CN110277142A - A kind of calculation method calculating ABO3 perovskite rock-steady structure and performance - Google Patents
A kind of calculation method calculating ABO3 perovskite rock-steady structure and performance Download PDFInfo
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Abstract
The invention discloses a kind of calculating ABO3 perovskite rock-steady structure and the calculation methods of performance, it is first perovskite-type material stable model in accordance with element building ABO3 of certain method and step to the specific position in the periodic table of elements of selection, it calculates and analyzes more different ABO3 knots and be configured to, phonon spectra, can be obtained respectively from thermodynamics and thermokinetics direction the structure stability how, then calculate separately its electronic structure and obtain its photoelectricity basic performance；The present invention provides a kind of method that can differentiation form stable perovskite structure, the second main group selection arbitrary element (in addition to radioactive element Ra), stable perovskite ABO3 structure is constituted in conjunction with+4 valence transition metal elements (defined herein as Zr, Ha) and O element from the periodic table of elements.If the compound of stable perovskite structure can be formed, first-principles calculations can be passed through and predict its substantially performance.
Description
Technical field
The invention belongs to materialogy fields, and in particular to ABO3 perovskite-type compounds performance and emulation mode.
Background technique
Perovskite oxide (ABO3) with the characteristics such as ferroelectricity, ferromagnetic, superconduction, piezoelectricity due to making it in optical waveguide, laser
Frequency multiplication, piezoelectric transducer, tunable capacitor, high-capacity storage unit etc. have a wide range of applications, and the discovery such as Park exists
It is very big there may be possessing by regulation vanadium ion valence state in the short cycle LaVO3/SrVO3 perovskite superlattices of charge order
One metastable state of polarization intensity, Fennie has found PbTiO3/BiFeO3 electromagnetism in seeking strong magneto-electric coupled materials process
Coupling mechanism is different, and Sonali calculates the electronic structure of para-electric BaTiO3, chemical bond and optical property, discloses its application
Great potential.Calculating forecasting research at present about ABO3 structure and aspect of performance is numerous, relative to the wide of zirconium base functional material
General application, search domestic and foreign literature have been found that it is seldom to the materials theory research of the AZrO3 structure of ABO3 structure, it is especially right
In ZrBeO3, almost there are no any correlative studys for two kinds of structures of ZrMgO3.Intend herein through first-principles calculations system point
The zirconates for the ABO3 structure that the second major element (Be/Mg/Ga/Sr/Ba) and Ti, Zr, Ha are constituted is analysed, to develop the Quito Zr function
Energy material provides certain theoretical reference.
Summary of the invention
To achieve the goals above, the present invention is to realize by the following technical solutions: a kind of calculating ABO3 perovskite
The calculation method of rock-steady structure and performance, first in accordance with certain method and step to the specific position in the periodic table of elements of selection
Element building ABO3 be perovskite-type material stable model, calculate and analyze more different ABO3 knot and be configured to, phonon spectra,
Can be obtained respectively from thermodynamics and thermokinetics direction the structure stability how, then calculate separately its electronic structure and obtain
Its photoelectricity basic performance out, the technical solution that the present invention takes is it is characterized in that, its step includes:
(1) structure of ABO3 type perovskite is simple cubic lattice, and each Prague structure cell has 5 atoms, space group Pm-3m
(221), wherein B occupies the body position of cubic lattice, and A occupies 8 vertex positions of cubic lattice, 6 center of area positions of structure cell
It sets and is occupied by O ion, ionic radius size when stable ABO3 structure depends primarily on the combination of different elements can be formed, abided by
From following rule:；RA, RB, RO are the ion for occupying the corresponding valence state of the vertex A position, the body-centered B position and O atom respectively in above-mentioned formula
Radius.T is tolerance factor, and value is between 0.78 ~ 1.10；
(2) to the second major element (Be/Mg/Ga/Sr/Ba), the atom of each element is obtained by the modes such as read up the literature, table look-up
Radius size is 1.13,1.60,1.97,2.15,2.24 and the ionic radius size of+2 valence is respectively as follows: 0.17,0.49,
0.99,1.12,1.34；+ 4 valence transition metal elements (Ti/Zr/Ha), atomic radius size are 1.40,1.60,1.59 and+4 valences
The ionic radius size of state is respectively as follows: 0.53,0.72,0.71；O Elements Atom radius 0.66 ,-divalent ionic radius 1.21；
(3) according to the ionic radius size of each atomic valence, for the structure t tolerance factor for making constructed ABO3 type perovskite
Value is limiting in range, and generally there is specific fixed structure in the position for being computed discovery A, B to different element combinations, can not
Arbitrarily to exchange；
(4) through repeatedly being calculated, experience provide general step can elder generation's reference ion radius size, if combined ionic radius size phase
Poor little, then two kinds of occupy-place modes of alkali metal element and transition metal element are likely to, and are needed to establish structure cell respectively and are gone to count
It calculates；If radius ionic radius size of the difference is greater than 0.2 or more, radius it is big occupy vertex A, radius it is small occupy body-centered B
Position, 6 face center of areas that O atom occupies structure cell are constant always；
(5) transition metal element selects Zr element, is respectively combined into five kinds of elements of the second main group (Be/Mg/Ga/Sr/Ba)
The structure of ABO3 type perovskite, since Zr ionic radius is 0.72, between Mg/Ga, and radial difference is all 0.2 or more,
Therefore it can filter out combine by way of direct reference ion radius size and constitute the stable perovskite structure of geometry；
(6) five kinds of second major elements can only be combined into five kinds of stable ABO3 perovskite structures with Zr element combinations respectively:
The position the AB selection of respectively ZrBe O3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3, various structures are unique, and others combination exists
It cannot be stabilized on geometry configuration；
(7) as Fig. 1 gives the perovskite structure illustraton of model embodiment that combines with Zr of the second major element selection Mg, wherein Mg is accounted for
According to body-centered position, Zr occupies vertex position, and O occupies center of area position；
(8) it after determining the stable possibility compound of geometry occupy-place, needs to model it respectively, finds out possible minimum energy structure
Type；
(9) compounds several for ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3 test the system that CaZrO3 can be achieved
It is standby, the initial parameter of other compounds can be obtained by the cell parameter of the perovskite structure CaZrO3 of experiment preparation；
(10) the identical CaO-ZrO2 powder mixing of molar percentage is taken to dissolve by ball milling, drying, and taken the photograph in 2500 or so
Slowly grow up to crystal under family name's degree high temperature；
(11) by crystal fracture, it is ground into the powder of 1 ~ 10000nm thickness, powder sample carries out x-ray x ray diffraction；
(12) the x-ray diffraction data for acquiring laboratory sample, which is passed to by general purpose data port
Masterial Studio software such as Fig. 2；
(13) in Masterial Studio software, reflex tools module is selected, experimental data put down except background
Sliding processing；
(14) main peak calibration is carried out using powder index function, parameter can take system default value；
(15) powder solve module is used, to calibration and the processed experimental diffraction spectral line spectrum of refine calculates, and obtains original
Structure cell lattice constant is a=b=c=0.4160nm；
(16) this cell model needs density functional theory to carry out structure optimization, selects in Masterial Studio software package
CASTEP module carries out structure optimization；
(17) local density approximation LDA method is selected, exchange correlation function selects CA-PZ, and the minimum convergence of gross energy is arranged
For 1 × 10-6 eV/atom, internal stress is less than 0.05Gpa, and less than 0.0001 nm, the maximum field of force is less than 0.03ev, optimization for displacement
The lattice constant of simple cubic cell afterwards is a=b=c=0.4062nm；
(18) from multiple such calculating, experience is obtained, it can be using the size of 0.4000nm as other compounds letter of same main group
The initial value of cubic cell lattice constant；
(19) initial value with lattice constant for 0.4000nm establishes simple cubic cell, is determined in compound according to (1) formula rule
A, B occupy-place adds O atom, by the setting in step 17 to institute in each compound structure cell respectively in the corresponding atom of A, B additions
There is atom to carry out full relaxation, so that compound structure is optimized to minimum energy state as far as possible；
(20) tetra- kinds of ZrBeO3, ZrMgO3, (CaZrO3), SrZrO3, BaZrO3 ABO3 compounds are implemented by above step, fills
Symmetry is constant after separation structure optimization, and the lattice constant after optimization is respectively 0.33895nm, 0.3733nm, (0.4062nm),
0.4183nm, 0.4153nm.For lattice constant after optimization in 4nm or so, initial value takes 4nm to obtain probably adding again from experimental data
Upper calculating experience is got；
(21) before it can carry out other photoelectric properties calculating to the model compounds of foundation, since compound is from element week
It directly combines and obtains in phase table, judge whether needing to be stabilized it, judge in terms of following 2:
A: thermodynamic stability: calculating the formation energy Ef of each compound, and calculation method is Ef=Et-EA-EB-3EO, above-mentioned formula
Middle Et is the opposite total energy size of compound after structure optimization, and EA is single A nuclear energy size, and EB is single B atomic energy
Size is measured, EO is single O atom energy size.Ef calculated result is showing that the structure can thermodynamically be stablized and depositing for negative value
?；To be formed to five kinds of ABO3 compounds of ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3 can calculate, and as a result distinguish
Be negative value for -47.93 eV, -42.82 eV, -23.81 eV, -13.61 eV, -92.02eV, illustrate this five kinds of structures from
Analysis can should all form stable compound on thermodynamics；
B: dynamic stability: carrying out lattice phonon scattering spectra to the compound structure after optimization, and phonon state density calculates, in conjunction with
Can the compound of phon scattering spectrum and density of states analysis ABO3 structure have formability in terms of dynamics.If phon scattering is composed
Then illustrate that the structural compounds are kinetically unstable in the presence of empty frequency, it is difficult to synthesize, empty frequency then illustrates that compound is steady if it does not exist
It is fixed, it is readily synthesized with the stable phase compound；
(22) phonon calculating, phonon are carried out to five kinds of ABO3 compounds of ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3
Scattering spectra and the density of states as shown in Fig. 3,4,5,6,7, can be seen that each compound is equal from ZrBeO3 to SrZrO3 respectively from spectral line
There is empty frequency, but the empty frequency phenomenon of phonon spectra gradually decreases, and shows that these compounds are high-temperature stable phase, but under low-temperature condition
Thermodynamic stability gradually increases, the no empty frequency of the phon scattering spectrum of BaZrO3, the phase Thermodynamically stable, dynamic stabilization,
Therefore it can be prepared under normal temperature and pressure with laboratory, such as sol-gal process.
It is to be noted that the temperature environment of first-principles calculations is corresponding 0K, therefore high temperature, the height of many compounds
Pressure stable phase will appear empty frequency when phonon calculates, and can simulate pressure change to different mutually stable influences.
By above step, we can pass through first-principles calculations in the case where known ion radius size substantially
It may determine that can certain two dvielement form the compound of stable ABO3 perovskite structure in periodic table out, the compound shape
At complexity how, experimental period and cost can be greatlyd save, and the phonon spectra calculated under high pressure, observation can be passed through
The more difficult experiment progress for forming stable compound and improvement direction are instructed in the variation of its spectral line with the situation of change of pressure.
Beneficial effects of the present invention: the present invention provides a kind of method that can differentiation form stable perovskite structure, from member
The second main group selection arbitrary element (in addition to radioactive element Ra), (limits herein in conjunction with+4 valence transition metal elements in plain periodic table
Be set to Zr, Ha) and O element constitute stable perovskite ABO3 structure.It, can if the compound of stable perovskite structure can be formed
To pass through first-principles calculations and predict its substantially performance, pass through the second major element of first-principles calculations network analysis
(Be/Mg/Ga/Sr/Ba) it with the zirconates of Ti, Zr, Ha ABO3 structure constituted, is provided centainly for the exploitation Quito Zr functional material
Theoretical reference.
Detailed description of the invention
Upon reading the detailed description of non-limiting embodiments with reference to the following drawings, other feature of the invention,
Objects and advantages will become more apparent upon:
Fig. 1 is ZrMgO3 of embodiment of the present invention cellular models figure.
Fig. 2 is the x-ray powder diffraction spectrum of CaZrO3.
Fig. 3 is ZrBeO3 structure cell phon scattering spectrum and density of states figure.
Fig. 4 is ZrMgO3 structure cell phon scattering spectrum and density of states figure.
Fig. 5 is CaZrO3 structure cell phon scattering spectrum and density of states figure.
Fig. 6 is SrZrO3 structure cell phon scattering spectrum and density of states figure.
Fig. 7 is BaZrO3 structure cell phon scattering spectrum and density of states figure.
Specific embodiment
To be easy to understand the technical means, the creative features, the aims and the efficiencies achieved by the present invention, below with reference to
Specific embodiment, the present invention is further explained.
Please refer to Fig. 1-Fig. 7, the present invention provides the calculation method of a kind of calculating ABO3 perovskite rock-steady structure and performance
Scheme:
A kind of calculation method calculating ABO3 perovskite rock-steady structure and performance, first in accordance with certain method and step to selection
The element building ABO3 of specific position is perovskite-type material stable model in the periodic table of elements, calculates and analyzes more different
ABO3 knot be configured to, phonon spectra, can be obtained respectively from thermodynamics and thermokinetics direction the structure stability how,
Its electronic structure is calculated separately again and obtains its photoelectricity basic performance, and the technical solution that the present invention takes is it is characterized in that, its step
Include:
(1) structure of ABO3 type perovskite is simple cubic lattice, and each Prague structure cell has 5 atoms, space group Pm-3m
(221), wherein B occupies the body position of cubic lattice, and A occupies 8 vertex positions of cubic lattice, 6 center of area positions of structure cell
It sets and is occupied by O ion, ionic radius size when stable ABO3 structure depends primarily on the combination of different elements can be formed, abided by
From following rule:；RA, RB, RO are the ion for occupying the corresponding valence state of the vertex A position, the body-centered B position and O atom respectively in above-mentioned formula
Radius.T is tolerance factor, and value is between 0.78 ~ 1.10；
(2) to the second major element (Be/Mg/Ga/Sr/Ba), the atom of each element is obtained by the modes such as read up the literature, table look-up
Radius size is 1.13,1.60,1.97,2.15,2.24 and the ionic radius size of+2 valence is respectively as follows: 0.17,0.49,
0.99,1.12,1.34；+ 4 valence transition metal elements (Ti/Zr/Ha), atomic radius size are 1.40,1.60,1.59 and+4 valences
The ionic radius size of state is respectively as follows: 0.53,0.72,0.71；O Elements Atom radius 0.66 ,-divalent ionic radius 1.21；
(3) according to the ionic radius size of each atomic valence, for the structure t tolerance factor for making constructed ABO3 type perovskite
Value is limiting in range, and generally there is specific fixed structure in the position for being computed discovery A, B to different element combinations, can not
Arbitrarily to exchange；
(4) through repeatedly being calculated, experience provide general step can elder generation's reference ion radius size, if combined ionic radius size phase
Poor little, then two kinds of occupy-place modes of alkali metal element and transition metal element are likely to, and are needed to establish structure cell respectively and are gone to count
It calculates；If radius ionic radius size of the difference is greater than 0.2 or more, radius it is big occupy vertex A, radius it is small occupy body-centered B
Position, 6 face center of areas that O atom occupies structure cell are constant always；
(5) transition metal element selects Zr element, is respectively combined into five kinds of elements of the second main group (Be/Mg/Ga/Sr/Ba)
The structure of ABO3 type perovskite, since Zr ionic radius is 0.72, between Mg/Ga, and radial difference is all 0.2 or more,
Therefore it can filter out combine by way of direct reference ion radius size and constitute the stable perovskite structure of geometry；
(6) five kinds of second major elements can only be combined into five kinds of stable ABO3 perovskite structures with Zr element combinations respectively:
The position the AB selection of respectively ZrBe O3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3, various structures are unique, and others combination exists
It cannot be stabilized on geometry configuration；
(7) as Fig. 1 gives the perovskite structure illustraton of model embodiment that combines with Zr of the second major element selection Mg, wherein Mg is accounted for
According to body-centered position, Zr occupies vertex position, and O occupies center of area position；
(8) it after determining the stable possibility compound of geometry occupy-place, needs to model it respectively, finds out possible minimum energy structure
Type；
(9) compounds several for ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3 test the system that CaZrO3 can be achieved
It is standby, the initial parameter of other compounds can be obtained by the cell parameter of the perovskite structure CaZrO3 of experiment preparation；
(10) the identical CaO-ZrO2 powder mixing of molar percentage is taken to dissolve by ball milling, drying, and taken the photograph in 2500 or so
Slowly grow up to crystal under family name's degree high temperature；
(11) by crystal fracture, it is ground into the powder of 1 ~ 10000nm thickness, powder sample carries out x-ray x ray diffraction；
(12) the x-ray diffraction data for acquiring laboratory sample, which is passed to by general purpose data port
Masterial Studio software such as Fig. 2；
(13) in Masterial Studio software, reflex tools module is selected, experimental data put down except background
Sliding processing；
(14) main peak calibration is carried out using powder index function, parameter can take system default value；
(15) powder solve module is used, to calibration and the processed experimental diffraction spectral line spectrum of refine calculates, and obtains original
Structure cell lattice constant is a=b=c=0.4160nm；
(16) this cell model needs density functional theory to carry out structure optimization, selects in Masterial Studio software package
CASTEP module carries out structure optimization；
(17) local density approximation LDA method is selected, exchange correlation function selects CA-PZ, and the minimum convergence of gross energy is arranged
For 1 × 10-6 eV/atom, internal stress is less than 0.05Gpa, and less than 0.0001 nm, the maximum field of force is less than 0.03ev, optimization for displacement
The lattice constant of simple cubic cell afterwards is a=b=c=0.4062nm；
(18) from multiple such calculating, experience is obtained, it can be using the size of 0.4000nm as other compounds letter of same main group
The initial value of cubic cell lattice constant；
(19) initial value with lattice constant for 0.4000nm establishes simple cubic cell, is determined in compound according to (1) formula rule
A, B occupy-place adds O atom, by the setting in step 17 to institute in each compound structure cell respectively in the corresponding atom of A, B additions
There is atom to carry out full relaxation, so that compound structure is optimized to minimum energy state as far as possible；
(20) tetra- kinds of ZrBeO3, ZrMgO3, (CaZrO3), SrZrO3, BaZrO3 ABO3 compounds are implemented by above step, fills
Symmetry is constant after separation structure optimization, and the lattice constant after optimization is respectively 0.33895nm, 0.3733nm, (0.4062nm),
0.4183nm, 0.4153nm.For lattice constant after optimization in 4nm or so, initial value takes 4nm to obtain probably adding again from experimental data
Upper calculating experience is got；
(21) before it can carry out other photoelectric properties calculating to the model compounds of foundation, since compound is from element week
It directly combines and obtains in phase table, judge whether needing to be stabilized it, judge in terms of following 2:
A: thermodynamic stability: calculating the formation energy Ef of each compound, and calculation method is Ef=Et-EA-EB-3EO, above-mentioned formula
Middle Et is the opposite total energy size of compound after structure optimization, and EA is single A nuclear energy size, and EB is single B atomic energy
Size is measured, EO is single O atom energy size.Ef calculated result is showing that the structure can thermodynamically be stablized and depositing for negative value
?；To be formed to five kinds of ABO3 compounds of ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3 can calculate, and as a result distinguish
Be negative value for -47.93 eV, -42.82 eV, -23.81 eV, -13.61 eV, -92.02eV, illustrate this five kinds of structures from
Analysis can should all form stable compound on thermodynamics；
B: dynamic stability: carrying out lattice phonon scattering spectra to the compound structure after optimization, and phonon state density calculates, in conjunction with
Can the compound of phon scattering spectrum and density of states analysis ABO3 structure have formability in terms of dynamics.If phon scattering is composed
Then illustrate that the structural compounds are kinetically unstable in the presence of empty frequency, it is difficult to synthesize, empty frequency then illustrates that compound is steady if it does not exist
It is fixed, it is readily synthesized with the stable phase compound；
(22) phonon calculating, phonon are carried out to five kinds of ABO3 compounds of ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3
Scattering spectra and the density of states as shown in Fig. 3,4,5,6,7, can be seen that each compound is equal from ZrBeO3 to SrZrO3 respectively from spectral line
There is empty frequency, but the empty frequency phenomenon of phonon spectra gradually decreases, and shows that these compounds are high-temperature stable phase, but under low-temperature condition
Thermodynamic stability gradually increases, the no empty frequency of the phon scattering spectrum of BaZrO3, the phase Thermodynamically stable, dynamic stabilization,
Therefore it can be prepared under normal temperature and pressure with laboratory, such as sol-gal process.
It is to be noted that the temperature environment of first-principles calculations is corresponding 0K, therefore high temperature, the height of many compounds
Pressure stable phase will appear empty frequency when phonon calculates, and can simulate pressure change to different mutually stable influences.
By above step, we can pass through first-principles calculations in the case where known ion radius size substantially
It may determine that can certain two dvielement form the compound of stable ABO3 perovskite structure in periodic table out, the compound shape
At complexity how, experimental period and cost can be greatlyd save, and the phonon spectra calculated under high pressure, observation can be passed through
The more difficult experiment progress for forming stable compound and improvement direction are instructed in the variation of its spectral line with the situation of change of pressure.
The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention, for this field skill
For art personnel, it is clear that invention is not limited to the details of the above exemplary embodiments, and without departing substantially from spirit of the invention or
In the case where essential characteristic, the present invention can be realized in other specific forms.Therefore, in all respects, should all incite somebody to action
Embodiment regards exemplary as, and is non-limiting, the scope of the present invention by appended claims rather than on state
Bright restriction, it is intended that including all changes that fall within the meaning and scope of the equivalent elements of the claims in the present invention
It is interior.Any reference signs in the claims should not be construed as limiting the involved claims.
In addition, it should be understood that although this specification is described in terms of embodiments, but not each embodiment is only wrapped
Containing an independent technical solution, this description of the specification is merely for the sake of clarity, and those skilled in the art should
It considers the specification as a whole, the technical solutions in the various embodiments may also be suitably combined, forms those skilled in the art
The other embodiments being understood that.
Claims (5)
1. a kind of calculation method for calculating ABO3 perovskite rock-steady structure and performance, first in accordance with certain method and step to selection
In the periodic table of elements specific position element building ABO3 be perovskite-type material stable model, calculate and analyze than less
It is configured to ABO3 knot, phonon spectra can obtain the stability of the structure such as from thermodynamics and thermokinetics direction respectively
What, then calculate separately its electronic structure and obtain its photoelectricity basic performance, the technical solution that the present invention takes is it is characterized in that, it is walked
Suddenly include:
The structure of ABO3 type perovskite is simple cubic lattice, and each Prague structure cell has 5 atoms, space group Pm-3m (221),
Wherein B occupies the body position of cubic lattice, and A occupies 8 vertex positions of cubic lattice, 6 face heart positions of structure cell by O from
Can son occupies, form ionic radius size when stable ABO3 structure depends primarily on the combination of different elements, defer to following
Rule:；RA, RB, RO are the ionic radius for occupying the corresponding valence state of the vertex A position, the body-centered B position and O atom respectively in above-mentioned formula.
2.t is tolerance factor, and value is between 0.78 ~ 1.10；
To the second major element (Be/Mg/Ga/Sr/Ba), the atom half of each element is obtained by the modes such as read up the literature, table look-up
Diameter size is 1.13,1.60,1.97,2.15,2.24 and the ionic radius size of+2 valence is respectively as follows: 0.17,0.49,0.99,
1.12 1.34；+ 4 valence transition metal elements (Ti/Zr/Ha), atomic radius size be 1.40,1.60,1.59 and+4 valence states from
Sub- radius size is respectively as follows: 0.53,0.72,0.71；O Elements Atom radius 0.66 ,-divalent ionic radius 1.21；
According to the ionic radius size of each atomic valence, to take the structure t tolerance factor of constructed ABO3 type perovskite
Value is limiting in range, and generally there is specific fixed structure in the position for being computed discovery A, B to different element combinations, it is not possible to
Arbitrarily exchange；
Repeatedly calculated, experience provide general step can first reference ion radius size, if combined ionic radius size differs
Less, then two kinds of occupy-place modes of alkali metal element and transition metal element are likely to, and are needed to establish structure cell respectively and are gone to calculate；
If radius ionic radius size of the difference is greater than 0.2 or more, radius it is big occupy vertex A, radius it is small occupy body-centered B, O
6 face center of areas that atom occupies structure cell are constant always；
Transition metal element selects Zr element, is respectively combined into ABO3 type to five kinds of elements of the second main group (Be/Mg/Ga/Sr/Ba)
The structure of perovskite, since Zr ionic radius is 0.72, between Mg/Ga, and radial difference is all 0.2 or more, therefore can
It filters out to combine in a manner of through direct reference ion radius size and is constituted the stable perovskite structure of geometry；
Five kind of second major element can only can be combined into five kinds of stable ABO3 perovskite structures with Zr element combinations respectively: respectively
The position AB selection for ZrBe O3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3, various structures is unique, and others combination is in geometry
It cannot be stabilized on structural configuration；
If Fig. 1 gives the perovskite structure illustraton of model embodiment that the second major element selection Mg is combined with Zr, wherein Mg is occupied
Body-centered position, Zr occupy vertex position, and O occupies center of area position；
It after determining the stable possibility compound of geometry occupy-place, needs to model it respectively, finds out possible minimum energy configuration；
Compounds several for ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3 test the preparation that CaZrO3 can be achieved,
The initial parameter of other compounds can be obtained by the cell parameter of the perovskite structure CaZrO3 of experiment preparation；
The identical CaO-ZrO2 powder mixing of molar percentage is taken to dissolve by ball milling, drying, and in 2500 or so degrees Celsius
Slowly grow up to crystal under high temperature；
By crystal fracture, it is ground into the powder of 1 ~ 10000nm thickness, powder sample carries out x-ray x ray diffraction；
The x-ray diffraction data for acquiring laboratory sample, which is passed to by general purpose data port
Masterial Studio software such as Fig. 2；
In Masterial Studio software, reflex tools module is selected, experimental data is carried out except background, it is smooth to locate
Reason；
Main peak calibration is carried out using powder index function, parameter can take system default value；
Using powder solve module, to calibration and the processed experimental diffraction spectral line spectrum of refine is calculated, and obtains primitive unit cell
Lattice constant is a=b=c=0.4160nm；
This cell model needs density functional theory to carry out structure optimization, selects in Masterial Studio software package
CASTEP module carries out structure optimization；
Select local density approximation LDA method, exchange correlation function select CA-PZ, setting the minimum convergence of gross energy be 1 ×
10-6 eV/atom, internal stress are less than 0.05Gpa, and displacement is less than 0.0001 nm, and the maximum field of force is less than 0.03ev, after optimization
The lattice constant of simple cubic cell is a=b=c=0.4062nm；
From multiple such calculating, experience is obtained, it can be using the size of 0.4000nm as other compounds letter cube of same main group
The initial value of structure cell lattice constant；
Initial value with lattice constant for 0.4000nm establishes simple cubic cell, determines that A, B are accounted in compound according to (1) formula rule
O atom is added, by the setting in step 17 to all atoms in each compound structure cell respectively in the corresponding atom of A, B additions in position
Full relaxation is carried out, so that compound structure is optimized to minimum energy state as far as possible；
Tetra- kinds of ZrBeO3, ZrMgO3, (CaZrO3), SrZrO3, BaZrO3 ABO3 compounds are implemented by above step, are sufficiently tied
Symmetry is constant after structure optimization, and the lattice constant after optimization is respectively 0.33895nm, 0.3733nm, (0.4062nm),
0.4183nm, 0.4153nm.
3. the lattice constant after optimization is in 4nm or so, initial value takes 4nm to obtain probably adding calculating experience from experimental data and obtain
Come；
Before it can carry out other photoelectric properties calculating to the model compounds of foundation, since compound is from the periodic table of elements
In directly combine and obtain, judge whether needing to be stabilized it, judge in terms of following 2:
A: thermodynamic stability: calculating the formation energy Ef of each compound, and calculation method is Ef=Et-EA-EB-3EO, above-mentioned formula
Middle Et is the opposite total energy size of compound after structure optimization, and EA is single A nuclear energy size, and EB is single B atomic energy
Size is measured, EO is single O atom energy size.
4.Ef calculated result shows that the structure can be thermodynamically stabilized for negative value；To ZrBeO3, ZrMgO3,
Five kinds of ABO3 compounds of CaZrO3, SrZrO3, BaZrO3 to be formed and can be calculated, and are as a result respectively -47.93 eV, -42.82
EV, -23.81 eV, -13.61 eV, -92.02eV, are negative value, and illustrating that this five kinds of structures are analyzed from thermodynamics should
Stable compound can all be formed；
B: dynamic stability: carrying out lattice phonon scattering spectra to the compound structure after optimization, and phonon state density calculates, in conjunction with
Can the compound of phon scattering spectrum and density of states analysis ABO3 structure have formability in terms of dynamics.
5. illustrating that the structural compounds are kinetically unstable if phon scattering composes and there is empty frequency, it is difficult to synthesize, if it does not exist
Empty frequency then illustrates that compound is stablized, and is readily synthesized with the stable phase compound；
(22) phonon calculating, phonon are carried out to five kinds of ABO3 compounds of ZrBeO3, ZrMgO3, CaZrO3, SrZrO3, BaZrO3
Scattering spectra and the density of states as shown in Fig. 3,4,5,6,7, can be seen that each compound is equal from ZrBeO3 to SrZrO3 respectively from spectral line
There is empty frequency, but the empty frequency phenomenon of phonon spectra gradually decreases, and shows that these compounds are high-temperature stable phase, but under low-temperature condition
Thermodynamic stability gradually increases, the no empty frequency of the phon scattering spectrum of BaZrO3, the phase Thermodynamically stable, dynamic stabilization,
Therefore it can be prepared under normal temperature and pressure with laboratory, such as sol-gal process.
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