MATERIALS 兴 HIENGE& ENGIEERING ELSEVIER Materials Science and Engineering A 438-440(2006)343-345 www.elsevier.com/locate/msea An alternative approach to the crystallography of martensitic transformation in Zro2 J F Nie. B C. Muddle Department of Materials Engineering, Monash University, Victoria 3800, Australia Received 20 June 2005; received in revised form 17 October 2005: accepted 20 December 2005 The crystallographic features of the tetragonal to monoclinic martensitic transformation in Zro2 have been analysed using the moire plane approach. It is found that the predicted orientation relationships and interface orientations of the transformations are in excellent agreement with those observed experimentally. The successful application of the approach indicates that such martensite interfaces are defined by edge-to-edge matching of lattice planes o 2006 Elsevier B v. All rights reserved Keywords: Crystallography: Lattice matching: Interface: Moire plane 1. Introduction of coupling crystallography and migration mechanisms more Zirconia(ZrO2) has a face-centred cubic structure(Fin3m) directly. It is the purpose of this paper to demonstrate appli- (P42/nmc)between 1200 and 2370.C and a primitive mono- [1,5 itic transformation in a Ceoz-stabilised ZrO2 at temperatures above 2370C, a primitive tetragonal structure martens clinic structure(P2,c)below 950C[1]. It is widely accepted that the structural change from tetragonal [2-7] to monoclinic in zirconia is displacive in nature, and under proper microstruc 2. Experimental observations tural design and control this transformation can be utilised to enhance the fracture toughness of zirconia and its alloys. In Fig. 1 shows a transmission electron microscopy image of the past 30 years, the crystallographic features of the tetrago- edge-on plates of the monoclinic phase and the corresponding nal => monoclinic transformation have been well documented selected area electron diffraction(SAED) pattern recorded from and it has been demonstrated [1-7)that such features can be these plates and the surrounding matrix of the tetragonal phase fully predicted by the phenomenological theory of martensitic [5. The image was obtained with the electron beam direction parallel to [00 1]. The orientation relationship implied by the A Moire plane approach, based on consideration of matching SAED pattern is such that(200)m//(200),[010Jm//[00 1] and of edges of lattice planes, has recently been developed [8, 9]to [00 1]m//[O 1 OJ. There are two variants in the image. For the account for the crystallography and migration mechanisms of plate labelled I in Fig. 1(a), the two broad surfaces of this plate planar interphase boundaries in phase transformations. with are parallel to each other and the angle between the broad surface input of lattice parameters and lattice plane correspondence, this and (200) is w16. While the orientation of the broad surface approach is capable of predicting the orientation relationship, does not appear to be parallel to any low-index planes of either and the orientation, structure and migration mechanisms of tragonal or monoclinic lattice, careful inspection of the image interphase boundaries. Compared to PTMC, this alternative and the corresponding SAED pattern suggests that the normal of approach is less complex mathematically and has the advantag the broad surface(habit plane)is parallel to the vector connectin (002)m and(020) reflections. If this observation is accepte as accurate and representative, then the habit plane of the plate Corresponding author. Tel: +61 399059605: fax: +6139905 4940 is parallel to the moire plane resulting from the intersection of E-mail address: nie@ spme. monash. edu. au (J.F. Nie) 002)m and(02 0) planes
Materials Science and Engineering A 438–440 (2006) 343–345 An alternative approach to the crystallography of martensitic transformation in ZrO2 J.F. Nie ∗, B.C. Muddle Department of Materials Engineering, Monash University, Victoria 3800, Australia Received 20 June 2005; received in revised form 17 October 2005; accepted 20 December 2005 Abstract The crystallographic features of the tetragonal to monoclinic martensitic transformation in ZrO2 have been analysed using the Moire plane ´ approach. It is found that the predicted orientation relationships and interface orientations of the transformations are in excellent agreement with those observed experimentally. The successful application of the approach indicates that such martensite interfaces are defined by edge-to-edge matching of lattice planes. © 2006 Elsevier B.V. All rights reserved. Keywords: Crystallography; Lattice matching; Interface; Moire plane ´ 1. Introduction Zirconia (ZrO2) has a face-centred cubic structure (Fm3¯m) at temperatures above 2370 ◦C, a primitive tetragonal structure (P42/nmc) between 1200 and 2370 ◦C and a primitive monoclinic structure (P21/c) below 950 ◦C [1]. It is widely accepted that the structural change from tetragonal [2–7] to monoclinic in zirconia is displacive in nature, and under proper microstructural design and control this transformation can be utilised to enhance the fracture toughness of zirconia and its alloys. In the past 30 years, the crystallographic features of the tetragonal⇒monoclinic transformation have been well documented and it has been demonstrated [1–7] that such features can be fully predicted by the phenomenological theory of martensitic crystallography (PTMC). A Moire plane approach, based on consideration of matching ´ of edges of lattice planes, has recently been developed [8,9] to account for the crystallography and migration mechanisms of planar interphase boundaries in phase transformations. With an input of lattice parameters and lattice plane correspondence, this approach is capable of predicting the orientation relationship, and the orientation, structure and migration mechanisms of interphase boundaries. Compared to PTMC, this alternative approach is less complex mathematically and has the advantage ∗ Corresponding author. Tel.: +61 3 9905 9605; fax: +61 3 9905 4940. E-mail address: nie@spme.monash.edu.au (J.F. Nie). of coupling crystallography and migration mechanisms more directly. It is the purpose of this paper to demonstrate application of this approach to the tetragonal⇒monoclinic martensitic transformation in a CeO2-stabilised ZrO2 [1,5,6]. 2. Experimental observations Fig. 1 shows a transmission electron microscopy image of edge-on plates of the monoclinic phase and the corresponding selected area electron diffraction (SAED) pattern recorded from these plates and the surrounding matrix of the tetragonal phase [5]. The image was obtained with the electron beam direction parallel to [0 0 1]t. The orientation relationship implied by the SAED pattern is such that (2 0 0)m//(2 0 0)t, [0 1 0] ¯ m//[0 0 1]t and [0 0 1]¯ m//[0 1 0] ¯ t. There are two variants in the image. For the plate labelled 1 in Fig. 1(a), the two broad surfaces of this plate are parallel to each other and the angle between the broad surface and (2 0 0)t is ∼16◦. While the orientation of the broad surface does not appear to be parallel to any low-index planes of either tetragonal or monoclinic lattice, careful inspection of the image and the corresponding SAED pattern suggests that the normal of the broad surface (habit plane) is parallel to the vector connecting (0 0 2)m and (0 2 0)t reflections. If this observation is accepted as accurate and representative, then the habit plane of the plate is parallel to the Moire plane resulting from the intersection of ´ (0 0 2)m and (0 2 0)t planes. 0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.12.064
J E Nie, B C Muddle/ Materials Science and Engineering A 438-440(2006)343-345 Fig. 1.(a) Transmission electron micrograph showing martensite plates of the monoclinic phase in the matrix of the tetragonal phase in a CeO2-stabilised ZrO2 loy, and (b)corresponding SAED pattern from the martensite plates labelled 1 and 2 and surrounding matrix. Electron beam is parallel to [0101//[001].The labelled reflections of the monoclinic phase in(b)refer to those from plate 1 in(a). The habit plane normal of plate 1 is indicated by the dash line in(b). Careful inspection of monoclinic plates reveals the exis- [001]t, if any, is accommodated plastically by dislocation loops, ce of another orientation relationship that can be described then the tetragonal to monoclinic transformation can be simpli by(002)m//(020)t, [0 1 0]m//00 1] and [100)m//[100J [6, 1 ]. fied into a two-dimensional case, as illustrated in Fig.2.For This second orientation relationship differs from the first one by this structural transformation, the(020) plane is sheared into a rotation of approximately 8.5 about the [01)m//[001] axis. (002)m, and the(200)t plane is expanded into(200)m.There The habit plane of monoclinic plates that are associated with the fore, s=tan A=tan(Pm-900), nx=d(oo2)m/(d(o20), sin Pm) second orientation relationship is about 5 from(020)t towards cm/at, ny= d(200m/d(200)=(am/at)sin Pm, where s is the (200)t magnitude of shear strain, nx is the dilatation of(02 O) in[01 OJt ny is the dilatation of (200)t in [100]t, and at, am, Cm and 3. Theoretical analysis are the lattice parameter of the tetragonal and monoclinic lat- tices, respectively. Substituting these parameters into following Inspection of the tetragonal and monoclinic lattices sug- equations [8] gests that the monoclinic lattice can be generated from the tetragonal lattice by shearing in the [0 10]t direction on(200) (1+n y)(nx+ny)+sn yV /52ny-(n2-1)(02-D and dilatation in the [0 101,[100]t and [001]t directions, COsp- (nx +nv)2+52n2 respectively(Fig. 2(a). Assuming that the misfit strain alon y t[1001t y si+(nx-1)-+ 2n(1-cos p+ ssin and assuming that at=0.5132 nm, Ct=0.5228 nm, am=0.5193nm,bm=0.5204nm,cm=0.5362nm,and [010 Bm=98.8%[1], the rotation angle, between the two lat- tices is predicted to be 0 and thus the monoclinic lattice is (200)t (200)m x expected to develop a rational orientation relationship with out of plane normal (001lt ut of plane normal [010)m he tetragonal lattice, i.e. (200hm/(200)t,[010Jm/00lt and [00 1]m/n[o i OJt. The theory also predicts that the habit y4(100 ▲00m (02 0)t and (002)m planes, is 16.15 clockwise from(200) i.e. B=(90-a)=16. 15, where a is the angle between the habit plane and(02 O)(Fig 3). These predictions are thus in excellent agreement with experimental observations(Fig. 1). It (200)m is to be emphasised that the predicted orientation relationship and the interface orientation in particular, are a function of the ratio of lattice parameters of the monoclinic and tetragonal lattices. The angle =0 only when n,=(am/at)sin Bm=1 out of plane normal [010]m Since(200)m and (200) planes are precisely parallel to each grams showing two possible structural transformat other and the macroscopic interface is inclined to them, the tetragonal to monoclinic lattices. The viewing direction is[0 10lm//1o macroscopic interface may adopt a form of regularly spaced
344 J.F. Nie, B.C. Muddle / Materials Science and Engineering A 438–440 (2006) 343–345 Fig. 1. (a) Transmission electron micrograph showing martensite plates of the monoclinic phase in the matrix of the tetragonal phase in a CeO2-stabilised ZrO2 alloy, and (b) corresponding SAED pattern from the martensite plates labelled 1 and 2 and surrounding matrix. Electron beam is parallel to [0 1 0] ¯ m//[0 0 1]t. The labelled reflections of the monoclinic phase in (b) refer to those from plate 1 in (a). The habit plane normal of plate 1 is indicated by the dash line in (b). Careful inspection of monoclinic plates reveals the existence of another orientation relationship that can be described by (0 0 2)m//(0 2 0)t, [0 1 0] ¯ m//[0 0 1]t and [1 0 0]m//[1 0 0]t [6,1]. This second orientation relationship differs from the first one by a rotation of approximately 8.5◦ about the [0 1 0] ¯ m//[0 0 1]t axis. The habit plane of monoclinic plates that are associated with the second orientation relationship is about 5◦ from (0 2 0)t towards (2 0 0)t. 3. Theoretical analysis Inspection of the tetragonal and monoclinic lattices suggests that the monoclinic lattice can be generated from the tetragonal lattice by shearing in the [0 1 0] ¯ t direction on (2 0 0)t and dilatation in the [0 1 0] ¯ t, [1 0 0]t and [0 0 1]t directions, respectively (Fig. 2(a)). Assuming that the misfit strain along Fig. 2. Schematic diagrams showing two possible structural transformations from tetragonal to monoclinic lattices. The viewing direction is [0 1 0] ¯ m//[0 0 1]t. [0 0 1]t, if any, is accommodated plastically by dislocation loops, then the tetragonal to monoclinic transformation can be simpli- fied into a two-dimensional case, as illustrated in Fig. 2. For this structural transformation, the (0 2 0)t plane is sheared into (0 0 2)m, and the (2 0 0)t plane is expanded into (2 0 0)m. Therefore, s = tan θ = tan(βm − 90◦), ηx = d(0 0 2)m /(d(0 2 0)t sin βm) = cm/at, ηy = d(2 0 0)m /d(2 0 0)t = (am/at) sin βm, where s is the magnitude of shear strain, ηx is the dilatation of (0 2 0)t in [0 1 0] ¯ t, ηy is the dilatation of (2 0 0)t in [1 0 0]t, and at, am, cm and βm are the lattice parameter of the tetragonal and monoclinic lattices, respectively. Substituting these parameters into following equations [8]: cos ϕ = (1 + ηxηy)(ηx + ηy) + sηy s2η2 y − (η2 x − 1)(η2 y − 1) (ηx + ηy) 2 + s2η2 y , (1) sin α = s cos ϕ + sin ϕ s2 + (ηx − 1)2 + 2ηx(1 − cos ϕ + ssin ϕ) , (2) and assuming that at = 0.5132 nm, ct = 0.5228 nm, am = 0.5193 nm, bm = 0.5204 nm, cm = 0.5362 nm, and βm = 98.8◦ [1], the rotation angle, ϕ, between the two lattices is predicted to be 0◦ and thus the monoclinic lattice is expected to develop a rational orientation relationship with the tetragonal lattice, i.e. (2 0 0)m//(2 0 0)t, [0 1 0] ¯ m//[0 0 1]t and [0 0 1]¯ m//[0 1 0] ¯ t. The theory also predicts that the habit plane, the Moire plane defined by the intersection of the sets of ´ (0 2 0)t and (0 0 2)m planes, is ∼16.15◦ clockwise from (2 0 0)t, i.e. β = (90◦ − α) = 16.15◦, where α is the angle between the habit plane and (0 2 0)t (Fig. 3). These predictions are thus in excellent agreement with experimental observations (Fig. 1). It is to be emphasised that the predicted orientation relationship, and the interface orientation in particular, are a function of the ratio of lattice parameters of the monoclinic and tetragonal lattices. The angle ϕ = 0 only when ηy = (am/at)sin βm = 1. Since (2 0 0)m and (2 0 0)t planes are precisely parallel to each other and the macroscopic interface is inclined to them, the macroscopic interface may adopt a form of regularly spaced
J F Nie, B.C. Muddle/ Materials Science and Engineering A 438-440(2006)343-345 yA [10011 monoclinic within the Moire plane(macroscopic) interface. The detailed analysis of such interfacial defects is, however, beyond the scope of the present paper. The structural change from the tetragonal lattice to the mon- aclinic lattice can also occur by shearing in the [100] direc tion on(020) and expanding in the [100] and the [01] tions, respectively(Fig. 2(b)). In this alternative transformation, the(200) plane is now sheared into(200)m and the (020) plane is expanded into(002)m. Therefore, s=tan 8=tan(90-Bm), nx=amat, ny=(cm/at)sin Bm For the lattice parameters used for the structural change depicted in Fig 2(a), and B are now predicted to be 0.141 and -4.32 respectively. The(002)m plane is rotated 0. 141 clockwise away from the(020)t, and thus the orientation relationship between estragon 1010). the two lattices is now near rational, and can be related to the first orientation relationship by a rotation of approximately 8.66 about the common axis of [0 10)m//00 1 ]t. The macroscopic interface is rotated 4.32 anti-clockwise from(020)t Since (002)m and(02 O)t planes are almost parallel to each other and the macroscopic interface is inclined to them, the inter- face may again adopt a form that is similar to that illustrated in Fig 3(b) Refe [1]R H.J. Hannink, P.M. Kelly, B.C. Muddle. J. Am. Ceram Soc. 83(2000) [2] PM. Kelly, L.R.F. Rose, Progr. Mater. Sci. 47(2002)463. [3] PM. Kelly, CJ. Ball, J Am. Ceram Soc. 69(1986)259 [5] B.C. Muddle, Mater Res. Soc. Symp Proc. 78(1987)3 [6 G.R. Hugo. B C Muddle, R H. Hannink, Mater. Sci. Forum 34-36(1988) Fig 3. Schematic diagrams showing the monoclinic/tetragonal interface that is F.R. Chien, FJ. Ubic, V. Prakash, A H. Heuer, Acta Mater. 46(1998) in the form of (a) Moire plane, and (b) terrace planes and structural disconnec- tions. Viewing direction is parallel to [0 1 01m/n[oo1- [8] J F Nie, Acta Mater. 52(2004)795. [9] J F. Nie, Scripta Mater. 52(2005)687 terrace planes, separated by structural ledges or structural [10] J.P. Hirth, R.C. Pond, Acta Mater. 44(1996)4749 disconnections[10, 11](Fig 3(b)). In terms of the Moire plane [I1 J.P. Hirth, Metall. Mater. Trans. A 25(1994)1885 approach [8], the migration of such macroscopic interfaces involves the formation and lateral sliding of moire ledges
J.F. Nie, B.C. Muddle / Materials Science and Engineering A 438–440 (2006) 343–345 345 Fig. 3. Schematic diagrams showing the monoclinic/tetragonal interface that is in the form of (a) Moire plane, and (b) terrace planes and structural disconnec- ´ tions. Viewing direction is parallel to [0 1 0] ¯ m//[0 0 1]t. terrace planes, separated by structural ledges or structural disconnections [10,11] (Fig. 3(b)). In terms of the Moire plane ´ approach [8], the migration of such macroscopic interfaces involves the formation and lateral sliding of Moire ledges ´ within the Moire plane (macroscopic) interface. The detailed ´ analysis of such interfacial defects is, however, beyond the scope of the present paper. The structural change from the tetragonal lattice to the monoclinic lattice can also occur by shearing in the [1 0 0]t direction on (0 2 0)t and expanding in the [1 0 0]t and the [0 1 0] ¯ t directions, respectively (Fig. 2(b)). In this alternative structural transformation, the (2 0 0)t plane is now sheared into (2 0 0)m, and the (0 2 0)t plane is expanded into (0 0 2)m. Therefore, s = tan θ = tan(90 − βm), ηx = am/at, ηy = (cm/at)sin βm. For the lattice parameters used for the structural change depicted in Fig. 2(a), ϕ and β are now predicted to be 0.141◦ and −4.32◦, respectively. The (0 0 2)m plane is rotated 0.141◦ clockwise away from the (0 2 0)t, and thus the orientation relationship between the two lattices is now near rational, and can be related to the first orientation relationship by a rotation of approximately 8.66◦ about the common axis of [0 1 0] ¯ m//[0 0 1]t. The macroscopic interface is rotated ∼4.32◦ anti-clockwise from (0 2 0)t. Since (0 0 2)m and (0 2 0)t planes are almost parallel to each other and the macroscopic interface is inclined to them, the interface may again adopt a form that is similar to that illustrated in Fig. 3(b). References [1] R.H.J. Hannink, P.M. Kelly, B.C. Muddle, J. Am. Ceram. Soc. 83 (2000) 461. [2] P.M. Kelly, L.R.F. Rose, Progr. Mater. Sci. 47 (2002) 463. [3] P.M. Kelly, C.J. Ball, J. Am. Ceram. Soc. 69 (1986) 259. [4] B.C. Muddle, R.H.J. Hannink, J. Am. Ceram. Soc. 69 (1986) 547. [5] B.C. Muddle, Mater. Res. Soc. Symp. Proc. 78 (1987) 3. [6] G.R. Hugo, B.C. Muddle, R.H.J. Hannink, Mater. Sci. Forum 34–36 (1988) 165. [7] F.R. Chien, F.J. Ubic, V. Prakash, A.H. Heuer, Acta Mater. 46 (1998) 2151. [8] J.F. Nie, Acta Mater. 52 (2004) 795. [9] J.F. Nie, Scripta Mater. 52 (2005) 687. [10] J.P. Hirth, R.C. Pond, Acta Mater. 44 (1996) 4749. [11] J.P. Hirth, Metall. Mater. Trans. A 25 (1994) 1885
