chemical bonds in changing the hardness of...

saqarTvelos mecnierebaTa erovnuli akademiis moambe, t. 10, #2, 2016

BULLETIN OF THE GEORGIAN NATIONAL ACADEMY OF SCIENCES, vol. 10, no. 2, 2016

© 2016 Bull. Georg. Natl. Acad. Sci.

Inorganic Chemistry

Chemical Bonds in Changing the Hardness ofNanomaterials

Giorgi Chiradze*, Alexi Gerasimov**, Giorgi Kvesitadze§,Mikhail Vepkhvadze**

*Department of Physics, Akaki Tsereteli State University, Kutaisi, Georgia** Georgian Technical University, Tbilisi, Georgia§Academy Member, Georgian National Academy of Sciences, Tbilisi, Georgia

ABSTRACT. Nanomaterials consisting of nanoparticles, in contrast to conventional materials, duringloading behave in a special way. The value and sometimes even the direction of the change initiated by theloading process depends on the size of their constituent nanoparticles. Despite many attempts theexplanation of these facts does not still exist. In this paper, we propose a new mechanism of changing themagnitude and direction of change initiated by a loading process in nanomaterials, depending on the sizeof the constituent nanoparticles. This mechanism is based on the new ideas about changing the atomposition in the material, which is determined by the change of quantum state of the chemical bonds of theatom. This change can be realized in different ways: by temperature, light, pressure, electric and magneticfields, reduction of the particle size of the material. This mechanism qualitatively explains all the experimentalfacts taking place during the loading of nanomaterials. © 2016 Bull. Georg. Natl. Acad. Sci.

Key words: nanomaterials, hardness, plasticity, fluidity, quantum state of chemical bonds

Materials of macroscopic size in the solid state(compact materials) at mechanical loading first expe-rience elastic deformation, then inelastic deformationtransferred into flexibility and later fluidity bringingto their mechanical destruction [1-3]. Depending uponthe nature of the material, some of these processescan be of such small intensity that it is very hard todetect them experimentally, for example, during brit-tle fracture of the material. In compact materials asthe load is increased, the inelastic deformation, plas-ticity, fluidity are also increased and mechanical de-struction occurs [2-3]. Nanomaterials composed of

nanoparticles behave quite differently: the volumeand sometimes even the direction of change initiatedby a loading process depends on the size of theirconstituent nanoparticles [4,5 ]. It was found that thedecrease of grain size to nanometer levels causes anincrease of the microhardness (MH) values innanomaterials and yield point (YP) in 4-5 times. Thistendency in case of the MH is described by the em-pirical Hall–Petch relation (H-P): H=H0+KL-1/2, whereH is nanomaterial hardness at a given value, H0 is thehardness of substance, K individual constant for eachmaterial, the so-called Hall–Petch coefficient, L is an

106 Giorgi Chiradze, Alexi Gerasimov, Giorgi Kvesitadze, Mikhail Vepkhvadze

Bull. Georg. Natl. Acad. Sci., vol. 10, no. 2, 2016

average size of nanoparticles [4, 5]. Similar expres-sion also describes the dependence of the yield stresson nanoparticles size. With decrease of nanoparticlessize the yield stress first increases similar to H-P law:ðT= ð0+KL-1/2 (ðT is yield point and ð0 - internal stresswhich hinders plastic shift in the material) and thendecreases [4, 5]. For numerous researchednanomaterials the Hall–Petch relation is fulfilled upto a certain grain size and for smaller grain sizes theinverse effect is observed: the values of hardnessand yield stress are decreased with the reduce ofnanograins size (Fig.1). The latter is considered ananomaly and called “anti H-P”. The increase in themicrohardness and yield stress values with a decreasein grain size to a nanosize is explained by a decreasein the number of dislocations in particles with reduc-tion of their size which is proved by X-ray and elec-tron microscopic investigations [4, 5].

It is believed that due to the fact that in the rangeof “anti- H-P” dislocation activity is not observed,reduction of hardness and yield point is caused bydifferent mechanisms. The fact that in case of brittlesubstances (oxides, nitrides, carbides, intermetallids),changing the grain size the value of hardnesschanges insignificantly [6, 7]. It is also known that

superplasticity phenomenon in nanomaterials is farhigher by value and occurs at lower temperaturesthan in compact materials that has big practical im-portance [4, 5]. Besides this, in nanomaterials cre-ated from metal alloys, intermetallids and high-melt-ing compounds are revealed higher speed and lowertemperatures of deformation processes than in thesame materials in polycrystalline state [4, 5]. Innanomaterials of oxides and silicium nitrides the low-est temperature, after which superplastisity occurs,is higher than in nanomaterials of other substances.In various works the results quantitatively differentfrom each other, nevertheless it can be stated thatchanges of hardness characteristics (MH, plasticity,yield point and mechanical destruction) innanomaterials are connected with the decrease ofnanoparticles size. In spite of numerous attempts,there is no explanation to these facts [4, 5]. On thebasis of new ideas about the change of the locationof an atom in the material which allowed to createelementary act of decreasing the hardness of the com-pact material, this work offers the mechanism of chang-ing in nanomaterials the value and direction of thechange initiated by loading of the processes depend-ing on the sizes of nanoparticles constituting them[8]. All above-mentioned processes on microscopiclevel are determined by the change of initial locationof atoms in the material which has been described tillnow from the viewpoint of molecular-kinetic theory(MKT) [9]. However, the MKT is valid at tempera-tures T=0.7 Tmp (Tmp – temperature of melting) andeven at these temperatures cannot explain many ex-perimental facts connected with the change of thelocation of the atom in the substance and totally pow-erless in interpretation of the phenomena taking placeat low temperatures [10]. This explains non-existenceof the elementary act of beginning the processes de-veloping in the loaded compact materials [8] and an-nounced in nanomaterials as “anomaly”, dependenceof the changes of directions and value initiated byloading processes on the size of nanoparticles [ 4, 5].

In the paper [ 8] it has been shown that the change

Fig. 1. The dependence of the hardness of nanomaterialfrom the grain size of the constituent nanoparticles:

1-area, complying with the law Hall-Patch relation2-anomalous range (anti Hall-Patch)

Chemical Bonds in Changing the Hardness of Nanomaterials 107


of the hardness of the usual materials as a result ofmechanical loading at a constant temperature is de-termined by decreasing the energy of chemical bondsbetween the atoms (molecules) composing given ma-terial. The energy of chemical bonds is decreasingdue to the appearance of additional antibonding elec-trons due to the approach of bonding and anti-bond-ing zones under the pressure [ 10]. The magnitude ofthis approach depends on the ratio direction of thepressure force and crystallographic direction [8].Therefore, the concentration of additionalantibonding electrons is unequal in all areas of mate-rial. The probability WA of change of atom location inthe substance is determined by the expression

phaABQPA WNnAW )/( , where A is almost con-stant value, ABQPn - concentration of AQP(antibonding quasi-particles – electrons inantibonding zone and holes in the bonding zone), Na

is concentration of atoms (molecules) of the sub-stance, is number of AQP near the given atom nec-essary for reduction of the height of potential barrierto zero, Wph is the probability of the phonons pres-ence of definite energy close to the given atom [8-10]. Clearly, the more n ABQP concentration of the AQP,the easier the change of atom location in the materialand beginning of the processes of decreasing hard-ness of the material. In case of nanomaterials it is

necessary to consider the specifics of the energy(quantum) states of the electrons participating in crea-tion of chemical bonds in nanoparticles.

Unlike compact solid bodies, during creation ofwhich from the multiplicity of the atoms, energy lev-els of atoms split and create bonding and anti-bond-ing zones, during the formation of the nanoparticles(clusters), the splitting of electronic levels of atomsto discrete bonding and anti-bonding energy levels(orbitals) occur. It will be recalled that electrons lo-cated in the bonding orbitals increase the energy ofchemical bond apart from electrons located onantibonding orbitals which decrease it. Therefore,the electrons located on the antibonding orbitals andvacant places on the bonding orbits on bonding or-bitals (holes) are the AQP. In big clusters the levelsare less split. A small cluster is similar to the moleculewith its discrete set of energy levels, bonding andantibonding orbitals. In nanoparticles the energy dis-tances between discrete levels are of such value thatelectrons can freely transit to the higher energy lev-els and move along the nanoparticle. Beginning fromthe certain sizes of nanoparticles, during its motionthe AQP reaching the surface of nanoparticle, aremostly reflected from them and remain in its volumeraising the AQP concentration unlike the compactsolid body of the same volume from which the AQP

Fig. 2. Schematic illustration of growth in ABQPs' concentration with reducing in nanoparticles size at given temperature.Increasing in AQPs the calculated real concentration for fixed concentration with decreasing in sizes: a) AQPtrajectory in compact solid's region with volume equal to the nanoparticle volume: two of them are leaving thevolume; b) in connection with the reflection from the boundary surface of the nanoparticle trajectory three AQP is init and they will be around more the number of atoms in this volume than in the case of a compact solid body; c) andd) with decreasing size of nanoparticles of the same three AQP will be near a larger number of atoms.

a) b) c) d)



can transit freely into the neighboring region (Fig.2).This can be described by real concentration of theAQP which is bigger as compared with the calcu-lated at the given temperature. The lessernanoparticles size, the bigger real concentration. Dueto the fact that AQP (during one period of atomicoscillation) appears near atoms more frequently innanopatricles than in compact solid body [10, 11]and weakening of their chemical bonds will be big-ger. Thus, with the decrease of nanoparticles size thereal concentration of AQP increases, chemical bondsweaken more, the probability of atoms motion growsand hardness decreases correspondingly.

It should be mentioned that in the near-surfacerange of the nanoparticle the AQP more frequentlyappear near the atoms, than in its volume due to thedirect and reverse direction of the AQP motion in thereflection process which will cause additional increaseof the real concentration of the AQPs. In its turn as aresult of increasing electron-hole screening will de-crease the distance between bonding and anti-bond-ing orbitals that will contribute to further increase ofthe AQPs because of thermal transitions and corre-spondingly further decrease of the distance betweenbonding and anti-bonding orbitals [11]. Thus, in thenear-surface range of the nanoparticle the real con-centration of the AQP (Fig.3) and respectively theprobability of the movement of atom is more than inthe volume. Thus, unlike compact materials during

loading of nanomaterials and increase in the AQPconcentration occurs not only as a result of pressurecaused by pressure but because of decreasing ofnanoparticles size.

Proceeding from the above-mentioned mechanismof changing at constant temperature, quantum stateof electrons participating in the creation of chemicalbonds in nanoparticles, it can be easily explained notonly the above mentioned experimental data but alsothe facts announced anomalies from the viewpointof MKT.

A decrease of the hardness value and yield pointwith decrease of nanograin sizes is naturally explainedby an increase of the AQP concentration and corre-sponding decrease of the energy of chemical bonds.

The thing that in case of fragile nanomaterials(oxides, nitrides, carbides, intermetallids) with thechange of the grains size the value of hardness ischanging less than in other nanomaterials [4, 5] isdue to the fact that at the uniform sizes of nanograinsin fragile nanomaterials of AQP concentration andtheir mobility is less because of bigger splitting ofatoms electron levels which decreases the possibil-ity of electrons transition to the overlying energylevels. Therefore, in materials with big splitting oflevels for achievement of the necessary AQP con-centration the sizes of nanoparticles must be smallerthan in materials with less splitting of levels. Figure 4shows that the anomaly for NiZr2 starts from com-

Fig. 3. Energy levels distributions in nanoparticle surface layer and bulk. Due to reflection from surface the probability ofAQPs appearance near atoms in the surface layer is higher than that in bulk, what a) decreases energy-differencebetween bonding and anti-bonding levels in semiconductor; b) in metals these levels are overlapped and pseudo-gapnear the surface is smaller than in the bulk and the concentration is incomparably higher.

Chemical Bonds in Changing the Hardness of Nanomaterials 109


paratively smaller nanotaprticles size than Fe-Mo-Si-B, the melting temperature of which is less than inNiZr2 (It is shown that [12, 13] in semiconductors andmetals the width of levels splitting is in correlationwith melting temperature). The same mechanism ex-plains the fact that in nanomaterials of oxides andsilicon nitrides the minimum temperature after whichsuperplacticity occurs is higher than in nanomaterialsof other substances.

As was mentioned above, in nanomaterials cre-ated from metal alloys intermettalids and refractorycompounds are revealed the higher speeds and lowertemperatures of deformation processes than in thesame materials in polycrystalline state. This is due tothe fact that the ratio of bulk and near-surface rangeof polycrystalline particles by order of magnitude isgreater than in nanoparticles and hence the increaseof the AQP concentration because of refraction isvery small compared with voluminous concentrationof AQP and contributes insignificantly in weakeningof chemical bonds.

According to a number of authors plastic defor-mation in materials always starts with athermal grainboundary microsliding [4, 5] which consists in thefact that at a certain loading of the solid body theshift of one of its parts in relation to another along

some plane can take place. In nanomaterials plasticmicrosliding occurs at considerably less loadingsthan in compact materials which is due to the addi-tional concentration of AQPs in nanoparticles but itis interesting to explain why the microsliding of oneof its parts in relation to another one along a certainplane and not plasticity of the whole material is ob-served. The microsliding in nanomaterials is easilyexplained by the new mechanism of change of at-oms location in materials offered by us in the fol-lowing way. In nanomaterials nanoparticles com-posing them are located chaotically in terms of theircrystallographic directions. Crystallographic direc-tions of nanoparticles composing nanomaterialmainly don’t coincide, i.e. these directions are lo-cated chaotically. On application of the loading tonanomaterial the direction of the pressure andcrystallographic directions will have different an-gles. At definite angles the approach of bondingand antibonding levels will take place. This willincrease the AQP concentration and correspond-ingly, the mobility of atoms, especially in sub-sur-face range of nanoparticle. In those directions ofthe nanomaterial where the amount of suchnanoparticles is more, the microsliding will occur(Fig.5).

Fig. 4. The dependence the hardness of nanomaterial,which had different melting point,from the size oftheir respective nanoparticles Tmel1< Tmel2

Fig. 5. Disposition of nanoparticles with differentcrystallographic orientation in the nanomaterial.1-micro sliding plane.



araorganuli qimia

qimiuri bmebi nanomasalebis sisalis cvlilebaSi

g. CiraZe,* a. gerasimovi,** g. kvesitaZe,§ m. vefxvaZe**

* akaki wereTlis saxelmwifo universiteti, fizikis departamenti, quTaisi, saqarTvelo** saqarTvelos teqnikuri universiteti, Tbilisi, saqarTvelo§ akademiis wevri, saqarTvelos mecnierebaTa erovnuli akademia, Tbilisi, saqarTvelo

datvirTvis qveS myofi nanonawilakebisagan Semdgari nanomasalebi iqcevian sruliadgansxvavebulad imave nivTierebis Cveulebrivi masalebisagan: datvirTviT gamowveuliTvisebebis cvlilebis sidide da zogjer mimarTulebac damokidebulia Semadgenelinanonawilakebis zomebze. miuxedavad mravali cdisa am fenomenis axsna jer ar arsebobda.mocemul naSromSi SemoTavazebulia am fenomenis axali meqanizmi. es meqanizmi dafuZnebuliaatomis adgilmonacvleobis axal warmodgenebze, romelic ganixilavs atomis qimiurbmebSi monawile eleqtronebis kvantur mdgomareobis cvlilebas. es cvlileba SeiZlebagamowveuli iyos sxadasxva saSualebiT: temperaturiT, sinaTliT, wneviT, eleqtruli damagnituri velebiT, nanonawilakebis zomebis SemcirebiT. SemoTavazebuli meqanizmiTvisebrivad xsnis nanomasalebis datvirTvasTan dakavSirebul yvela eqsperimentul faqts.

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Received March, 2016

chemical bonds in changing the hardness of...

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