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A non-convex free energy function is constructed to characterize different polarization orientations in the materials.
A non-convex free energy function is constructed to characterize different polarization orientations at mesoscale in the materials.
For the purpose, we confine our discussion here with perovskite-type materials, and in a one-dimensional description.
It is easy to show that hysteresis loops observed in the electric field in the materials are embedded in the above constitutive laws.
Hall, Journal of Materials Science, Vol. 36, (2001), 4575- 4601

Computational Materials Science 42.4(2008):537-549
Journal of Materials Processing Tech 151.1(2004):63-69
Journal of Materials Processing Tech 177.1-3(2006):197-201
International Journal of Minerals Metallurgy and Materials 16.2(2009):177-183
Materials & Design 31.4(2010):2001-2010

Laser technology is one of the most versatile techniques used in a variety of materials processing for wide range of materials.
Dutkiewicz: Texturization of multicrystalline silicon by wet chemical etching for silicon solar cells, Journal of Materials Science, Vol.40, No 6, (2004), p. 1459 - 1463
Chibani: Characterization of texture surface for solar cells, Journal of Applied Science, Vol. 10 (3) (2010), p. 231 - 234
Zięba: Laser surface treatment of multicrystalline silicon for enhancing optical properties, Journal of Materials Processing Technology, 201 (2008), p. 291 - 296
Drygała: Laser processing of multicrystalline silicon for texturization of solar cells, Journal of Materials Processing Technology, 191 (2007), p. 228 - 231

Table 1: Material alloys with their refractive indexes.
Materials used for mirror simulations are shown together with their refractives indexes in Table 1.
Same materials are used for all the VCSEL structures as only I-V characteristics (Power, Voltage and Current) are studied by only varying the number of QWs and reflectivity of the two bragg stacks.
F.R.S., "Xxxiv. on the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 47, no. 287, pp. 375-384, 1899
Han, "Distributed bragg reflectors for gan-based vertical-cavity surface-emitting lasers," Applied Sciences, vol. 9, p. 1593, 04 2019

Journal of Electronic Materials (2011)
Journal of Electronic Materials.
ProQuest Science Journals, 35 (2006) 1017
Materials Letters. 65(2011) 3216–3218 [13] Huang, Z.F., Conway, P.P, Jung, E., Thomson, R.C, Liu, C.Q, and Loeher T..
Journal of Electronic Materials. 35(2006)1761-1772.

Materials and methods Materials.
Liu: Journal of Building Structures J., 28(1): 64-71. (2007) [4] S.
Huang and Y.Zhu: Jiangxi Forestry Science and Technology J., 6: 54, 62. (2008) [6] J.Gilfillang, S.Gilbert, and G.Patrick: Journal of Reinforced Plastics J., 22(15): 1373-1387. (2000) [7] J.
Dias: Material Research J., 6(2): 193-202. (2003) [8] D.Svecova and R.Eden J: Canadian Journal of Civil Engineering J., 31: 45-55. (2004) [9] A.Borri, M.Corradi, and A.Grazini: Composites: Part B. 36: 143-153. (2005) [10] J.
Thesis, College of Materials Science and Technology, Beijing Forestry University. (2008) [11] Y.

TRUSM utilizes the vibration of the elastic body (stator) in the ultrasonic frequency band and the reverse piezoelectric effect of piezoelectric materials.
Models above did not take into account the radial slide between the stator and the rotor and the transformation efficiency of the piezoelectric materials.
Smart Materials and Structures, 1998, 7,pp:352-368
Journal of Intelligent Material Systems and Structures, 2003, 14(10),pp:657-667
Mechanical Science and Technology, 2005, 24(12),pp:1411-1415.

Material and Experimental Method Experimental materials.
Design of process parameters for dual phase steel production with strip rolling using the finite-element method [J], Journal of Materials Processing Technology, 92-93(1999): 486-493 [5] X.H.Xue, Y.Y.Shan, L.Zheng, et al.
Materials Science and Engineering A, 438–440 (2006): 285-287 [6] A.
Materials Letters, 56 (2002): 200-209 [7] R.
Journal of Iron and Steel Research International, 19 (2012): 37-41

Materials and methods Materials and reagents.
West China Journal of Pharmaceutical Sciences,2012,6
Study on Leucaena leaf flavonoids [J]; Journal of Hainan Normal University;2008 02 [5] LI J X.
Isolation and identification of a sterol composition parsley [J]. traditional Chinese medicinal materials，2000，23(9):546
Henan Vocational Technical Teachers College Journal，2004，32(1):48-50.

There is a growing interest in use of the nickel-based alloy Inconel 625 coatings due to its ability to improve base materials high temperature properties.
Sampath, "Substrate temperature effects on the splat formation, microstructure development and properties of plasma sprayed coating", Materials Science and Engineering Vol.
Okumiya, "Characterization and properties of splats sprayed with different cast iron powders", Materials Letters Vol. 58, (2004), p. 2481
Herman, "Rapid solidification and microstructure development during plasma spray deposition", Journal of Thermal Spray Technology, Vol. 5(4) (1996)
Grant, "Characterization of electric arc spray formed Ni superalloy IN718", Materials Science and Engineering Vol.