CN101004395A - Lossless method for measuring coefficient of thermal expansion of Nano grain - Google Patents

Abstract

A method for nondestructive-measuring heat expansion coefficient of nanoparticle includes scattering nanoparticle material into base material, using X- ray absorption fine structure chart to measure distance between nearest adjacent nanopartide atoms in base material and to measure square relative displacement of distance between adjacent atoms as well as to measure cubic relative displacement of distance between adjacent atoms then utilizing formula to calculate out heat expansion coefficient of nanoparticle.

Description

The method of nondestructively measuring nano grain thermal expansivity

Technical field

The present invention relates to a kind of method of nondestructively measuring nano grain thermal expansivity.

Background technology

The compound substance mesostroma that is mixed with metal nanoparticle is isolated from each other nano particle, forms quantum dot.When the de Broglie wavelength of the size of nano particle and electronics, relevant wavelength and exciton Bohr radius can be compared, will cause quantum size effect.Simultaneously, when the size of nano particle during much smaller than the light field wavelength, act on the macroscopic field that electric field on the nano particle obviously is different from surrounding medium, polarization process has changed the specific inductive capacity of local, produce the dielectric confinement effect, the generation local fields strengthens, and causes bigger third-order nonlinear optical effect, and this class material has potential using value in fields such as light transmission, optical storage and all-optical switchs.

Utilize methods such as thermal dilatometer, fiber grating, electronic speckle pattern interferometry and elastic modulus experimental provision can measure the material coefficient of thermal expansion coefficient at present, but can only measuring body material coefficient of thermal expansion coefficient, the not thermal expansivity of energy measurement nano particle.Along with reducing of particle size, increasing of the increase of specific area and surface atom number, small-size effect, surface effect and quantum size effect appear in nano particle, nano particle are had be different from the special performance of block materials, reduce catalytic activity raising and absorption peak blue shift etc. as fusing point.How to distinguish unknownly but the thermal expansivity of nano particle and body material have, this just has influence on the design and the assembling of nano-device.Therefore, the thermal expansivity of measurement nano particle is imperative.But, also do not have at present a kind of method that can the analysis to measure coefficient of thermal expansion of Nano grain.

Summary of the invention

The present invention is in order to overcome the deficiencies in the prior art, a kind of method of nondestructively measuring nano grain thermal expansivity to be provided.

The present invention is achieved through the following technical solutions:

A kind of method of nondestructively measuring nano grain thermal expansivity, it is characterized in that, nano-particle material is dispersed in the host material, the most contiguous interatomic distance of nano particle that is dispersed in the host material with X ray absorption fine structure spectrometry is r then, square relative displacement σ of distance between adjacent atom ², cube relative displacement C of distance between adjacent atom ₃, according to formula $\mathrm{\&alpha;}=\frac{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20071003664900081.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}{\mathrm{rT}{\mathrm{\&sigma;}}^2}\frac{3z(1+z)\ln (1/z)}{(1-z)(1+10z+z^2)}$ Calculate the thermal expansivity of nano particle, in the formula, r is the most contiguous interatomic disance, R be all atoms in the same coordination shell to the mean distance between the central atom, T is for measuring temperature, σ ²=C ₂=＜(r-R) ²Be square relative displacement of distance between adjacent atom, C ₃=＜(r-R) ³Be cube relative displacement of distance between adjacent atom, $z=\exp (-\frac{{\mathrm{\&theta;}}_E}{T})$ 。θ _EBe nano particle Einstein temperature, θ _ECalculate by following formula:

σ under the different temperatures ²Can obtain by the EXAFS analysis of spectrum,

Be Planck's constant, m _rBe the reduced mass of nano particle, k _BBe Boltzmann constant, therefore can calculate Einstein temperature θ _EWith static degree of disorder factor sigma may ² _s

Wherein, described nano-particle material is the metal nanoparticle material, and described host material is selected from amorphous glass, organism, crystalline material.

The present invention has following beneficial effect: what other patent was measured is body material coefficient of thermal expansion coefficient, belongs to the scope of macroscopic view; What the present invention measured is the thermal expansivity of nano particle, belongs to the scope of microcosmic.The present invention can be indirect measurement, by measuring the nano particle interatomic disance, cube relative displacement of distance between square relative displacement of distance and adjacent atom between adjacent atom is measured the thermal expansivity of nano particle, indirectly to the testing sample not damaged.

Description of drawings:

The transmission electron microscope photo of three kinds of different silver nano-grain glass samples of Fig. 1;

The K limit expansion X ray of Fig. 2 Ag body material absorbs fine structure spectroscopy and corresponding fourier transform thereof;

The Ag K limit expansion X ray of Fig. 3 sample Ag1 absorbs fine structure spectroscopy and corresponding fourier transform thereof;

The Ag K limit expansion X ray of Fig. 4 sample Ag2 absorbs fine structure spectroscopy and corresponding fourier transform thereof;

The Ag K limit expansion X ray of Fig. 5 sample Ag3 absorbs fine structure spectroscopy and corresponding fourier transform thereof;

Arest neighbors Ag-Ag interatomic disance in three kinds of different silver nano-grain glass samples of Fig. 6.

The Ag-Ag arest neighbors coordination shell C of different samples under Fig. 7 different temperatures ₂Value.

The C of the Ag-Ag arest neighbors coordination shell of different samples under Fig. 8 different temperatures ₃Value

The silver foil that Fig. 9 calculates according to the XAFS analysis result and the thermal expansivity of silver nano-grain.

Embodiment:

The thermal expansivity that absorbs silver nano-grain in the fine structure spectroscopy EXAFS measurement glass with the expansion X ray is embodiment:

1, the preparation of silver nano-grain glass: at first, commercial sodium-calcium-silicate sheet glass is cut into 20mm * 20mm sample,, make the sample that thickness is 0.12-0.16mm by attenuate, polishing.This sample is immersed AgNO ₃+ NaNO ₃Mixed molten liquid in, make 1000g NaNO ₃In 0.5g AgNO is arranged ₃, carry out ion-exchange, take out sample behind the cool to room temperature, in air, heat-treat.Detailed technological parameter sees Table 1.The massfraction of soda lime glass consists of: 71.87SiO ₂-13.3Na ₂O-8.69CaO-4.15MgO-0.59Al ₂O ₃-K0.31 ₂O-0.01BaO-0.079TiO ₂-0.148SO ₃-0.865Fe ₂O ₃

Sample	Particle size/nm	Ion-exchange			Thermal treatment
								?AgNO 3Concentration [%]	Temperature [℃]	Time [h]	Temperature [℃]	Time [h]
?Ag1		?7.0	?0.05	?330	?382	?380 ?600							?432 ?97
	?Ag2						?4.0	?0.05	?330	?429	?380 ?480	?810 ?384
?Ag3		?2.8	?0.05	?330	?426	?410							?459

With Phillips CM200 transmission electron microscope (TEM) observation sample Ag1, silver nano-grain among the Ag2 and Ag3, diameter is respectively 7nm, 4nm and 2.8nm, as shown in Figure 1.

2, the sign of silver nano-grain structure: the measurement temperature range is 12K-298K.Analyze Ag K limit X ray with commercial UWXAFS 3.0 routine packages and absorb fine structure spectroscopy.Ag K limit X ray absorbs fine structure spectroscopy and is collected in Hamburg, Germany synchrotron radiation center X1 experiment centre.Utilize theoretical phase function and the amplitude function of theoretical EXAFS Equation for Calculating Ag, and come EXAFS resonance spectrum χ (k) that match experiment obtains and corresponding Fourier Tranform to compose (Fouriertransform-FT) with them.Concrete formula is as follows:

$\mathrm{\&chi;}\left(k\right)=\underset{\mathrm{<figure-callout\; id="0"\; label="j\; S"\; filenames="A20071003664900081.png,A20071003664900091.png"\; state="\{\{state\}\}">j</figure-callout>}}{\mathrm{\&Sigma;}}{S}_{}^{}{}_0^2{N}_j\frac{F_j\left(k\right)}{k{{\mathrm{<figure-callout\; id="2"\; label="R\; j"\; filenames="A20071003664900081.png,A20071003664900091.png"\; state="\{\{state\}\}">R</figure-callout>}}_j}^2}\&times;\sin (2k{R}_j+{\mathrm{\&phi;}}_j\left(k\right))e^{-2R_j/\mathrm{\&lambda;}\left(k\right)}{e}^{-2{{\mathrm{\&sigma;}}_j}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20071003664900081.png,A20071003664900091.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}$

Wherein: k is the photoelectron wave number; S ₂ ⁰Be that amplitude reduces the factor; N _jBe j layer atom number; F _j(k) be j layer atom backward scattering amplitude; R _jBe that j layer atom is to the distance between the central atom; 2kR _jDrift mutually when representing transmitted wave to be got back to starting point by the backward scattering of j layer atom; φ _j(k) be the additional phase drift of central atom; λ (k) is photoelectronic mean free path; σ _j ²Be the j layer atomic disorder degree factor, also write as C ₂It comprises two parts:: the unordered and structural disorder of heat.In order to analyze the EXAFS spectrum effectively, draw its structural parameters exactly, following formula is transformed into

$<\mathrm{\&chi;}\left(k\right)>=\frac{\mathrm{NF}(k,\mathrm{kR})e^{-2R/\mathrm{\&lambda;}}}{\mathrm{<figure-callout\; id="2"\; label="k\; R"\; filenames="A20071003664900081.png,A20071003664900091.png"\; state="\{\{state\}\}">k</figure-callout>}{R}^{}{}^2}\exp [-2C_2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20071003664900081.png,A20071003664900091.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+\frac{2}{3}{C}_4{k}^2-...]\sin [2\mathrm{kR}+\mathrm{\&phi;}\left(k\right)-\frac{4}{3}{C}_3{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="A20071003664900081.png"\; state="\{\{state\}\}">k</figure-callout>}}^3+...]$

Wherein: C ₂=＜(r-R) ²Be square relative displacement of distance between adjacent atom, be the Debye-Waller factor again, C ₃=＜(r-R) ³Be cube relative displacement of distance between adjacent atom, bond distance's asymmetry distribution that the anharmonic oscillation of atom causes has been described.R is that arbitrary atom in the same coordination shell is to the mean distance between the central atom, R=＜r 〉.When n 〉=4, C _n=0 (n is a positive integer).

EXAFS function χ (k) is through k ²After the weighting, adopt the Hanning window function that coordination shell is mated.Wave number (k) matching range is 2-16  ^-1, interatomic disance (R) matching range is 1.0-4.0 .Wherein the maximum error scope of co-ordination distance R is ± 0.006  (298K), and the least error scope of co-ordination distance R is ± 0.001  (12K).

Ag body material, the Ag K limit expansion X ray of sample Ag1～Ag3 absorbs fine structure spectroscopy and Fig. 2～Fig. 5 is seen in corresponding Fourier conversion.

3, the acquisition of silver nano-grain structural parameters: utilize UWXAFS 3.0 routine packages to analyze Ag-Ag arest neighbors coordination shell interatomic disance r as shown in Figure 6, square relative displacement C of distance between adjacent atom ₂As shown in Figure 7, cube relative displacement C of distance and between adjacent atom ₃As shown in Figure 8.

4, for the silver nano-grain in Ag body material and the glass, its thermal expansivity can be calculated by following formula:

$\mathrm{\&alpha;}=\frac{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20071003664900081.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}{\mathrm{rT}{\mathrm{\&sigma;}}^2}\frac{3z(1+z)\ln (1/z)}{(1-z)(1+10z+z^2)}$

R is the arest neighbors interatomic disance in the following formula, R be all atoms in the same coordination shell to the mean distance between the central atom, T is for measuring temperature, σ ²=C ₂=＜(r-R) ²Be square relative displacement of distance between adjacent atom, and claim the Debye-Waller factor again, the degree of disorder of atom is described.C ₃=＜(r-R) ³Be cube relative displacement of distance between adjacent atom, bond distance's asymmetry distribution that the anharmonic oscillation of description atom causes, $z=\exp (-\frac{{\mathrm{\&theta;}}_E}{T})$ , θ _EBe nano particle einstein (Einstein) temperature.Present embodiment thermal expansivity result of calculation as shown in Figure 9.As shown in Figure 9, under the room temperature, the room temperature thermal linear expansion coefficient that calculates the silver foil of gained is 1.72 * 10 ^-5K ^-1, approach experiment value 1.89 * 10 ^-5K ^-1, show that these computing method are reliable.7.0nm the room temperature thermal expansivity of 4.0nm and 2.8nm silver nano-grain is respectively 1.72 * 10 ^-5K ^-1, 2.0 * 10 ^-5K ^-1With 2.7 * 10 ^-5K ^-1, along with particle size reduces, the thermal linear expansion coefficient of Ag nano particle increases.When Ag nanoparticle size during greater than 7nm (volume fraction of silver atoms is 21%), the thermal linear expansion coefficient basically identical of the thermal linear expansion coefficient of silver nano-grain and silver foil.Other thermal linear expansion coefficient of measuring under the temperature is seen Fig. 9.

Above-mentioned description to embodiment is can understand and apply the invention for the ease of these those skilled in the art.The person skilled in the art obviously can easily make various modifications to these embodiment, and needn't pay through creatively work being applied in the General Principle of this explanation among other embodiment.Therefore, the invention is not restricted to the embodiment here, those skilled in the art enlighten according to the present invention, all should be within protection scope of the present invention for the modification that is equal in fact that the present invention makes.

Claims (3)

1, a kind of method of nondestructively measuring nano grain thermal expansivity, it is characterized in that, nano-particle material is dispersed in the host material, and the most contiguous interatomic distance of nano particle that is dispersed in the host material with X ray absorption fine structure spectrometry is r then, according to formula $\mathrm{\&alpha;}=\frac{c_3}{\mathrm{rT}{\mathrm{\&sigma;}}^2}\frac{3z(1+z)\ln (1/z)}{(1-z)(1+10z+z^2)}$ Calculate the thermal expansivity of nano particle, in the formula, r is the most contiguous interatomic disance, R be all atoms in the same coordination shell to the mean distance between the central atom, T is for measuring temperature, σ ²=C ₂=＜(r-R) ²Be square relative displacement of distance between adjacent atom, C ₃=＜(r-R) ³Be cube relative displacement of distance between adjacent atom, $z=\exp (-\frac{{\mathrm{\&theta;}}_E}{T}),$ θ _EBe the nano particle Einstein temperature.

2, the method for nondestructively measuring nano grain thermal expansivity according to claim 1 is characterized in that, described nano-particle material is the metal nanoparticle material.

3, the method for nondestructively measuring nano grain thermal expansivity according to claim 1 is characterized in that, described host material is selected from amorphous glass, organism, crystalline material.

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