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Effect of Surface Layer on Young’s Modulus of Ultrathin Nanofilms: A Theoretical Model Yi’ao Jia1,2,3,a, Yehejong Saqier1,2,3,b* and Bai Narsu1,2,3,c* 1College of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China 2Modern Physics Research Center, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China 3Inner Mongolia Key Laboratory of Physics and Chemistry of Functional Materials, Hohhot, 010022, People’s Republic of China a985853010@qq.com, bsaqier@imnu.edu.cn, cnars@imnu.edu.cn Keywords: Ultrathin nanofilm, Young’s modulus, Surface effect.
For the elastic stiffness tensor, different crystal structures have different elastic stiffness tensors; cubic crystals have 3 independent elastic constants, hexagonal crystals have 5, and monoclinic crystals have 13 independent elastic constants.
This paper discusses only cubic crystals, with the elastic stiffness matrix cij as follows: cijcubic =c11c12c12000c12c11c12000c12c12c11000000c44000000c44000000c44 #4 Hence, from Eq. 4, the elastic energy for each crystal structure can be derived [18]: Eelasticcubic=12c11ϵ12+ϵ22+ϵ32+c12ϵ1ϵ2+ϵ2ϵ3+ϵ3ϵ1+12c44ϵ42+ϵ52+ϵ62 #5 This paper focuses solely on the cubic crystal (111) thin film system, namely, a system with cylindrical symmetry in its elastic properties.
International journal of Solids and Structures, 14.6 (1978) 431-440

The diffraction peaks were indexed to the (100), (002), (101), (110), (103), and (112) planes, corresponding to the wurtzite crystal structure of ZnO.
D=Kλβcosθ (1) Where; D is crystallite size K is the shape factor, typically around 0.9 for rod-like structure λ is wavelength of the X-ray used(A0) β is full width at half maximum (FWHM) of diffraction peak, in radians θ is Bragg angle(radians) Fig. 2.
Journal of Materials Chemistry C, 5, (2017) 6640–6646
Construction of a ZnO heterogeneous structure using CO3O4 as a co-catalyst to enhance photoelectrochemical performance, Materials 17 (2023) 146

When r < 1-1.5 nm where the particles consist of only several ten to hundred atoms, a cluster structure is formed, which differs from the corresponding bulk structure, while Eq. 57 is valid only when the particle has the same structure of the bulk.
This granular structure is similar to a random structure of a chain polymer modeled by a trajectory of a self-avoiding walk with a fractal dimension of d = 4/3 [130].
According to general quantum chemistry consideration [138], all thermodynamic quantities are roughly linear function of 1/r that corresponds to the surface/volume ratio of particles.
Ubbelohde: Melting and Crystal Structure (Clarendon press, Oxford, 1965), p. 171
Weast: CRC Handbook of Chemistry and Physics, 69 th edition (Boca Raton, FL, CRC Press, 1988-1989), p.

The inclusion of ternary elements ‘Zr’ and ‘Al’ to binary Mg-Zn was made in attempts to control the corrosion rate of the alloys, improve alloy strength and refine grain structure [7, 8].
Backscatter images for the surfaces of the experimental alloys did not reveal any regions of contrast for distinguishable phases in the Mg-Zn-Se alloy, although notable phase contrast was seen for the Mg-Zn-Cu alloy along the grain boundary structure of the alloy as shown in Figures 7 and 8, respectively.
Principles of Colloid and Surface Chemistry, (1997), 3rd Edition, Marcel Dekker, Inc
Wetting, Spreading, and Penetration, in: Handbook of Applied Surface and Colloid Chemistry. (2002), K.

Mechanical Behaviors of HDPE Fiber Reinforced Cement Mortar Trithos Kamsuwan1,a, Taweechai Amornsakchai2,b, Toemsak Srikhirin3,c 1 Materials Science and Engineering Program, School of Materials Science and Engineering, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand 2Department of Chemistry, Faculty of Science, Mahidol University, Phuttamonthon 4 Road, Salaya, Nakhon Pathom 73170, Thailand 3Department of Physics, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand a skamsuwan@yahoo.com, b taweechai.amo@mahidol.ac.th, c toemsak.sri@mahidol.ac.th Keywords: Mechanical Behaviors, High Density Polyethylene (HDPE) Fiber, Reinforced, Cement Mortar Abstract.
Fiber reinforced cement composites has so far been successfully used in slabs on grade, shotcrete, architectural panels, precast products, offshore structures, structures in seismic regions, thin and thick repairs, crash barriers, footings, hydraulic structures and many other applications.

Figure 1 shows the structure change and Raman spectrum of fullerenes when they were heated in a vacuum.
Fig. 1 Changes of structure and Raman spectrum of mixed fullerenes (influences of raised temperature) Weight Wheel Rotate plate Achlil plate Fixed wax Silicon wafer Bolt MotorWheel hold plate Weight Wheel Rotate plate Achlil plate Fixed wax Silicon wafer Bolt MotorWheel hold plate Heating at 1013K 10μm Heating at 1013K 10μm10μm Heating at 1073K 10μm Heating at 1073K 10μm10μm Room temperature Room temperature Heating at 973K Heating at 973K Heating at 1073K Heating at 1073K Fig. 2 Schematic diagram of polishing apparatus When fullerenes were heated, however, each peak sharpened at 973 K, but the peaks broadened at 1073 K.
If the temperature was settled over 873 K while fabricating the fullerene wheel, graphitisation of fullerenes and fracturing of the fullerene structure occurred.
Saitou: Chemistry and Physics of Fullerene, Nagoya Univesity Publisher (2000) p.6

The last segment designed was the base of the structure which held the Apollo capsule in the wind tunnel and also acted as a reservoir for the pressure tappings and electrode wires to pass through.
Material of structure An important consideration of both the design and manufacturing process is the material used to build the individual components of the model Apollo Capsule.
[8]Lien, J. and Ahmed N.A., Chemistry, Emission Control, Radioactive Pollution and Indoor Air Quality, Chap. 20, Mazzeo, N.
[55]Findanis, N., and Ahmed, N.A., ‘The interaction of an asymmetrical localised synthetic jet on a side supported sphere,’ Journal of Fluids and Structures, Vol. 24, No. 7, 2008, pp. 1006-1020 [56]Findanis, N., and Ahmed, N.A., ‘Three-dimensional flow reversal and wake characterisation of a sphere modified with active flow control using synthetic jet,’ Advances and Applications in Fluid Mechanics, Vol. 9, No. 1, 2011, pp.17-76

Hence, the utilization of nanotechnology across many scientific disciplines is a significant instrument for achieving optimal applications and investigations in physics, biology, chemistry, and engineering, specifically at the atomic and molecular scales [27,28].
Regarding the matter above CdO, oxides of elements and metals are highly intriguing due to their distinct composition and specialized structure, which allows for the manipulation of their significant mechanical, thermal, optical, and electrical properties [20,22].
This reference card corresponds to CdO with a cubic crystalline structure with a facing orientation.
Additionally, the EDX analysis verified that all CdO NPs possessed a distinct compositional structure and maintained a constant shape.

The fillers with thermal insulation property with hollow structures would stop heat convection, especially when the diameter of pores is less than 4nm [4].
This is because the nano-SnO2 forms large molecular structure in binder system which creates more air-pockets at the liquid-solid-air interphase, that minimizes the contact area to glass substrate [13, 14].
Pekala, "Correlation between structure and thermal conductivity of organic aerogels," Journal of Non-Crystalline Solids, vol. 188, no. 3, pp. 226-234, 1995
Yuan, "Photoluminescence properties of SnO2 nanoparticles synthesized by sol− gel method," The Journal of Physical Chemistry B, vol. 108, no. 24, pp. 8119-8123, 2004.

Thus, the mixing properties i.e. thermodynamic, microscopic, mechanical, thermal, surface, transport, magnetic properties, structure and phase diagram of FeSi and FeSi-based multicomponent alloys have attracted the attentiveness of several researchers [4-10].
Feng, Stability, electronic structure mechanical and thermodynamic properties of Fe-Si binary compounds, J.
Singh, Quasi-lattice model for the thermodynamic properties and microscopic structure of molten Fe-Si alloy, Physica B, 406, (2011), 4338-4341 [14] D.
Moelwyn-Hughes, Physical Chemistry, Pergamon Press, (1961) [29] G.