CN109061304B - Method for calculating conductivity variation of palladium in extremely dilute hydrogen environment - Google Patents
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Abstract
The invention discloses a method for calculating the conductivity variation of palladium in an extremely dilute hydrogen environment. The method can calculate the conductivity variation of the palladium in the extremely-dilute hydrogen environment, and provides a theoretical basis for weak hydrogen detection. According to the invention, by establishing a theoretical structure model of hydrogen adsorption of metal palladium, under the condition of extremely thin environmental hydrogen, the change of the structure and the electronic characteristic of palladium after hydrogen adsorption is researched by utilizing a first principle, so that the resistivity change of the palladium is deduced, and the conductivity change quantity of the palladium before and after hydrogen atom adsorption is obtained. The method has strong objectivity, is not interfered by the outside, and has high calculation result precision.
Description
Technical Field
The invention relates to the technical field of metal conductivity calculation, in particular to a method for calculating the conductivity variation of palladium in an extremely dilute hydrogen environment.
Background
In industrial technical applications, palladium is often used to extract high purity hydrogen. This is because both palladium and hydrogen have a relatively large valence from the extra-nuclear valence electron arrangement, particularly palladium as a transition metal has a valence of +2, +3, +4, and hydrogen also has a valence of ± 1, 0, and both elements have the same electronegativity of 2.20 on the leinas karl borlin scale. Therefore, in theory, the two elements can be "miscible" with each other in any proportion. When the metal palladium is exposed in an environment containing hydrogen, with the gradual increase of the hydrogen content, hydrogen atoms adsorbed on the atomic layer on the surface of the palladium will be gradually merged into the second and third … atomic layers positioned in the inner layer, the energy of the whole system will be gradually reduced, and the lost energy is used for forming the bonding energy between the palladium and the hydrogen. The limit would then be perfect mutual solubility of palladium and hydrogen, with the two elements forming a nested face-centered cubic structure, similar to the unit cell structure of sodium chloride, with a ratio of 1: 1. However, the actual situation cannot achieve the perfect 1:1 situation due to the complexity of the environment, the objective existence of impurity atoms, defects, and the like. According to a large number of experimental studies, two coexistence forms exist between palladium and hydrogen: an alpha phase and a beta phase. Wherein the alpha phase is a liquid phase and the lattice structure of the system is substantially similar to the unit cell structure of the metal, and the molar ratio of hydrogen to palladium is 0.03 at room temperature. As more and more hydrogen is incorporated into the palladium metal, the limiting case is the beta phase, with a molar ratio of the two elements of 0.6. In practical situations, palladium can absorb hydrogen gas violently, and when hydrogen gas needs to be purified in various mixed gases containing hydrogen gas, the hydrogen gas can be stored in metal palladium by utilizing the palladium-hydrogen mutual solubility, and then the palladium is heated in a proper environment to enable the hydrogen gas to escape, so that the hydrogen gas with high purity can be obtained.
After the palladium absorbs hydrogen, the conductivity of the palladium can be changed sensitively, and the method for acquiring the hydrogen concentration value by measuring the change of the conductivity of the metal palladium by utilizing the characteristic has wide application prospect in aerospace hydrogen detection/detection. This is because even very small amounts of hydrogen, for example, on the order of parts per million by volume of hydrogen to ambient gas, the relative value of the change in resistance of metallic palladium can be as much as a few thousandths of a meter above its measurement limit, and thus this method is extremely suitable for weak hydrogen detection. But the relative change of the resistance of the palladium is very small, so that the signal to noise ratio is higher when the resistance is measured. The change reason and the change size of the conductivity of the conductive material are theoretically analyzed by the invention and compared with the experimental measurement result. Therefore, the reliability and the accuracy of resistance change measurement can be improved, and the method has profound theoretical guiding significance for weaker hydrogen detection based on analysis of a real physical image.
Disclosure of Invention
In view of this, the invention provides a method for calculating the conductivity variation of palladium in an extremely dilute hydrogen environment, which can calculate the conductivity variation of palladium in the extremely dilute hydrogen environment and provide a theoretical basis for weak hydrogen detection.
The method for calculating the conductivity variation of the palladium in the extremely-dilute hydrogen environment comprises the following steps of:
step 3, based on the concentration of hydrogen in the current environment, determining the proportional value of hydrogen atoms on the atomic layer on the palladium surface according to the relationship between the gas density and the surface density to obtain the palladium atom number of the atomic layer on the palladium surface required for adsorbing one hydrogen atom, and expanding the super unit cell determined in the step 2 to the palladium atom number of the atomic layer on the palladium surface to form a super unit cell β with a palladium atom-hydrogen atom structure1The palladium atom-hydrogen atom structure super unit cell β1The hydrogen atom in (b) is removed to form a control palladium atom structure super unit cell β2Separately calculating the palladium atom-hydrogen atom structure of the super cell β by using the first principle1Palladium atomic structure super cell β in comparison2Energy state density distribution information of (a);
and 4, respectively integrating the electron energy state densities of the two structural super unit cells, and calculating the conductivity variation of the palladium after hydrogen adsorption according to the variation value of the electron energy state density integration of the two structural super unit cells.
Further, in the step 4, the electron energy state densities of the two super crystal cells are respectively integrated within the range of positive and negative 3 KT of the Fermi surface, and the super crystal cell β with the palladium atom-hydrogen atom structure is obtained1Integrated energy state density of (a) and comparative palladium atomic structure super cell β2Where K is the boltzmann constant and T is the kelvin temperature.
Further, the first principle calculation software VASP is used for structural modeling and first principle calculation.
Further, the number of layers of the super cell constructed in step 2 is 4.
Further, when the VASP is used for calculating the system total energy of the super unit cell in the step 2 and the energy state density distribution information of the super unit cell with the structure in the step 3, passivation treatment is carried out on the atom on the lowest layer of palladium, and then structural relaxation is carried out on each atom.
Has the advantages that:
first, the first principle calculation is an experiment from the viewpoint of calculation, and the most probable result is obtained from a strict inference logic. From a narrow point of view, the first calculation is from the beginning (ab initio), specifically excluding any empirical parameters, the parameters required being only a constant quantity in nature: and calculating parameters such as electron quality, light speed and the like. Therefore, the first principle calculation is based on the most basic state equation of the material structure, and the most basic physical property parameters of the material are obtained by performing the calculation of a multivariate parallel equation system on the basis of the most basic interaction assumption. Therefore, for the measurement capability which cannot be achieved by the existing experimental technical means, the theoretical 'experimental measurement' is carried out, the objectivity is strong, the external interference is avoided, and the calculation result precision is high.
Secondly, the lattice nesting process of the mutual-soluble system formed by palladium and hydrogen is different from that of other mutual-soluble systems, and in alpha and beta formed, two elements mutually occupy octahedral positions of a unit cell structure. More particularly, when a foreign element is absorbed in a metal (which is essentially a face-centered cubic structure), it typically first occupies non-face-centered cubic octahedral sites, whereas for hydrogen absorbed into palladium, it first occupies face-centered cubic sites. Therefore, when very small amounts of hydrogen are adsorbed to the atomic layer on the surface of palladium, theoretical analysis is required to determine the most likely occupied position of the hydrogen atom when all positions are unoccupied and selective occupancy occurs, thereby making the theoretical basis of the method of the present invention even more stringent.
And thirdly, the conductivity change condition of the palladium in the extremely trace hydrogen environment can be obtained through the method, on the basis of the method, the specific relation between the metal palladium and the adsorption quantity of the hydrogen is continuously and deeply researched, and for a specific palladium sensor, the conductivity change curve of the palladium in the extremely trace hydrogen environment is drawn through theoretical analysis, so that the specific concentration value of the spatial trace hydrogen can be reversely deduced. The method has important research value for space hydrogen detection and space astronavigation hydrogen detection technologies.
Drawings
FIG. 1 shows various cases where hydrogen atoms are adsorbed on the crystal plane of an atomic layer (111) on the surface of palladium.
FIG. 2 shows various cases where hydrogen atoms are adsorbed on the crystal plane of an atomic layer (100) on the surface of palladium.
FIG. 3 shows various cases where hydrogen atoms are adsorbed on the crystal plane of the atomic layer (110) on the surface of palladium.
Wherein, the atoms in fig. 1 to 3 are palladium atoms, and the star marks represent the positions of hydrogen atom adsorption.
Fig. 4 is a visualization model constructed when hydrogen atoms are adsorbed on the palladium (111) plane and adsorbed at the fcc position.
FIG. 5 is a first-type full quantum computing commerce software VASP interface relying on Shanghai super computing center.
FIG. 6 is a block diagram of a unit cell of face centered cubic palladium of palladium constructed in the commercial application software materials Studio.
FIG. 7 is a diagram of a constructed palladium 16X 16 super cell.
FIG. 8 is a diagram showing the structure of four positions of hydrogen adsorbed on the palladium (111) crystal face.
Fig. 9 is a relative total energy for the four-position system of fig. 8.
Fig. 10 is a cross-sectional schematic of charge density.
β in FIG. 111And β2The charge densities on the (111) and (010) planes were compared.
β in FIG. 121And β2And the integrated energy state density.
FIG. 13 is a flow chart of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a method for calculating the conductivity variation of palladium in an extremely-dilute hydrogen environment, which is characterized in that a theoretical structure model of metal palladium for absorbing hydrogen is established, and the change of the structure and the electronic characteristic of palladium after absorbing hydrogen is researched by utilizing a first principle under the condition that the environmental hydrogen is extremely dilute (the hydrogen content is less than 0.1ppm), so that the resistivity change of the palladium is deduced, and the conductivity variation of the palladium before and after hydrogen atom absorption is obtained.
The method specifically comprises the following steps:
The method utilizes a first principle to calculate the change of the structure and the electronic characteristic of palladium before and after hydrogen adsorption so as to obtain the conductivity variation of the palladium; in the embodiment, the software VASP is directly utilized to calculate the first principle, and the software has high calculation precision, visualized input and output and convenient operation; however, the present invention is not limited to this software, and may be any software as long as it can construct a super cell based on the first principle and realize calculation of the structure and electronic characteristics of the super cell.
In the VASP: describing the interaction between basic particles such as ions and atoms by adopting a pseudopotential, namely describing the interaction between the particles by adopting a plane wave amplification projection algorithm; the exchange interaction between charged particles is described by a generalized gradient approximation; when different calculation steps are carried out, the size of the set Monkhorst-Pack grid is gradually changed; in the plane wave vector calculation, the initial range of the truncation energy adopted by the invention is 150-650 millielectron volts, and the optimal truncation energy value obtained through optimization is 350 millielectron volts. The use of such truncation can achieve the computational accuracy requirement at an approximation.
And 2, establishing an adsorption structure model of hydrogen atoms on the atomic layer on the surface of the palladium and determining the actual adsorption condition.
The lattice constant of metallic palladium is a known quantity at room temperature, but in order to maintain the uniformity of the simulation calculation, the lattice constant of metallic palladium at room temperature needs to be determined by calculation: under the calculation setting, a model of the metal palladium face-centered cubic is constructed by using VASP, the energy of a palladium unit cell system corresponding to different lattice constants is calculated, and the lowest point of the energy is taken as the most probable lattice constant. The lattice constant is used as the lattice constant of the palladium unit cell for subsequent calculation.
In the extremely dilute hydrogen environment, hydrogen atoms are only adsorbed on the atomic layer on the palladium surface, and even all possible occupied vacancies in the atomic layer on the palladium surface are not occupied, so that the specific adsorption position of the hydrogen atoms on the palladium surface layer needs to be determined. A number of known experiments have established that hydrogen atoms are first adsorbed on the (111) crystal planes of metallic palladium. However, there are several different adsorption sites, so it is necessary to determine which one the real situation belongs to, i.e., to determine the specific position of the hydrogen atom on the atomic layer on the palladium surface. Therefore, the invention constructs different adsorption structure situations of hydrogen atoms on atomic layers on the surface of palladium, calculates the total unit cell energy under each adsorption situation, and takes the situation that the total unit cell energy is the lowest, namely the situation that the system structure is the most stable, namely the most possible adsorption situation of the hydrogen atoms. The method comprises the following specific steps:
the palladium metal is of a typical face-centered cubic lattice structure, and in order to obtain a specific adsorption structure situation of hydrogen atoms on an atomic layer on the surface of palladium, palladium unit cells are firstly constructed, and then various adsorption position situations of the hydrogen atoms on the palladium unit cells are analyzed; considering boundary effect and other factors, 5-20 unit cells are constructed to simulate various adsorption positions of one hydrogen atom on an atomic layer on the surface of palladium. The crystal plane of the atomic layer on the surface of palladium is generally (111), (100) or (110), and the adsorption condition of the three planes is analyzed for comprehensive examination.
When the crystal plane of the atomic layer on which hydrogen atoms are adsorbed on the palladium surface is (111), 4 cases are divided: a hydrogen atom is located in the middle of two palladium atoms, called a bridge structure; hydrogen is adsorbed directly above one palladium atom (top); the hydrogen atom is positioned among 3 palladium atoms, and one palladium atom is positioned below the (111) surface to form a regular hexagonal structure (hcp); the hydrogen atom is located among 3 palladium atoms, and no palladium atom is present directly below the (111) plane, which forms a nested face-centered-cubic structure (fcc) with the palladium unit cell, as shown in fig. 1.
When hydrogen is adsorbed on the (100) face of palladium, there are 3 adsorption structures: the hydrogen atom is positioned among 4 palladium atoms to form a hollow structure; the hydrogen atom is positioned among 2 palladium atoms to form a bridge structure; the hydrogen atoms are adsorbed directly above one of the palladium atoms to form a top structure, as shown in figure 2.
When hydrogen is adsorbed on the (110) face of palladium, there are 5 adsorption structures: the first type of asymmetric structure observed experimentally, known as pseudo-triple-fold structure (pseudo-triple-fold), is not validated in theoretical calculations, but has been found experimentally; the hydrogen atom is positioned among 4 palladium atoms to form a hollow structure; the hydrogen atoms are positioned among 2 palladium atoms which are relatively close to each other to form a short bridge structure; the hydrogen atom is positioned among 2 palladium atoms which are far away from each other to form a longbridge structure; the hydrogen atom is adsorbed directly above one palladium atom (top) as shown in fig. 3.
Then, the adsorption model of various hydrogen atoms on the atomic layer on the surface of palladium, namely a super cell α, is constructed in large-scale computer commercial software materials Studioi(i ═ 1,2,3, …). For example, when hydrogen atoms were adsorbed on the palladium (111) plane and adsorbed at the fcc position, the model constructed was visualized as shown in fig. 4.
Calculated by taking the palladium-hydrogen adsorption model constructed in the materials Studio as the VASPStructural input document POSCAR in VASP for each super cell αi(i ═ 1,2,3, …) and the total energy E of the system of super cells can be obtained in the output file OUTCAR of VASPi(i ═ 1,2,3, …). The method comprises the following steps of selecting i with the lowest energy, namely the actual adsorption condition of hydrogen atoms on an atomic layer on the surface of palladium, and determining a corresponding adsorption model, namely a determined palladium-hydrogen adsorption model.
Step 3, establishing palladium-hydrogen adsorption super cell β of complete system1And control supercell β2Pairs β in turn by the VASP according to its own computational flow1And β2And performing structure optimization, static calculation and system energy state density calculation.
Deriving a proportional numerical value of hydrogen atoms on a palladium surface atomic layer according to the concentration of hydrogen in the current environment and the relation between gas bulk density and surface density, then obtaining the number of palladium surface atomic layers required for adsorbing one hydrogen atom according to the proportional numerical value of the hydrogen atoms on the palladium surface atomic layer, and then expanding the palladium-hydrogen adsorption model determined in the step (2) to the determined palladium atom number of the palladium surface atomic layer according to the obtained palladium surface atomic layer to form a complete system of palladium-hydrogen adsorption super unit cell β1I.e. the period of the metal palladium lattice is enlarged, so that the model is closer to the real situation. In order to retain the bulk material characteristics of palladium and ensure the calculation efficiency, atomic layers of palladium are constructed as much as possible, and passivation treatment is carried out on atoms at the lowest layer of palladium to ensure the symmetry and the accuracy of results.
The palladium atom-hydrogen atom structure super cell β1The hydrogen atom in (b) is removed to form a control palladium atom structure super unit cell β2I.e. the palladium supercell before hydrogen atom adsorption.
Next to the super cell β1And β2Performing first principle calculation to obtain super cell β1And β2Charge distribution information and electron energy state density distribution information of (1):
in the software VASP, first, the super cell β is fixed1And β2All the lowest layer atoms, using VASP pairsThe structure of the system is optimized, namely the position of each atom (including palladium atom and hydrogen atom) except the lowest layer of atoms in the unit cell is continuously relaxed to obtain the point with the lowest energy of the system, namely the most probable position of all atoms.
In the VASP output file of the structure calculation, the CONTCAR file is used as the structure input file again, all atoms of the super unit cell are fixed, and the whole system is subjected to one-time self-consistent static calculation, so that the charge distribution information of the whole system can be obtained.
At this time, the files CHG and CHGCAR representing the charge distribution information in the previous calculation result are used as input files of VASP, and the whole system is subjected to one-time self-consistent calculation, so that the electron energy state density distribution information of the system is obtained and reflected in the DOSCAR of the VASP output file.
First according to step 3 with respect to the super cell β1And β2The method mainly considers two points that firstly, for the palladium-hydrogen system, valence electrons around palladium atoms occupy most of the proportion in the whole system, and only 1 hydrogen atom in the whole system brings 1 valence electron, so that the influence on the valence electrons of the whole system is very small, the influence on the electron mobility and the electron effective mass of the whole valence electron system is very small1And performing cross-section charge density analysis on the position of the middle hydrogen atom to determine whether the bonding strength between the hydrogen valence electron and the palladium valence electron forms a shared electron cloud or not, thereby verifying the influence of the valence electron of the external hydrogen atom on the whole system. By verification it can be determined that: after introduction of hydrogen atoms, the influence on the electron mobility and the electron effective mass of the whole valence electron system is negligibleAnd (6) counting.
After verifying the above assumptions, proceed to pair β1And β2Analysis of the electron energy state density distribution information of the system of (1). The integrated energy state density near the fermi surface, based on the electron energy state density of the system, is used as input data for the following theoretical derivation.
Specifically, as previously mentioned, the overall system still maintains the metallic character when metallic palladium adsorbs a small amount of hydrogen to form a palladium-hydrogen "miscible" α phase, where the molar ratio of hydrogen to palladium is 0.03, and for super cell β when the hydrogen is extremely dilute1For example, the entire system can be considered metallic, so the conductivity of the analytical system uses the metal electron theory:
when a constant electric field E is applied to the metal, a stable current density j is actually established in a time of the order of femtoseconds, obeying ohm's law:
j＝σE
where σ is the conductivity.
The nature of the steady current reflects that, under constant external field, the electrons reach a new steady state statistical distribution, which can also be described by a distribution function f (k) similar to that at equilibrium, and once the distribution function f (k) is determined, the current density can be directly calculated.
It is well known that in simple electronic theory, the main physical basis for explaining ohm's law is:
(i) electrons are accelerated under the action of an electric field E;
(ii) electrons lose directional motion due to collision
For (i), it can be shown by band theory that under the action of E, all electronic state changes obey:
where k is an electron wave vector, t is time, E is an applied electric field, q is a basic charge amount, and h is a boltzmann constant.
Whereas for (ii) the electrons, assuming a certain collision free time τ, completely lose the directional motion obtained in the electric field once subjected to a collision. In order to quantitatively research the theory of electron motion, a differential equation, boltzmann equation, with respect to an electron transport distribution function is introduced. The boltzmann equation is established from an examination of how the electron transport distribution function varies over time, and the variation of the electron transport distribution function has two sources:
"Drift" of statistical distribution in k-space caused by ambient conditions "
ii, collision, the electrons continuously jump from one state k to another state k' due to vibration of lattice atoms or the presence of impurities, and the change of the electron state is called scattering. Assuming that the final and initial states of the collision can be simplified as b and a, the boltzmann equation can be simplified as:
wherein f is0Is the fermi function at equilibrium, f ═ f (k), and τ is a parameter introduced and called relaxation time. Using the basic relation of the energy bands:
the final current density formula is:
the above equation is expressed in terms of components:
finally, the conductivity is obtained:
notably, the above formula appears
It is shown that the contribution of the integral comes mainly from E ═ EFNearby, i.e. the conductivity is mainly determined by the fermi plane E ═ EFThe situation of the vicinity. Assuming that the metal conduction band electrons can be basically used with a single effective mass m*The following steps are described:
by unfolding the integral, ignoring higher order terms, the metal conductivity can be written as:
wherein σ0Representative tensor σαβScalar value of (c) in the above pair of supercells β1And β2It has been clarified from the analysis of the charge distribution information of the system (1) that the electron mobility (relaxation time) τ (E) for the valence electrons of the entire palladium system after hydrogen adsorptionF) And electron effective mass m*Do not change and thus have a conductivity σ for the system0The influence of (a) is attributed to the electron density n.
It is noted that n is the number density of valence electrons near the Fermi surface of the system, since the electron distribution function of the whole system is unchanged before and after adsorption, the electron energy state density distribution obtained in step 3 is combined with the palladium-hydrogen adsorption super cell β1And control Palladium UlipropateStage unit cell β2And integrating the electron energy state density near the Fermi surface (within plus or minus 3 KT ranges of the Fermi surface), and comparing the change values of the electron energy state density integrals of the two super unit cells to obtain the conductivity change condition of the system after the palladium adsorbs the hydrogen. Wherein K is Boltzmann constant, T is Kelvin, and the conductivity characteristics of the crystal can be well reflected by the electron energy state density within plus or minus 3 KT of the Fermi surface.
It is noted that palladium-hydrogen adsorption super cell β may also be used1And control palladium supercell β2The electron energy state densities of the palladium and the hydrogen adsorption are respectively subjected to integration treatment in a full range, and the conductivity change amount of the palladium after hydrogen adsorption is calculated by using the integration results in the full range.
Thus, the conductivity change value of palladium under the given extremely dilute hydrogen environment is obtained.
With a specific very dilute hydrogen concentration of 9 × 1026The specific way of calculating the change of the palladium conductivity in the invention is illustrated by taking the adsorption per cubic meter on the (111) surface of the metal palladium as an example.
The concentration of hydrogen was 9 × 1026Per cubic meter, i.e., just near the experimental measurement limit, and literature reports the amount of conductivity change of metallic palladium, which can be used to validate the calculations of the present invention, can be deduced from the lattice constant of palladium at room temperature, 9 × 10261 hydrogen atom per cubic meter is adsorbed on the (111) face of palladium, and the palladium surface atomic layer has 16 atoms.
FIG. 5 shows a first exemplary full-quantum computing commercial software VASP, whose version is vasp.5.3.5, used in the computing of the present invention, and the super computer group used in the computing of Shanghai super computing center. The pseudopotential used was PAW-GGA.
The lattice constant of palladium is known, but to ensure consistency in this study, the lattice constant of palladium was calculated using the first principles of principle calculation tool VASP, first constructing a unit cell of face centered cubic palladium in the commercial application software materialas Studio, as shown in fig. 6.
The structure information is used as input, a structure input file POSCAR of VASP is written, the unit cell basis vector length of the Pd face-centered cubic is calculated to be a ═ b ═ c ═ 391.82pm through lattice relaxation, and the unit cell basis vector length of the Pd face-centered cubic structure is 389.07pm under room temperature (300K) through experiment. Therefore, the adopted calculation tool is verified to be more matched with the actual situation.
When hydrogen is adsorbed on the surface atomic layer (111) of palladium, there are four adsorption sites of fcc, hcp, top and bridge, as discussed above. Then a comparison of the magnitude of their probability of being attracted to different locations is required. By calculating the total energy of the palladium-hydrogen system at different adsorption sites, it can be determined that the system with the lowest energy is the most stable, i.e. the most likely adsorption site.
Combining with practical situation, firstly constructing four layers of palladium atoms, wherein the crystal face index of each layer is (111), and finally passivating the last layer to retain the characteristics of the bulk material, namely the structure of the palladium-16 × 16 × 16 × 16 super unit cell. The four layers of palladium atoms are constructed, so that the structural stability of the palladium atoms is guaranteed, the specific surface area of the palladium atoms is increased, and the detection efficiency is improved. As in fig. 7, 25 palladium atoms per layer are shown in fig. 7, but due to translational symmetry, each layer actually contains 16 palladium atoms. The supercell palladium: 16 x 16 lattice relaxation was first performed based on the palladium lattice basis vector 391.82pm calculated in the first step. The structure file is first exported from the materials Studio, which is fixed (F) for passivating the last layer, and the remaining upper three layers of atoms are continuously relaxed in position. The atomic coordinates of each layer are finally determined by calculation through VASP.
Based on the above calculation results, a structural super cell α with hydrogen adsorbed at four positions of palladium (111) crystal face was constructed1，α2，α3，α4I.e. fcc, hcp, top, bridge four positions in sequence, as shown in fig. 8, α for the four super cells1，α2，α3，α4After structural relaxation, in the output file OUTCAR of VASP, the relative total energy of the system can be obtained, the result of which is shown in fig. 9.
The results show that after fcc adsorption, the system has the lowest binding energy, which indicates that the fcc adsorption structure is consistent with a large number of experimental observations, namely the most likely adsorption position.
When the specific adsorption position of the hydrogen atom is determined, the calculation precision is improved, namely, a larger calculation amount is set in a step size KPOINTS file of an inverted lattice space taken during representing VASP calculation, and the adsorption super cell β of the complete fcc palladium: 16 × 16 × 16 × 16-hydrogen: 1 system is obtained1Next, under the same accuracy KPOINTS files, a comparative group of 16 × 16 × 16 × 16 super cells β was created2。
β need to be paired before calculating the system energy state density1And β2The static self-consistent calculation is that each atom position is fixed, the continuous self-iterative calculation is carried out on the whole system from the most basic Schrodinger equation, finally the most reliable configuration of the whole system is obtained within the set precision range, the charge density distribution of the whole system can be obtained through the static calculation, and then the comparison β is carried out1And β2The charge distribution on the (111) and (010) planes, FIG. 10 is a charge density cross-sectional schematic, where the build-up of four atomic layers of palladium can be seen, as well as the hydrogen atom adsorbed at the uppermost fcc position (within the black circle), the vertical cut is the (010) plane, and the horizontal cut is the (111) plane1And β2Charge density ratio of (111) plane and (010) plane as shown in FIG. 11 Palladium-Hydrogen represents super cell β1Palladium stands for super cell β2。
β1And β2The coordinates of the charge density planes on the (111) plane and the (010) plane are the same, and the scales of the charge density sizes (colors) are the same. It can be seen that after hydrogen atoms are adsorbed, hydrogen and the nuclear valence electron of palladium do not form a shared electron cloud, so that the electron mobility (relaxation time) and the electron effective mass of the valence electron of the whole palladium system are not changed after hydrogen is adsorbed.
The previous analysis showed that hydrogen and palladium form a miscible body with a more typical metal lattice structure when hydrogen is rarer, for β1The conductivity scalar value calculation formula is as follows:
after hydrogen is adsorbed, the electron mobility (relaxation time) and the electron effective mass of the valence electrons of the whole palladium system are not changed, so that the influence factors on the conductivity of the system are attributed to the electron density n. And n is the number density of valence electrons near the fermi surface of the system.
In the results of the static calculation of the previous step, two groups of super cell systems β were obtained1And β2The self-consistent charge density of (A) is shown in the output files CHGCAR and CHG of VASP, and then the previous step is carried out to β1And β2At this time, when the input file INCAR is set, the ICHAGR in the input file is changed to be 2 or 11, which means that the already calculated input files CHGCAR and CHG are adopted, and at this time, the calculation precision of KPOINTS is further increased, and meanwhile, the coordinates of the fixed atoms are still obtained β1And β2The distribution of the energy state density and the integrated energy state density of (a) are shown in fig. 12.
By accumulating the density of integrated states around the fermi level
And performing weighted average comparison to obtain the super cell β after hydrogen adsorption1Comparative control palladium super cell β2The integrated energy state density reduction was 0.249%. The electron distribution function of the whole system is unchanged before and after adsorption, so the number density n of valence electrons near the fermi surface of the system, i.e. the conductivity reduction of the system is also 0.249%, which is consistent with the literature report that the conductivity reduction of palladium after hydrogen adsorption is about 0.203% -0.547%.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A method for calculating the conductivity variation of palladium in an extremely dilute hydrogen environment is characterized by comprising the following steps:
step 1, constructing all possible structure models of hydrogen atoms adsorbed on atomic layers on the surface of palladium;
step 2, respectively constructing super unit cells of palladium atoms-hydrogen atoms of each structure model obtained in the step 1; calculating the total energy of the system of each super unit cell by utilizing a first principle, wherein the super unit cell corresponding to the minimum total energy of the system is the real adsorption condition of one hydrogen atom on the atomic layer on the surface of palladium;
step 3, based on the concentration of hydrogen in the current environment, determining the proportional value of hydrogen atoms on the atomic layer on the palladium surface according to the relationship between the gas density and the surface density to obtain the palladium atom number of the atomic layer on the palladium surface required for adsorbing one hydrogen atom, and expanding the super unit cell determined in the step 2 to the palladium atom number of the atomic layer on the palladium surface to form a super unit cell β with a palladium atom-hydrogen atom structure1The palladium atom-hydrogen atom structure super unit cell β1The hydrogen atom in (b) is removed to form a control palladium atom structure super unit cell β2Separately calculating the palladium atom-hydrogen atom structure of the super cell β by using the first principle1Palladium atomic structure super cell β in comparison2Energy state density distribution information of (a);
and 4, respectively integrating the electron energy state densities of the two structural super unit cells, and calculating the conductivity variation of the palladium after hydrogen adsorption according to the variation value of the electron energy state density integration of the two structural super unit cells.
2. The method for calculating the conductivity change of palladium in an extremely dilute hydrogen environment according to claim 1, wherein in the step 4, the electron energy state densities of two structural super cells are respectively integrated within plus and minus 3 KT ranges of Fermi surface to obtain β of palladium atom-hydrogen atom structural super cell1Integrated energy state density of (a) and a comparable palladium atomic structure super cellβ2Where K is the boltzmann constant and T is the kelvin temperature.
3. The method for calculating the conductivity change amount of palladium in an extremely dilute hydrogen environment according to claim 1, wherein the structural modeling and the first-principle calculation are performed by using first-principle calculation software VASP.
4. The method for calculating the conductivity change of palladium in an extremely dilute hydrogen environment according to claim 3, wherein the number of layers of the super unit cell constructed in the step 2 is 4.
5. The method for calculating the conductivity change of palladium in an extremely dilute hydrogen environment according to claim 3, wherein when the VASP is used to calculate the system total energy of the super cell in step 2 and the energy state density distribution information of the structured super cell in step 3, the passivation treatment is performed on the atom on the lowest layer of palladium, and then the structural relaxation is performed on each atom except the atom on the lowest layer.
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5330855A (en) * | 1991-09-23 | 1994-07-19 | The United States Of America, As Represented By The Secretary Of Commerce | Planar epitaxial films of SnO2 |
| EP0961334A2 (en) * | 1998-06-01 | 1999-12-01 | Matsushita Electric Industrial Co., Ltd. | Method for activating fuel cell |
| US7389671B1 (en) * | 2004-12-01 | 2008-06-24 | Uchicago Argonne, Llc | Ultrafast and ultrasensitive hydrogen sensors based on self-assembly monolayer promoted 2-dimensional palladium nanoclusters |
| CN104538070A (en) * | 2014-12-08 | 2015-04-22 | 中广核工程有限公司 | Method, device and system for measuring concentration of hydrogen in nuclear power station containment vessel |
| CN107301758A (en) * | 2017-08-08 | 2017-10-27 | 肇庆高新区长光智能技术开发有限公司 | A kind of hydrogen prior-warning device |
| CN107548456A (en) * | 2014-12-10 | 2018-01-05 | Bp北美公司 | The estimation of nano-porous materials electrical conductivity |
| CN107543924A (en) * | 2017-09-06 | 2018-01-05 | 重庆医科大学 | Biology sensor detection myeloperoxidase based on copper palladium platinum mesh nanometer material |
| CN108172849A (en) * | 2018-03-06 | 2018-06-15 | 中国科学院上海高等研究院 | Based on the monoatomic manganese dioxide-carbon nano tube composite catalyst of palladium and its preparation |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7815843B2 (en) * | 2007-12-27 | 2010-10-19 | Institute Of Nuclear Energy Research | Process for anode treatment of solid oxide fuel cell—membrane electrode assembly to upgrade power density in performance test |
-
2018
- 2018-07-09 CN CN201810744952.2A patent/CN109061304B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5330855A (en) * | 1991-09-23 | 1994-07-19 | The United States Of America, As Represented By The Secretary Of Commerce | Planar epitaxial films of SnO2 |
| EP0961334A2 (en) * | 1998-06-01 | 1999-12-01 | Matsushita Electric Industrial Co., Ltd. | Method for activating fuel cell |
| US7389671B1 (en) * | 2004-12-01 | 2008-06-24 | Uchicago Argonne, Llc | Ultrafast and ultrasensitive hydrogen sensors based on self-assembly monolayer promoted 2-dimensional palladium nanoclusters |
| CN104538070A (en) * | 2014-12-08 | 2015-04-22 | 中广核工程有限公司 | Method, device and system for measuring concentration of hydrogen in nuclear power station containment vessel |
| CN107548456A (en) * | 2014-12-10 | 2018-01-05 | Bp北美公司 | The estimation of nano-porous materials electrical conductivity |
| CN107301758A (en) * | 2017-08-08 | 2017-10-27 | 肇庆高新区长光智能技术开发有限公司 | A kind of hydrogen prior-warning device |
| CN107543924A (en) * | 2017-09-06 | 2018-01-05 | 重庆医科大学 | Biology sensor detection myeloperoxidase based on copper palladium platinum mesh nanometer material |
| CN108172849A (en) * | 2018-03-06 | 2018-06-15 | 中国科学院上海高等研究院 | Based on the monoatomic manganese dioxide-carbon nano tube composite catalyst of palladium and its preparation |
Non-Patent Citations (2)
| Title |
|---|
| Influence of hydrogen adsorption on conductivity of ultrathin Pd films;Litovchenko et al.;《PHYSICS OF LOW-DIMENSIONAL STRUCTURES》;20021231;第77-86页 * |
| 化学镀钯膜提高直接甲醇燃料电池阻醇性能的应用;索春光 等;《功能材料与器件学报》;20080430;第422-425页 * |
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