Arrangement of dislocation networks in hot-pressed titanium diboride

Suipta~aetMataiataialia,

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ARRANGEMENT OF DISLOCATION NETWORKS IN HOT-PRESSED TITANIUM DIBORIDE D.A. Hoke and G.T. Gray III MaterialsDivision, Los Alamos National Laboratory Los Alamos, New Mexico, 87545 USA (Received November 29,1994)

Introduction

The high internal stresses required to create defects in ceramic materials dictates that most dislocations are formed during exposum to extreme conditions such as high temperatures or pressures, when slip systems start to become active. However, upon cooling I?om high temperature processing, for example, defect energy can be lowered through the rearrangement of dislocations into equilibrium substructures. That is, interaction between sets of common Burg& vector dislocations, leading to the formation of dislocation networks, is one way the defect energy can be reduced in materials where long range motion leading to annihilation is not possible. For example, Amelinckx observed hexagonal and square dislocation networks in undeformed rock salt (1) and potassium chloride (2). Hexagonal networks were similarly observed by Silk and Barnes (3) in cleaved mica, and by Cockayne et al. (4) in hexagonal cadmium suhide. It is not clear what role dislocation networks play, if any, on the subsequent mechanical behavior of brittle mater&. It is genemlly accepted that most ceramic materials, at room temperature, fail through the process of critical crack growth coupled with fast propagation The contribution of dislocations to the failme of ceramics is thought to be negligible compared with that of crack propagation (5). Planar dislocation networks, however, can form energetically stable sub-grain boundaries, which may impede slip at high temperatures or pressums. Therefore, understanding the structure and relationship of the dislocations found in as-processed ceramics may play an important role in understanding the behavior of this class of materials when subjected to applied loads. TiB, is a covalently-bonded ceramic, with a hexagonal crystal structure typified by AlB, (6), in which layers of titauium and boron atoms alternate in hexagonal coordination. The AlB* type structure is shown in Figure 1. Several investigators have examined the possible operating slip systems in TiB, loaded in compression at high temperature. Nakano, Imura, and Taken&i (7) and Nakano, Matsubar, and Imura (8) concluded that the primary slip system in titanium diboride at high temperatures was ( lOlO). Ramberg and Wilhams (9) proposed two alternate primary slip systems at high temperatures: { lOTO}[0002] and (OOO2)~lOTO>.Wang and Arsenault (10) reported three observed slip directions in TiB, deformed at various strain rates at high temperature: l/34110>, [0002], and l/361 13>, and Vanderwalker and Crofi (11) reported that prismatic { lOTO} and basal (0002) slip occur in shock-loaded TiB,. The observation of dislocationnetworks in titanium diboride has not been reported to date in the literature. The purpose of tbis paper is to report some recent observations of dislocation networks in hot-pressed titanium diboride.

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Boron o Titanium

l

Figure 1. Cryal strwture of titanium diboride typified by that of ALB,(6).

Material and Emerimental

Procedureg

Monolithic titanium diboride was obtained from the Cercom Corporation, Vista, CA, for this investigation. The material was prepared by hot-pressing from powders. The average grain size was 10 f 1 microns as determmed by the linear intercept method The as-received material was sectioned into wafers nominally 250 microns thick for examination in the transmission electron microscope (TEM) using a low-speed diamond saw, The disks were mechanically dimpled using 6 micron diamond paste to a center thickness of approximately 20 microns and then ion-thinned using a 6 kV ion source at a grazing angle of 12- 15 degrees. Foils were examined at 300 kV using a Philips CM30 (Philips Electronic Instruments Corp., Inc., Mahwah, NJ) equipped with a double-tilt stage.

Two types of dislocation networks were commonly found within the as-received TiB,: hexagonal and square. Hexagonal-type networks, shown in Figure 2a, predominately formed large two-dimensional grids, while the square dislocation networks, Figure 2b, tended to form more compact structures. The two dimensional nature of the hexagonal and square networks results in the formation of low angle subgram boundaries, dividing individual grams into two or more smaller subgrains with misorientations of less than 5” as shown in Figure 3.

(4

@I

Figure 2. (a) Typical hexagonal dislocation network in Ti&, (b) Typical square dislocation nelsvork in T&.

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Figure 3. Typical dislocation networks in as-received Tia, viewed on edge as low angle sub-grain boundaries.

ml Networks

Figure 4 shows a hexagonal dislocation network which lies in (0002). Difhaction contrast analysis of the hexagonal dislocation structure, Figure 5, reveals that the network is composed entirely of “a”type dislocations along the close-packed directions, with Burgers vectors of the type 1/3<1120>. Under [rlOO] di&ction conditions, Figure 5a, the dislocation segments labeled AB and BC are visible while segment BD is not. Correspondingly, under the di&cting conditions of [lOTO] and [OlTO], Figures 5b and 5c, respectively, dislocation segments BC and AB, are not visible. Therefore, the dislocations labeled AB, BC, and BD have Burgers vectors of 1/3[1120], 1/3[zllO], and 1/3[121O],respectively. In this case, the 1/3<1120> type dislocations he on individual prism planes and make up the hexagonal geometry visible in Figure 4. ‘Ihe regular hexagons consist of pure edge dislocations due to the fact that their line images lie perpendicular to the {OlTO)-type planes, and the 1/3<112@-type Burgers vectors. Furthermore, the dislocations must have equal line tensions to produce a network of evenly distributed dislocations 120” apart. Formation of the network can be described by the following reaction: $ [li20]+ + [2iio]- f [i2io]. Using the b* criterion for dislocation energy per unit length, it can be shown that formation of a hexagonal dislocation network results in a decrease in energy and is therefore an energetically favorable reaction:

Figure 4. Extended dislocatioa r&work which lies in (0002) in TiF&

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Figue 5. Diflktion contrast analysis of hexagonal dislocation network which lies in (0002). In (a), taken in [TlOO], diskations andBCarevisibleandaD~~~)~in[10~O],ABandBDarevisible,andBCdisappears;in(c)takenin[OlTO],BCand BDarevisibleattdABdisppem Usingasecoadreflectiogcaditionforcase@)itwasw~thattheAB.BC,andBDdislocations are all “a” type dislocations with burgers vectors of li3[1120], 1/3[% lo], and 1/3[1210], respectively.

AES

Applying the rules derived by Frank (12) concerning the combination of dislocation lines, it is clear that the hexagonal networks evolve ti the interacti~ between two sets of l&l 1ZO>type dislocations on the basal plane. The resulting network forms a pure low angle tilt boundary as &tied by Ball and Hirsch (13). Because the “a” type 1/3<1120> dislocations reside at the intersection between the basal (0002) and prism {0 1TO) planes, and the network is energetically stable, slip on these systems may be impeded. 2. Sauare Networks The square dislocation network shown in Figure 6 lies in (lOT4). Using diEaction contrast analysis, Figure 7, the square dislocation network was de&mined to be composed of “a”, “c”,and “a+c” type dislocations. Under [0002] d&-acting uxxlitions, Figure 7a, the dislccation segmenta labeled AB and BC are visible while segment BD is not. Under the diffracting conditions of [OlTO],Figure 7b, the segments labeled BC are not visible. Under the di&actjng conditions of [OlTl], Figure 7c, the small segments labeled AB are not visible.

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Figure 6. Extended square dishcatioll nebvork which lies in (1014) in T&

Therefore, the dislocation segments labeled BC, BD, and AB have Burgers vectors of l/36110>, and 1/3Gl3> respectively, corresponding to the reaction shown below:

;

[2110]

l

[OOol] q f

4)001>,

[2113].

In contrast to the energy-reducing reaction which forms the hexagonal network, formation of the square network does not result in a decrease in strain energy as shown below, and is therefore considered an energetically unstable quasi-equilibrium structure: (4) However, continuity of the long-range square geometty suggests that long-range stress fields associated with a non-equilibrium structure are not present. Thesqurnenetworksrevealacolnplex~~~ofbasal(0002)<1120>,prismatic (OlTO}[OOOl],and pyramidal {OlTl }<1123>slip leading to the “lozenge-type” shapes (1) observed in Figure 7. Although Frank (12) predicted that square dislocation networks be made of intersecting parallel dislocation lines, Amelinckx (1) observed that sing&&es cau lead to formation of the lozenge-shaped networks imaged in Figure 7. Hirth ad L.&he (14) consider dislocations with the l/3 < 1123> type burgers vector to be only marginally stable in HCP crystals, then&m the square dislocation networks are potentially more likely to dissociate or reorganize during deformation than the 1/3<1120> type dislocations in the more energetically stable hexagonal coordination. The hexagonal and square dislocation networks form as a result of polygonization, the recovery process following hot press& Randon@ oriented dislocations introduced during hot-pressing rearrage themselves into sub-grain boumhuies, reducing the overall strain energy of the crystal. Rearrangement from the random disl~tion distribution into sub-grain boundaries involves only minor movement, and can be accOmplished through climb while the TiB, remains at an elevated temperature (15). Because titanium diboride is a hexagonal material with a c/aratio of 1.06, thermal expansion in the c-direction is greater than in the adirection. Therefore, upon processing, the grams expand or contract according to their specific orientation cmating areas of localized stress. While geometrical mismatches of this type are accommodated through the formation of intra-grain microcracks, when the grain size reaches approximately 15 pm (9), it is not clear if the dislocation sub-grain boundary networks are affected.

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F&n-e 7. DiEaction contrast analysis of square dislocation network which lies in (lOT4). IO (a), taken in [OOOZ],dichations AB and BCareviPibleeodBD~in(bXtakmin[Ol~O],dislocationsABandBDarevisibleaadBC~;in(c~takenin[OlTl], dislocatiws BC and BD are visible and AB diqpeax. Tberefore, tbe dislocation segments labelled BC, BD, and AB have burgers vectors of 1/3[C!llO], [OOOl], and lL+[2TTT], respectively.

conclusions Transmission electron microscopy identified two types of dislocation networks in as-received titauium diboride. Hexagonal dislocation networks composed of l/34 120> type dislocations were identified and are a result of the interaction between parallel sets of “a” type dislocations on individual prism planes. Dislocations forming the hexagonal networks result in a reduction of energy, and are considered equilibrium &u&n-es. Square dislocation networks composed of l/34 120>, [OOOl],and l/34 123> type dislocations on basal, prism, aud pryamidal plaues wete identified and are the result of parallel sets of “a”type dislocations reacting with parallel sets of “c” type dislocations to form unstable short dislocation segments composed of “a+c”type dislocations. Dislocations arranged in square networks do not result in an energy reduction, and are considered quasi-equilibrium configurations, more likely to dissociate or reorganize during deformation or further thermal processing than dislocations in the hexagonal coordination.

This work was performed under the auspices of the U.S. Department of Energy.

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Refemmes 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14. 15.

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