature change. The system uses a piston to introduce/remove the sample to/from the magnetic field (μ0∆His up to 1.7T) created by an ordinary electromagnet. The temperature of the sample is controlled by a double pipe heat exchanger operating by the electrical heater and air flow circulation from a Dewar with liquid nitrogen to the sample holder assembly.We have measured the adiabatic temperature change, ΔTad, of two polycrystalline samples: Gd and Ni50Mn35In15Heusler alloy. At the second-order magnetic phase transitions (18oC for Gd and 42oC for Ni50Mn35In15), ΔTadunder μ0∆H=1.7T are 3.8±0.1oC for Gd and 1.9±0.1oC for Ni50Mn35In15. The Heusler alloy shows an inverse magnetocaloric effect: ΔTadis-1.5±0.1oC on cooling and-1.6±0.1oC on heating at the martensitic transformation temperatures of ~24oC and ~29oC, respectively.

Magnetic phase transitions and large magnetic entropy change with a wide temperature span in HoZn

CsCl-type HoZn undergoes two successive magnetic phase transitions: (i) paramagnetic to ferromagnetic (FM) at TC∼72K and (ii) a spin reorientation (SR) at TSR∼26K. Magnetization and modified Arrott plots indicate that HoZn undergoes a second-order magnetic phase transition around TC. The obtained critical exponents have some small deviations from the mean-field theory, indicating a short range or a local magnetic interaction which is properly related to the coexistence of FM and SR transitions at low temperature. Two successive magnetic transitions in HoZn induce one broad pronounced peak together with a shoulder in the temperature dependence of the magnetic entropy change −ΔSM(T) curves, resulting in a wide temperature range with a large relative cooling power (RCP). For a field change of 0–7T, the maximum value of −ΔSM is 15.2J/kgK around TC with a large RCP value of 1124J/kg. The large reversible magnetocaloric effect (MCE) and RC indicate that HoZn is a good candidate for active magnetic refrigeration.

Critical behavior and spontaneous magnetization estimation in La0.5Sr0.5MnO3 compound

We report the critical behavior in La0.5Sr0.5MnO3 perovskite oxide manganite using methods including modified Arrott plot, Kouvel–Fisher plot, and critical isotherm analysis. By means of the above techniques around the ferromagnetic–paramagnetic (FM–PM) transition, the magnetic data analyzed shows the sample attending the second-order magnetic phase transition with the critical parameters β = 0.553±0.020 with TC=352.02±0.63K (from the spontaneous magnetization MS(T) below TC) and γ =1.169±0.058 with TC=352.49±0.85K (from the inverse initial susceptibility χ0−1(T) above TC). The exponent δ =3,216 independently obtained from the critical magnetization isotherm satisfies the Widom scaling relationδ=1+β/γ. Moreover, the critical exponents are in the theoretically expected values for mean-field interaction model rather than the other universal theory and also follow the single scaling equation of M(H,ε)ε−β=f±(H/εβ+γ). Furthermore, to estimate the spontaneous magnetization of La0.5Sr0.5MnO3 perovskite, we used the magnetic entropy change (−ΔSM), obtained from isothermal magnetization. The results of this approach are compared to results obtained from classical analysis using Arrott curves.

3D-Ising ferromagnetic characteristics and magnetocaloric study in Pr0.4Eu0.2Sr0.4MnO3 manganite

The structure, critical exponents and magnetocaloric effect (MCE) of Pr0.4Eu0.2Sr0.4MnO3 were investigated in detail. A solid state reaction method was used in the preparation phase. Phase purity, structure, size, and crystallinity were investigated using XRD and SEM. The Reitveld refinement of XRD pattern shows that the sample adopts an orthorhombic structure with Pnma space group. Analyzing temperature and field dependences of magnetization around the ferromagnetic–paramagnetic transition reveals the sample undergoing the second-order magnetic phase transition with the critical parameters TC∼238K, β=0.310(3), γ=1.264(1) and δ=4.761(9).The exponents are close to 3D-Ising values. This reflects an existence of ferromagnetic short-range order in our sample. With these values one can scale the magnetization below and above TC following a single equation of state. However, it is noteworthy that the scaling relations are obeyed indicating renormalization of interactions around the TC. Temperature variation in effective exponents βeff and γeff resemble with those for disordered ferromagnet. In the vicinity of TC, the magnetic entropy change ΔS reached maximum values of 2.80 and 5.32J/kgK under magnetic field variations of 2 and 5T, respectively. The field dependence of the magnetic entropy changes are also analyzed, which show power law dependence ΔSMmax≈aμ0Hn at transition temperature. The critical exponent analysis related to magnetocaloric effect is described. Moreover, the temperature dependence of the exponent n for a different magnetic field is also studied. The values of n obey to the Curie Weiss law above the transition temperature. In particularly, n can be related to the critical exponents β, γ and δ at the magnetic transition. We used the scaling hypotheses to scale the magnetic entropy change and heat capacity changes to a single universal curve respectively for Pr0.4Eu0.2Sr0.4MnO3 sample.

Study of critical behavior of perovskite La0.8Ca0.2−xPbxFeO3 (x = 0.0, 0.1 and 0.2) compounds

The critical properties of ferrite perovskite La0.8Ca0.2−xPbxFeO3 (x=0.0, 0.1 and 0.2) compounds at the ferromagnetic–paramagnetic (FM–PM) transition have been analyzed. Experimental results revealed that all samples exhibit a second-order magnetic phase transition. The estimated critical exponents derived from the magnetic data using various techniques such as modified Arrott plot, Kouvel–Fisher method, and critical magnetization isotherms M (TC, H). The critical exponent values for all samples are in a close agreement with those predicted for the mean-field theory. The reason for this behavior may be long-range interactions between spins in this system.

Critical behavior and magnetocaloric effect of Pr1−xCaxMnO3

The critical behavior of Pr1−xCaxMnO3 samples with x = 0.25, 0.27, and 0.29 has been investigated. Detailed analyses of magnetic-field dependences of magnetization at temperatures around the paramagnetic-ferromagnetic transition, M(H, T), reveal that the samples undergo a second-order magnetic phase transition. The Arrott plot method predicts the values of critical parameters to be TC ≈ 118 K, β = 0.351 ± 0.003, γ = 1.372 ± 0.002, and δ = 4.90 ± 0.02 for x = 0.25; TC ≈ 116 K, β = 0.362 ± 0.002, γ = 1.132 ± 0.004, and δ = 4.09 ± 0.03 for x = 0.27; and TC ≈ 110 K, β = 0.521 ± 0.002, γ = 0.912 ± 0.005, and δ = 2.71 ± 0.02 for x = 0.29. The values of β = 0.351 (for x = 0.25) and β = 0.362 (for x = 0.27) are close to the value β = 0.365 expected for the 3D Heisenberg model, proving an existence of short-range ferromagnetic interactions in these samples. A slight increase in Ca-doping content (x = 0.29) leads to the shift of the β value (=0.521) towards that of the mean-field theory (with β = 0.5) characteristic of long-range ferromagnetic interactions. The samples also exhibit a magnetocaloric effect: around TC of Pr1−xCaxMnO3 compounds, magnetic-entropy change reaches the maximum values of about 5.0, 4.1, and 2.5 J kg−1 K−1 for x = 0.25, 0.27, and 0.29, respectively, under an applied-field change of 50 kOe. Magnetic-field dependences of the maximum magnetic-entropy change (ΔSmax) obey a power law |ΔSmax(H)| ∝ Hn, where exponent values n = 0.68–0.74 are close to those obtained from the theoretical relation n = 1 + (β − 1)/(β + γ).

High-entropy bulk metallic glasses as promising magnetic refrigerants

In this paper, the Ho20Er20Co20Al20RE20 (RE = Gd, Dy, and Tm) high-entropy bulk metallic glasses (HE-BMGs) with good magnetocaloric properties are fabricated successfully. The HE-BMGs exhibit a second-order magnetic phase transition. The peak of magnetic entropy change (ΔSMpk) and refrigerant capacity (RC) reaches 15.0 J kg−1 K−1 and 627 J kg−1 at 5 T, respectively, which is larger than most rare earth based BMGs. The heterogeneous nature of glasses also contributes to the large ΔSMpk and RC. In addition, the magnetic ordering temperature, ΔSMpk and RC can be widely tuned by alloying different rare earth elements. These results suggest that the HE-BMGs are promising magnetic refrigerant at low temperatures.

Critical Behavior of La0.67Ba0.33Mn0.95Fe0.05O3 Manganite

The critical behavior of perovskite manganite La0.67Ba0.33Mn0.95Fe0.05O3 at the ferromagnetic–paramagnetic has been analyzed. The results show that the sample exhibited the second-order magnetic phase transition. The estimated critical exponents derived from the magnetic data using various such as modified d’Arrott plot Kouvel–Fisher method and critical magnetization M(TC, H). The critical exponents values for the La0.67Ba0.33Mn0.95Fe0.05O3 are close to those expected from the mean field model β = 0.504 ± 0.01 with TC = 275661 ± 0.447 (from the temperature dependence of the spontaneous magnetization below TC), γ = 1.013 ± 0.017 with TC = 276132 ± 0.452 (from the temperature dependence of the inverse initial susceptibility above TC), and δ = 3.0403 ± 0.0003. Moreover, the critical exponents also obey the single scaling equation of M(H, e) = |e|βf±(H/|e|β+γ).

Critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.7Ca0.2Sr0.1Mn1−xCrxO3 compounds (0 < x < 0.1)

The critical behavior of the La0.7Ca0.2Sr0.1Mn1−xCrxO3 (0<x<0.1) was carried out by measurement of the magnetization around the Curie temperature TC. Experimental results revealed that these samples exhibit a second-order magnetic phase transition. The critical properties are investigated through various techniques such as modified Arrott plot, Kouvel–Fisher methods and critical isotherm to analyze magnetic-field dependences of magnetization. The values of critical exponents which are derived from the magnetic data, using the above methods, yield 0.24⩽β⩽0.25 and 1.01⩽γ⩽1.08 with TC in the range of 255–294K. The critical isotherm M(TC, H) gives δ=4.9±0.1. Thus, the scaling law γ+β=δβ is fulfilled. The critical exponents obey the single scaling equation of state Mμ0H,ε=εβf±μ0H/εβ+γ, where f+ for T>TC and f− for T<TC. The estimated critical exponents are close to the tricritical mean field model for the Cr doped sample suggesting short-range interaction.

Coexistence of short- and long-range ferromagnetic order in La0.7Sr0.3Mn1−xCoxO3 compounds

Polycrystalline La0.7Sr0.3Mn1−xCoxO3 (x = 0.0–1.0) samples were synthesized by solid-state reaction. Structural and magnetization studies reveal the replacement of Co for Mn in La0.7Sr0.3Mn1−xCoxO3, and the decrease of the Curie temperature (TC) from 360 K (for x = 0) to 224 K (for x = 1). Positive slopes observed in the H/M versus M2 curves prove all the samples undergo a second-order magnetic phase transition. By analysis of the M(H) data at temperatures around TC using the Kouvel-Fisher method, we obtained the values of critical parameters (TC, β, γ, and δ). The results suggest an existence of short-range FM order in the sample x = 0 with β = 0.377. Meanwhile, for the case of Co-doped samples, their β values in the range of 0.403–0.457 indicate a coexistence of short and long-range FM order. This means that Co-doping favors establishing FM long-range order in La0.7Sr0.3Mn1−xCoxO3. From M(H) data, we have also determined the magnetic entropy change (ΔSm) for the samples. We have found that the ΔSm(T) curves for different applied fields are collapsed onto a universal curve by normalizing the ΔSm(T) curves to their respective maximum value ΔSmax (i.e., ΔSm(T)/ΔSmax) and rescaling the temperature axis above and below TC with θ=(T−TC)/(Tr−TC), where Tr is the reference temperature.

Magnetic Properties and Large Magnetocaloric Effect in Amorphous Fe-Ag-Ni-Zr for Room-Temperature Magnetic Refrigeration

This paper reveals that a partial replacement of Fe by Ni (5%) and/or Ag (2%) in amorphous Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">85-x</sub> Ag <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> Zr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> (x = 0 and 2) alloys leads to the shift of T toward room temperature (RT) (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> = 308 and 303 K for x = 0 and 2, respectively). Basing on isothermal magnetization data, the magnetic entropy change (ΔS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ) of the amorphous alloys was calculated. Their maximum ΔS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> values (|ΔS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> |) achieve just around RT, corresponding to the ferromagnetic-paramagnetic (FM-PM) phase transition of the amorphous phase. Under a magnetic field change of 10 kOe, |ΔS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> | values are ~1 J · kg <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> · K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . We have also used different methods, such as the modified Arrott plots, the Kouvel-Fisher method, and critical isotherm analysis to study their critical property around the FM-PM phase transition. Our results suggest that the amorphous Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">85-x</sub> Ag <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> Zr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> alloys exhibit a second-order magnetic phase transition with the critical exponents of β = 0.389-0.396 and y = 1.279-1.334 close to those expected for the 3-D Heisenberg model. This proves the existence of short-range FM interactions in these alloys.

Influence of Crystallite Size on Magnetocaloric Effect and Critical Behavior La&lt;sub&gt;0.7&lt;/sub&gt;Sr&lt;sub&gt;0.3&lt;/sub&gt;Mn&lt;sub&gt;0.92&lt;/sub&gt;Co&lt;sub&gt;0.08&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; Nanoparticles

Four samples of La0.7Sr0.3Mn0.92Co0.08O3 (LSMCO) with different crystallite sizes were prepared by the combination of solid-state reaction and mechanical milling methods. Based on isothermal magnetization data, ${M}$ ( $\boldsymbol {H}$ ), temperature dependences of magnetic entropy change, $\Delta \boldsymbol {S} _{m} {T}$ , of the samples under a magnetic field change of 10 kOe were calculated. The maximum values of magnetic entropy change (| $\Delta {S} _{\mathrm {max}}$ |) at room temperature are in the range of 0.9–1.4 J $\cdot $ $\mathrm{kg}^{{\mathbf {-1}}}\cdot $ $\mathrm{K}^{{\mathbf {-1}}}$ , corresponding to ferromagnetic (FM)–paramagnetic phase transition. In addition, ${M} ^{{\mathbf {2}}}$ versus ${H}/{M}$ curves at temperatures around ${T} _{C}$ prove the samples exhibiting a second-order magnetic phase transition. The critical exponents $\beta $ , $\gamma $ , and $\delta $ were determined using the modified Arrott plot method and critical isotherm analysis. Here, these exponent values are located in between those expected for the mean-field theory and 3-D Heisenberg model. It means the coexistence of short-range and long-range FM interactions in LSMCO nanoparticles.

Magnetism and Magnetocaloric Effect in EuAuZn

The magnetic properties and magnetocaloric effect (MCE) in the ternary intermetallic compound EuAuZn have been studied via magnetization and heat capacity measurements. The compound orders ferromagnetically below T C ~ 52 K with a spin reorientation transition at T SR ~ 19 K. A large reversible MCE has been observed in EuAuZn accompanied by a second-order magnetic phase transition from a paramagnetic to a ferromagnetic state. Under a field change of 5 T, the maximum values of magnetic entropy change (-ΔS M max ) and adiabatic temperature change (ΔT ad max ) are 9.1 J/kg·K and 3.8 K, respectively, the corresponding relative cooling power is 318 J/kg.

Magnetic properties and magnetocaloric effect at room temperature of Ni50−x Ag x Mn37Sn13 alloys

In this work, we present a detailed study of the magnetic properties and the magnetocaloric effect at room temperature of Ni50−xAgxMn37Sn13 alloys with x = 1, 2, and 4, which were prepared by using an arc-melting method. Experimental results reveal that a partial replacement of Ag for Ni leads to a decrease in the anti-FM phase in the alloys. In addition, the martensitic-austenitic phase transition shifts towards lower temperature and is broaded. The Curie temperature (TCA) for the austenitic phase also shifts toward to lower temperature, but not by much. The Curie temperature was found to be 308, 305, and 298 K for x = 1, 2, and 4, respectively. The magnetic entropy change (ΔSm) of the samples was calculated by using isothermal magnetization data. Under an applied magnetic field change of 10 kOe, the maximum value of ΔSm (|ΔSmax|) was achieved at around room temperature and did not change much (~0.8 J·kg−1·K−1) with increasing Ag-doping concentration. Particularly, the M2 vs. H/M curves prove that all the samples exhibited a second-order magnetic phase transition. Based on Landau’s phase-transition theory and careful analyses of the magnetic data around the TCA, we have determined the critical parameters β, γ, δ, and TC. The results show that the β values are located between those expected for the 3D-Heisenberg model (β = 0.365) and mean-field theory (β = 0.5). Such a result proves the coexistence of short-range and long-range ferromagnetic interactions in Ni50−xAgxMn37Sn13 alloys. The nature of the changes in the critical parameters and the |ΔSmax| is thoroughly discussed by means of structural analyses.

Structure, magnetic properties and magnetocaloric effect in LaMnSbO0.8 F0.2 oxypnictide material

We have investigated the structural, magnetic properties and magnetocaloric effect (MCE) in LaMnSbO0.8F0.2. The compound has the ZrCuSiAs-type structure with P4/nmm space group. For a field change of 0–5 T, the maximum entropy change (–ΔSM) is calculated to be 0.074 J kg−1 K by using the Maxwell's relations from the magnetic isotherms. The relative cooling power was increasing from 0.67 to 3.74 J kg−1 with the increases of magnetic field changes from 0–1 to 0–5 T. The observed reversible MCE is related to a second-order magnetic phase transition.

Critical behavior near the ferromagnetic–paramagnetic phase transition in La0.65Eu0.05Sr0.3Mn1−xCrxO3 (x=0.10 and x=0.15)

The critical properties of perovskite manganite La0.65Eu0.05Sr0.3Mn1−xCrxO3 (x=0.10 and x=0.15) around the paramagnetic–ferromagnetic phase transition are investigated through various techniques such as the modified Arrott plot, Kouvel–Fisher method, and critical isotherm analysis. The experimental results have revealed that the samples exhibited the second-order magnetic phase transition and the critical exponents of β and γ for La0.65Eu0.05Sr0.3Mn1−xCrxO3 (x=0.10) are consistent with the prediction of the mean field model. Furthermore, the estimated critical exponents of La0.65Eu0.05Sr0.3Mn1−xCrxO3 (x=0.15) are close to those found out by the 3D-Heisenberg model. The magnetization–field–temperature M–H–T behaviors of all compounds at below and above TC were properly renormalized following the scaling of state equation M(H,ε)=|ε|βf±(H/|ε|β+γ), where ε=(T−TC)/TC, f+ for T>TC and f− for T<TC. This confirms that the obtained values of the critical exponent as well as TC are reasonably accurate and unambiguous.

Giant dielectric permittivity and magneto-capacitance effects in low doped manganites

The effect of giant dielectric permittivity due to phase separation accompanied by charged inhomogeneities in low-doped manganites is discussed. The effect appears in the vicinity of the second-order magnetic phase transition and is caused by long-range Coulomb forces. The long-range Coulomb interaction is responsible for the formation of inhomogeneous charged states and determines their characteristic length scales. We derive the phase diagram of the inhomogeneous charged states in the framework of the phenomenological theory of phase transitions. The large value of the static dielectric function reduces the characteristic value of the Coulomb energy of the inhomogeneous state and makes the appearance of the magnetoelectric effect possible. We discuss the formation of a state with giant dielectric permittivity and magneto-capacitance effects in that case.