CN109061304A - A kind of palladium conductivity variations amount calculation method in extremely thin hydrogen environment - Google Patents
A kind of palladium conductivity variations amount calculation method in extremely thin hydrogen environment Download PDFInfo
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Abstract
Conductivity variations amount calculation method that the invention discloses a kind of palladiums in extremely thin hydrogen environment.Palladium conductivity variations amount in extremely thin hydrogen environment can be calculated using the present invention, provides theoretical foundation for faint hydrogen detection.The present invention adsorbs the theoretical construct model of hydrogen by establishing Metal Palladium, in the extremely thin situation of environment hydrogen, conductivity variations amount size of the palladium before and after Hydrogen chemisorption is obtained to derive its change in resistance using the variation of structure and characteristic electron after first principle research palladium absorption hydrogen.Objectivity of the present invention is strong, and not by external interference, computational solution precision is high.
Description
Technical field
The present invention relates to conductivity metal computing technique fields, and in particular to a kind of palladium conductance in extremely thin hydrogen environment
Rate variable quantity calculation method.
Background technique
In industrial technology application, palladium is often used to extract the hydrogen of high-purity.This is because arranging from core Outer valence electrons
From the point of view of, palladium and hydrogen all have more chemical valence, especially as the palladium of transition metal, with+2 ,+3 ,+4 chemical valence, and
Hydrogen also has ± 1,0 chemical valence, and on the electronegativity table of Linus karr Pauling scale, and two kinds of elements have phase
Same electronegativity is 2.20.So theoretically two kinds of elements can be with arbitrary proportion mutually " dissolving each other ".Contain when Metal Palladium is exposed to
Have in the environment of hydrogen, with gradually increasing for hydrogen content, the hydrogen atom for being adsorbed on palladium surface atom layer will gradually incorporate
The energy of a atomic layer positioned at second, third of internal layer ..., whole system will gradually decrease, and the energy of loss is used to be formed
Combination bond energy between palladium-hydrogen.So the case where limit will be that the perfection of palladium and hydrogen is dissolved each other, and two kinds of elements form nested against one another
Face-centred cubic structure, similar to the cell configuration of sodium chloride, the ratio of two kinds of elements is 1:1 at this time.But actual conditions are but
Because of the objective reality of the complexity of environment, foreign atom, defect etc., it is unable to reach perfect 1:1 situation.It is ground according to many experiments
Study carefully verifying, there are two kinds between palladium and hydrogen to coexist form: α phase and β phase.Wherein α phase is known as liquid phase phase, the lattice structure base of system
This is similar to the cell configuration of metal, and at room temperature, the mole ratio of hydrogen and palladium is 0.03.As more and more hydrogen incorporate palladium
In metal, limit situations are β phase, and the mole ratio of two kinds of elements is 0.6.In a practical situation, palladium can tempestuously be inhaled
Receive hydrogen, when need in the various mixed gases of hydrogen purifying hydrogen of hydrogen, so that it may utilize above-mentioned palladium-hydrogen " dissolving each other ", by hydrogen
Then gas " storage " heats palladium in suitable environment in Metal Palladium, so that hydrogen " evolution ", so that it is very high to obtain purity
Hydrogen.
After absorbing hydrogen, conductivity can occur sensitively to change very much palladium, using this characteristic, by measuring metal
The variation of palladium conductivity obtains this method of density of hydrogen numerical value, has in aerospace hydrogen detection/detection wide
Application prospect.This is because the even extremely small hydrogen of content, for example, hydrogen and environmental gas volume ratio be million/
When one magnitude, the resistance variations relative value of Metal Palladium is up to some thousandths of, and on its measuring limit, institute is in this way extremely
Suitable for faint hydrogen detection.But since the opposite variation of palladium resistance is very small, in measurement, its noise is relatively high.Through the invention
The reason of changes and variation size of its conductivity are theoretically analyzed, and is compared with experimental measurements.So not only
The reliability and accuracy of its resistance change measurement, and the analysis based on its actual physical image can be improved, it can be to more
There is far-reaching theory directive significance for faint hydrogen detection.
Summary of the invention
In view of this, the present invention provides a kind of palladiums in extremely thin hydrogen environment conductivity variations amount calculation method, energy
Palladium conductivity variations amount in extremely thin hydrogen environment is enough calculated, provides theoretical foundation for faint hydrogen detection.
The palladium of the invention conductivity variations amount calculation method in extremely thin hydrogen environment, includes the following steps:
Step 1, a Hydrogen chemisorption is constructed in all possible structural model of palladium surface atom layer；
Step 2, the super structure cell of palladium atom-hydrogen atom for each structural model that construction step 1 obtains respectively；Utilize first
Property principle, calculate the system gross energy of each super structure cell, super structure cell corresponding to minimum system gross energy is as true
Absorption situation of one hydrogen atom in palladium surface atom layer；
Step 3, the concentration based on hydrogen in current environment determines hydrogen original according to the relationship of gas volume density and surface density
Son is in the proportional numerical value of palladium surface atom layer, the palladium atom number of palladium surface atom layer needed for obtaining one hydrogen atom of absorption；
The palladium atom number that the super structure cell that step 2 determines is extended to identified palladium surface atom layer, forms palladium atom-hydrogen atom
The super structure cell β of structure1；By the super structure cell β of palladium atom-hydrogen atom structure1In hydrogen atom removal, palladium in contrast is former
The super structure cell β of minor structure2；Using first principle, the super structure cell β of palladium atom-hydrogen atom structure is calculated separately1With the palladium of control
The super structure cell β of atomic structure2Energy state density distributed intelligence；
Step 4, the density of electronic states of two super structure cells of structure is done into Integral Processing respectively, it is super according to two structures
The changing value of the density of electronic states integral of structure cell calculates conductivity variations amount of the palladium after adsorbing hydrogen.
Further, in the step 4, the density of electronic states of two super structure cells of structure is respectively in Fermi surface positive and negative 3
It is integrated within the scope of a KT, obtains the super structure cell β of palladium atom-hydrogen atom structure1Integral energy state density and control palladium atom
The super structure cell β of structure2Integral energy state density, wherein K is Boltzmann constant, and T is Kelvin.
Further, structural modeling and first-principles calculations are carried out using first-principles calculations software VASP.
Further, the number of plies for the super structure cell that step 2 constructs is 4.
Further, structure described in the system gross energy of super structure cell described in step 2, step 3 is calculated in utilization VASP to surpass
Grade structure cell energy state density distributed intelligence when, Passivation Treatment is done to one layer of the bottom atom of palladium, then to each atom into
Row structure Relaxation.
The utility model has the advantages that
Firstly, first-principles calculations are tested from the angle of calculating, obtain most from strict inference logic
Probable result.Primary calculating i.e. HF Ab initio (ab initio) are carried out from the angle of narrow sense, are specifically exactly to arrange
Except any empirical parameter, required parameter is the constant basis of nature: electron mass, and the parameters such as light velocity go to be calculated.
Thus, first-principles calculations are set out with the most basic state equation of the structure of matter, are assumed from most basic interaction
On the basis of carry out polynary parallel equation group calculating to obtain the most basic physical-property parameter of substance.So for existing reality
It tests for the measurement capability that technological means is unable to reach, carries out theoretical " experiment measurement ", objectivity is strong, not by external interference, meter
It is high to calculate result precision.
Secondly, the lattice nested procedure of " dissolving each other " system that palladium and hydrogen are formed is different from other bodies that " dissolve each other ", it is formed by α
In β, two kinds of elements are all occupied mutually on the octahedral site of its cell configuration.More particularly, when certain external member
When element is absorbed in metal (being all substantially face-centred cubic structure), what is generally occupied first is non-face-centered cubic octahedral position
It sets, and for hydrogen is absorbed into palladium, what is occupied first is face-centered cubic position.So when extremely micro hydrogen adsorbs
When to palladium surface atom layer, when all positions are not occupied, and when selectivity occur and occupying, it is necessary to which theory analysis determines
Hydrogen atom is the most possible to plant oneself, so that the method for the present invention theoretical basis is more rigorous.
Again, by the invention it is obtained that conductivity variations situation of the palladium in extremely trace hydrogen environment, in this hair
On the basis of bright, the physical relationship between research Metal Palladium and the adsorbance of hydrogen is continued deeper into, palladium specific for one passes
Sensor depicts conductivity variations curve of the palladium in denier hydrogen environment by theory analysis, it is micro- counter can to release space
Measure the specific concentration values of hydrogen.This is all with important research for the detection of space hydrogen, space aerospace hydrogen Detection Techniques
Value.
Detailed description of the invention
Fig. 1 is various situations of the Hydrogen chemisorption in palladium surface atom layer (1 1 1) crystal face.
Fig. 2 is various situations of the Hydrogen chemisorption in palladium surface atom layer (1 0 0) crystal face.
Fig. 3 is various situations of the Hydrogen chemisorption in palladium surface atom layer (1 1 0) crystal face.
Wherein, the atom in FIG. 1 to FIG. 3 is palladium atom, and star mark represents the position of Hydrogen chemisorption.
Fig. 4 is the visualization mould of building when Hydrogen chemisorption is on palladium (1 1 1) face, and is adsorbed on the position fcc
Type.
Fig. 5 is the full interface quantum calculation business software VASP of the primary for relying on Shanghai Supercomputer Center.
Fig. 6 is the cell configuration figure of the face-centered cubic palladium of the palladium constructed in business application software Materias Studio.
Fig. 7 is the super cell configuration figure of palladium 16 × 16 × 16 × 16 of building.
Fig. 8 is four kinds of position assumption diagrams that hydrogen is adsorbed on palladium (1 1 1) crystal face.
Fig. 9 is the opposite total energy of the system of the tetra- kinds of positions Fig. 8.
Figure 10 is the signal of charge density section.
Figure 11 is β1And β2It is compared in the charge density in (1 1 1) face and (0 1 0) face.
Figure 12 is β1And β2Energy state density distribution with integral energy state density.
Figure 13 is flow chart of the present invention.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
Conductivity variations amount calculation method that the present invention provides a kind of palladiums in extremely thin hydrogen environment, by establishing metal
Palladium adsorbs the theoretical construct model of hydrogen, in the extremely thin situation of environment hydrogen (hydrogen content is less than 0.1ppm), utilizes the primary
Principle research palladium adsorbs the variation of structure and characteristic electron after hydrogen, to derive its change in resistance, obtains palladium in hydrogen atom
Adsorb the conductivity variations amount size of front and back.
Specifically comprise the following steps:
Step 1, the calculating input setting of first-principles calculations software VASP is determined the use of.
The present invention is the variation using structure and characteristic electron of the first-principles calculations palladium before and after adsorbing hydrogen, thus
To the conductivity variations amount of palladium；The present embodiment is the calculating that first principle is directly carried out using software VASP, the meter of the software
Calculate precision height, input and output visualize, is easy to operate；But the present invention is not limited to the softwares, as long as the primary can be based on
Principle constructs super structure cell, and realizes to the structure of super structure cell and the calculating of characteristic electron.
In VASP: the interaction between the elementary particles such as ion, atom is described by pseudo potential, i.e., it is logical
Plane wave amplification projection algorithm is crossed the interaction between particle is described；Exchange interaction between charged particle is
It is described by generalized gradient approximation；When carrying out different calculating steps, the Monkhorst-Pack grid of setting is big
It is small to gradually change；When plane wave vector calculates, the truncation energy initial range that the present invention takes is 150 to 650 milli electron-volts,
It obtains that energy value is most preferably truncated to be 350 milli electron-volts by optimization.Meter can be reached under approximation using such truncation
Calculate the demand of precision.
Step 2, hydrogen atom is established in the adsorption structure model of palladium surface atom layer and determines practical absorption situation.
At room temperature, the lattice constant of Metal Palladium is known quantity, but the uniformity in order to keep simulation to calculate, and need to pass through calculating
It determines the lattice constant of Metal Palladium at normal temperature: under above-mentioned calculating and setting, constructing Metal Palladium face-centered cubic using VASP
Model, calculate the corresponding palladium structure cell maximum system energy of different lattice constants, take minimum energy point be most probable lattice constant.
Using this lattice constant as the lattice constant of palladium structure cell, subsequent calculating is carried out.
In extremely thin hydrogen environment, hydrogen atom is only adsorbed on the atomic layer on palladium surface, or even does not all occupy palladium surface
All vacancy that may be occupied in atomic layer, it is thus necessary to determine that specific absorption position of the hydrogen atom on palladium surface layer.It is a large amount of known
Experiment, which has determined hydrogen atom first, can be adsorbed on Metal Palladium (1 1 1) crystal face.But there can be several different absorption positions,
So it needs to be determined that truth is to belong to any, i.e., specific location of the determining hydrogen atom in palladium surface atom layer.For this purpose, this
Invention constructs hydrogen atom in the different adsorption structure situations of palladium surface atom layer, calculates the structure cell total energy under each absorption situation,
The situation for taking structure cell total energy minimum, the as most stable of situation of architecture, that is, the most probable absorption situation of hydrogen atom.Tool
Body is as follows:
Metal Palladium is typical centroid cubic lattice structure, to obtain hydrogen atom in the specific adsorption structure of palladium surface atom layer
Then situation, first building palladium structure cell analyze hydrogen atom in the various absorption position situations of palladium structure cell；In view of boundary effect etc.
Factor constructs 5~20 structure cells to simulate a hydrogen atom in the various absorption position situations of palladium surface atom layer.Palladium surface is former
Crystal face is generally (1 1 1) face, (1 0 0) face or (1 1 0) face where sublayer, and to investigate comprehensively, the present invention is to these three faces
Absorption situation all analyzed.
When Hydrogen chemisorption is when crystal face where palladium surface atom layer is (1 1 1), be divided into 4 kinds of situations: hydrogen atom is located at
The centre of two palladium atoms, referred to as bridge shape structure (bridge)；Hydrogen is adsorbed on the surface (top) of a palladium atom；Hydrogen atom
There is a palladium atom to be located at the lower section in (1 1 1) face among 3 palladium atoms, and immediately below it, forms a regular hexagon
Structure (hcp)；Hydrogen atom is located among 3 palladium atoms, and the lower section for being located at (1 1 1) face immediately below it does not have palladium atom to deposit
Face-centred cubic structure nested against one another (fcc) is formed in, this structure and palladium structure cell, as shown in Figure 1.
When hydrogen is adsorbed on (1 0 0) face of palladium, share 3 kinds of adsorption structures: hydrogen atom is located among 4 palladium atoms,
Form hollow structure；Hydrogen atom is located among 2 palladium atoms, forms bridge structure；Hydrogen chemisorption is in a palladium atom
Surface, formed top structure, as shown in Figure 2.
When hydrogen is adsorbed on (1 1 0) face of palladium, share 5 kinds of adsorption structures: the first by experimental observation to one kind
Unsymmetric structure, referred to as counterfeit triple stack structures (pseudo-three-fold), can not verify in theoretical calculation, but in reality
It tests and has been found that；Hydrogen atom is located among 4 palladium atoms, forms hollow structure；Hydrogen atom is located at 2 at a distance of closer palladium
Among atom, short bridge structure is formed；Hydrogen atom is located among 2 palladium atoms apart from each other, forms long
Bridge structure；Hydrogen chemisorption is in the surface (top) of a palladium atom, as shown in Figure 3.
Then above-mentioned various hydrogen atoms are constructed in mass computing business software Materias Studio in palladium surface atom
The Adsorption Model of layer, i.e., super structure cell αi(i=1,2,3 ...).For example, when Hydrogen chemisorption is on palladium (1 1 1) face, and
When being adsorbed on the position fcc, the model visualization of building is as shown in Figure 4.
The palladium constructed in Materias Studio-hydrogen Adsorption Model is exported to the structure input file calculated for VASP
POSCAR, to each super structure cell α in VASPi(i=1,2,3 ...) carries out structural relaxation, in the output file OUTCAR of VASP
In, the system total energy E of available each super structure celli(i=1,2,3 ...).Wherein choose the i of minimum energy, as hydrogen atom
In the practical absorption situation of palladium surface atom layer, corresponding Adsorption Model is determining palladium-hydrogen Adsorption Model.
Step 3, the palladium-hydrogen for establishing complete system adsorbs super structure cell β1And the super structure cell β of control2.By VASP according to
The calculation process of its own is successively to β1And β2Structure optimization, static calculation and system energy state density is carried out to calculate.
According to the concentration of hydrogen in current environment, according to the relationship of gas volume density and surface density, derive that hydrogen atom exists
The proportional numerical value of palladium surface atom layer；Then, one hydrogen of absorption is obtained in the proportional numerical value of palladium surface atom layer according to hydrogen atom
The number of palladium surface atom layer needed for atom；Then, according to the number of resulting palladium surface atom layer, step 2 is determined
Palladium-hydrogen Adsorption Model extends to the palladium atom number of identified palladium surface atom layer, and the palladium-hydrogen absorption for forming complete system is super
Grade structure cell β1, that is, expand the period of Metal Palladium lattice, so that model is closer to truth.In order to which the body material for retaining palladium is special
Sign, while under the premise of guaranteeing computational efficiency, the atomic layer of building palladium as much as possible is answered, and do to palladium lowest level atom blunt
Change handles the accuracy to guarantee symmetry and result.
By the super structure cell β of palladium atom-hydrogen atom structure1In hydrogen atom removal, palladium atomic structure in contrast
Super structure cell β2, i.e., the super structure cell of palladium before Hydrogen chemisorption.
Next to super structure cell β1And β2First-principles calculations are carried out, super structure cell β is obtained1And β2Distribution of charges
Information and density of electronic states distributed intelligence:
In software VASP, firstly, fixed super structure cell β1And β2All bottom one layer of atoms, using VASP to system
Carry out structure optimization, as in structure cell in addition to bottom one layer of atom other each atom (including palladium atom and hydrogen it is former
Son) position constantly carry out relaxation, obtain the minimum point of maximum system energy, as all atoms position the most probable.
In the VASP output file of Structure Calculation, it regard CONTCAR file as structure input file again, fixation is super
All atoms of structure cell do whole system primary from the static calculation being in harmony, it can obtain the distribution of charges letter of whole system
Breath.
At this point, the file CHG and CHGCAR of distribution of charges information will be represented as the defeated of VASP in previous step calculated result
Enter file, whole system once just obtained the density of electronic states distributed intelligence of system from calculating is in harmony, be reflected in
In the DOSCAR of VASP output file.
Step 4, super structure cell β is analyzed in the density of electronic states distributed intelligence being calculated in conjunction with VASP1And β2Conductance
Rate situation of change.
It first has to according to step 3 about super structure cell β1And β2System distribution of charges information, judge hydrogen atom bring
Influence situation of the electronics to the electronic system of entire Metal Palladium system.Here mainly consider two o'clock: first is that for this individual of palladium-hydrogen
For system, the valence electron around palladium atom occupies most ratios in whole system, and there was only 1 hydrogen in whole system
Atom brings 1 valence electron, so the influence for whole system valence electron is very small.It is embodied in entire valence electron body
The electron mobility of system and the influence of electron effective mass are very small.The second aspect is exactly on theory analysis to above-mentioned vacation
If verifying.The present invention utilizes the calculated result of VASP, adsorbs super structure cell β to palladium-hydrogen1Do section in middle hydrogen atom position
Charge density analysis, the bonding specified between hydrogen atom valence electron and palladium valence electron are strong and weak, if form communization electronics
Cloud, to verify the influence size of the valence electron pair whole system of external hydrogen atom.It can be determined by verifying: introduce hydrogen atom
Afterwards, the influence of the electron mobility to entire valence electron system and electron effective mass can be ignored.
After verifying above-mentioned hypothesis, then carry out to β1And β2System density of electronic states distributed intelligence analysis.According to
Integral energy state density of the density of electronic states of system near Fermi surface, the input data as following theory deductions.
Specifically: according to aforementioned, when Metal Palladium, which adsorbs a small amount of hydrogen, forms the α phase of palladium-hydrogen " dissolving each other ", whole system is still
Metallicity so is remain, the ratio between molal quantity of hydrogen and palladium is 0.03 at this time.And when hydrogen is extremely thin, for super structure cell β1
For, whole system can regard metallicity as completely, therefore the conductivity for analyzing system uses electron theory of metals:
As soon as actually will form one within the time of femtosecond magnitude after to metal application steady electric field E and stablize electricity
Current density j obeys Ohm's law:
J=σ E
Wherein, σ is conductivity.
The essence of stable electric current reflects, it is constant it is outer off field, electronics reaches a new stationary state statistical distribution, this
Static distribution can also describe with one with similar distribution function f (k) when balance, once it is determined that distribution function f (k),
It can direct calculating current density.
It is well known that explaining that the Main physical basis of Ohm's law is in simple electron theory:
(i): electronics accelerates under electric field E effect；
(ii): electronics loses directed movement due to collision
For (i), by band theory it can be proved that under the action of E, all electronic states, which change, is obeyed:
Wherein, k is electronics wave vector, and t is the time, and E is extra electric field, and q is elementary charge amount, and h is Boltzmann constant.
And for (ii), it is assumed that electronics has certain collision free time τ, completely loses once by collision in electric field
Obtained in directed movement.In order to which quantitative study electron motion is theoretical, the differential side about electron transport distribution function is introduced
Journey --- Boltzmann equation.Boltzmann equation is how to change over time and establish from investigation electron transport distribution function
, there are two sources for the variation of electron transport distribution function:
I: " drift " of the statistical distribution as caused by external condition in k-space
Ii: collision, since the vibration of lattice atoms or concrete reasons, the electronics such as presence of impurity are constantly occurring
This variation of leap from a state k to another state k ', electronic state is called scattering.Assuming that the final states and initial state of collision
It can simplify as b and a, then Boltzmann equation can simplify are as follows:
For the gradient of f (k)；The integral of collision term b-a includes unknown distribution function, therefore, Boltzmann
Equation is an Integral-differential Equations formula, under normal circumstances, cannot obtain simple analytical form solution, in practice, one
It is extensive approximately as described below:
Wherein f0The Fermi function when being balance, f=f (k), τ are the parameter introduced, and are called the relaxation time.It utilizes
The basic relational expression of energy band:Electron current density equation can finally be obtained are as follows:
Above formula representation in components:
Finally obtain conductivity:
It is worth noting that, above formula occursShow the contribution of integral mainly from E=EFNear, it is, conductance
Rate depends mainly on Fermi surface E=EFNeighbouring situation.Assuming that metal conduction band electron can use single effective mass m substantially*It retouches
It states:
Integral is unfolded, ignores high-order term, conductivity metal may finally be write as:
Wherein, σ0Represent tensor σαβScalar value.Above-mentioned to super structure cell β1And β2System distribution of charges information point
It has been specified in analysis, after absorption hydrogen for the valence electron of entire palladium system, electron mobility (relaxation time) τ (EF)
With electron effective mass m*It does not change, hence for system conductivityσ0Influence factor just sum up in the point that electronics volume density n.
It is worth noting that, n at this time is the number density of valence electron near system Fermi surface.For absorption front and back,
The Electron distribution function of whole system is constant, therefore the density of electronic states distribution for combining step 3 to obtain, super to palladium-hydrogen absorption
Structure cell β1With the super structure cell β of palladium of control2, do the density of electronic states of (within the scope of positive and negative 3 KT of Fermi surface) near its Fermi surface
Integrate, then compare two super structure cells of structure density of electronic states integral changing value, so that it may obtain palladium absorption hydrogen it
The conductivity variations situation of system afterwards.Wherein, K is Boltzmann constant, and T is Kelvin, within the scope of positive and negative 3 KT of Fermi surface
Density of electronic states can be very good the conductance feature for reflecting crystal.
It should be noted that super structure cell β can also be adsorbed to palladium-hydrogen1With the super structure cell β of palladium of control2Electron energy state
Density does the Integral Processing in gamut respectively, calculates conductivity of the palladium after adsorbing hydrogen using the integral result in gamut
Variable quantity.
The conductivity variations value of palladium under set extremely thin hydrogen environment is obtained as a result,.
Below with a specific extremely thin hydrogen concentration: 9 × 1026A/cubic meter is adsorbed on (1 1 1) face of Metal Palladium
For, illustrate that the present invention calculates the specific practice of the situation of change of palladium conductivity.
The concentration of hydrogen is 9 × 1026A/cubic meter that is, just close to experiment measuring limit, and has document report gold
Belong to the conductivity variations amount of palladium, can be used to verify calculated result of the invention.It can be pushed away by the lattice constant of palladium at room temperature
Export, 9 × 1026Corresponding 1 Hydrogen chemisorption of a/cubic meter is on (1 1 1) face of palladium, and palladium surface atom layer has 16 originals
Son.
Fig. 5 is that the present invention calculates the primary full quantum calculation business software VASP, the version vasp.5.3.5 used,
Supercomputing unit used is Shanghai Supercomputer Center.It the use of pseudo potential is PAW-GGA.
The lattice constant of palladium is known, but the consistency in order to guarantee this research, utilizes first-principles calculations tool
VASP calculates the lattice constant of palladium, and the crystalline substance of face-centered cubic palladium is constructed first in business application software Materias Studio
Born of the same parents, as shown in Figure 6.
Using structural information as input, the structure input file POSCAR that VASP is written calculates Pd by lattice relaxation
Face-centred cubic structure cell basic vector length is a=b=c=391.82pm, and tests and measure, under room temperature (300K), Pd face-centered cubic
Structure structure cell basic vector length is 389.07pm.Therefore the calculating instrument for demonstrating use is more identical actual conditions.
When hydrogen palladium surface atom layer (1 1 1) absorption when, it is already discussed above, share fcc, hcp, top, bridge
Four kinds of absorption positions.A possibility that being adsorbed on different location to it size is so needed to compare.By calculating different adsorption potentials
Palladium-hydrogen system the total energy set, that is, can determine minimum energy system be it is most stable, also as most probable absorption position.
In conjunction with actual conditions, four layers of palladium atom are constructed first, every layer of the indices of crystallographic plane are (1 1 1), and the last layer is done
Passivation Treatment retains the feature of its body material, as palladium: 16 × 16 × 16 × 16 super cell configurations.Construct four layers of palladium original
Son can increase its specific surface area while guaranteeing its structural stability, improve detection efficient.Such as Fig. 7, it is shown as in Fig. 7
Every layer of 25 palladium atom, but due to translational symmetry, it is 16 that every layer of reality, which contains palladium atom number,.It is calculated first according to the first step
Palladium lattice basic vector 391.82pm out, to super structure cell palladium: 16 × 16 × 16 × 16 carry out lattice relaxation.First from
Export structure file in Materias Studio has carried out fixing process (F) to it to be passivated the last layer,
Remaining three layers of atom above carry out the continuous relaxation processing in position.It is calculated by VASP, every layer of atomic coordinates has finally been determined.
According to above-mentioned calculated result, the super structure cell α of structure that hydrogen is adsorbed on four kinds of positions of palladium (1 1 1) crystal face is constructed1,
α2, α3, α4, that is, it respectively is the tetra- kinds of positions fcc, hcp, top, bridge.As shown in Figure 8.To these four super structure cell α1,
α2, α3, α4After carrying out structural relaxation, in the output file OUTCAR of VASP, the opposite total energy of available system, result
As shown in Figure 9.
The result shows that system has minimum combination energy after fcc absorption, illustrate that fcc adsorption structure and many experiments are seen
Survey result is consistent, as the position of most probable absorption.
After the specific absorption position of hydrogen atom has been determined, computational accuracy is improved, i.e., is taken down when characterizing VASP and calculating
Bigger calculation amount is provided in the step-length KPOINTS file of lattice space.Fcc palladium: 16 × 16 × 16 × 16- hydrogen: 1 is obtained
The super structure cell β of the absorption of complete system1.Then under the KPOINTS file of same accuracy, contrast groups palladium is established: 16 × 16
× 16 × 16 super structure cell β2。
Before counting system energy state density, need to β1And β2The static calculation for carrying out structural relaxation and being in harmony certainly.It is so-called quiet
State as fixes the position of each atom from calculatings is in harmony, and from most basic Schrodinger equation, carries out constantly to whole system
Self iterative calculation, finally in set accuracy rating, obtain the most confidence configuration of whole system.It is counted by static state
It calculates, the charge density distribution of whole system can be obtained.Then β is compared1And β2Charge point on (1 1 1) and (0 1 0) face
Cloth, Figure 10 are the signal of charge density section.Wherein, it is seen that four layers of palladium atomic layer of building, and inhaled in the position of the top fcc
Attached hydrogen atom (in black circles), vertical section is (0 1 0) face, and horizontal section is (1 1 1) face.Section is all
It is intercepted along the coordinate position center of Hydrogen chemisorption, is the influence in order to accurately describe proton exoelectron to whole system.
β1And β2It is as shown in figure 11 in the comparison of the charge density in (1 1 1) face and (0 1 0) face.Palladium-hydrogen represents super structure cell β1, palladium generation
The super structure cell β of table2。
β1And β2Coordinate, the charge density size (face of charge density plane are intercepted on (1 1 1) face and (0 1 0) face
Color) scale is identical.As it can be seen that the core Outer valence electrons of hydrogen and palladium is there is no communization electron cloud is formed, to test after hydrogen ion adsorption
Absorption hydrogen is demonstrate,proved later for the valence electron of entire palladium system, electron mobility (relaxation time) and electron effective mass are not
It changes.
Front analysis shows, when hydrogen is more thin, the mutual solution that hydrogen and palladium are formed has more brilliant than more typical metal
Lattice structure, for β1, conductivity scalar value calculation formula are as follows:
Hydrogen is adsorbed later for the valence electron of entire palladium system, electron mobility (relaxation time) and the effective matter of electronics
Amount does not change, and just sums up in the point that electronics volume density n hence for the influence factor of system conductivity.And n is system Fermi surface
The number density of neighbouring valence electron.
In the result of previous step static calculation, two groups of super structure cell system β have been obtained1And β2Be in harmony charge density certainly, body
In the output file CHGCAR and CHG of present VASP, then previous step, to β1And β2Carry out energy state density calculating.At this time, if
When setting input file INCAR, the ICHAGR=2 of the inside will be changed to ICHARG=11, represent what use had calculated
Input file CHGCAR and CHG at this time further increase the computational accuracy of KPOINTS, while the still seat of fixed atom
Mark.β has been calculated1And β2Energy state density distribution with integral energy state density, as a result as shown in figure 12.
By adding up to the integral DOS near fermi levelWeighted average is done again to compare, and is obtained
Super structure cell β to after absorption hydrogen1Structure cell β super compared with control group palladium2Integrating energy state density reduction amount is 0.249%.For inhaling
For attached front and back, the Electron distribution function of whole system is constant, therefore the number density n of the neighbouring valence electron of system Fermi surface, that is,
System conductivity reduction amount is also 0.249%, and under this hydrogen concentration of document report, conductivity is about in a small amount after palladium absorption hydrogen
0.203%-0.547% more coincide.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (5)
1. a kind of palladium conductivity variations amount calculation method in extremely thin hydrogen environment, which comprises the steps of:
Step 1, a Hydrogen chemisorption is constructed in all possible structural model of palladium surface atom layer；
Step 2, the super structure cell of palladium atom-hydrogen atom for each structural model that construction step 1 obtains respectively；Utilize primary original
Reason calculates the system gross energy of each super structure cell, and super structure cell corresponding to minimum system gross energy is true one
Absorption situation of the hydrogen atom in palladium surface atom layer；
Step 3, the concentration based on hydrogen in current environment determines that hydrogen atom exists according to the relationship of gas volume density and surface density
The proportional numerical value of palladium surface atom layer, the palladium atom number of palladium surface atom layer needed for obtaining one hydrogen atom of absorption；It will step
The rapid 2 super structure cells determined extend to the palladium atom number of identified palladium surface atom layer, form palladium atom-hydrogen atom structure
Super structure cell β1；By the super structure cell β of palladium atom-hydrogen atom structure1In hydrogen atom removal, palladium atom knot in contrast
The super structure cell β of structure2；Using first principle, the super structure cell β of palladium atom-hydrogen atom structure is calculated separately1With the palladium atom of control
The super structure cell β of structure2Energy state density distributed intelligence；
Step 4, the density of electronic states of two super structure cells of structure is done into Integral Processing respectively, according to two super structure cells of structure
The changing value of density of electronic states integral calculate conductivity variations amount of the palladium after adsorbing hydrogen.
2. palladium as described in claim 1 conductivity variations amount calculation method in extremely thin hydrogen environment, which is characterized in that institute
It states in step 4, the density of electronic states of two super structure cells of structure integrates within the scope of positive and negative 3 KT of Fermi surface respectively, obtains
To the super structure cell β of palladium atom-hydrogen atom structure1Integral energy state density and control the super structure cell β of palladium atomic structure2Integral
Energy state density, wherein K is Boltzmann constant, and T is Kelvin.
3. palladium as described in claim 1 conductivity variations amount calculation method in extremely thin hydrogen environment, which is characterized in that benefit
Structural modeling and first-principles calculations are carried out with first-principles calculations software VASP.
4. palladium as claimed in claim 3 conductivity variations amount calculation method in extremely thin hydrogen environment, which is characterized in that step
The number of plies of the super structure cell of rapid 2 building is 4.
5. palladium as claimed in claim 3 conductivity variations amount calculation method in extremely thin hydrogen environment, which is characterized in that
It is distributed using the energy state density of the super structure cell of structure described in the system gross energy of super structure cell described in VASP calculating step 2, step 3
When information, Passivation Treatment is done to one layer of the bottom atom of palladium, structure Relaxation then is carried out to each atom.
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