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Crystals are the solid of regular geometric shape with the certain arrangement of atoms, ions or molecules in the space, which contains monocrystals and polycrystals (owing to the periodic arrangement destroyed by grain boundaries), almost all of the metals macroscopically appear polycrystalline.
The hidden mathematical laws in the quasicrystals According to a number of studies currently, quasicrystals were found to have magical mathematical laws that three concepts related with the quasicrystals were Penrose puzzles [3], Fibonacci sequence and golden section. 1) Penrose puzzles in crystal structure A typical quasicrystal structure is three-dimensional Penrose puzzles like the mode of paving bricks with translational asymmetry, long-range ordered structure, and five rotational symmetry not allowed in common crystals (refer with: Fig. 2) [4].
In 1976, Roger Penrose constructed a new puzzle method with only two kinds of two-dimensional Penrose puzzles, a fat diamond and a thin diamond (their interior angle were 72o, 108o and 36o, 144o, respectively) (refer with: Fig. 2(c)), the length of each side: a, which can fill up a two-dimensional plane without gap or overlap, as a result of the pattern with five rotational symmetry. 2) Fibonacci Sequence and golden section Scientists found that all the spacing between diffraction spots and the center spot in quasicrystal, a series of irrational numbers, conform to the Fibonacci sequence.
In mathematics, Fibonacci sequence is defined with recursive method (refer with: Eq. 1): ,, (1) Literally, Fibonacci sequence begins with 0 and 1, and then the new Fibonacci coefficient equals the sum of previous two numbers.
The more backward, the more close to golden section is the ratio of two adjacent numbers (an infinite acyclic decimal similar with PI, its value is approximately 1.62), that is (refer with: Eq. 2, Eq. 3): (2) (3) The ratio of the distance between the atoms in quasicrystal tends to approach φ (the golden ratio).

If joining them with each other the fusion welding process number is low.
The different melting points limit the applicable welding process number.
Test number Parameters 1 2 3 4 5 6 7 Pressure [PSI] 35 Welding time [s] 1 A friction amplitude [μm] 54 B friction amplitude [μm] 30 32 34 30 32 34 32 Amplitude step time [s] 0.5 0.5 0.5 0.35 0.35 0.35 0.15 Power [W] 2060 1940 1920 2580 2740 2620 - Maximum Tensile force [N] 451 422 426 609 658 635 - 3.
It seems from Table 2. that as a function of joint strengths, the best parameters for the USW earned from the number 5 test.
Nazarov: Ultrasonic Welding of Nickel with Coarse and Ultrafine Grained Structures.

The volume increase can also put existing crack into compression with fracture toughness enhancement, extending reliability and lifetime of stabilized zirconia Cations incorporation with small valence numbers such as the alkaline earth or stable rare earth cations (RE+ or Y3+) at pure zirconia can cause substitutional solid solution formation.
Controlled powder synthesis and ceramic processing can lead to higher densities and nonometric grain sizes.
Spectrum form at low wave number do not show peaks related to monoclinic zirconia (Fig 2 (a)).
Wave Features of ceramic powders obtained by Pechini Wave Number (cm-1) Functional Group. 3440 OH 2930 Ethyleneglicol (CH) 2350 CO 1630 Yttrium Oxide 586,462 Zr-OH2 Laser particle size analysis (Fig. 3) indicate that synthesized powder have narrow particle/agglomerate distribution, with medium size of 2.8117 μm.
Forms and position of bands of low wave numbers permits qualitative phases identification.

Two titanium silicides such as TiSi2 (ICDD card number: 35-785) and Ti5Si3 (ICDD card number: 29-1362) are marketed in the world.
Among them, pentatitanium trisilicide, Ti5Si3 (Chemical Abstracts Service (CAS) registry number: 12067-57-1) has been shown to be potentially useful intermediate material.
The grain size of as-received powder was about 5 to 10 mm.
Acknowledgments This presentation was supported by the Cooperative Research Program of Network Joint Research Center for Materials & Devices, Japan by Tohoku University, Japan (Grant Number: 2015286 and 20164006).

Table 2 Penetration height of each group proportion Number Admixture Water reducing agent Penetration height S1 JM- 33.8 S2 coal ash SP8 17.6 S3 slag powder SP8 14.5 S4 slag powder SP8 18.1 S5 slag powder SP1 16.2 2.2 Frost-resistance We test frost-resistance of the five specimens by slowly frozen method, freezethaw cycle for 300 times, then test the strength and mass loss rate.
Table 3 Result of resistance to freezing and thawing test of concrete Number Admixture Water reducing agent Mass loss rate Strength loss rate S1 JM- 0 3.5 S2 coal ash SP8 0.20 -2.1 S3 slag powder SP8 -0.19 7.8 S4 slag powder SP8 -0.29 5.1 S5 slag powder SP1 -0.30 1.3 From the table we can see that the strength of all in addition to S2 is declined, but strength loss is small.
Table 4 Result of attack test in the 10%sodium sulfate liquor number Strength soaked in water Strength soaked in sulfuric acid solution Strength loss rate S1 71.6 70.5 -1.5 S2 88.2 91.5 3.7 S3 91.3 95.0 4.0 S4 92.4 98.4 6.5 S5 92.6 96.3 4.7 Due to Table 4, the strength of specimens except S1 is unexpected increased.
It is not only because that the specimens are close-grained and impervious, but also they are mixed with coal ash and ground slag which are significant to resistance of sulfate eroding[4].
The changing process is shown in Fig.2 Table 5 Shrinkage rate in different curing age Number Shrinkage rate (μm/m) 1d 3d 7d 14d 28d 56d 90d S1 35.2 76.3 90.3 130.3 180.3 253.1 311.6 S2 97.6 143.6 183.5 230.5 290.6 370.6 410.5 S3 106.3 146.2 170.8 224.7 280.6 362.5 422.3 S4 101.4 146.9 190.4 234.1 274.5 330.8 370.6 S5 63.9 98.3 120.6 170.8 264.3 304.8 389.2 Fig.2 Shrinkage rate of the specimens in different curing age Conclusions From the test, we can see that S5 group is the optimal proportion.It has the feature of high strength and durability.This is mainly because coal ash and slag powder have been mixed into the specimens, and on the other hand, the polycarboxylate water reducer has some positive effect just as increasing anti-permeability and reducing the shrinkage crack.

The relationship between total strain amplitude and the failure cycle number was well expressed by Manson-Coffin formula.
There are elastic and plastic deformation two parts in this equation: (2) Whereis total strain amplitude;is the elastic component of total strain amplitude; is the plastic component of total strain amplitude;is the coefficient of fatigue strength;is the coefficient of plastic fatigue;is the index of fatigue strength;is the index of plastic fatigue;is the number of cycles.
Calculation results are shown in Tab.1: Tab. 1 Fatigue calculation results of each node Node 170035 141617 170076 170075 Maximum stress value (Pa) 0.6545E9 0.4199E9 0.1687E9 0.15317E9 Cycles N 10000 10000 10000 10000 Stress amplitude 0.3273E9 0.166E9 0.7971E8 0.8293E8 Maximum allowable cycles 0.1E8 0.156E8 0.338E8 0.427E8 Tab.1 shows that stress amplitude is higher in the area of stress concentrations, and that allows the less number of cycles , the cumulative fatigue damage coefficient is greater as well.
(2) Stress amplitude is higher in the area of stress concentrations, and that allows the less number of cycles , the cumulative fatigue damage coefficient is greater as well.
[7] Wang Zhixing,Zhou Dian.Fine grain microstructure of hot die ring and the high cycle fatigue performance of GH4169

Technology Number Allocation: The technology number is allocated as per the following procedure: 1.
Then a Technology Number Allocation Register is consulted to find the numbers available for allocation in the technology group.
The allocated technology number and sheet number are also inscribed on the tape as illustrated in the figure much like would be the case with a book number on the spine of a book.
Litter and its removal 664.6-664.7 Technology and processing of cereal grains TP368-456 Food processing and manufacture 664.6 Baking.
Grain processing TD429.5-480.7 Water purification.

The bubbles have tended to distribute along some line in grain body.
In contrast, the specimen implanted deuterium ions formed a large number of defects.
From (a) to (c), the number density after aged gradually increased.
The larger number density, the larger the bubbles growed up whose break need more irradiated dose.

It was found that the introduction of hollow ceramic microspheres into fine-grained sand concrete to a certain extent provides the formation of the concrete structure with a longer "safety zone" (i.e. the stage when the load increase does not lead to a substantial increase in acoustic emission energy and strains).
Results and discussions Earlier [9], the number of ultrasound pulses N and the amplitude A were studied for the analysis of acoustic emission parameters of the samples of high-lightweight concrete during the mechanical testing of compressive strength.
It was determined that the character of the change in the number of AE signals and the total value of the amplitude have similar appearance.
Fig. 2 shows that the application of complex nanomodifier on the surface of ceramic microspheres allows increasing the strength of lightweight concrete in proportion to the number of hollow filler.

Number one marks the base material, number two the heat affected zone and number three the fusion zone.
Fig. 3: Micrograph of an H340LAD welding seam (Nd:YAG) The base material of H340LAD is fine grained ferrite-perlitic.
After the heat influence of the laser beam, the structure is coarse-grained with martensitic areas.
Number one shows the base material, number two the heat affected zone, number three the fusion zone and additionally number four the 0.2 mm gap.
Influence of the number of linear bead-on-plate welding seams.