The Debye temperature of quasi-equi-atomic α-Fe–Cr alloys

Cieślak, J.; Costa, B.F.O.; Dubiel, S.

doi:10.1088/0953-8984/18/48/017

Cited by 6 publications

(8 citation statements)

References 14 publications

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“…The value of the vibrational entropy measured at 298 K for the α-phase agrees quite well with inelastic neutron scattering results on samples of similar composition [14]. Also the difference in the entropy values, ∆S = S σ − S α = 0.095 ± 0.009k B as determined in the present experiment from the Fe-partial DOS agrees well with the corresponding difference calculated from the equation ∆S = 3k B ln(Θ Dσ /Θ Dα ) = 0.07k B , where k B is the Boltzmann constant and Θ Di is the Debye temperature as determined from the second-order Doppler shift for the α (i = α) and the σ (i = σ) phase, respectively [3]. The corresponding theoretical value of ∆S is equal to 0.058 k B .…”

supporting

confidence: 90%

“…Its physical properties are, in general, quite different than those of the α-phase of similar composition. Some properties, like the magnetic ones, are even dramatically different [2], other properties, like the Debye temperature, seem to be very similar [3]. The latter is rather unexpected as the hardness of the σ-phase is by a factor of ∼ 3 larger than that of the α-phase.…”

mentioning

confidence: 91%

“…5 Cr 47.5 sample was approximated by a σ-Fe 53. 3 Cr 46.7 one. The latter was studied in the 1×1×1 tetragonal supercell with 30 atoms (16 Fe and 14 Cr atoms).…”

mentioning

confidence: 98%

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Vibrational Properties ofα- andσ-Phase Fe-Cr Alloy

Dubiel¹,

Cieślak²,

Sturhahn³

et al. 2010

Phys. Rev. Lett.

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Experimental investigation as well as theoretical calculations, of the Fe-partial phonon density-ofstates (DOS) for nominally Fe52.5Cr47.5 alloy having (a) α-and (b) σ-phase structure were carried out. The former at sector 3-ID of the Advanced Photon Source, using the method of nuclear resonant inelastic X-ray scattering, and the latter with the direct method [K. Parlinski et al., Phys. Rev. Lett. 78, 4063 (1997)]. The characteristic features of phonon DOS, which differentiate one phase from the other, were revealed and successfully reproduced by the theory. Various data pertinent to the dynamics such as Lamb-Mössbauer factor, f , kinetic energy per atom, E k , and the mean force constant, D, were directly derived from the experiment and the theoretical calculations, while vibrational specific heat at constant volume, CV , and vibrational entropy, S were calculated using the Fe-partial DOS. Using the values of f and CV , we determined values for Debye temperatures, ΘD. An excellent agreement for some quantities derived from experiment and first-principles theory, like CV and quite good one for others like D and S was obtained.For many years Fe-Cr alloy system has been of exceptional scientific and technological interest. The former stems on one hand from its interesting physical properties such as magnetic ones, and on the other hand from the fact that it forms a solid solution within the whole concentration range preserving, at least metastably, the same crystallographic structure (bcc). This, in turn, gives a unique chance for investigating the influence of the composition on various physical properties within the same structure as well as adequatly testing different theoretical models and theories. The latter follows from the fact that Fe-Cr alloys constitute the basic ingredient of stainless steels (SS) that for a century have been one of the most important structural materials [1], and, consequently, some properties of SS are inherited from the parent alloy. To the latter belongs a σ-phase that can precipitate if a quasi-equiatomic Fe-Cr alloy undergoes an isothermal annealing in the temperature range ∼ 800K≤T≤∼ 1100 K. The σ-phase has a tetragonal structure (type D 14 4h P4 2 /mnm) with 30 atoms distributed over five different sites (Table 1). Its physical properties are, in general, quite different than those of the α-phase of similar composition. Some properties, like the magnetic ones, are even dramatically different [2], other properties, like the Debye temperature, seem to be very similar [3]. The latter is rather unexpected as the hardness of the σ-phase is by a factor of ∼ 3 larger than that of the α-phase. To clarify this situation a more detailed knowledge of vibrational properties of the σ-and α-phases is essential. In addition, the σ-phase belongs to an important family of tetrahedrally close-packed FrankKasper phases and is one of the closest low-order crystalline approximants for dodecagonal quasicrystals which have similar local structural properties with the icosahedral glass (ICG) [4]. The...

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confidence: 90%

mentioning

confidence: 91%

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Vibrational Properties ofα- andσ-Phase Fe-Cr Alloy

Dubiel¹,

Cieślak²,

Sturhahn³

et al. 2010

Phys. Rev. Lett.

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“…The Θ D -values shown in Fig. 5 are very close to those found for α-FeCr alloys of similar composition [26]. This is rather an unexpected result as the Debye temperature is thought to reflect a toughness or stiffness of a solid state material, Fig.…”

Section: Determination Of the Debye Temperaturesupporting

confidence: 73%

Sigma phase—one of the main reasons for deterioration of stainless steels properties

Dubiel

2009

Hyperfine Interact

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“…These figures can be compared with the value of 398 K derived from f as determined from the room temperature PDOS recorded on Fe 52.5 Cr 47.5 alloy. 66 It is interesting to note that for the α-FeCr alloys of similar compositions, D parallels the behaviour found for σ , though its values are shifted downwards by ∼10 K. 76 In the Fe-V system, where the range of σ occurrence is much wider, D shows a non-monotonic behavior as a function of composition with its extreme values between ∼425 K for x ≈ 40 and ∼600 K for x ≈ 60. A local maximum of ∼525 K was found to exist at x ≈ 43.…”

Section: Debye Temperaturementioning

confidence: 59%

Sigma-Phase in Fe-Cr and Fe-V Alloy Systems and its Physical Properties

Dubiel

Cieślak

2011

Critical Reviews in Solid State and Materials Sciences

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This review addresses the physical properties of the σ -phase in Fe-Cr and Fe-V alloy systems as revealed both with experimental-mostly with the Mössbauer spectroscopy-and theoretical methods. In particular, the following questions relevant to the issue have been addressed: identification of σ and determination of its structural properties, kinetics of α-to-σ and σ -to-α phase transformations, Debye temperature and Fe-partial phonon density of states, Curie temperature and magnetization, hyperfine fields, isomer shifts and electric field gradients.

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The Debye temperature of quasi-equi-atomic α-Fe–Cr alloys

Cited by 6 publications

References 14 publications

Vibrational Properties ofα- andσ-Phase Fe-Cr Alloy

Vibrational Properties ofα- andσ-Phase Fe-Cr Alloy

Sigma phase—one of the main reasons for deterioration of stainless steels properties

Sigma-Phase in Fe-Cr and Fe-V Alloy Systems and its Physical Properties

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