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The structure and thermal parameters of ordered Cu65Fe10Pd25 ternary alloy
Physica B 461 (2015) 129–133
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Physica B journal homepage: www.elsevier.com/locate/physb
The structure and thermal parameters of ordered Cu65Fe10Pd25 ternary alloy N. Ahmad a, A.B. Ziya a,n, A. Ibrahim b, S. Atiq b, S. Ahmad a, F. Bashir c a
Department of Physics, Bahauddin Zakariya University, Multan 60800, Pakistan Institute of Advanced Materials, Bahauddin Zakariya University, Multan 60800, Pakistan c L. C. W. University, Lahore, Pakistan a
art ic l e i nf o
a b s t r a c t
Article history: Received 21 October 2014 Received in revised form 6 January 2015 Accepted 7 January 2015 Available online 8 January 2015
Structural and thermal parameters have been studied in Cu65Fe10Pd25 alloy during order–disorder (O–D) transformation using differential scanning calorimetry (DSC) and high temperature X-ray diffraction (HTXRD). The results reveal that the Cu65Fe10Pd25 alloy undergoes an O–D transformation at Tc ¼ 797 K. The alloy shows L12 type ordering below Tc and has disordered face centered cubic (fcc) structure above Tc. The lattice parameter shows a positive deviation from Vegard’s rule which may be related to the weakening of interatomic forces by the addition of Fe. The integrated intensity data obtained from the diffraction experiments was utilized to determine the coefficient of thermal expansion (α(T)), mean square amplitude of vibration ( u2 (T )) and Debye temperatures (ΘD) during the O–D transformation. The abrupt change in the value of lattice parameter and coefficient of thermal expansion at Tc shows that the nature of O–D transition is first order. These results have been discussed by comparing them to those for Cu3Pd alloy. & 2015 Elsevier B.V. All rights reserved.
Keywords: Lattice parameter Structure X-ray diffraction O–D transition
1. Introduction The formation of ordered structures and the development of long-range order (LRO) in the arrangement of atoms of different type is characteristic of many alloy systems. Atomically ordered alloys possess specific physical properties. The copper–palladium (Cu–Pd) alloys are of great interest with regard to their application as well as from the point of view of the scientific understanding. Structurally ordered Cu3Pd alloys have a face centered cubic (fcc) lattice of the L12 type, which depends on temperature, composition and thermal treatment [1,2]. Ordered Cu–Pd and other transition metals alloys are extensively used in electronic industry as electro-contact materials. Therefore, it is necessary to know the role of the mechanisms of scattering of charge carriers and the peculiarities of the Fermi surface in the development of transport properties of such alloys [3]. These alloys have received a lot of attention from researchers because Cu–Pd alloys exhibit variety of ordered phases. It has been reported that disordered fcc Cu–Pd alloys, in the range of about 8–30 at% Pd, transform into a variety of ordered structures below 773 K [4]. Thermal expansion is one of the fundamental physical properties in materials science and engineering. INVAR alloys are one n
Corresponding author. Fax: þ 92 61 9210068. E-mail address: [email protected] (A.B. Ziya).
http://dx.doi.org/10.1016/j.physb.2015.01.004 0921-4526/& 2015 Elsevier B.V. All rights reserved.
of the examples which are being used in precise mechanical machines [5]. The mechanical properties of alloys are also directly linked to their characteristic Debye temperature (ΘD). Determination of Debye temperature is given of great importance in crystallography because of its use in structural refinement and explanation of various properties. The scientific understanding and technological importance of thermal expansion of the alloys has lead to its measurement for various materials [6,8,17]. The structural properties of alloys can be modified by the addition of ternary alloying elements. The addition of Fe in Cu–Pd alloys is expected to improve the order–disorder transformation temperature (Tc) and magnetic properties of these alloys. In the present study, structure and thermal properties of Cu65Fe10Pd25 alloy are investigated by using high temperature X-ray diffraction (HTXRD). Thermal parameters were determined by using the Bragg line displacement method [6]. Thermal parameters of Cu65Fe10Pd25 alloy in both ordered and disordered states have been determined and compared.
2. Experimental method The sample of Cu65Fe10Pd25 alloy (5 g) was prepared from spectroscopically pure Cu, Fe and Pd metals by using arc-melting furnace with water cooled copper hearth under an atmosphere of purified argon. The samples were remelted six times to ensure the
130
N. Ahmad et al. / Physica B 461 (2015) 129–133
homogeneity of the alloy constituents. The ingot was sealed in quartz tubes under a vacuum of 2.0 10 3 Pa and annealed for 20 h at 1273 K in order to homogenize them. Thin slices were cut from the ingot, one of which was annealed at 723 K for one week and subsequently furnace cooled to room temperature to avoid the accumulation of surplus vacancies. The composition of Cu65Fe10Pd25 alloy was determined by using electron probe microanalyzer (EPMA, JXA-8100, JEOL). The composition was measured at ten different points and the average composition was taken as the true composition of the alloy. The homogeneity variation of the alloy was found to be less than 1 at%. The sample was then grinded and polished to produce a smooth surface suitable for HTXRD experiments. The HTXRD experiments were performed on a Bruker D8 AXS diffractometer fitted with an evacuated chamber having a Pt–Rh heater and precise temperature measurement arrangement. Diffraction patterns were taken in the scattering angle range of 15–135° under θ– θ geometry with divergence and receiving slits of 0.5° using Nifiltered CuKα radiation. The tube parameters were 45 kV and 40 mA. The HTXRD experiments were performed in the range of 300–1173 K with an increment of 50 K in general but 10 K near the order–disorder (O–D) transition temperature (Tc). The data was corrected for instrumental errors by using a highly pure silicon powder as external standard. The thermal analysis of the sample was performed on a differential scanning calorimeter (DSC, model SBT-Q600) under nitrogen atmosphere at a heating rate of 20 K/min up to a temperature of 1500 K.
3. Results and evaluation 3.1. Differential scanning calorimetry Fig. 1 shows the DSC thermograms of Cu65Fe10Pd25 alloy. The change in heat flow beyond 1395 K reflects the on-set of melting of the alloys. A small endothermic peak at 797 K was observed which shows change of phase from ordered to disordered. These results are consistent with those obtained from HTXRD explained later. 3.2. Structural study by X-ray diffraction Fig. 2 shows the X-ray diffraction patterns of Cu65Fe10Pd25 alloy taken at various temperatures. The prominent feature of all
Fig. 1. Thermogram of Cu65Fe10Pd25 alloy recorded on a differential scanning calorimeter at a heating rate of 20 K/min.
Fig. 2. X-ray diffraction patterns of Cu65Fe10Pd25 alloy taken at various temperatures during in-situ diffraction experiments.
patterns is the presence of sharp (100)-, (110)-, and (210)-superlattice reflections and (111)-, (200)-, (220)-, (311)-, (222)-, (400)and (331)-fundamental reflections. The small peak adjacent to (200) originated from the Pt–Rh heater used in the HTXRD experiments. The superlattice reflections disappear above 797 K, which indicate the O–D transformation. The structure factor for Cu65Fe10Pd25 alloy with L12 type ordered structure is:
F Fundamental = c Pd fPd + 3 (cCu fCu + c Fe fFe )
(1)
F Superlattice = c Pd fPd − (cCCu fCu + c Fe fFe )
(2)
The observed superlattice and fundamental reflections obey Eqs. (1) and (2), respectively, which confirm that the alloy has L12 type ordered structure. The true value of lattice parameter at room temperature was obtained by the extrapolation of lattice parameters for each reflection against Nelson–Riley function and was found to be 3.697 70.002 Å. The value of lattice parameter shows a positive deviation from Vegard's rule (3.673 Å). This result is consistent with the Cu3Pd alloy [4]. The data obtained from HTXRD experiments was utilized to obtain the temperature dependence of lattice parameter (Fig. 3(a)) and the thermal parameters (Figs. 3 (b) and 4(a and b)). The O–D transition observed in diffraction patterns at Tc ¼797 K is also reflected in Fig. 3(a). The sudden change in lattice parameter at Tc indicates that this transition is a first order transition [16]. A change Δa = 0.010 Å was observed in the value of lattice parameter at Tc. Two methods have been reported for the determination of thermal parameters from the X-ray diffraction data. One is the use of integrated intensity data of all Bragg reflections in the pattern at a fixed temperature (usually referred to as Wilson-plot method [18]). The second method employs the temperature dependence of integrated intensity of a high angle Bragg reflection (usually referred to a Bragg-line displacement method) and is used to eliminate the effects of preferred orientation. The later method has been used in the present study and results are given in the following sections.
N. Ahmad et al. / Physica B 461 (2015) 129–133
Fig. 3. Temperature dependence of ordered and disordered Cu65Fe10Pd25 alloy (a) lattice parameter a(Å) and (b) coefficient of thermal expansion (α(T)).
131
Iobs ) for Cu 65Fe10Pd 25 alloy and Ical vibration u2 (T ) of Cu Fe Pd alloy.
Fig. 4. (a) The temperature dependence of (a) ln ( (b) Mean-square amplitude of thermal
65
10
25
3.3. Thermal expansion The temperature dependence of coefficient of thermal expansion (α(T)) is shown in Fig. 3(b). The value of α(T) was determined by least square fitting of a second degree polynomial1 to the data of lattice parameter a(Å) shown in Fig. 3(a):
1 ⎛ da (T ) ⎞ 1 α (T ) = (B + 2CT ) ⎜ ⎟= a (T ) ⎝ dT ⎠ a (T )
a (T ) = A + BT + CT
Temperature range (K)
α ( 10 6) (K 1) A (Å)
R.T.–793 803–1173
9.973–10.716 16.264–17.221
B ( 10 5) (Å K 1)
3.687 3.502 3.681 5.200
C ( 10 9) (Å K 2) 3.104 5.356
(3)
where A is a temperature independent term and corresponds to the lattice parameter at absolute zero. B and C represent the coefficients of the linear and quadratic terms, respectively. The thermal properties include contributions from both lattice vibrations and electrons. The electronic contribution is dominant usually at low temperatures [6]. Keeping in view the temperature range in this work, it can be concluded that the thermal expansion is mainly due to lattice vibrations. The values of coefficients A, B and C are listed in Table 1. Since, dependence of lattice parameter on temperature is linear, the coefficient of thermal expansion increases linearly with increase of temperature. The variation in α(T) as a function of temperature is shown in 1
Table 1 Coefficient of thermal expansion (α(T)) for Cu65Fe10Pd25 alloy.
Fig. 3(b). A sudden change in its value near Tc can be clearly seen in Fig. 3(b). 3.4. Mean square amplitude of vibration Mean square amplitude of vibration of an atom ( u2 (T )) was determined from temperature dependence of the normalized integrated intensity (Iobs/Ical) of a high angle fundamental reflection. The integrated intensity of the reflection (hkl) of a polycrystalline sample was calculated using the relation:
Ical = Kp F 2 LPe−2M
(4)
where K is a scale factor, p is the multiplicity factor, F is the structure factor, LP is the Lorentz-polarization factor. The
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N. Ahmad et al. / Physica B 461 (2015) 129–133
experimental value of integrated intensity (Iobs) was determined by using a diffraction software and
Mi = Bi ( sin2θ /λ2),
i = Cu, Fe or Pd
(5)
B is the temperature factor, θ the Bragg angle and λ is the wavelength of the incident X-rays. Since, the temperature factor for Cu, Fe and Pd atoms were nearly identical [9], an assumption B (T ) = BCu (T ) = BFe (T ) = BPd (T ) was made to obtain the value ofB (T ) . Fig. 4(a) shows the plot of ln
( ) as a function of temIobs Ical
perature T, the slope of which gives the value of B (T ) . Debye's high temperature approximation relates the temperature factor B (T ) to mean square amplitude of vibration ( u2 (T )) as [7]:
B (T ) = 8π 2 u2 (T )
(6)
The abrupt change in a(T) linked to first order transition seen earlier is again reflected in the plot of ln
( ) vs. T as well. It can be Iobs Ical
seen that value of u2 (T )in the disordered state is larger than that of the ordered state. 3.5. Debye temperature Debye's high temperature approximation yields [7]:
⎛ 6h2T ⎞ ⎟⎟ + B0. B (T ) = ⎜⎜ ⎝ mkΘ D2 ⎠
(7)
where, B0 is the static part of the temperature factor. The values of ΘD obtained using Eq. (7) for the ordered and disordered are listed in Table 2. The theoretical value of ΘD was obtained from the following relationship [18]: −2 −2 −2 Θ−2 = cCu ΘCu + c Fe Θ Fe + c Pd Θ Pd
(8)
The value of ΘD obtained by Eq. (8) is greater than the experimental value for the disordered case. Fig. 4(b) shows that extrapolated u2 (T ) curve approaches zero value at absolute zero which indicates that the static part of temperature factor B0 is very small.
4. Discussion The O–D transition temperature Tc for Cu3Pd alloy is 781 K [4]. The Tc in the present case is 797 K. i.e. addition of Fe to Cu–Pd leads to an increase in Tc. It can be shown on the basis of method of static concentration wave that the presence of Fe in Cu–Pd suppresses evolution of all other types of waves except L12-type wave which is active upon ordering [12]. This leads to an increase in the value of Tc. The melting point of Cu65Fe10Pd25 was found to be 1395 K. Pure Cu, Fe and Pd have melting points of 1358 K, 1811 K and 1827 K, respectively. The Cu3Pd alloy has a melting of 1405 K [14]. The melting point of Cu65Fe10Pd25 alloy calculated by Lindemann's rule [10] gives a value of 1416 K. Since, the composition of the investigated alloy lies close to that of Cu3Pd, the decrease in the Table 2 Debye temperature (ΘD) of ordered and disordered Cu65Fe10Pd25 alloy. Cu65Fe10Pd25
ΘD (K)
Ordered Disordered
373 7 0.9 314 7 1
value of melting point can be attributed to the weakening of bonding forces resulting from addition of Fe. A material melts at that temperature for which the amplitude of thermal vibration is a certain fraction of the interatomic distance in the crystal. It has been reported that addition of Fe to Cu3Pd leads to a change in the value of lattice parameter [1]. The present study has shown that the addition of the Fe in Cu3Pd alloy results in a larger value of lattice parameter, thermal expansion and mean square amplitude of vibration. In other words, the Fe addition induces static expansion and dynamic softening in the crystal lattice. Substitution of Cu atoms with Fe atoms weakens the interatomic bonding force [14]. This is in accordance with the expectations as the atomic radius of Fe atom (1.27 Å) is comparable to the radii of Cu (1.28 Å) and Pd (1.38 Å) [16]. It can be seen from Fig. 3(a and b) that the relationship between the lattice parameter and the coefficient of thermal expansion is linear in the case of both ordered and disordered states. The equilibrium interatomic distance depends on the forces between atoms. These forces help the lattice to resist any change in its size caused by thermal effects [13]. This may a possible explanation for the observed relationship observed between the lattice parameter and the coefficient of thermal expansion. The value of u2 (T ) increases with the increase of the temperature. This is due to the fact that there is an increase in lattice vibration with the increase of temperature. This is in close agreement with prediction based on theory [14]. The temperature factor B (T ) usually contains two parts i.e. a temperature dependent part B (T ) and the static part B0 . The static component arises due to difference in atomic size of the constituents atoms. Since, the atomic sizes of Cu-, Fe- and Pd-atoms are nearly equal, so the contribution from static part of temperature factor (B0) is expected to be extremely small. The experiments show that the value of B0 was nearly zero. Although, there is a small difference in the thermal parameters of Cu65Fe10Pd25 and Cu3Pd alloys, both have smaller coefficient of thermal expansion than that of pure Pd and binary Cu3Pd alloy [11,15]. The slope of α(T) curves in ordered state is less than that of disordered state. The slight increase in slope of α(T) curve in the later case might be related to anharmonicity of the lattice. The relation between ΘD and stiffness constant c44 is given below [19]:
θD =
1/2 h ⎛ 3N ⎞1/3 ⎛ c44 ⎞ ⎜ ⎟ ⎜ ⎟ k B ⎝ 4π V ⎠ ⎝ ρ ⎠
(9)
where, (N/V) is the number of atoms per unit cell. The other symbols have usual meanings. It can be clearly seen from Eq. (9) that ΘD is directly proportional to c44 . Therefore, increase or decrease in the value of ΘD will depend directly on the stiffness constant i.e. a material with large stiffness constant will be expectedly harder and vice versa. In the present case, the ΘD for Cu65Fe10Pd25 ordered alloy is large as compared to that of Cu3Pd. The addition of Fe to Cu–Pd alloy weakens the interatomic bonding in the disordered state as indicated by the results for melting temperature. The ΘD therefore decreases and the alloy becomes softer. But the interatomic interactions of Fe with Cu and Pd in the ordered state are such that they lead to an increase in the value of stiffness constant. Hence, the ΘD is large and alloy becomes harder. The results show that the thermal parameters change drastically when the sample undergoes a phase change at Tc. The value of all the thermal parameters reduce when the sample is in ordered state. This shows that the degree of thermal expansion can be controlled by two ways: (i) by the ternary addition of various
N. Ahmad et al. / Physica B 461 (2015) 129–133
elements and (ii) by ordering. This provides a method for practical application of these alloys. More detailed investigation of thermal properties in ordered alloys are necessary for finding out ways to improve properties of materials and their application in the field of thermo-engineering.
Acknowledgment
5. Conclusions
References
Structural and thermal parameters have been studied in Cu65Fe10Pd25 alloy during order–disorder transformation using differential scanning calorimetry and high temperature X-ray diffraction. The results show that: i. The Cu65Fe10Pd25 alloy undergoes an O–D transformation at Tc ¼797 K. The alloy shows L12 type ordering below Tc and has disordered fcc structure above Tc. ii. The lattice parameter shows a positive deviation from Vegard's rule which may be related to the weakening of interatomic forces by the addition of Fe in the disordered state. iii. The integrated intensity data obtained from the X-ray diffraction experiments was utilized to determine the coefficient of thermal expansion (α(T)), mean square amplitude of vibration ( u2 (T )) and Debye temperatures (ΘD) in both ordered and disordered state. iv. The abrupt change in the value of lattice parameter (a(T)) and coefficient of thermal expansion (α(T)) at Tc shows that the nature of O–D transition is first order.
133
One of the authors Naseeb Ahmad wishes to acknowledge the financial support of Higher Education Commission (H. E. C.), Government of Pakistan, Islamabad, during the course of this work.
[1] [2] [3] [4] [5] [6] [7] [8]
[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
N.I. Kourov, et al., Phys. Met. Metall. 75 (2010) 337. A. Hussain, et al., Chin. J. Phys. 47 (2009) 344. N.I. Kourov, et al., J. Phys. Met. Metall. 104 (2007) 232. P.R. Subramanian, et al., J. Phase Equilib. 12 (1991) 231. E. Ahmed, et al., J. Alloy. Compd. 473 (2009) 1. A.B. Ziya, et al., J. Alloy. Compd. 479 (2009) 60. B.D. Cullity, et al., Elements of X-Ray diffraction, third ed., Prentice Hall, Pearson, 2001. D.B. Williams, et al., Transmission Electron Microscopy: A Textbook for Materials Science, second ed., Springer Science and Business Media, USA (2009) 262. J.A. Ibers, et al., International Tables for X-ray Crystallography, The Kynoch Press, Birmingham, 1974. S.A. Cho, et al., J. Phys. F: Met. Phys. 12 (1982) 1069. Y. Sato, et al., J. Phys. Rev. B 1 (1970) 1402. A.G. Khachaturyan, et al., Prog. Mater. Sci. 22 (1978) 1. Y.C. Venudhar, et al., J. Less-Common Met. 116 (1986) 341. S.O. Kart, et al., J. Achiev. Mater. Manuf. Eng. 31 (2008) 41–46. J.W. Arblaster, et al., J. Platin. Met. Rev. 56 (2012) 181. P.M. Chaikin, et al., Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, 1998. Z. Jun, et al., J. Sci. China Ser. G-Phys. Mech. Astron. 52 (2009) 1039. A.B. Ziya, et al., J. Alloy. Compd. 425 (2006) 123. W.P. Mason, Physical Acoustics, Part B-Lattice Dynamics, 3, Academic Press, New York, 1965.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
The structure and thermal parameters of ordered Cu65Fe10Pd25 ternary alloy N. Ahmad a, A.B. Ziya a,n, A. Ibrahim b, S. Atiq b, S. Ahmad a, F. Bashir c a
Department of Physics, Bahauddin Zakariya University, Multan 60800, Pakistan Institute of Advanced Materials, Bahauddin Zakariya University, Multan 60800, Pakistan c L. C. W. University, Lahore, Pakistan a
art ic l e i nf o
a b s t r a c t
Article history: Received 21 October 2014 Received in revised form 6 January 2015 Accepted 7 January 2015 Available online 8 January 2015
Structural and thermal parameters have been studied in Cu65Fe10Pd25 alloy during order–disorder (O–D) transformation using differential scanning calorimetry (DSC) and high temperature X-ray diffraction (HTXRD). The results reveal that the Cu65Fe10Pd25 alloy undergoes an O–D transformation at Tc ¼ 797 K. The alloy shows L12 type ordering below Tc and has disordered face centered cubic (fcc) structure above Tc. The lattice parameter shows a positive deviation from Vegard’s rule which may be related to the weakening of interatomic forces by the addition of Fe. The integrated intensity data obtained from the diffraction experiments was utilized to determine the coefficient of thermal expansion (α(T)), mean square amplitude of vibration ( u2 (T )) and Debye temperatures (ΘD) during the O–D transformation. The abrupt change in the value of lattice parameter and coefficient of thermal expansion at Tc shows that the nature of O–D transition is first order. These results have been discussed by comparing them to those for Cu3Pd alloy. & 2015 Elsevier B.V. All rights reserved.
Keywords: Lattice parameter Structure X-ray diffraction O–D transition
1. Introduction The formation of ordered structures and the development of long-range order (LRO) in the arrangement of atoms of different type is characteristic of many alloy systems. Atomically ordered alloys possess specific physical properties. The copper–palladium (Cu–Pd) alloys are of great interest with regard to their application as well as from the point of view of the scientific understanding. Structurally ordered Cu3Pd alloys have a face centered cubic (fcc) lattice of the L12 type, which depends on temperature, composition and thermal treatment [1,2]. Ordered Cu–Pd and other transition metals alloys are extensively used in electronic industry as electro-contact materials. Therefore, it is necessary to know the role of the mechanisms of scattering of charge carriers and the peculiarities of the Fermi surface in the development of transport properties of such alloys [3]. These alloys have received a lot of attention from researchers because Cu–Pd alloys exhibit variety of ordered phases. It has been reported that disordered fcc Cu–Pd alloys, in the range of about 8–30 at% Pd, transform into a variety of ordered structures below 773 K [4]. Thermal expansion is one of the fundamental physical properties in materials science and engineering. INVAR alloys are one n
Corresponding author. Fax: þ 92 61 9210068. E-mail address: [email protected] (A.B. Ziya).
http://dx.doi.org/10.1016/j.physb.2015.01.004 0921-4526/& 2015 Elsevier B.V. All rights reserved.
of the examples which are being used in precise mechanical machines [5]. The mechanical properties of alloys are also directly linked to their characteristic Debye temperature (ΘD). Determination of Debye temperature is given of great importance in crystallography because of its use in structural refinement and explanation of various properties. The scientific understanding and technological importance of thermal expansion of the alloys has lead to its measurement for various materials [6,8,17]. The structural properties of alloys can be modified by the addition of ternary alloying elements. The addition of Fe in Cu–Pd alloys is expected to improve the order–disorder transformation temperature (Tc) and magnetic properties of these alloys. In the present study, structure and thermal properties of Cu65Fe10Pd25 alloy are investigated by using high temperature X-ray diffraction (HTXRD). Thermal parameters were determined by using the Bragg line displacement method [6]. Thermal parameters of Cu65Fe10Pd25 alloy in both ordered and disordered states have been determined and compared.
2. Experimental method The sample of Cu65Fe10Pd25 alloy (5 g) was prepared from spectroscopically pure Cu, Fe and Pd metals by using arc-melting furnace with water cooled copper hearth under an atmosphere of purified argon. The samples were remelted six times to ensure the
130
N. Ahmad et al. / Physica B 461 (2015) 129–133
homogeneity of the alloy constituents. The ingot was sealed in quartz tubes under a vacuum of 2.0 10 3 Pa and annealed for 20 h at 1273 K in order to homogenize them. Thin slices were cut from the ingot, one of which was annealed at 723 K for one week and subsequently furnace cooled to room temperature to avoid the accumulation of surplus vacancies. The composition of Cu65Fe10Pd25 alloy was determined by using electron probe microanalyzer (EPMA, JXA-8100, JEOL). The composition was measured at ten different points and the average composition was taken as the true composition of the alloy. The homogeneity variation of the alloy was found to be less than 1 at%. The sample was then grinded and polished to produce a smooth surface suitable for HTXRD experiments. The HTXRD experiments were performed on a Bruker D8 AXS diffractometer fitted with an evacuated chamber having a Pt–Rh heater and precise temperature measurement arrangement. Diffraction patterns were taken in the scattering angle range of 15–135° under θ– θ geometry with divergence and receiving slits of 0.5° using Nifiltered CuKα radiation. The tube parameters were 45 kV and 40 mA. The HTXRD experiments were performed in the range of 300–1173 K with an increment of 50 K in general but 10 K near the order–disorder (O–D) transition temperature (Tc). The data was corrected for instrumental errors by using a highly pure silicon powder as external standard. The thermal analysis of the sample was performed on a differential scanning calorimeter (DSC, model SBT-Q600) under nitrogen atmosphere at a heating rate of 20 K/min up to a temperature of 1500 K.
3. Results and evaluation 3.1. Differential scanning calorimetry Fig. 1 shows the DSC thermograms of Cu65Fe10Pd25 alloy. The change in heat flow beyond 1395 K reflects the on-set of melting of the alloys. A small endothermic peak at 797 K was observed which shows change of phase from ordered to disordered. These results are consistent with those obtained from HTXRD explained later. 3.2. Structural study by X-ray diffraction Fig. 2 shows the X-ray diffraction patterns of Cu65Fe10Pd25 alloy taken at various temperatures. The prominent feature of all
Fig. 1. Thermogram of Cu65Fe10Pd25 alloy recorded on a differential scanning calorimeter at a heating rate of 20 K/min.
Fig. 2. X-ray diffraction patterns of Cu65Fe10Pd25 alloy taken at various temperatures during in-situ diffraction experiments.
patterns is the presence of sharp (100)-, (110)-, and (210)-superlattice reflections and (111)-, (200)-, (220)-, (311)-, (222)-, (400)and (331)-fundamental reflections. The small peak adjacent to (200) originated from the Pt–Rh heater used in the HTXRD experiments. The superlattice reflections disappear above 797 K, which indicate the O–D transformation. The structure factor for Cu65Fe10Pd25 alloy with L12 type ordered structure is:
F Fundamental = c Pd fPd + 3 (cCu fCu + c Fe fFe )
(1)
F Superlattice = c Pd fPd − (cCCu fCu + c Fe fFe )
(2)
The observed superlattice and fundamental reflections obey Eqs. (1) and (2), respectively, which confirm that the alloy has L12 type ordered structure. The true value of lattice parameter at room temperature was obtained by the extrapolation of lattice parameters for each reflection against Nelson–Riley function and was found to be 3.697 70.002 Å. The value of lattice parameter shows a positive deviation from Vegard's rule (3.673 Å). This result is consistent with the Cu3Pd alloy [4]. The data obtained from HTXRD experiments was utilized to obtain the temperature dependence of lattice parameter (Fig. 3(a)) and the thermal parameters (Figs. 3 (b) and 4(a and b)). The O–D transition observed in diffraction patterns at Tc ¼797 K is also reflected in Fig. 3(a). The sudden change in lattice parameter at Tc indicates that this transition is a first order transition [16]. A change Δa = 0.010 Å was observed in the value of lattice parameter at Tc. Two methods have been reported for the determination of thermal parameters from the X-ray diffraction data. One is the use of integrated intensity data of all Bragg reflections in the pattern at a fixed temperature (usually referred to as Wilson-plot method [18]). The second method employs the temperature dependence of integrated intensity of a high angle Bragg reflection (usually referred to a Bragg-line displacement method) and is used to eliminate the effects of preferred orientation. The later method has been used in the present study and results are given in the following sections.
N. Ahmad et al. / Physica B 461 (2015) 129–133
Fig. 3. Temperature dependence of ordered and disordered Cu65Fe10Pd25 alloy (a) lattice parameter a(Å) and (b) coefficient of thermal expansion (α(T)).
131
Iobs ) for Cu 65Fe10Pd 25 alloy and Ical vibration u2 (T ) of Cu Fe Pd alloy.
Fig. 4. (a) The temperature dependence of (a) ln ( (b) Mean-square amplitude of thermal
65
10
25
3.3. Thermal expansion The temperature dependence of coefficient of thermal expansion (α(T)) is shown in Fig. 3(b). The value of α(T) was determined by least square fitting of a second degree polynomial1 to the data of lattice parameter a(Å) shown in Fig. 3(a):
1 ⎛ da (T ) ⎞ 1 α (T ) = (B + 2CT ) ⎜ ⎟= a (T ) ⎝ dT ⎠ a (T )
a (T ) = A + BT + CT
Temperature range (K)
α ( 10 6) (K 1) A (Å)
R.T.–793 803–1173
9.973–10.716 16.264–17.221
B ( 10 5) (Å K 1)
3.687 3.502 3.681 5.200
C ( 10 9) (Å K 2) 3.104 5.356
(3)
where A is a temperature independent term and corresponds to the lattice parameter at absolute zero. B and C represent the coefficients of the linear and quadratic terms, respectively. The thermal properties include contributions from both lattice vibrations and electrons. The electronic contribution is dominant usually at low temperatures [6]. Keeping in view the temperature range in this work, it can be concluded that the thermal expansion is mainly due to lattice vibrations. The values of coefficients A, B and C are listed in Table 1. Since, dependence of lattice parameter on temperature is linear, the coefficient of thermal expansion increases linearly with increase of temperature. The variation in α(T) as a function of temperature is shown in 1
Table 1 Coefficient of thermal expansion (α(T)) for Cu65Fe10Pd25 alloy.
Fig. 3(b). A sudden change in its value near Tc can be clearly seen in Fig. 3(b). 3.4. Mean square amplitude of vibration Mean square amplitude of vibration of an atom ( u2 (T )) was determined from temperature dependence of the normalized integrated intensity (Iobs/Ical) of a high angle fundamental reflection. The integrated intensity of the reflection (hkl) of a polycrystalline sample was calculated using the relation:
Ical = Kp F 2 LPe−2M
(4)
where K is a scale factor, p is the multiplicity factor, F is the structure factor, LP is the Lorentz-polarization factor. The
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experimental value of integrated intensity (Iobs) was determined by using a diffraction software and
Mi = Bi ( sin2θ /λ2),
i = Cu, Fe or Pd
(5)
B is the temperature factor, θ the Bragg angle and λ is the wavelength of the incident X-rays. Since, the temperature factor for Cu, Fe and Pd atoms were nearly identical [9], an assumption B (T ) = BCu (T ) = BFe (T ) = BPd (T ) was made to obtain the value ofB (T ) . Fig. 4(a) shows the plot of ln
( ) as a function of temIobs Ical
perature T, the slope of which gives the value of B (T ) . Debye's high temperature approximation relates the temperature factor B (T ) to mean square amplitude of vibration ( u2 (T )) as [7]:
B (T ) = 8π 2 u2 (T )
(6)
The abrupt change in a(T) linked to first order transition seen earlier is again reflected in the plot of ln
( ) vs. T as well. It can be Iobs Ical
seen that value of u2 (T )in the disordered state is larger than that of the ordered state. 3.5. Debye temperature Debye's high temperature approximation yields [7]:
⎛ 6h2T ⎞ ⎟⎟ + B0. B (T ) = ⎜⎜ ⎝ mkΘ D2 ⎠
(7)
where, B0 is the static part of the temperature factor. The values of ΘD obtained using Eq. (7) for the ordered and disordered are listed in Table 2. The theoretical value of ΘD was obtained from the following relationship [18]: −2 −2 −2 Θ−2 = cCu ΘCu + c Fe Θ Fe + c Pd Θ Pd
(8)
The value of ΘD obtained by Eq. (8) is greater than the experimental value for the disordered case. Fig. 4(b) shows that extrapolated u2 (T ) curve approaches zero value at absolute zero which indicates that the static part of temperature factor B0 is very small.
4. Discussion The O–D transition temperature Tc for Cu3Pd alloy is 781 K [4]. The Tc in the present case is 797 K. i.e. addition of Fe to Cu–Pd leads to an increase in Tc. It can be shown on the basis of method of static concentration wave that the presence of Fe in Cu–Pd suppresses evolution of all other types of waves except L12-type wave which is active upon ordering [12]. This leads to an increase in the value of Tc. The melting point of Cu65Fe10Pd25 was found to be 1395 K. Pure Cu, Fe and Pd have melting points of 1358 K, 1811 K and 1827 K, respectively. The Cu3Pd alloy has a melting of 1405 K [14]. The melting point of Cu65Fe10Pd25 alloy calculated by Lindemann's rule [10] gives a value of 1416 K. Since, the composition of the investigated alloy lies close to that of Cu3Pd, the decrease in the Table 2 Debye temperature (ΘD) of ordered and disordered Cu65Fe10Pd25 alloy. Cu65Fe10Pd25
ΘD (K)
Ordered Disordered
373 7 0.9 314 7 1
value of melting point can be attributed to the weakening of bonding forces resulting from addition of Fe. A material melts at that temperature for which the amplitude of thermal vibration is a certain fraction of the interatomic distance in the crystal. It has been reported that addition of Fe to Cu3Pd leads to a change in the value of lattice parameter [1]. The present study has shown that the addition of the Fe in Cu3Pd alloy results in a larger value of lattice parameter, thermal expansion and mean square amplitude of vibration. In other words, the Fe addition induces static expansion and dynamic softening in the crystal lattice. Substitution of Cu atoms with Fe atoms weakens the interatomic bonding force [14]. This is in accordance with the expectations as the atomic radius of Fe atom (1.27 Å) is comparable to the radii of Cu (1.28 Å) and Pd (1.38 Å) [16]. It can be seen from Fig. 3(a and b) that the relationship between the lattice parameter and the coefficient of thermal expansion is linear in the case of both ordered and disordered states. The equilibrium interatomic distance depends on the forces between atoms. These forces help the lattice to resist any change in its size caused by thermal effects [13]. This may a possible explanation for the observed relationship observed between the lattice parameter and the coefficient of thermal expansion. The value of u2 (T ) increases with the increase of the temperature. This is due to the fact that there is an increase in lattice vibration with the increase of temperature. This is in close agreement with prediction based on theory [14]. The temperature factor B (T ) usually contains two parts i.e. a temperature dependent part B (T ) and the static part B0 . The static component arises due to difference in atomic size of the constituents atoms. Since, the atomic sizes of Cu-, Fe- and Pd-atoms are nearly equal, so the contribution from static part of temperature factor (B0) is expected to be extremely small. The experiments show that the value of B0 was nearly zero. Although, there is a small difference in the thermal parameters of Cu65Fe10Pd25 and Cu3Pd alloys, both have smaller coefficient of thermal expansion than that of pure Pd and binary Cu3Pd alloy [11,15]. The slope of α(T) curves in ordered state is less than that of disordered state. The slight increase in slope of α(T) curve in the later case might be related to anharmonicity of the lattice. The relation between ΘD and stiffness constant c44 is given below [19]:
θD =
1/2 h ⎛ 3N ⎞1/3 ⎛ c44 ⎞ ⎜ ⎟ ⎜ ⎟ k B ⎝ 4π V ⎠ ⎝ ρ ⎠
(9)
where, (N/V) is the number of atoms per unit cell. The other symbols have usual meanings. It can be clearly seen from Eq. (9) that ΘD is directly proportional to c44 . Therefore, increase or decrease in the value of ΘD will depend directly on the stiffness constant i.e. a material with large stiffness constant will be expectedly harder and vice versa. In the present case, the ΘD for Cu65Fe10Pd25 ordered alloy is large as compared to that of Cu3Pd. The addition of Fe to Cu–Pd alloy weakens the interatomic bonding in the disordered state as indicated by the results for melting temperature. The ΘD therefore decreases and the alloy becomes softer. But the interatomic interactions of Fe with Cu and Pd in the ordered state are such that they lead to an increase in the value of stiffness constant. Hence, the ΘD is large and alloy becomes harder. The results show that the thermal parameters change drastically when the sample undergoes a phase change at Tc. The value of all the thermal parameters reduce when the sample is in ordered state. This shows that the degree of thermal expansion can be controlled by two ways: (i) by the ternary addition of various
N. Ahmad et al. / Physica B 461 (2015) 129–133
elements and (ii) by ordering. This provides a method for practical application of these alloys. More detailed investigation of thermal properties in ordered alloys are necessary for finding out ways to improve properties of materials and their application in the field of thermo-engineering.
Acknowledgment
5. Conclusions
References
Structural and thermal parameters have been studied in Cu65Fe10Pd25 alloy during order–disorder transformation using differential scanning calorimetry and high temperature X-ray diffraction. The results show that: i. The Cu65Fe10Pd25 alloy undergoes an O–D transformation at Tc ¼797 K. The alloy shows L12 type ordering below Tc and has disordered fcc structure above Tc. ii. The lattice parameter shows a positive deviation from Vegard's rule which may be related to the weakening of interatomic forces by the addition of Fe in the disordered state. iii. The integrated intensity data obtained from the X-ray diffraction experiments was utilized to determine the coefficient of thermal expansion (α(T)), mean square amplitude of vibration ( u2 (T )) and Debye temperatures (ΘD) in both ordered and disordered state. iv. The abrupt change in the value of lattice parameter (a(T)) and coefficient of thermal expansion (α(T)) at Tc shows that the nature of O–D transition is first order.
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One of the authors Naseeb Ahmad wishes to acknowledge the financial support of Higher Education Commission (H. E. C.), Government of Pakistan, Islamabad, during the course of this work.
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