Dmitriev, Andrey I.

Nikonov, Anton Yu.

Sharkeev, Yuriy P.

English

Tomsk State University Repository

Molecular dynamics study of the inﬂuence of the parameters of the crystallizationprocess during selective laser sintering of alloy Ti-NbMolecular dynamics study of the inﬂuence of theparameters of the crystallization process duringselective laser sintering of alloy Ti-NbAnton Yu. Nikonov, Andrey I. Dmitriev, Yuriy P. Sharkeevanickonoﬀ@ispms.ruAbstractIn the paper the study of the processes occurring at diﬀerent stages ofthe process of laser sintering is performed using the method of computer sim-ulation on the atomic scale. The initial conﬁguration of the system is twospherical crystallites with properties of titanium and niobium, with the inter-face. Interatomic interaction was described by the embedded atom method.We analyzed the eﬀect of cooling rate on the resulting crystal structure of thealloy Ti-Nb. We also investigated the dependence of the resistance forces tobreak of sintered particles on the heating time of the system and its rate ofcooling. It is shown that the main parameter which determines the adhesiveproperties of sintered particles is the contact area obtained during sinteringprocess. The simulation results can not only deﬁne the technological parame-ters of the process to provide the desired mechanical properties of the resultingproducts, but also are a necessary basis for calculations on large scale levelsin order to study the behavior of implants in actual use.1 IntroductionCurrently, one of the dominant material for the production of bio-implants is tita-nium and titanium alloys. Along with the recognized advantages of titanium as theimplant material (magnetic inertia, bio-compatibility, low density combined withhigh strength, high corrosion resistance and others.), titanium has a relatively highmodulus of elasticity. It was found that from attractive high biomechanical com-patibility point of view beta alloys of titanium-niobium, which may also have theeﬀect of pseudoelasticity, bringing them closer in properties to the properties ofcortical bone may be considered. [1, 2]. Metallurgical methods for producing suchalloys are well known but they are complicated, laborious and expensive. This iscaused, in particular, by a large diﬀerence between the melting points and densitiesof titanium and niobium. It should be noted that the titanium and niobium have avery signiﬁcantly diﬀerent in thermal properties (thermal conductivity, speciﬁc heat,coeﬃcient of linear expansion). Manufacturing also requests complex multistep ther-momechanical methods in order to generate alloys with homogeneous structure and345Proceedings of XLIV International Summer School  Conference APM 2016chemical composition. Furthermore, during such treatments the preform lost to halfvolume.Recently use of the additive technology, in particular, methods of synthesis of layeredlaser solves the above problems and achieves the objectives of personalized medicine[3, 4]. Advantages of additive technology and selective laser sintering are especiallythe possibility of forming not only the volume of the product, but also the internalstructure. When forming structure it is possible simultaneously to synthesize a newmaterial (alloy), using as the starting powder mixture components in the desiredproportions.Obviously, the physical properties of samples are determined primarily by processingconditions and the properties of the starting powder. In turn, the problem of deter-mining the optimal impact parameters on the starting powder to produce sampleswith desired mechanical properties requires a deep understanding of mechanismsthat are taking place during laser sintering at diﬀerent scale levels. A short time du-ration and high power laser beam makes particularly diﬃcult to direct experimentalstudy the eﬀects of high-energy impact. One of the research directions allowing usto identify the main regularities of the formation of Ti-Nb alloy by layering lasersynthesis, depending on the parameters and intensive modes of heating is the usingof methods of numerical modeling. Thus using the numerical method of ab initialcalculations described in [5] the optimal stoichiometry to obtain the desired elasticmodulus for Ti-Nb alloy system was found. In the present paper, mathematicalmodel of the process of low modulus β-Ti-Nb alloy system formation produced bylaser sintering from titanium and niobium powders was developed. For this aim,the particle based method of atomic-scale - the method of molecular dynamics wasused to simulate processes of alloy crystallization under diﬀerent temperature gradi-ents conditions. Varying the temperature gradients was determined by the originaltemperature conditions of the system and by changing the heat sink intensity givenby the thermo-physical properties of the substrate. Future the adhesion proper-ties between particles of obtained Ti-Nb alloy, determines by the duration of thehigh-energy laser exposure were estimated.2 Results of calculation2.1 Features of Ti-Nb alloy crystallizationTo study the features of Ti-Nb alloy crystallization under diﬀerent temperaturegradient conditions on the scale of single atoms the method of molecular dynamicsin the form of LAMMS software [6] was used. Interatomic interaction was describedusing an interatomic potential calculated in the framework of the embedded atommethod [7, 8], which had earlier been veriﬁed in test problems on the calculation ofelastic and energy characteristics. The simulated system consisted of two sphericalcrystallites, one of which was corresponded to the lattice of titanium, and the secondone - niobium. The diameter of each sphere was 10 nm, which is 5 times less thanthe characteristic size of the powder particles used for laser synthesis. The totalnumber of atoms exceeds 150000. The initial sample structure is shown in Fig. 1a.In order to study the eﬀect of varying duration of a laser beam exposure the high-346Molecular dynamics study of the inﬂuence of the parameters of the crystallizationprocess during selective laser sintering of alloy Ti-Nba) b) c)d) e)Figure 1: (a) The initial structure of the modeled particles of Ti (dark gray) and Nb(light gray) and structure corresponds to diﬀerent moments of time of the high-speedheating process up to 6000 K: (b) 30 ps, (c) 70 ps, (d) 120 ps and (e) 220 ps.speed warm-up of two particles up to temperature of 6000 K, 5000 K and 3000 Kin various tasks was realized. Snapshots given on Figures 1b-d demonstrate thestructure of the modeled system at diﬀerent moments of time corresponding to theheating process. As a result of warm up stage the uniform melting for both metalswithin one particle was achieved as shown in Figure 1e.The future solidiﬁcation procedure during which a linearly decreasing of the systemtemperature from high value to ambient (300 K) one was carried out. The followingcooling rates of the modeled ensemble of atoms were studied: 9.5, 5.7 and 3.1 K/ps.The corresponding time dependencies of the temperature changing for the modeledsystem during cooling stage are shown in Figure 2. Note that in order to achievethe cooling rate of 3.1 K/ps the resulting temperature of the system after heatingstage was decreased to 5000 K. The resulting structure of the sample after coolingwas analyzed using the algorithm which allows one to determine the local topologyof interatomic structure corresponding to bcc, fcc and hcp crystal lattices. Theinﬂuence of cooling rate on the ratio of atoms with bcc local topology of Ti-Nb alloywas studied.The resulting structures for considered variants of cooling rates are shown in Fig-ures 3a-c. Percentage of bcc atoms for the resultant state depends on the coolingrate and amounts to 11.2%, 56.2% and 87.7%, respectively. A further reduction of347Proceedings of XLIV International Summer School  Conference APM 2016Figure 2: Time dependencies of the system temperature and parts of fcc atoms forthree cooling rates.the rate of the system cooling has not led to a noticeable change in the proportion ofatoms with a bcc lattice in the resulting state. Thus, by trying of diﬀerent coolingmodes of the system we found that the cooling rate of 3.1 K/ps or less for two-component system is suﬃcient to ensure that to form the resulting polycrystallinestructure of Ti-Nb beta-alloy. The remaining 12% corresponds to the surface atoms,and atoms located near the formed grain boundaries.a) b) c)Figure 3: The ﬁnal structure of the modeled sample after crystallization with dif-ferent cooling rates: (a) 9.5 K/ps, (b) 5.7 K/ps and (c) 3.1 K/ps.These results allow the use of mechanical and physical characteristics of the formedparticles of the Ti-Nb alloy as the parameters needed to describe the interactionbetween particles for models of a mesoscopic scale. We can also note the qualita-tive agreement between results of simulation and existing experimental data on theeﬀect of pre-heating the powder mixture and the use of the substrate during thepreparation of beta-titanium-niobium alloy under selective laser sintering.348Molecular dynamics study of the inﬂuence of the parameters of the crystallizationprocess during selective laser sintering of alloy Ti-Nb2.2 Adhesion properties of Ti-Nb particlesNext stage of research was devoted to study the inﬂuence of the alloy particle systemheating duration and its cooling rate on the value of the resulting adhesive force.For this purpose two hemisphere-shaped particles with an internal structure corre-sponding to the structure of the β-alloy Ti-Nb system obtained by as a result of thecrystallization process were simulated. Testing was carried out as follows. Initiallyhemisphere from their tops converged to a distance of about 1 nm. Obtained inthis way conﬁguration of the modeled system is shown in Figure 4a. The crystallo-graphic orientation of the particles was chosen so that, in the area of convergenceof the particles grain boundary was formed.By the next stage of testing a local heating of both particles in the region of topsconvergence by adding the kinetic energy to the surface atoms of the ratio of 1 eV/psfor the entire system was simulated. As a result melting of the hemispheres andtheir subsequent sintering were occurred. Depending on the duration of heating thesintering area has changed. The resulting structure, corresponding to the contactarea of 8500 A2 is shown in Figure 4b.This conﬁguration was obtained by heatingthe modeled system in the area of convergence of particles tops to ≈ 3000 K within50 ps, followed by cooling.a) b)Figure 4: The structure of the modeled setup of Ti-Nb β-alloy at diﬀerent stage:(a) before heating, (b) after heating.To assess the adhesive force the conﬁguration, not only with diﬀerent values of thecontact square, but with a diﬀerent structure of resulting contact were created. Themodiﬁcations in the structure were achieved by changing the cooling rate of themolten area. At low cooling rates the crystallization of the molten contact areawith formation of a grain boundary was observed. At relatively high cooling ratesthe amorphization of a conjugated area was taking place. The ﬁnal stage of adhesiveforces estimation consists into modeling of rupture of the formed coupling. To thisend, the movement with constant velocities of atoms located at the base of thehemispheres was modeled. Velocities were oriented in opposite directions along axisX. Figure 5 shows the dependence of the resistance force on the initial value ofthe square of molten area. It can be seen very well pronounced linear dependence349Proceedings of XLIV International Summer School  Conference APM 2016between forces and squares for all considered cases. In these particular cases featuresof structure of the molten area does not have a signiﬁcant impact on the resultingdependence.Figure 5: The dependence of adhesion strength on the square and the structurefeatures of the molten area of two particles of Ti-Nb β-alloy.Thus, the main factor determining the magnitude of the adhesive force is the squareof the area involved in the contact between two particles. This parameter directlydepends on the duration of thermal exposure. The cooling rate and the relatedstructure of the molten area almost no eﬀect on the resulting adhesion properties.3 ConclusionsComputer simulation results of the melting process, followed by crystallization ofa mixture of particles of titanium and niobium, for diﬀerent values of the temper-ature gradient allowed to determine the conditions necessary to obtain a systemwith a maximum content of beta-crystal structure of the alloy Ti-Nb. It was foundthat the cooling rate of 3.1 K/ps or less for considered two-component system issuﬃcient to ensure that the resulting polycrystalline structure was beta alloy witha maximum content of the bcc lattice. At that variation of the temperature gra-dients determined by the initial system temperature and a diﬀerent heat removalintensity deﬁned by thermo-physical properties of the substrate. It should be notedthat the obtained results qualitatively agree with experimental data on the eﬀect ofpreheating the powder mixture and the use of substrate during the production ofbeta-alloy of titanium-niobium system by selective laser sintering [9, 10]. Accordingto the simulation results it was shown that the main factor determining the valueof the adhesion forces between the particles is the area of the region involved in the350REFERENCEScontact between two particles. The rate of cooling and the structure of the obtainedcontact region almost no eﬀect on the properties of the resulting adhesive. Theobtained result will be used to specify the mechanical and physical characteristics ofthe formed powder particles of the alloy Ti-Nb in the description of the interactionbetween the particles in the model of a mesoscopic scale.AcknowledgementsThe research work was supported by the Russian Science Foundation, Grant No15-19-00191.References[1] Y. Bai, Y. Deng, Y. Zheng, Y. Li, R. Zhang, Y. 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IOP Conf.Ser.: Mater. Sci. Eng. 91 (2015) 012031Nikonov A.Yu., Akademichesky 2/4, 634055, Tomsk, RussiaDmitriev A.I., Akademichesky 2/4, 634055, Tomsk, RussiaSharkeev Yu.P., Akademichesky 2/4, 634055, Tomsk, Russia351

Molecular dynamics study of the influence of the parameters of the crystallization process during selective laser sintering of alloy Ti-Nb

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Molecular dynamics study of the influence of the parameters of the crystallization process during selective laser sintering of alloy Ti-Nb

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