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What is the LCM of 2156 484 11858?
The LCM of 2156, 484, 11858 is: 23,716.
How many gigabytes in 11858 megabytes?
11858 times 1024. 1 Megabyte = 1024 Kilobytes.
What is the LCM of 215 and 484 and 11858?
104060.
What are the release dates for Days of Our Lives - 1965 1-11858?
Days of Our Lives - 1965 1-11858 was released on: USA: 6 June 2012
What is the Least common multiple of 2156484 and 11858?
168205752
What numbers should be added to 11158 to make it exactly divisible by 77?
11158 ÷ 77 = 144 r 70 Thus an extra 77 - 70 = 7 needs to be added to make it divisible by 77. A further 77 can also be added which will still result in a multiple of 77, ie adding 84 will also result in a multiple of 77. Thus the one "of the following" to add is the one which is one of: 7, 84, 161, 238, 315, 392, 469, 546, 623, 700, 777, 854, 931, 1008, 1085, 1162, 1239, 1316, 1393, 1470, 1547, 1624, 1701, 1778, 1855, 1932, 2009, 2086, 2163, 2240, 2317, 2394, 2471, 2548, 2625, 2702, 2779, 2856, 2933, 3010, 3087, 3164, 3241, 3318, 3395, 3472, 3549, 3626, 3703, 3780, 3857, 3934, 4011, 4088, 4165, 4242, 4319, 4396, 4473, 4550, 4627, 4704, 4781, 4858, 4935, 5012, 5089, 5166, 5243, 5320, 5397, 5474, 5551, 5628, 5705, 5782, 5859, 5936, 6013, 6090, 6167, 6244, 6321, 6398, 6475, 6552, 6629, 6706, 6783, 6860, 6937, 7014, 7091, 7168, 7245, 7322, 7399, 7476, 7553, 7630, 7707, ...
What verses in the bible is it is written?
In the King James versionthe phrase - it is written - appears 80 times6034 Jos 8:31 As Moses the servant of the LORD commanded the children of Israel, as it is written in the book of the law of Moses, an altar of whole stones, over which no man hath lift up any iron: and they offered thereon burnt offerings unto the LORD, and sacrificed peace offerings.8041 2 Sam 1:18 (Also he bade them teach the children of Judah the use of the bow: behold, it is written in the book of Jasher.)8774 1 Kin 2:3 And keep the charge of the LORD thy God, to walk in his ways, to keep his statutes, and his commandments, and his judgments, and his testimonies, as it is written in the law of Moses, that thou mayest prosper in all that thou doest, and whithersoever thou turnest thyself:10187 2 Kin 23:21 And the king commanded all the people, saying, Keep the passover unto the LORD your God, as it is written in the book of this covenant.11675 2 Chr 23:18 Also Jehoiada appointed the offices of the house of the LORD by the hand of the priests the Levites, whom David had distributed in the house of the LORD, to offer the burnt offerings of the LORD, as it is written in the law of Moses, with rejoicing and with singing, as it was ordained by David.11709 2 Chr 25:4 But he slew not their children, but did as it is written in the law in the book of Moses, where the LORD commanded, saying, The fathers shall not die for the children, neither shall the children die for the fathers, but every man shall die for his own sin.11858 2 Chr 31:3 He appointed also the king's portion of his substance for the burnt offerings, to wit, for the morning and evening burnt offerings, and the burnt offerings for the sabbaths, and for the new moons, and for the set feasts, as it is written in the law of the LORD.11979 2 Chr 35:12 And they removed the burnt offerings, that they might give according to the divisions of the families of the people, to offer unto the LORD, as it is written in the book of Moses. And so did they with the oxen.12100 Ezr 3:2 Then stood up Jeshua the son of Jozadak, and his brethren the priests, and Zerubbabel the son of Shealtiel, and his brethren, and builded the altar of the God of Israel, to offer burnt offerings thereon, as it is written in the law of Moses the man of God.12102 Ezr 3:4 They kept also the feast of tabernacles, as it is written, and offered the daily burnt offerings by number, according to the custom, as the duty of every day required;12170 Ezr 6:18 And they set the priests in their divisions, and the Levites in their courses, for the service of God, which is at Jerusalem; as it is written in the book of Moses.12509 Neh 8:15 And that they should publish and proclaim in all their cities, and in Jerusalem, saying, Go forth unto the mount, and fetch olive branches, and pine branches, and myrtle branches, and palm branches, and branches of thick trees, to make booths, as it is written.12584 Neh 10:34 And we cast the lots among the priests, the Levites, and the people, for the wood offering, to bring it into the house of our God, after the houses of our fathers, at times appointed year by year, to burn upon the altar of the LORD our God, as it is written in the law:12586 Neh 10:36 Also the firstborn of our sons, and of our cattle, as it is written in the law, and the firstlings of our herds and of our flocks, to bring to the house of our God, unto the priests that minister in the house of our God:14533 Psa 40:7 Then said I, Lo, I come: in the volume of the book it is written of me,18904 Isa 65:6 Behold, it is written before me: I will not keep silence, but will recompense, even recompense into their bosom,22001 Dan 9:13 As it is written in the law of Moses, all this evil is come upon us: yet made we not our prayer before the LORD our God, that we might turn from our iniquities, and understand thy truth.23174 Mat 2:5 And they said unto him, In Bethlehem of Judaea: for thus it is written by the prophet,23213 Mat 4:4 But he answered and said, It is written, Man shall not live by bread alone, but by every word that proceedeth out of the mouth of God.23215 Mat 4:6 And saith unto him, If thou be the Son of God, cast thyself down: for it is written, He shall give his angels charge concerning thee: and in their hands they shall bear thee up, lest at any time thou dash thy foot against a stone.23216 Mat 4:7 Jesus said unto him, It is written again, Thou shalt not tempt the Lord thy God.23219 Mat 4:10 Then saith Jesus unto him, Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.23469 Mat 11:10 For this is he, of whom it is written, Behold, I send my messenger before thy face, which shall prepare thy way before thee.23839 Mat 21:13 And said unto them, It is written, My house shall be called the house of prayer; but ye have made it a den of thieves.24078 Mat 26:24 The Son of man goeth as it is written of him: but woe unto that man by whom the Son of man is betrayed! it had been good for that man if he had not been born.24085 Mat 26:31 Then saith Jesus unto them, All ye shall be offended because of me this night: for it is written, I will smite the shepherd, and the sheep of the flock shall be scattered abroad.24217 Mar 1:2 As it is written in the prophets, Behold, I send my messenger before thy face, which shall prepare thy way before thee.24469 Mar 7:6 He answered and said unto them, Well hath Esaias prophesied of you hypocrites, as it is written, This people honoureth me with their lips, but their heart is far from me.24550 Mar 9:12 And he answered and told them, Elias verily cometh first, and restoreth all things; and how it is written of the Son of man, that he must suffer many things, and be set at nought.24551 Mar 9:13 But I say unto you, That Elias is indeed come, and they have done unto him whatsoever they listed, as it is written of him.24775 Mar 14:21 The Son of man indeed goeth, as it is written of him: but woe to that man by whom the Son of man is betrayed! good were it for that man if he had never been born.24781 Mar 14:27 And Jesus saith unto them, All ye shall be offended because of me this night: for it is written, I will smite the shepherd, and the sheep shall be scattered.24996 Luk 2:23 (As it is written in the law of the LORD, Every male that openeth the womb shall be called holy to the Lord;)25029 Luk 3:4 As it is written in the book of the words of Esaias the prophet, saying, The voice of one crying in the wilderness, Prepare ye the way of the Lord, make his paths straight.25067 Luk 4:4 And Jesus answered him, saying, It is written, That man shall not live by bread alone, but by every word of God.25071 Luk 4:8 And Jesus answered and said unto him, Get thee behind me, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.25073 Luk 4:10 For it is written, He shall give his angels charge over thee, to keep thee:25222 Luk 7:27 This is he, of whom it is written, Behold, I send my messenger before thy face, which shall prepare thy way before thee.25777 Luk 19:46 Saying unto them, It is written, My house is the house of prayer: but ye have made it a den of thieves.26037 Luk 24:46 And said unto them, Thus it is written, and thus it behoved Christ to suffer, and to rise from the dead the third day:26288 Joh 6:31 Our fathers did eat manna in the desert; as it is written, He gave them bread from heaven to eat.26302 Joh 6:45 It is written in the prophets, And they shall be all taught of God. Every man therefore that hath heard, and hath learned of the Father, cometh unto me.26594 Joh 12:14 And Jesus, when he had found a young ass, sat thereon; as it is written,26943 Act 1:20 For it is written in the book of Psalms, Let his habitation be desolate, and let no man dwell therein: and his bishoprick let another take.27158 Act 7:42 Then God turned, and gave them up to worship the host of heaven; as it is written in the book of the prophets, O ye house of Israel, have ye offered to me slain beasts and sacrifices by the space of forty years in the wilderness?27457 Act 15:15 And to this agree the words of the prophets; as it is written,27739 Act 23:5 Then said Paul, I wist not, brethren, that he was the high priest: for it is written, Thou shalt not speak evil of the ruler of thy people.27947 Rom 1:17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.27986 Rom 2:24 For the name of God is blasphemed among the Gentiles through you, as it is written.27995 Rom 3:4 God forbid: yea, let God be true, but every man a liar; as it is written, That thou mightest be justified in thy sayings, and mightest overcome when thou art judged.28001 Rom 3:10 As it is written, There is none righteous, no, not one:28039 Rom 4:17 (As it is written, I have made thee a father of many nations,) before him whom he believed, even God, who quickeneth the dead, and calleth those things which be not as though they were.28152 Rom 8:36 As it is written, For thy sake we are killed all the day long; we are accounted as sheep for the slaughter.28168 Rom 9:13 As it is written, Jacob have I loved, but Esau have I hated.28188 Rom 9:33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.28203 Rom 10:15 And how shall they preach, except they be sent? As it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!28217 Rom 11:8 (According as it is written, God hath given them the spirit of slumber, eyes that they should not see, and ears that they should not hear;) unto this day.28235 Rom 11:26 And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:28264 Rom 12:19 Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord.28291 Rom 14:11 For it is written, As I live, saith the Lord, every knee shall bow to me, and every tongue shall confess to God.28306 Rom 15:3 For even Christ pleased not himself; but, as it is written, The reproaches of them that reproached thee fell on me.28312 Rom 15:9 And that the Gentiles might glorify God for his mercy; as it is written, For this cause I will confess to thee among the Gentiles, and sing unto thy name.28324 Rom 15:21 But as it is written, To whom he was not spoken of, they shall see: and they that have not heard shall understand.28382 1 Cor 1:19 For it is written, I will destroy the wisdom of the wise, and will bring to nothing the understanding of the prudent.28394 1 Cor 1:31 That, according as it is written, He that glorieth, let him glory in the Lord.28403 1 Cor 2:9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.28429 1 Cor 3:19 For the wisdom of this world is foolishness with God. For it is written, He taketh the wise in their own craftiness.28549 1 Cor 9:9 For it is written in the law of Moses, Thou shalt not muzzle the mouth of the ox that treadeth out the corn. Doth God take care for oxen?28574 1 Cor 10:7 Neither be ye idolaters, as were some of them; as it is written, The people sat down to eat and drink, and rose up to play.28699 1 Cor 14:21 In the law it is written, With men of other tongues and other lips will I speak unto this people; and yet for all that will they not hear me, saith the LORD.28763 1 Cor 15:45 And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.28872 2 Cor 4:13 We having the same spirit of faith, according as it is written, I believed, and therefore have I spoken; we also believe, and therefore speak;28947 2 Cor 8:15 As it is written, He that had gathered much had nothing over; and he that had gathered little had no lack.28965 2 Cor 9:9 (As it is written, He hath dispersed abroad; he hath given to the poor: his righteousness remaineth for ever.29112 Gal 3:10 For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them.29115 Gal 3:13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:29153 Gal 4:22 For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman.29158 Gal 4:27 For it is written, Rejoice, thou barren that bearest not; break forth and cry, thou that travailest not: for the desolate hath many more children than she which hath an husband.30140 Heb 10:7 Then said I, Lo, I come (in the volume of the book it is written of me,) to do thy will, O God.30390 1 Pet 1:16 Because it is written, Be ye holy; for I am holy.
What are the first 2000 multiples of 11?
The first 2000 multiples of 11 can be calculated by multiplying 11 by each natural number starting from 1. The first few multiples are 11, 22, 33, 44, and so on. To find the 2000th multiple, you would multiply 11 by 2000, which equals 22,000.
What influence does grain size have on mechanical properties of metal?
Influence of grain size on following properties of meatals:- Hardness Strength Impactness Toughness Creep Fatigue Ductility Malleability Durability Brittleness INTRODUCTION Yttria-stabilized tetragonal zirconia polycrystals (Y-TZP) have proved to be important structural ceramics. High strength and fracture toughness make them attractive candidates for a number of demanding applications. It was established that these advantageous properties are strongly influenced by the ceramic microstructure [1]. The relationships between microstructure and mechanical properties in Y-TZP ceramics have been studied extensively over the past two decades. It is now generally agreed that the transformation toughening effect (stress-induced tetragonal to monoclinic phase transformation) in Y-TZP ceramics is grain size dependent [2 7]. The larger the tetragonal grains the greater propensity to undergo stress-induced transformation to an equilibrium structure, resulting in an enhanced toughness. The maximum toughness lies near the critical grain size, where the tetragonal grains undergo spontaneous tetragonal to monoclinic transformation [7]. It was found that this critical grain size depends on the yttria content [6, 7]. However, the critical grain size, cited for 3Y-TZP (3 mol% Y2O3), which is the most common zirconia ceramic material, varies significantly (from 1 to 6 µm) [3, 8-9]. This could be attributed to different processing procedures that result in different ceramic microstructures. Thus, microstructural parameters like porosity, grain size distribution, yttrium distribution in grains, purity, phase assemblage, etc. need to be taken into account for evaluating the microstructure. In contrast to the fracture toughness the strength of 3Y-TZP reaches its maximum usually at smaller grain size [5, 10]. Increasing size of failure origin coupled with microstructural coarsening was identified as the reason for strength decrease in ceramics with large grains [11]. However, the increase of strength with decreasing grain size cannot be extended to the nanocrystalline range in 3Y-TZP. Eichler et al. [10] determined the strength maximum for 3Y-TZP in the submicron range and noted a clear strength decrease in the nanocrystalline grain size range (~100 nm). In this case, the strength decrease was attributed to the grain size dependence of fracture toughness. A decrease in the fracture toughness was observed as the grain size changed from the submicrometre to the nanometre range [10, 12]. These results validate the assumption that the increase of critical defects during microstructural coarsening is connected with the formation of stress induced transformed regions at the free surface and takes place preferentially in ceramics with grains near the critical size [11]. Nevertheless, special processing of TZP ceramics has been reported, which can partially eliminate the increase of critical defects during coarsening, resulting in almost constant strength, independent of grain size [8, 9]. Original papers Ceramics − Silikáty 52 (3) 165-171 (2008) 165 EFFECT OF GRAIN SIZE ON MECHANICAL PROPERTIES OF 3Y-TZP CERAMICS MARTIN TRUNEC Department of Ceramics and Polymers, Brno University of Technology Technicka 2896/2, 616 69 Brno, Czech Republic E-mail: trunec@fme.vutbr.cz Submitted June 21, accepted September 4, 2008 Keywords: Zirconia, Nanoceramics, Transformation toughening, Microstructure, Mechanical properties The dependence of mechanical properties of 3Y-TZP ceramics on their grain sizes in the range from 0.19 µm to 2.15 µm has been investigated. Vickers indentation tests were used to determine hardness and fracture toughness. The hardness decreased with increasing grain size. The fracture toughness was almost constant for ceramics with the grain size up to 0.40 µm and then grew with increasing grain size up to 7.8 MPam0.5 for ceramics with grain size of 1.8 µm. Above this grain size a spontaneous transformation from tetragonal to monoclinic phase occurred. Ceramic samples with grain sizes of 0.30 µm and 0.78 µm yielded similar bending strength, 1020 and 1011 MPa, respectively. The microstructural coarsening required for achieving larger grain size resulted in a higher scatter of strength values, which was demonstrated by a lower Weibull modulus (13.0 vs. 7.54). The mechanical properties of nanocrystalline 3Y-zirconia ceramics coarsened to the grain size range from 0.085 to 0.70 µm were also investigated and compared. Differences in mechanical behaviour of investigated ceramics were observed and their possible causes discussed. The objective of the present investigation was to describe the dependence of mechanical properties of commercial submicrometre-grained 3Y-TZP ceramics on grain size and to compare their mechanical properties to the mechanical properties of nanocrystalline zirconia ceramics and nanocrystalline ceramics coarsened to the submicrometre range. EXPERIMENTAL Two zirconia powders stabilized by 3 mol% Y2O3 were used for the preparation of test specimens. Commercial zirconia powder TZ-3YB (Tosoh, Japan) was cold isostatically pressed at 300 MPa into disk-shaped bodies (diameter 28 mm; thickness 5 mm). For comparison, a nanocrystalline zirconia powder B261 (BUT, Czech Republic) was used. Details of the preparation of the nanopowder can be found in [13]. Nanocrystalline powder was cold isostatically pressed at 1000 MPa without additives. The pressed bodies were 18 mm in diameter and 5 mm thick. These bodies were ground to a thickness of 1.5 mm prior to sintering. Both types of bodies were densified by pressureless sintering in air at temperatures from 1100 to 1650°C and dwell times ranging from 0 to 50 hours. The density of sintered specimens was determined by the Archimedes method [14] with distilled water as the immersing medium. The relative density of all ceramic bodies was calculated using the value 6.1 g·cm-3 for the theoretical density of 3Y-TZP. The grain size of the sintered ceramics was evaluated by linear intercept method (without correction) on scanning electron microscopy (SEM) micrographs of polished and thermally etched samples, in a similar way as in [15]. At least three micrographs and total of 300 intersects were evaluated to determine the average grain size for each sintering batch. The phase composition of the sintered ceramics was determined by X-ray diffraction (XRD) analysis (X´pert, Philips, the Netherlands). The X-ray spectra of polished and fracture surface were obtained and the phase content was quantified using Rietveld analysis. For hardness and fracture toughness evaluation Vickers indentation tests (LV 700, Leco, USA) were used. Prior to indentation ceramic disks were mounted in a resin and their surfaces ground and polished (finishing with 1 µm diamond polishing fluid). Hardness tests were performed at a load of 9.8 N (1 kg) and a hold of 15 s. For determining the Vickers hardness, HV (MPa), the following expression was used: HV = 1.8544 P/d 2, (1) where P is the applied load and d is the average diagonal line length of the indentation. Ten indentations were made for each sample. Toughness was calculated directly from the crack lengths produced by Vickers indentation at higher loads. Applied loads were 49.05 N (5 kg), 98.1 N (10 kg), 196.2 N (20 kg) and 294.3 N (30 kg) always with a hold of 15 s. The crack lengths were measured immediately after indentation using a calibrated optical microscope. The fracture toughness, KIc (MPam0.5), was calculated using the equation given by Niihara et al. [16] for Palmqvist cracks: KIc = 9.052 × 10-3 H3/5 E2/5 d c-1/2 , (2) where H is the hardness, E the Young modulus (a value of 210 GPa has been assumed for all the samples), d is the average diagonal line length of the indentation and c is the length of the Palmqvist crack. Ten valid measurements were determined for each sample. The valid measurements had to satisfy the requirements of the JIS R 1607 [17] on acceptable indentation cracks. The flexural strength was determined for selected ceramic samples in four-point bending at a crosshead speed of 2 mm/min, using fully articulated fixture with a 10 mm inner and 20 mm outer span (in the "A" arrangement according to the EN 843-1 [18]). Ceramic bars with dimensions ca. 2.5 × 2 × 25 mm3 were cut from the disks, ground and polished (finally with 1-2 µm grained diamond paste). The parameters of the Weibull strength distribution were calculated numerically, in compliance with the ENV 843-5 [19]. RESULTS AND DISCUSSION Microstructure and phase analysis Various sintering schedules were applied to zirconia green bodies to obtain dense sintered ceramics with different grain sizes. Only those sintering schedules that resulted in sintered densities exceeding 99% of theoretical density (% t.d.) were employed. A temperature of 1400°C was the lowest temperature used in sintering the TZ-3YB ceramics; this was necessary to obtain a dense sintered body. Larger grains were obtained by the action of both higher sintering temperatures and longer sintering times. Sintering schedules and resulting densities and grain sizes are shown in Table 1. The density of sintered TZ-3YB bodies was constant up to the sintering temperature of 1650°C. At the sintering temperature of 1650°C the density of TZ-3YB ceramics decreased with increasing sintering time. The structure of ceramics remained dense but the theoretical density of these ceramics decreased due to spontaneous transformation of the tetragonal into the monoclinic phase (see Table 1). The average grain size of TZ-3YB ceramics ranged from 0.19 µm (sintered at 1400°C/2 h) to 2.15 µm (sintered at 1650°C/50 h). The Trunec M. 166 Ceramics − Silikáty 52 (3) 165-171 (2008) critical grain size for spontaneous transformation from tetragonal to monoclinic phase lies between 1.8 and 2.15 µm, where the content of monoclinic phase in TZ 3YB ceramics increased dramatically. The sample sintered at 1650°C for 50 hours consisted of 77 % monoclinic phase and was severely cracked due to volume changes accompanying t→m transformation. Mechanical properties could not be determined for these ceramics. Several authors [8, 9, 11] have found large cubic grains in thermally treated 3Y-TZP samples. In our case no exaggerated grain growth was observed during the microstructural coarsening. The zirconia nanopowder B261 could be sintered to dense bulk ceramics already at the temperature of 1100°C and dwell time of 4 hours. The microstructure remained nanoscaled with an average grain size of 85 nm. Microstructural coarsening occurred at higher sintering temperatures. However, the grain growth kinetics of B261 ceramics was different from that in TZ 3YB ceramics. B261 ceramics sintered at 1550°C/5 h had larger grains than TZ 3YB ceramics sintered under the same conditions (0.70 vs. 0.48 µm). Moreover, the density of B261 ceramics decreased sharply already at small grain sizes where no monoclinic phase was detected. Figure 1 shows the density as a function of grain size for both TZ-3YB and B261 ceramics. The reason for the density change in B261 ceramics is not completely clear. According to the equilibrium phase diagram given by Scott [20] the maximum amount of cubic phase occurring in 3 mol% Y2O3-ZrO2 ceramics sintered at 1550°C can be about 28 %. Matsui et al. [21] showed that in tetragonal zirconia ceramics similar to TZ-3YB the Y3+ ions segregated at grain boundaries over a width of ~10 nm. Consequently, the cubic phase started to form from grain boundaries and a triple junction, at which Y3+ ions were segregated. A mixed tetragonal- cubic structure was confirmed in TZ-3YB ceramics by XRD analysis. In B261 ceramics the nanocrystalline structure probably allowed other mechanisms of phase structure development to take place that resulted in the one-phase tetragonal structure. This fact could explain the faster grain growth found in B261 ceramics. Typical microstructures of TZ-3YB ceramics are shown in Figures 2-4 and microstructures of B261 ceramics are shown in Figures 5 and 6. The holes and voids visible in micrographs on Figures 4 and 6 are believed not to be pores but rather to result from pulling out the grains during grinding and polishing. Effect of grain size on mechanical properties of 3Y-TZP ceramics Ceramics − Silikáty 52 (3) 165-171 (2008) 167 Table 1. Sintering schedules of zirconia ceramics and resulting density, grain size and monoclinic phase content. Sintering schedule Density Relative density Grain size m - ZrO2 Powder/Sample (°C)/(h) (g/cm3) (% t.d.) (µm) (%) TZ - 3YB 1400/2 6.07 99.5 0.19 0 TZ - 3YB 1500/2 6.08 99.7 0.30 0 TZ - 3YB 1550/0 6.09 99.8 0.29 0 TZ - 3YB 1550/2 6.09 99.8 0.40 0 TZ - 3YB 1550/5 6.09 99.8 0.48 0 TZ - 3YB 1550/10 6.09 99.8 0.54 0 TZ - 3YB 1600/2 6.09 99.8 0.53 0 TZ - 3YB 1600/5 6.09 99.8 0.68 0 TZ - 3YB 1600/10 6.08 99.7 0.78 0 TZ - 3YB 1650/10 6.08 99.6 0.99 3 TZ - 3YB 1650/20 6.08 99.6 1.37 6 TZ - 3YB 1650/30 6.04 99.1 1.79 13 TZ - 3YB 1650/50 5.68 93.1 2.15 77 B 261 1100/4 6.07 99.4 0.085 0 B 261 1300/6 6.04 99.0 0.19 0 B 261 1450/2 5.93 97.3 0.33 0 B 261 1550/5 5.71 93.6 0.70 0 Figure 1. Density of TZ-3YB and B261 ceramics as a function of grain size. Grain size (µm) Density (g cm-3) 5.9 5.7 0.0 6.1 0.4 1.6 2.0 6.0 5.8 6.2 1.2 0.8 TZ-3YB B261 Mechanical properties Ten Vickers hardness tests were performed for each ceramic. Average hardness values and their standard deviation are given in Table 2. The hardness of TZ-3YB ceramics clearly decreased with increasing grain size from HV = 12620 MPa at grain size of 0.19 µm to HV = 10971 MPa at grain size of 1.79 µm. The graph in Figure 7 shows the hardness of TZ-3YB ceramics as a function of the inverse square root of grain size. The values in the graph could be reasonably fitted with a line (r2 = 0.94), which means that this dependence followed the Hall-Petch relationship. The hardness of B261 ceramics showed a higher dispersion but the linear fit seems to be also reasonable. Different parameters of the fits (lower hardness of B261 compared with TZ-3YB ceramics) could be attributed to different phase structure (mixed tetragonal-cubic vs. pure tetragonal). Trunec M. 168 Ceramics − Silikáty 52 (3) 165-171 (2008) Figure 2. SEM micrograph showing the microstructure of the TZ-3YB ceramics sintered at 1400°C for 2 h. Figure 3. SEM micrograph showing the microstructure of the TZ-3YB ceramics sintered at 1650°C for 20 h. 1 µm 5 µm Figure 4. SEM micrograph showing the microstructure of the TZ-3YB ceramics sintered at 1650°C for 50 h. Figure 5. SEM micrograph showing the microstructure of the B261 ceramics sintered at 1100°C for 4 h. 5 µm 500 nm Figure 6. SEM micrograph showing the microstructure of the B261 ceramics sintered at 1550°C for 5 h. 2 µm Different loads of Vickers indenter in the range from 49.05 N (5 kg) to 294.3 N (30 kg) were used to generate cracks in ceramic samples. It was verified that in all cases only Palmqvist cracks were produced. Fracture toughness values calculated from crack lengths using Equation (2) at different loads are shown in Table 2. The indenter load of 49.05 N (5 kg) generated unstable cracks that grew further after load release. It was not possible to measure the crack length reliably, therefore the fracture toughness calculated from this load was not included in the Table 2. The graph in Figure 8 shows the dependence of fracture toughness of TZ-3YB ceramics at different loads on grain size. The values of fracture toughness determined at different loads varied significantly. Nevertheless, the dependence of toughness on grain size showed the same trend for all loads. To obtain the most reliable value for the fracture toughness, an average of values determined at different loads was calculated (see Table 2). Figure 9 gives the dependence of the average fracture toughness on grain size for both TZ-3YB and B261 ceramics. This dependence can be divided in two areas. The toughness was almost constant (~ 5.1 MPam0.5) up to a grain size of 0.4 µm. In ceramics with larger grains, the toughness increased linearly up to the grain size of 1.8 µm, where the maximum toughness (7.8 MPam0.5) was found. Above this grain size spontaneous transformation to the monoclinic phase occurred. Figure 9 shows that both ceramics, TZ-3YB and B261, followed the same toughness dependence on grain size. It also follows from this figure that the transformation toughness effect is grain size dependent only above a particular tetragonal grain size (approx. 0.4 µm). Effect of grain size on mechanical properties of 3Y-TZP ceramics Ceramics − Silikáty 52 (3) 165-171 (2008) 169 Table 2. Hardness, HV, fracture toughness, KIc, and their standard deviations, s, of zirconia ceramics. Fracture toughness Sintering Hardness 10 kg 20 kg 30 kg Average schedule HV s KIc s KIc s KIc s KIc Sample (°C)/(h) (MPa) (MPam0.5) TZ - 3YB 1400/2 12620 186 4.94 0.07 5.29 0.06 5.49 0.05 5.24 TZ - 3YB 1500/2 12264 135 4.91 0.06 5.20 0.08 5.41 0.05 5.17 TZ - 3YB 1550/0 12137 224 4.89 0.29 5.10 0.06 5.38 0.05 5.12 TZ - 3YB 1550/2 12007 103 4.89 0.05 5.14 0.03 5.40 0.03 5.14 TZ - 3YB 1550/5 11970 113 5.06 0.07 5.23 0.05 5.45 0.06 5.25 TZ - 3YB 1550/10 11738 127 5.53 0.13 5.41 0.07 5.62 0.07 5.52 TZ - 3YB 1600/2 11858 363 5.15 0.16 5.29 0.07 5.57 0.04 5.34 TZ - 3YB 1600/5 11849 551 5.80 0.21 5.43 0.05 5.62 0.04 5.62 TZ - 3YB 1600/10 11588 176 6.39 0.09 5.53 0.03 5.72 0.03 5.88 TZ - 3YB 1650/10 11361 293 6.75 0.21 5.82 0.12 5.87 0.06 6.15 TZ - 3YB 1650/20 11145 341 7.11 0.12 6.52 0.10 6.09 0.06 6.57 TZ - 3YB 1650/30 10971 293 7.94 0.24 7.50 0.54 7.80 0.15 7.77 B 261 1100/4 12867 789 4.89 0.08 5.35 0.14 - - 5.12 B 261 1300/6 12485 218 4.79 0.07 5.15 0.12 5.38 0.08 5.11 B 261 1450/2 10587 657 4.73 0.09 5.30 0.27 - - 5.02 B 261 1550/5 10080 435 5.98 0.45 5.79 0.21 5.99 0.40 5.92 Figure 7. The dependence of the hardness of TZ-3YB and B261 ceramics on the inverse square root of grain size. d-1/2 (µm-1/2) Hardness (MPa) 11 000 10 000 0.4 12 000 0.8 2.0 2.4 11 500 10 500 12 500 1.6 1.2 13 000 2.8 3.2 3.6 TZ-3YB B261 Figure 8. Fracture toughness of TZ-3YB ceramics as a function of grain size determined at different indentation loads. Grain size (µm) Fracture toughness (MPa m0.5) 6 4 0.0 8 0.4 1.6 2.0 7 5 9 1.2 0.8 10 kg load 20 kg load 30 kg load Recently Vickers indentation fracture toughness tests (VIF) were reviewed in detail [22]. It was concluded that VIF techniques are not suitable for reliable measurement of fracture toughness, KIc, because the crack arrest process occurs in a multiple-crack environment and in highly complex residual stress conditions. To verify our fracture toughness results determined by the indentation method, two standardized methods were applied. Unfortunately, the results obtained by "Chevron V Notch" method (CVN) and "Single Edged V Notch Beam" method (SEVNB) showed extremely high scatter (5-12 MPam0.5), thus it was not possible to find any dependence on grain size. The reason for such high variance is not clear and may be connected with the toughening effect in TZP ceramics. From this point of view the indentation method utilized in the present investigation provided more consistent results compared with the CVN and SEVNB methods. The four-point bending strength of TZ-3YB bars with a grain size of 0.30 µm (sintered at 1500°C/2 h) and 0.78 µm (sintered at 1600°C/10 h) was determined and compared. Figure 10 shows the Weibull plot of both materials. Although the average strength of samples varying in grain size was similar (1020 MPa vs. 1011 MPa), it can be seen in the graph that the scatter of strength values was higher for TZ-3YB ceramics with larger grains. This observation was confirmed by calculation of Weibull moduli. The Weibull modulus was m = 13.0 for ceramics with the grain size of 0.30 µm and m = 7.54 for ceramics with the grain size of 0.78 µm. It was verified statistically that these values are significantly different. According to the linear fracture mechanics the body with higher fracture toughness should possess the higher strength. In our case TZ-3YB ceramics with a grain size of 0.78 µm had higher toughness than ceramics with a grain size of 0.30 µm (5.88 vs. 5.17 MPam0.5). Unfortunately, the effect of higher toughness was suppressed by an effect of bigger critical defects due to microstructural coarsening [10]. The competition of these two effects resulted in ceramics with strengths apparently independent of grain size. However, the size and distribution of defects during coarsening cannot be efficiently controlled, which resulted in the lower Weibull modulus for ceramics sintered at higher temperature. CONCLUSION The effect of grain size on mechanical properties of commercial submicrometre-grained 3Y-TZP ceramics (TZ-3YB) and nanocrystalline 3Y-zirconia ceramics (B261) was investigated. The following conclusions could be drawn: 1.The hardness of both TZ-3YB and B261 ceramics decreased with increasing grain size. However, the hardness was lower in coarsened nanoceramics. This could be attributed to different mechanisms of the development of phase structure in nanoceramics compared with submicrometre-grained ceramics. 2.The fracture toughness was almost constant (5.1 MPam0.5) up to the grain size of 0.4 µm. Above this grain size, the fracture toughness started to grow and reached the maximum of 7.8 MPam0.5 at the grain size of 1.8 µm. Further grain growth resulted in spontaneous transformation from tetragonal to monoclinic phase and damage of the samples due to cracking. Both ceramics followed the same grain size depen-dence of fracture toughness. 3.The four-point bending strength of TZ-3YB ceramics with grain size of 0.30 and 0.78 µm was similar, 1020 MPa and 1011 MPa, respectively. The higher Trunec M. 170 Ceramics − Silikáty 52 (3) 165-171 (2008) Figure 9. Average fracture toughness of TZ-3YB and B261 ceramics as a function of grain size. Grain size (µm) Fracture toughness (MPa m0.5) 6 4 0.0 8 0.4 1.6 2.0 7 5 9 1.2 0.8 TZ-3YB B261 Figure 10. Weibull plot of the bending strength data for TZ-3YB ceramics sintered at 1500°C for 2 h and at 1600°C for 10 h. ln (bending strength, MPa) ln{ln[1/(1-P)]} -3 -5 6.6 -1 6.7 7.0 7.1 -2 -4 0 6.9 6.8 TZ-3YB - 1500°C/2 h TZ-3YB - 1600°C/10 h 1 2 7.2 fracture toughness inherent to ceramics with larger grain size was counterbalanced with an increase of critical defects due to microstructural coarsening. Moreover, the Weibull modulus declined from m = 13 at a grain size of 0.30 µm to m = 7.54 at a grain size of 0.78 µm. Acknowledgement The author gratefully acknowledges the funding provided by the Czech Ministry of Education under grant MSM 0021630508. Dr. A. Buchal and Mrs. D. Janova are kindly acknowledged for providing XRD analyses and SEM images, respectively. The author wishes to thank Mrs. Z. Skalova for her help with the experimental work. References 1. Hannink R. H. J., Kelly P. M., Muddle B. C.: J.Am.Ceram. Soc. 83, 461 (2000). 2. Lange F. F.: J. Mater.Sci. 17, 225 (1982). 3. Lange F. F.: J.Mater.Sci. 17, 240 (1982). 4. Becher P. F., Swain M. V.: J.Am.Ceram.Soc. 75, 493 (1992). 5. Wang J, Rainforth M., Stevens R.: Br.Ceram.Trans.J. 88, 1 (1989). 6. Suresh A., Mayo M. J., Porter W. D., Rawn C. J.: J.Am. Ceram.Soc. 86, 360 (2003). 7. Bravo-Leon A., Morikawa Y., Kawahara M., Mayo M. J.: Acta Mater. 50, 4555 (2002). 8. Ruiz L., Readey M. J.: J.Am.Ceram.Soc. 79, 2331 (1996). 9. Casellas D., Feder A., Llanes L., Anglada M.: Scr.Mater. 45, 213 (2001). 10. Eichler J., Rödel J., Eisele U., Hoffman M.: J.Am.Ceram. Soc. 90, 2830 (2007). 11. Casellas D., Alcala J., Llanes L., Anglada M.: J.Mater.Sci. 36, 3011 (2001). 12. Cottom B. A., Mayo M. J.: Scr.Mater. 34, 809 (1996). 13. Trunec M., Maca K.: J.Am.Ceram.Soc. 90, 2735 (2007). 14. EN 623-2: Advanced Technical Ceramics - Monolithic Ceramics. General and Texture Properties. Part 2: Determination of Density and Porosity, CEN, Brussels 1993. 15. Maca K., Trunec M., Chmelik R.: Ceramics-Silikaty 51, 94 (2007). 16. Niihara K., Morena R., Hasselman D. P. H.: J.Mater.Sci. Lett. 1, 13 (1982). 17. JIS R 1607: Testing Methods for Fracture Toughness of High Performance Ceramics, Japanese Standards Association, Tokyo 1990. 18. EN 843-1: Advanced Technical Ceramics - Monolithic Ceramics. Mechanical Properties at Room Temperature. Part 1: Determination of Flexural Strength, CEN, Brussels 1995. 19. ENV 843-5: Advanced Technical Ceramics - Monolithic Ceramics. Mechanical Properties at Room Temperature. Part 5: Statistical Analysis, CEN, Brussels 1996. 20. Scott H. G.: J.Mater.Sci. 10, 1527 (1975). 21. Matsui K., Horikoshi H., Ohmichi N., Ohgai M.: J.Am. Ceram.Soc. 86, 1401 (2003). 22. Quinn G. D., Bradt R. C.: J.Am.Ceram.Soc. 90, 673 (2007). Effect of grain size on mechanical properties of 3Y-TZP ceramics Ceramics − Silikáty 52 (3) 165-171 (2008) 171 VLIV VELIKOSTI ZRN NA MECHANICKÉ VLASTNOSTI 3Y-TZP KERAMIKY MARTIN TRUNEC Odbor keramiky a polymerù, Vysoké uèení technické v Brnì, Technická 2896/2, 616 69 Brno Mechanické vlastnosti 3Y-TZP keramiky byly zkoumány v závislosti na velikosti zrn v rozsahu od 0,19 µm do 2,15 µm. Vickersovy indentaèní testy byly použity pro stanovení tvrdosti a lomové houževnatosti. Tvrdost klesala s rostoucí velikostí zrn. Lomová houževnatost byla témìø konstantní pro keramiky se zrny do 0,4 µm a poté rostla se zvyšující se velikosti zrn až na 7,8 MPam0,5 u keramiky se zrny o velikosti 1,8 µm. U vìtších zrn došlo ke spontánní transformaci tetragonální fáze na monoklinickou. Keramické vzorky s velikostí zrn 0,30 µm a 0,78 µm mìli podobnou pevnost v ohybu, 1020 a 1011 MPa. Mikrostrukturní zhrubnutí, které bylo nezbytné pro dosažení vìtších zrn, vedlo k vyššímu rozptylu pevností, což se projevilo snížením Weibullova modulu (13,0 vs. 7,54). Pro srovnání byly také zkoumány mechanické vlastnosti nanokrystalické 3Y-ZrO2 keramiky, jejíž zrna byla zhrublá na velikost od 0,085 do 0,70 µm. Byly zjištìny rozdíly v mechanických vlastnostech zkoumaných keramik. Možné pøíèiny tìchto rozdílù byly diskutovány.
What are all the numbers 1-1000000?
Numbers 1 to 30,000!1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 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618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 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27857, 27858, 27859, 27860, 27861, 27862, 27863, 27864, 27865, 27866, 27867, 27868, 27869, 27870, 27871, 27872, 27873, 27874, 27875, 27876, 27877, 27878, 27879, 27880, 27881, 27882, 27883, 27884, 27885, 27886, 27887, 27888, 27889, 27890, 27891, 27892, 27893, 27894, 27895, 27896, 27897, 27898, 27899, 27900, 27901, 27902, 27903, 27904, 27905, 27906, 27907, 27908, 27909, 27910, 27911, 27912, 27913, 27914, 27915, 27916, 27917, 27918, 27919, 27920, 27921, 27922, 27923, 27924, 27925, 27926, 27927, 27928, 27929, 27930, 27931, 27932, 27933, 27934, 27935, 27936, 27937, 27938, 27939, 27940, 27941, 27942, 27943, 27944, 27945, 27946, 27947, 27948, 27949, 27950, 27951, 27952, 27953, 27954, 27955, 27956, 27957, 27958, 27959, 27960, 27961, 27962, 27963, 27964, 27965, 27966, 27967, 27968, 27969, 27970, 27971, 27972, 27973, 27974, 27975, 27976, 27977, 27978, 27979, 27980, 27981, 27982, 27983, 27984, 27985, 27986, 27987, 27988, 27989, 27990, 27991, 27992, 27993, 27994, 27995, 27996, 27997, 27998, 27999, 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28143, 28144, 28145, 28146, 28147, 28148, 28149, 28150, 28151, 28152, 28153, 28154, 28155, 28156, 28157, 28158, 28159, 28160, 28161, 28162, 28163, 28164, 28165, 28166, 28167, 28168, 28169, 28170, 28171, 28172, 28173, 28174, 28175, 28176, 28177, 28178, 28179, 28180, 28181, 28182, 28183, 28184, 28185, 28186, 28187, 28188, 28189, 28190, 28191, 28192, 28193, 28194, 28195, 28196, 28197, 28198, 28199, 28200, 28201, 28202, 28203, 28204, 28205, 28206, 28207, 28208, 28209, 28210, 28211, 28212, 28213, 28214, 28215, 28216, 28217, 28218, 28219, 28220, 28221, 28222, 28223, 28224, 28225, 28226, 28227, 28228, 28229, 28230, 28231, 28232, 28233, 28234, 28235, 28236, 28237, 28238, 28239, 28240, 28241, 28242, 28243, 28244, 28245, 28246, 28247, 28248, 28249, 28250, 28251, 28252, 28253, 28254, 28255, 28256, 28257, 28258, 28259, 28260, 28261, 28262, 28263, 28264, 28265, 28266, 28267, 28268, 28269, 28270, 28271, 28272, 28273, 28274, 28275, 28276, 28277, 28278, 28279, 28280, 28281, 28282, 28283, 28284, 28285, 28286, 28287, 28288, 28289, 28290, 28291, 28292, 28293, 28294, 28295, 28296, 28297, 28298, 28299, 28300, 28301, 28302, 28303, 28304, 28305, 28306, 28307, 28308, 28309, 28310, 28311, 28312, 28313, 28314, 28315, 28316, 28317, 28318, 28319, 28320, 28321, 28322, 28323, 28324, 28325, 28326, 28327, 28328, 28329, 28330, 28331, 28332, 28333, 28334, 28335, 28336, 28337, 28338, 28339, 28340, 28341, 28342, 28343, 28344, 28345, 28346, 28347, 28348, 28349, 28350, 28351, 28352, 28353, 28354, 28355, 28356, 28357, 28358, 28359, 28360, 28361, 28362, 28363, 28364, 28365, 28366, 28367, 28368, 28369, 28370, 28371, 28372, 28373, 28374, 28375, 28376, 28377, 28378, 28379, 28380, 28381, 28382, 28383, 28384, 28385, 28386, 28387, 28388, 28389, 28390, 28391, 28392, 28393, 28394, 28395, 28396, 28397, 28398, 28399, 28400, 28401, 28402, 28403, 28404, 28405, 28406, 28407, 28408, 28409, 28410, 28411, 28412, 28413, 28414, 28415, 28416, 28417, 28418, 28419, 28420, 28421, 28422, 28423, 28424, 28425, 28426, 28427, 28428, 28429, 28430, 28431, 28432, 28433, 28434, 28435, 28436, 28437, 28438, 28439, 28440, 28441, 28442, 28443, 28444, 28445, 28446, 28447, 28448, 28449, 28450, 28451, 28452, 28453, 28454, 28455, 28456, 28457, 28458, 28459, 28460, 28461, 28462, 28463, 28464, 28465, 28466, 28467, 28468, 28469, 28470, 28471, 28472, 28473, 28474, 28475, 28476, 28477, 28478, 28479, 28480, 28481, 28482, 28483, 28484, 28485, 28486, 28487, 28488, 28489, 28490, 28491, 28492, 28493, 28494, 28495, 28496, 28497, 28498, 28499, 28500, 28501, 28502, 28503, 28504, 28505, 28506, 28507, 28508, 28509, 28510, 28511, 28512, 28513, 28514, 28515, 28516, 28517, 28518, 28519, 28520, 28521, 28522, 28523, 28524, 28525, 28526, 28527, 28528, 28529, 28530, 28531, 28532, 28533, 28534, 28535, 28536, 28537, 28538, 28539, 28540, 28541, 28542, 28543, 28544, 28545, 28546, 28547, 28548, 28549, 28550, 28551, 28552, 28553, 28554, 28555, 28556, 28557, 28558, 28559, 28560, 28561, 28562, 28563, 28564, 28565, 28566, 28567, 28568, 28569, 28570, 28571, 28572, 28573, 28574, 28575, 28576, 28577, 28578, 28579, 28580, 28581, 28582, 28583, 28584, 28585, 28586, 28587, 28588, 28589, 28590, 28591, 28592, 28593, 28594, 28595, 28596, 28597, 28598, 28599, 28600, 28601, 28602, 28603, 28604, 28605, 28606, 28607, 28608, 28609, 28610, 28611, 28612, 28613, 28614, 28615, 28616, 28617, 28618, 28619, 28620, 28621, 28622, 28623, 28624, 28625, 28626, 28627, 28628, 28629, 28630, 28631, 28632, 28633, 28634, 28635, 28636, 28637, 28638, 28639, 28640, 28641, 28642, 28643, 28644, 28645, 28646, 28647, 28648, 28649, 28650, 28651, 28652, 28653, 28654, 28655, 28656, 28657, 28658, 28659, 28660, 28661, 28662, 28663, 28664, 28665, 28666, 28667, 28668, 28669, 28670, 28671, 28672, 28673, 28674, 28675, 28676, 28677, 28678, 28679, 28680, 28681, 28682, 28683, 28684, 28685, 28686, 28687, 28688, 28689, 28690, 28691, 28692, 28693, 28694, 28695, 28696, 28697, 28698, 28699, 28700, 28701, 28702, 28703, 28704, 28705, 28706, 28707, 28708, 28709, 28710, 28711, 28712, 28713, 28714, 28715, 28716, 28717, 28718, 28719, 28720, 28721, 28722, 28723, 28724, 28725, 28726, 28727, 28728, 28729, 28730, 28731, 28732, 28733, 28734, 28735, 28736, 28737, 28738, 28739, 28740, 28741, 28742, 28743, 28744, 28745, 28746, 28747, 28748, 28749, 28750, 28751, 28752, 28753, 28754, 28755, 28756, 28757, 28758, 28759, 28760, 28761, 28762, 28763, 28764, 28765, 28766, 28767, 28768, 28769, 28770, 28771, 28772, 28773, 28774, 28775, 28776, 28777, 28778, 28779, 28780, 28781, 28782, 28783, 28784, 28785, 28786, 28787, 28788, 28789, 28790, 28791, 28792, 28793, 28794, 28795, 28796, 28797, 28798, 28799, 28800, 28801, 28802, 28803, 28804, 28805, 28806, 28807, 28808, 28809, 28810, 28811, 28812, 28813, 28814, 28815, 28816, 28817, 28818, 28819, 28820, 28821, 28822, 28823, 28824, 28825, 28826, 28827, 28828, 28829, 28830, 28831, 28832, 28833, 28834, 28835, 28836, 28837, 28838, 28839, 28840, 28841, 28842, 28843, 28844, 28845, 28846, 28847, 28848, 28849, 28850, 28851, 28852, 28853, 28854, 28855, 28856, 28857, 28858, 28859, 28860, 28861, 28862, 28863, 28864, 28865, 28866, 28867, 28868, 28869, 28870, 28871, 28872, 28873, 28874, 28875, 28876, 28877, 28878, 28879, 28880, 28881, 28882, 28883, 28884, 28885, 28886, 28887, 28888, 28889, 28890, 28891, 28892, 28893, 28894, 28895, 28896, 28897, 28898, 28899, 28900, 28901, 28902, 28903, 28904, 28905, 28906, 28907, 28908, 28909, 28910, 28911, 28912, 28913, 28914, 28915, 28916, 28917, 28918, 28919, 28920, 28921, 28922, 28923, 28924, 28925, 28926, 28927, 28928, 28929, 28930, 28931, 28932, 28933, 28934, 28935, 28936, 28937, 28938, 28939, 28940, 28941, 28942, 28943, 28944, 28945, 28946, 28947, 28948, 28949, 28950, 28951, 28952, 28953, 28954, 28955, 28956, 28957, 28958, 28959, 28960, 28961, 28962, 28963, 28964, 28965, 28966, 28967, 28968, 28969, 28970, 28971, 28972, 28973, 28974, 28975, 28976, 28977, 28978, 28979, 28980, 28981, 28982, 28983, 28984, 28985, 28986, 28987, 28988, 28989, 28990, 28991, 28992, 28993, 28994, 28995, 28996, 28997, 28998, 28999, 29000, 29001, 29002, 29003, 29004, 29005, 29006, 29007, 29008, 29009, 29010, 29011, 29012, 29013, 29014, 29015, 29016, 29017, 29018, 29019, 29020, 29021, 29022, 29023, 29024, 29025, 29026, 29027, 29028, 29029, 29030, 29031, 29032, 29033, 29034, 29035, 29036, 29037, 29038, 29039, 29040, 29041, 29042, 29043, 29044, 29045, 29046, 29047, 29048, 29049, 29050, 29051, 29052, 29053, 29054, 29055, 29056, 29057, 29058, 29059, 29060, 29061, 29062, 29063, 29064, 29065, 29066, 29067, 29068, 29069, 29070, 29071, 29072, 29073, 29074, 29075, 29076, 29077, 29078, 29079, 29080, 29081, 29082, 29083, 29084, 29085, 29086, 29087, 29088, 29089, 29090, 29091, 29092, 29093, 29094, 29095, 29096, 29097, 29098, 29099, 29100, 29101, 29102, 29103, 29104, 29105, 29106, 29107, 29108, 29109, 29110, 29111, 29112, 29113, 29114, 29115, 29116, 29117, 29118, 29119, 29120, 29121, 29122, 29123, 29124, 29125, 29126, 29127, 29128, 29129, 29130, 29131, 29132, 29133, 29134, 29135, 29136, 29137, 29138, 29139, 29140, 29141, 29142, 29143, 29144, 29145, 29146, 29147, 29148, 29149, 29150, 29151, 29152, 29153, 29154, 29155, 29156, 29157, 29158, 29159, 29160, 29161, 29162, 29163, 29164, 29165, 29166, 29167, 29168, 29169, 29170, 29171, 29172, 29173, 29174, 29175, 29176, 29177, 29178, 29179, 29180, 29181, 29182, 29183, 29184, 29185, 29186, 29187, 29188, 29189, 29190, 29191, 29192, 29193, 29194, 29195, 29196, 29197, 29198, 29199, 29200, 29201, 29202, 29203, 29204, 29205, 29206, 29207, 29208, 29209, 29210, 29211, 29212, 29213, 29214, 29215, 29216, 29217, 29218, 29219, 29220, 29221, 29222, 29223, 29224, 29225, 29226, 29227, 29228, 29229, 29230, 29231, 29232, 29233, 29234, 29235, 29236, 29237, 29238, 29239, 29240, 29241, 29242, 29243, 29244, 29245, 29246, 29247, 29248, 29249, 29250, 29251, 29252, 29253, 29254, 29255, 29256, 29257, 29258, 29259, 29260, 29261, 29262, 29263, 29264, 29265, 29266, 29267, 29268, 29269, 29270, 29271, 29272, 29273, 29274, 29275, 29276, 29277, 29278, 29279, 29280, 29281, 29282, 29283, 29284, 29285, 29286, 29287, 29288, 29289, 29290, 29291, 29292, 29293, 29294, 29295, 29296, 29297, 29298, 29299, 29300, 29301, 29302, 29303, 29304, 29305, 29306, 29307, 29308, 29309, 29310, 29311, 29312, 29313, 29314, 29315, 29316, 29317, 29318, 29319, 29320, 29321, 29322, 29323, 29324, 29325, 29326, 29327, 29328, 29329, 29330, 29331, 29332, 29333, 29334, 29335, 29336, 29337, 29338, 29339, 29340, 29341, 29342, 29343, 29344, 29345, 29346, 29347, 29348, 29349, 29350, 29351, 29352, 29353, 29354, 29355, 29356, 29357, 29358, 29359, 29360, 29361, 29362, 29363, 29364, 29365, 29366, 29367, 29368, 29369, 29370, 29371, 29372, 29373, 29374, 29375, 29376, 29377, 29378, 29379, 29380, 29381, 29382, 29383, 29384, 29385, 29386, 29387, 29388, 29389, 29390, 29391, 29392, 29393, 29394, 29395, 29396, 29397, 29398, 29399, 29400, 29401, 29402, 29403, 29404, 29405, 29406, 29407, 29408, 29409, 29410, 29411, 29412, 29413, 29414, 29415, 29416, 29417, 29418, 29419, 29420, 29421, 29422, 29423, 29424, 29425, 29426, 29427, 29428, 29429, 29430, 29431, 29432, 29433, 29434, 29435, 29436, 29437, 29438, 29439, 29440, 29441, 29442, 29443, 29444, 29445, 29446, 29447, 29448, 29449, 29450, 29451, 29452, 29453, 29454, 29455, 29456, 29457, 29458, 29459, 29460, 29461, 29462, 29463, 29464, 29465, 29466, 29467, 29468, 29469, 29470, 29471, 29472, 29473, 29474, 29475, 29476, 29477, 29478, 29479, 29480, 29481, 29482, 29483, 29484, 29485, 29486, 29487, 29488, 29489, 29490, 29491, 29492, 29493, 29494, 29495, 29496, 29497, 29498, 29499, 29500, 29501, 29502, 29503, 29504, 29505, 29506, 29507, 29508, 29509, 29510, 29511, 29512, 29513, 29514, 29515, 29516, 29517, 29518, 29519, 29520, 29521, 29522, 29523, 29524, 29525, 29526, 29527, 29528, 29529, 29530, 29531, 29532, 29533, 29534, 29535, 29536, 29537, 29538, 29539, 29540, 29541, 29542, 29543, 29544, 29545, 29546, 29547, 29548, 29549, 29550, 29551, 29552, 29553, 29554, 29555, 29556, 29557, 29558, 29559, 29560, 29561, 29562, 29563, 29564, 29565, 29566, 29567, 29568, 29569, 29570, 29571, 29572, 29573, 29574, 29575, 29576, 29577, 29578, 29579, 29580, 29581, 29582, 29583, 29584, 29585, 29586, 29587, 29588, 29589, 29590, 29591, 29592, 29593, 29594, 29595, 29596, 29597, 29598, 29599, 29600, 29601, 29602, 29603, 29604, 29605, 29606, 29607, 29608, 29609, 29610, 29611, 29612, 29613, 29614, 29615, 29616, 29617, 29618, 29619, 29620, 29621, 29622, 29623, 29624, 29625, 29626, 29627, 29628, 29629, 29630, 29631, 29632, 29633, 29634, 29635, 29636, 29637, 29638, 29639, 29640, 29641, 29642, 29643, 29644, 29645, 29646, 29647, 29648, 29649, 29650, 29651, 29652, 29653, 29654, 29655, 29656, 29657, 29658, 29659, 29660, 29661, 29662, 29663, 29664, 29665, 29666, 29667, 29668, 29669, 29670, 29671, 29672, 29673, 29674, 29675, 29676, 29677, 29678, 29679, 29680, 29681, 29682, 29683, 29684, 29685, 29686, 29687, 29688, 29689, 29690, 29691, 29692, 29693, 29694, 29695, 29696, 29697, 29698, 29699, 29700, 29701, 29702, 29703, 29704, 29705, 29706, 29707, 29708, 29709, 29710, 29711, 29712, 29713, 29714, 29715, 29716, 29717, 29718, 29719, 29720, 29721, 29722, 29723, 29724, 29725, 29726, 29727, 29728, 29729, 29730, 29731, 29732, 29733, 29734, 29735, 29736, 29737, 29738, 29739, 29740, 29741, 29742, 29743, 29744, 29745, 29746, 29747, 29748, 29749, 29750, 29751, 29752, 29753, 29754, 29755, 29756, 29757, 29758, 29759, 29760, 29761, 29762, 29763, 29764, 29765, 29766, 29767, 29768, 29769, 29770, 29771, 29772, 29773, 29774, 29775, 29776, 29777, 29778, 29779, 29780, 29781, 29782, 29783, 29784, 29785, 29786, 29787, 29788, 29789, 29790, 29791, 29792, 29793, 29794, 29795, 29796, 29797, 29798, 29799, 29800, 29801, 29802, 29803, 29804, 29805, 29806, 29807, 29808, 29809, 29810, 29811, 29812, 29813, 29814, 29815, 29816, 29817, 29818, 29819, 29820, 29821, 29822, 29823, 29824, 29825, 29826, 29827, 29828, 29829, 29830, 29831, 29832, 29833, 29834, 29835, 29836, 29837, 29838, 29839, 29840, 29841, 29842, 29843, 29844, 29845, 29846, 29847, 29848, 29849, 29850, 29851, 29852, 29853, 29854, 29855, 29856, 29857, 29858, 29859, 29860, 29861, 29862, 29863, 29864, 29865, 29866, 29867, 29868, 29869, 29870, 29871, 29872, 29873, 29874, 29875, 29876, 29877, 29878, 29879, 29880, 29881, 29882, 29883, 29884, 29885, 29886, 29887, 29888, 29889, 29890, 29891, 29892, 29893, 29894, 29895, 29896, 29897, 29898, 29899, 29900, 29901, 29902, 29903, 29904, 29905, 29906, 29907, 29908, 29909, 29910, 29911, 29912, 29913, 29914, 29915, 29916, 29917, 29918, 29919, 29920, 29921, 29922, 29923, 29924, 29925, 29926, 29927, 29928, 29929, 29930, 29931, 29932, 29933, 29934, 29935, 29936, 29937, 29938, 29939, 29940, 29941, 29942, 29943, 29944, 29945, 29946, 29947, 29948, 29949, 29950, 29951, 29952, 29953, 29954, 29955, 29956, 29957, 29958, 29959, 29960, 29961, 29962, 29963, 29964, 29965, 29966, 29967, 29968, 29969, 29970, 29971, 29972, 29973, 29974, 29975, 29976, 29977, 29978, 29979, 29980, 29981, 29982, 29983, 29984, 29985, 29986, 29987, 29988, 29989, 29990, 29991, 29992, 29993, 29994, 29995, 29996, 29997, 29998, 29999, 30000 and beyond!
