Wednesday, September 24, 2014
Sunday, December 8, 2013
1. Расчеты по Ашкрофту и Мермину.
2. Расчет по рассмотренным в работе моделям.
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| Cu | | | | |
| Ag | | | | |
| Al | | | | |
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| Cs | | | | |
| Cu | | | | |
| Ag | | | | |
| Al | | | | |
Thursday, December 5, 2013
ON THE PROBLEM OF CRYSTAL METALLIC LATTICE IN THE DENSEST PACKINGS OF CHEMICAL ELEMENTS
© Henadzi Filipenka
AbstractThe literature generally describes a metallic bond as the one formed by means of mutual bonds between atoms' exterior electrons and not possessing the directional properties. However, attempts have been made to explain directional metallic bonds, as a specific crystal metallic lattice.
This paper demonstrates that the metallic bond in the densest packings (volume-centered and face-centered) between the centrally elected atom and its neighbours in general is, probably, effected by 9 (nine) directional bonds, as opposed to the number of neighbours which equals 12 (twelve) (coordination number).
Probably, 3 (three) "foreign" atoms are present in the coordination number 12 stereometrically, and not for the reason of bond. This problem is to be solved experimentally.
Introduction
At present, it is impossible, as a general case, to derive by means of quantum-mechanical calculations the crystalline structure of metal in relation to electronic structure of the atom. However, Hanzhorn and Dellinger indicated a possible relation between the presence of a cubical volume-centered lattice in subgroups of titanium, vanadium, chrome and availability in these metals of valent d-orbitals. It is easy to notice that the four hybrid orbitals are directed along the four physical diagonals of the cube and are well adjusted to binding each atom to its eight neighbours in the cubical volume-centered lattice, the remaining orbitals being directed towards the edge centers of the element cell and, possibly, participating in binding the atom to its six second neighbours /3/p. 99.
Let us try to consider relations between exterior electrons of the atom of a given element and structure of its crystal lattice, accounting for the necessity of directional bonds (chemistry) and availability of combined electrons (physics) responsible for galvanic and magnetic properties.
According to /1/p. 20, the number of Z-electrons in the conductivitiy zone has been obtained by the authors, allegedly, on the basis of metal's valency towards oxygen, hydrogen and is to be subject to doubt, as the experimental data of Hall and the uniform compression modulus are close to the theoretical values only for alkaline metals. The volume-centered lattice, Z=1 casts no doubt. The coordination number equals 8.
The exterior electrons of the final shell or subcoats in metal atoms form conductivity zone. The number of electrons in the conductivity zone effects Hall's constant, uniform compression ratio, etc.
Let us construct the model of metal - element so that external electrons of last layer or sublayers of atomic kernel, left after filling the conduction band, influenced somehow pattern of crystalline structure (for example: for the body-centred lattice - 8 'valency' electrons, and for volume-centered and face-centred lattices - 12 or 9).
ROUGH, QUALITATIVE MEASUREMENT OF NUMBER OF ELECTRONS IN CONDUCTION BAND OF METAL - ELEMENT. EXPLANATION OF FACTORS, INFLUENCING FORMATION OF TYPE OF MONOCRYSTAL MATRIX AND SIGN OF HALL CONSTANT.
(Algorithm of construction of model)
The measurements of the Hall field allow us to determine the sign of charge carriers in the conduction band. One of the remarkable features of the Hall effect is, however, that in some metals the Hall coefficient is positive, and thus carriers in them should, probably, have the charge, opposite to the electron charge /1/. At room temperature this holds true for the following: vanadium, chromium, manganese, iron, cobalt, zinc, circonium, niobium, molybdenum, ruthenium, rhodium, cadmium, cerium, praseodymium, neodymium, ytterbium, hafnium, tantalum, wolfram, rhenium, iridium, thallium, plumbum /2/. Solution to this enigma must be given by complete quantum - mechanical theory of solid body.
Roughly speaking, using the base cases of Born-Karman, let us consider a highly simplified case of one-dimensional conduction band. The first variant: a thin closed tube is completely filled with electrons but one. The diameter of the electron roughly equals the diameter of the tube.
With such filling of the area at local movement of the electron an opposite movement of the 'site' of the electron, absent in the tube, is observed, i.e. movement of non-negative sighting. The second variant: there is one electron in the
tube - movement of only one charge is possible - that of the electron with a negative charge. These two opposite variants
show, that the sighting of carriers, determined according to the Hall coefficient, to some extent, must depend on the
filling of the conduction band with electrons. Figure 1.
Figure 1. Schematic representation of the conduction band of two different metals. (scale is not observed).
a) - the first variant;
b) - the second variant.
The order of electron movement will also be affected by the structure of the conductivity zone, as well as by the temperature, admixtures and defects. Magnetic quasi-particles, magnons, will have an impact on magnetic materials.
Since our reasoning is rough, we will further take into account only filling with electrons of the conductivity zone. Let us fill the conductivity zone with electrons in such a way that the external electrons of the atomic kernel affect the formation of a crystal lattice. Let us assume that after filling the conductivity zone, the number of the external electrons on the last shell of the atomic
kernel is equal to the number of the neighbouring atoms (the coordination number) (5).
The coordination number for the volume-centered and face-centered densest packings are 12 and 18, whereas those
for the body-centered lattice are 8 and 14 (3).
The below table is filled in compliance with the above judgements.
| Element | RH . 1010 (м3/K) | Z. (number) | Z kernel (number) | Lattice type |
| Na | -2,30 | 1 | 8 | body-centered |
| Mg | -0,90 | 1 | 9 | volume-centered |
| Al | -0,38 | 2 | 9 | face-centered |
| Al | -0,38 | 1 | 12 | face-centered |
| K | -4,20 | 1 | 8 | body-centered |
| Ca | -1,78 | 1 | 9 | face-centered |
| Ca | T=737K | 2 | 8 | body-centered |
| Sc | -0,67 | 2 | 9 | volume-centered |
| Sc | -0,67 | 1 | 18 | volume-centered |
| Ti | -2,40 | 1 | 9 | volume-centered |
| Ti | -2,40 | 3 | 9 | volume-centered |
| Ti | T=1158K | 4 | 8 | body-centered |
| V | +0,76 | 5 | 8 | body-centered |
| Cr | +3,63 | 6 | 8 | body-centered |
| Fe | +8,00 | 8 | 8 | body-centered |
| Fe | +8,00 | 2 | 14 | body-centered |
| Fe | Т=1189K | 7 | 9 | face-centered |
| Fe | Т=1189K | 4 | 12 | face-centered |
| Co | +3,60 | 8 | 9 | volume-centered |
| Co | +3,60 | 5 | 12 | volume-centered |
| Ni | -0,60 | 1 | 9 | face-centered |
| Cu | -0,52 | 1 | 18 | face-centered |
| Cu | -0,52 | 2 | 9 | face-centered |
| Zn | +0,90 | 2 | 18 | volume-centered |
| Zn | +0,90 | 3 | 9 | volume-centered |
| Rb | -5,90 | 1 | 8 | body-centered |
| Y | -1,25 | 2 | 9 | volume-centered |
| Zr | +0,21 | 3 | 9 | volume-centered |
| Zr | Т=1135К | 4 | 8 | body-centered |
| Nb | +0,72 | 5 | 8 | body-centered |
| Mo | +1,91 | 6 | 8 | body-centered |
| Ru | +22 | 7 | 9 | volume-centered |
| Rh | +0,48 | 5 | 12 | face-centered |
| Rh | +0,48 | 8 | 9 | face-centered |
| Pd | -6,80 | 1 | 9 | face-centered |
| Ag | -0,90 | 1 | 18 | face-centered |
| Ag | -0,90 | 2 | 9 | face-centered |
| Cd | +0,67 | 2 | 18 | volume-centered |
| Cd | +0,67 | 3 | 9 | volume-centered |
| Cs | -7,80 | 1 | 8 | body-centered |
| La | -0,80 | 2 | 9 | volume-centered |
| Ce | +1,92 | 3 | 9 | face-centered |
| Ce | +1,92 | 1 | 9 | face-centered |
| Pr | +0,71 | 4 | 9 | volume-centered |
| Pr | +0,71 | 1 | 9 | volume-centered |
| Nd | +0,97 | 5 | 9 | volume-centered |
| Nd | +0,97 | 1 | 9 | volume-centered |
| Gd | -0,95 | 2 | 9 | volume-centered |
| Gd | T=1533K | 3 | 8 | body-centered |
| Tb | -4,30 | 1 | 9 | volume-centered |
| Tb | Т=1560К | 2 | 8 | body-centered |
| Dy | -2,70 | 1 | 9 | volume-centered |
| Dy | Т=1657К | 2 | 8 | body-centered |
| Er | -0,341 | 1 | 9 | volume-centered |
| Tu | -1,80 | 1 | 9 | volume-centered |
| Yb | +3,77 | 3 | 9 | face-centered |
| Yb | +3,77 | 1 | 9 | face-centered |
| Lu | -0,535 | 2 | 9 | volume-centered |
| Hf | +0,43 | 3 | 9 | volume-centered |
| Hf | Т=2050К | 4 | 8 | body-centered |
| Ta | +0,98 | 5 | 8 | body-centered |
| W | +0,856 | 6 | 8 | body-centered |
| Re | +3,15 | 6 | 9 | volume-centered |
| Os | <0 | 4 | 12 | volume-centered |
| Ir | +3,18 | 5 | 12 | face-centered |
| Pt | -0,194 | 1 | 9 | face-centered |
| Au | -0,69 | 1 | 18 | face-centered |
| Au | -0,69 | 2 | 9 | face-centered |
| Tl | +0,24 | 3 | 18 | volume-centered |
| Tl | +0,24 | 4 | 9 | volume-centered |
| Pb | +0,09 | 4 | 18 | face-centered |
| Pb | +0,09 | 5 | 9 | face-centered |
Conclusions
In spite of the rough reasoning the table shows that the greater number of electrons gives the atom of the element to the conductivity zone, the more positive is the Hall's constant. On the contrary the Hall's constant is negative for the elements which have released one or two electrons to the conductivity zone, which doesn't contradict to the conclusions of Payerls. A relationship is also seen between the conductivity electrons (Z) and valency electrons (Z kernel) stipulating the crystal structure.
The phase transition of the element from one lattice to another can be explained by the transfer of one of the external electrons of the atomic kernel to the metal conductivity zone or its return from the conductivity zone to the external shell of the kernel under the
influence of external factors (pressure, temperature).
We tried to unravel the puzzle, but instead we received a new puzzle which provides a good explanation for the physico-chemical properties of the elements. This is the "coordination number" 9 (nine) for the face-centered and volume-centered lattices.
This frequent occurrence of the number 9 in the table suggests that the densest packings have been studied insufficiently.
Using the method of inverse reading from experimental values for the uniform compression towards the theoretical calculations and the formulae of Arkshoft and Mermin (1) to determine the Z value, we can verify its good agreement with the data listed in Table 1.
The metallic bond seems to be due to both socialized electrons and "valency" ones - the electrons of the atomic kernel.
Literature:
1) Solid state physics. N.W. Ashcroft, N.D. Mermin. Cornell University, 1975
2) Characteristics of elements. G.V. Samsonov. Moscow, 1976
3) Grundzuge der Anorganischen Kristallchemie. Von. Dr. Heinz Krebs. Universitat Stuttgart, 1968
4) Physics of metals. Y.G. Dorfman, I.K. Kikoin. Leningrad, 1933
5) What affects crystals characteristics. G.G.Skidelsky. Engineer N 8, 1989
Appendix 1
Metallic Bond in Densest Packing (Volume-centered and face-centered)
It follows from the speculations on the number of direct bonds ( or pseudobonds, since there is a conductivity zone between the neighbouring metal atoms) being equal to nine according to the number of external electrons of the atomic kernel for densest packings that similar to body-centered lattice (eight neighbouring atoms in the first coordination sphere). Volume-centered and face-centered lattices in the first coordination sphere should have nine atoms whereas we actually have 12 ones. But the presence of nine neighbouring atoms, bound to any central atom has indirectly been confirmed by the experimental data of Hall and the uniform compression modulus (and from the experiments on the Gaase van Alfen effect the oscillation number is a multiple of
nine.
In Fig.1,1. d, e - shows coordination spheres in the densest hexagonal and cubic packings.
Fig.1.1. Dense Packing.
It should be noted that in the hexagonal packing, the triangles of upper and lower bases are unindirectional, whereas in the hexagonal packing they are not unindirectional.
Literature:
- Introduction into physical chemistry and chrystal chemistry of semi-conductors. B.F. Ormont. Moscow, 1968.
Theoretical calculation of the uniform compression modulus (B).
B = (6,13/(rs/ao))5* 1010 dyne/cm2
Where B is the uniform compression modulus ao is the Bohr radius rs - the radius of the sphere with the volume being equal to
the volume falling at one conductivity electron.
rs=(3/4p n)1/3,
Where n is the density of conductivity electrons.
Table 1. Calculation according to Ashcroft and Mermine Element Z rs/ao theoretical calculated
| Z | rs/a0 | B theoretical | B calculated | |
| Cs | 1 | 5.62 | 1.54 | 1.43 |
| Cu | 1 | 2.67 | 63.8 | 134.3 |
| Ag | 1 | 3.02 | 34.5 | 99.9 |
| Al | 3 | 2.07 | 228 | 76.0 |
| Z | rs/a0 | B theoretical | B calculated | |
| Cs | 1 | 5.62 | 1.54 | 1.43 |
| Cu | 2 | 2.12 | 202.3 | 134.3 |
| Ag | 2 | 2.39 | 111.0 | 99.9 |
| Al | 2 | 2.40 | 108.6 | 76.0 |
Literature:
- Solid state physics. N.W. Ashcroft, N.D. Mermin. Cornell University, 1975
Monday, May 4, 2009
固体物理学入門。
伝導電子が金属の低熱にデュロンプティ（法律）貢献しています。理論的な計算は、同じドルーデモデルには、暑さの中では、電子の貢献相当する必要がありますを示しています。金属原子の密度が、 1つだけ残していないパックのパッケージのいくつかの種類-結晶格子。だから離れて金属の結晶格子の形成には、高密度包装からも、役割と原子（核骨格）の化学的特性を演じました。金属結合の金属原子の電子のいくつかの外郭団体に一般的に登場する予定ですが、これらの電子は、伝導帯。ゾーンは、現在の短期的な制動時に、以前は、コイルを推進し、ホールの伝導電子の数が決まるまでの実験で生じたとして、よく知られている経験に示すの存在。どのように原子骨格の"プロパティ"を定義するために化学？これを行うには、伝導帯に惹かれるの骨格ハイブリッド軌道に囲まれた原子の数を定義します。最寄りのtsentralnoizbrannogo原子のダイヤモンドの結晶格子の原子の密度包装34 ％ 、配位数と同じです（コード） 4です。 1つの混成軌道原子ダイヤモンド34 4で割った値を占めて、ナトリウム原子68 8で割った値に等しい厚さ8.5 protsentov.Po類似のパッケージ74 8,5 ravno9ことでパソコンの分割に相当する原子の混成軌道の8.5 protsentov.Otsyuda番号に等しい。 （軌道） 。紙の"化学的要素の内の金属製パッキン密結合の問題について"に記載 http://kristall.lan.krasu.ru/Science/publ_grodno.html http://sciteclibrary.ru/eng/catalog/pages/5216.html （ ） inEnglish 外殻電子、または最初のハイブリッド軌道podobolochek記入して、残りの電子伝導度のゾーンに配置されています。おそらく、電気伝導度のゾーンを実空間では、細胞表面ウィグナーの近くに位置する必要がありますZeyttsa 。大体、それはくしに似ている。このため、低熱伝導電子が金属のように貢献する実際には2次元の空間は、複雑な面があります。結晶内の伝導電子のための周波数だけでなく、格子定数とは、接続されている固体形状ハイブリッド（価）の原子軌道の殻を持つ。デostsilyatsiiハースほかの実験ではフェルミ面のファンアルフエン研究している。上記の規定を設定すると、原子は、シェルや伝導帯の電子申告の仕組みとお支払いのレベルが異なる場合が明確であることを考える必要があります。良い記事を見られていることは、材料特性の計算化学的要素をすぐには空のキューバ生まれではないことが、カルマン。これはおそらく量子力学ため、反対意見を許容されるdikovato 。 金属monocrystalsで超電導 なぜ格子からの原子の熱振動超電導の出現をリンクすることを決めたか？のための材料を超伝導転移温度の状態では、要素の異なる同位体がある。もちろん、このような信頼性ですが、無視されています。 Sverhrovodimost格子の種類に依存しない。多くの指揮者のテーブルには、ニオブ超伝導体ではなく、周辺を超えています。ほぼ同じの原子の熱振動。なぜか、他の金属超電導から発見されていませんか？原子の熱揺らぎの主な超伝導のメカニズムではない！電気伝導度の温度に依存します。しかし、銅、銀、最低気温超電導でいくつかの理由で、多くの銅と銀はより悪化していた車掌がニオブ、高温超電導観測されていません。それはより困難と銅の結晶格子の種類につながる。ここでは、電気伝導度のゾーンの一部のプロセスは、主には熱の変動を意味する。検討のために、電子の数は、電気伝導度のゾーンに設定の格子の各原子を知る必要がある。 BCSが作家ごとに10個の電子では、超伝導が関係していると剛体の理論への単純な伝導1 〜約3原子から電子を一からの参加によると主張し、約10分の1または100番目の電子ごと。それにもかかわらず、多くの超伝導電流が正常の伝導電流！何かは、伝導帯の電子を発生する！タスクを設定します。電気伝導度のゾーンを私にするように細胞表面ウィグナー- Zeyttsaは、結晶格子の原子の間に位置しています。大電子伝導度は、どこにも、一度、この表面に滞在する。伝導電子のゾーンでは、超伝導状態への移行、またはお互いに依存するようになるのチームを結成する必要があります。だから伝導電子のゾーンでは、アトムを与える銅、ニッケル、銀、超伝導体ではないと比較して大きくなるはずです。金属の伝導電子の数の要素は、仕事ではhttp ： / / kristall.lan.krasu.ru /サイエンス/ publ_grodno.html ūバナジウム、ニオブ、タンタル、原子の5伝導電子と、結果的に提示されると、温度変化フランス領極南諸島= 5.30 。 .. 9.26と4.48 K. ù 、ハフニウム、チタン、 3電子にジルコニウム、とTC = 0.09 ... 0.39と0.65 K.表の右側の要素をしようと、鉛、スズ、 4-5電子とアルミニウム、 galy 、インジウム、タリウム、 2-3電子がTC = 1196 ... 1091 ... 3.40 ... 2 39は、それぞれ。また、スズフランス領極南諸島= 7.19 、 3.72 、それぞれリードしている。何を証明するために必要だった。これは、表面部分の電気伝導度、電子、その社会で自分の組織内の伝導電子のスピンが背中を通して作業によるものです。 -------------------------------------------------- ------------------------------ここでは、伝導電子のコースだと言っているのは、一体ではないとしてBCSが、原子の数千もの距離にはより多くの電子の間にし、 " mate商品"再生を開始します。また、電気伝導度のゾーンでは、エネルギーレベルの数を伝導電子の数に一致しないことは明らかである（量子力学のように）は、結晶格子の量、すなわち原子からの伝導電子の数に等しいです1-5またはもう少し。 -------------------------------------------------- ------------------------------伝導電子が金属の低熱にデュロンプティ（法律）貢献しています。同じドルーデモデルの理論的な計算は、暑さの中では、電子の貢献相当する必要がありますを示しています。おそらく、電気伝導度のゾーンを実空間では、細胞表面ウィグナーの近くに位置する必要がありますZeyttsa 。大体、それはくしに似ている。このため、低熱伝導電子が金属のように貢献する実際には2次元の空間は、複雑な面があります。このエラードルーデ。結晶内の伝導電子のための周波数だけでなく、格子定数とは、接続されている固体形状ハイブリッド（価）の原子軌道の殻を持つ。デostsilyatsiiハースほかの実験ではフェルミ面のファンアルフエン研究している。 •ジョセフソン効果？超電導磁気現象は、多くのレポートが関連付けられていた。そのため、 2つの超伝導体の間に強磁性体（鉄などの薄い層を配置する） 、または銅diamagnetics面白いようだし、その結果を分析します。これらのサンドイッチ高いTCをしないのか？ •はTCを増やす。下の上を設定してください。金属ではTCを改善するために以下を提供することができます。否定的な金属製のサンプルを請求してテストします。
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