Fe ve Fe - %25 Al için maksimum streslerin (hkl) düzlemlerinde teorik olarak hesaplanması

Yıl 2017, Cilt: 19 Sayı: 3, 23 - 30, 07.12.2017

Hamza Yaşar Ocak Ali Çetin Gencer Sarıoğlu

https://doi.org/10.25092/baunfbed.363741

Öz

Oda
sıcaklığında Fe ve Fe-% 25 Al (Fe₃Al) kristalleri bcc yapıda olup,
deneysel örgü parametreleri (a₀) 
2.87 Å ve 2,8964 Å dur. İç etkileşme enerjileri birbirlerine çok yakın
olan Fe ve Fe₃Al kristallerinin, fiziksel özellikleri birçok yönden
incelenmektedir. Temel fiziksel parametreler (hkl) kristal düzlemlerinde,
farklı büyüklüklere sahiptir. Bu çalışmada, elastik parametrelerden, maksimum
stressler (T_hkl),   hem Fe hem
de Fe₃Al kristalleri için (hkl) düzlemlerinde incelendi. Bunun için,
öncelikle Wien2k yöntemi kullanılarak ikinci derece elastik sabitler (C₁₁,
C₁₂ ve C₄₄) kübik simetri için hesaplandı. Kristallerin
örgü parametreleri ve saçılma açıları (2θ) pik genişliklerini (β_hkl)
bulmak için kullanıldı. Düzlemlere göre hesaplanan bazı elastik parametreler,
farklı denklemlerden hesaplanan sonuçlarla karşılaştırıldı. Kristal boyutlarına
(D_hkl) bağlı olan dislokasyon yoğunluğunlukları (δ_hkl) da
(hkl) düzlemlerinde incelendi. Elde edilen tüm sonuçlar, (hkl) düzlemleri ve
bazı [hkl] doğrultularına göre yorumlanarak, yakın çalışma sonuçları ile
karşılaştırıldı. Bu tarz analitik incelemelerin (222) düzlemine kadar
genişletilmesinin yeterli olabileceği sonucuna ulaşıldı.

Anahtar Kelimeler

Fe ve Fe - % 25 Al, maksimum stres, young sabiti, pik genişliği, kristal boyutu, dislokasyon yoğunluğu

Theoretical calculation of maximum stresses (hkl) planes for Fe and Fe - 25% Al

Öz

At room temperature, Fe
and Fe-25% Al (Fe₃Al) crystals are in bcc structure and the
experimental lattice parameters (a₀) are 2.87 Å and 2.8964 Å. The
physical properties of Fe and Fe₃Al crystals, whose internal
interaction energies are very close to each other, are investigated from many
perspectives. The basic physical parameters have different sizes in the (hkl)
crystal planes. In this study, the maximum stresses (T_hkl) were
investigated from the elastic parameters in the (hkl) planes for both Fe and Fe₃Al
crystals. For this, second order elastic constants (C₁₁, C₁₂
and C₄₄) were calculated first for cubic symmetry by using the
Wien2k method. The lattice parameters of the crystals and scattering angles
(2θ) were used to find the peak widths (β_hkl). Some elastic
parameters calculated with respect to the planes were compared with the results
calculated from different equations. The dislocation densities (δhkl) related
to crystal dimensions (D_hkl) were also studied in planes (hkl). All
the obtained results were interpreted according to (hkl) planes and some [hkl]
directions and compared with the results of other close studies. It has been
reached that such analytical investigations could be extended to the (222)
plane.

Anahtar Kelimeler

Fe and Fe3Al, maximum stress, young stability, peak width, crystal dimension, dislocation intensity

Kaynakça

• Gargicevich, D., Galvan Josa, V.M., Blanco, C., Lambri, O.A. and Cuello, G.J., Structure determination of Fe-Al-Ge alloys. Journal of Physics Conference Series, 663, 01204 (2015).
• Alonso, P.R., Gargano, P.H., Bozzano, P.B., Ramirez-Caballero, G.E., Balbuena, P.B. and Rubiolo, G.H., Combined ab initio and experimental study of A2+L21 coherent equilibria in the Fe-Al-X (X=Ti, Nb, V) systems. Intermetallics, 19, 1157-1167 (2011).
• Ucgun, E. and Ocak, H.Y., Electronic properties of austenite and martensite Fe-9%Mn alloys. Central Eurpean Journal of Physics, 6, 4, 880-811 (2008).
• Bremers, H., Hesse, J., Ahlers, H., Sievert, J. and Zachmann, D., Order and magnetic properties of Fe89-xMn11Alx alloys: magnetization measurement and X-ray diffraction. Journal of Alloys and Compounds, 366, 67-75 (2004). Eumann, M., Sauthoff, G. and Palm, M., Phase equilibria in the Fe–Al–Mo system – Part I: Stability of the Laves phase Fe2Mo and isothermal section at 800°C. Intermetallics, 16, 706-716 (2008).
• Kim, H., Suh, D. and Kim, N.J., Fe-Al-Mn-C Lightweight structural alloys: a review on the microstructures and mechanical properties. Science Technology Advance Mater, 14, 014205 (2013).
• Lung, C.W. and March, N.H., Mechanical Properties of Metals : Atomistic and Fractal Continuum Approaches, World Scientific Pub. Co. Inc., Singapore, (1999).
• Milstein, F., Mechanical stability of crystal lattices with two-body ınteractions. Physcal Review B, 2, 2, 512-518 (1970). Milstein, F. and Rasky, D.J., Volumetric and structural contributions to the ınteratomic potentials and elstic moduli of cubic metals. Physcal Review B, 33, 4, 2341-2349 (1986).
• Borchi, E., Bruzzi, M., Biggeri, U., Furetta, C. and Lemeilleur, F., Elastic moduli of polycrystalline diamond. European Organization for Nuclear Research, 94, 20, (1994).
• Gu, J., Gu, S., Xue, L., Wu, S. and Yan, Y., Microstructure and mechanical properties of in-situ Al13Fe4/Al composites prepared by mechanical alloying and spark plasma sintering. Material Sciences and Engineerinig, 558, 684-691 (2012).
• Skiba, T., Haušild, P., Karlík, M., Vanmeensel, K. and Vleugels, J., Mechanical properties of spark plasma sintered FeAl intermetallics. Intermetallics, 18, 1410-1414 (2010).
• Goulart, P.R., Spinelli, J.E., Cheung, N. and Gargia, A., The effect of cell spacing and distribution of intermetallic fibers on the mechanical properties of hypoeutectic Al-Fe alloys. Materials Chemistry and Physics, 119, 1-2, (2010).
• Leamy, H.J., The elastic stiffness coefficients of ıron-aluminium alloys-II the effect of long range order. Acta Metallurciga, 15, 12, 1839-1851 (1967).
• Rudman, P.S., A zeroth approximation calculation of order with application to the phase diagram. Acta Metallurciga, 8, 5, 321-327 (1960).
• Milstein, F., Morse function description of anharmonicity in pressure-volume relarions of cubic metals. Physica Status Solidi, 48, 2, 681-688 (1971).
• Najafabadi, R. and Kalonji, G., Mechanical stability criteria for ınteratomic potential functions used in computer simulations of materials. Acta Metallurciga, 36, 4, 917-927 (1988).
• Jamal, M., Asadabadi, S.J., Ahmad, I. and Aliabad, H.A., Elastic constants of cubic crystals. Computational Material Sciences 95, 592-599 (2014).
• Gonzales-Ormeño, G.P., and Petrilli, M.H., Ab-initio calculations of the formation energies of BCC-based superlattices in the Fe-Al system. Calphad, 26, 4, 573-582 (2002).
• Zhang, H., Punkkinen, M.P.J., Johansson, B., Hertzman, S. and Vitos, L., Single-crystal elastic constants of ferronagnetic bcc Fe-based random alloys from first-principles theory. Physcal Review B, 81, 184105 (2010).
• Arıkan, N., Ersen, M., Ocak, H.Y, Iyıgör, A, Candan, A., Uğur, Ş., Uğur G., Khenata, R. and Varshney, D., Ab initio study of phonon dispersion and elastic properties of L12 intermetallics Ti3Al and Y3Al. Modern Physics Letters B, 27, 30, 1350224 (2013).
• Bai, Y., Xing, J., Wu, H., Liu, Z., Gao, Y. and Ma, S., Study on Preparation and mechanical Properties of Fe3Al-20wt.%Al2O3 Composites. Materials and Desing, 39, (2012).
• Ocak H.Y., Uçgun E. ve Ünal R., “Experimental and first-principles investigation of the crystal structure of powder metallurgy Al-1.1Sc and Al-2Sc alloys”, Transactions of Nonferrous Metals Society of China, 23, 3020-3026, (2013).
• Wang, J., Xing, J., Cao, L., Su, W. and Gao, Y., Dry sliding wear behavior of Fe3Al alloys prepared by mechanical alloying and plasma activated sintering. Wear, 268, 3-4, (2010).
• Eumann, M., Palm, M. and Sauthoff, G., Alloys based on Fe3Al or FeAl with strengthening Mo3Al precipitates. Intermetallics, 12, 625-633 (2004).
• Nan-xian, C., Atomistic analysis of the field-ion micropcopy image of Fe3Al. Physcal Review B, 57, 22, 8842 (1998). Milstein, F. and Chantasiriwan, S., Theoretical study of the response of 12 cubic metals to uniaxialloading. Physcal Review B, 58, 10, 6006 (1998).
• Yue-Lin, L., Li-Jiang, G. and Shuo, J., Ab-initio investigation on mechanical properties of copper. Chinese Physics B, 21, 9, 1045 (2004).
• Milstein, F., Hill, R. and Huang, K., Theory of the Response of an Cubic Crystals to [111] Loading. Physcal Review B , 21, 10, 4282-4291 (1980).
• Blaha P., Schwarz K.,. Madsen G.K.H, Kvasnich D. ve Luitz J., WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties. Technical Universty, Wien, (2001).
• Karakose E. ve Keskin M., Structural investigations of mechanical properties of Al based rapidly solidified alloys. Materials and Design, 32, 4970–4979 (2011).
• Friák, M., Deges, J., Krein, R. Frommeyer, G. and Neugebauer, J., Combined ab initio and experimental study of structural and elastic properties of Fe3Al-based ternaries, Intermetallics, 18, 1310-1315 (2010).
• Osman Örnek, L12 fazda Rh3La bileşiğinin ab inito çalışması, Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20, 3, 591-595 (2016).
• Cullity, B.D, X- Işınları Difraksiyonu, (Çev. Sümer A.) İTÜ Yayınları, (1966).
• Taylor A. and Jones R.M., Constitution and magnetic properties of ıron-rich ıron-aluminum alloys. Journal of Physics and Chemistry of Solids, 6, 16-37, (1958).
• Peiqing L., Yupeng W., Ruijiao L., Yang Z. and Yang Y., Effect of Mn element on microstructure and mechanical properties of bulk nanocrystalline Fe3Al based materials prepared by aluminothermic reaction, Materials Science and Engineering A, 527, 2313–2319 (2010).
• Schmid E. and Boas W., Plasticity of Crystals. Hughes F.A. and Co. Ltd., London. (1950).
• Hualei Z, Marko P.J. Punkkinen, Johansson B. and Vitos, L., Theoretical elastic moduli of ferromagnetic bcc Fe alloys, Journal of Physics: Condensed Matter, 22, 275402 (2010).
• Foruts, E., Morris, D.G. and Muñoz-Morris, M.A., Evaluation of elastic modulus and hardness of FeeAl base intermetallics by nano-indentation techniques, Intermetallics 38, 1-3 (2013).
• Zamanzade, M., Vehoff, H. and Barnoush, A. Effect of chromium on elastic and plastic deformation of Fe3Al intermetallics, Intermetallics 41, 28-34 (2013).