Phase Transitions in Iron-Platinum

Transcription

1 Phase Transitions in Iron-Platinum Hannah E. Herde Department of Physics, Wellesley College, Wellesley, MA Regan Lab Department of Physics and Astronomy, University of California - Los Angeles, Los Angeles, CA (Dated: Summer 2013) 1

2 CONTENTS List of Figures 3 List of Tables 4 Introduction 5 Iron Platinum: Expectations and Theory 6 Face Centered Cubic and Face Centered Tetragonal Structure 7 fcc and fct Structures in Reciprocal Space 8 fcc and fct Lattice Vectors, Basis Atom Positions, and Reciprocal Lattice Vectors 9 Structure Factors 11 General Properties of FePt 17 Temperature Related Properties of FePt 18 FePt Binary Phase Diagram 20 fcc fct Transition: Temperature Dependent Magnetic and Structural Ordering 21 Curie Temperature 22 Melting 23 Magnetic Properties of FePt 25 Experiments 26 in situ TEM Experiments by other Groups 27 Our Experimental Plan 28 Control Samples 29 Checking for Beam Induced Effects 30 Proposed Experiment 34 2

3 Acknowledgments 36 Appendix 36 A: Atomic Form Factors for Diffraction Calculations 36 B: Calculated Radii of Diffraction Rings in fcc and fct FePt, FePt 3, and Pt 36 References 37 LIST OF FIGURES 1 Hard disk drive, labeled by Microtech.com [1] fcc diffraction rings within the first three graphene rings fct diffraction rings within the first three graphene rings Bulk Iron-Platinum phase diagram, from Whang et al Numbers of Fe and Pt atoms as a function of time. The initial total number of atoms in the model is 1.25x10 4, the estimated number of atoms in one 7nm-diameter FePt nanoparticle Atomic resolution TEM image of pure Pt on SiN x membrane of 14 August Sample kev Low Magnification TEM image of 14 August Sample, prepared by Brad Parks A pair of Pt nanoparticles sinters under the TEM s condensed electron beam Stills from the diffraction of multiple FePt nanoparticles on heated graphene substrate Still from TEM video of nanoparticle movement when heated. Note the damaged MgO coats

4 11 Stills from 29 July movie 8 showing the shrinking nanoparticle LIST OF TABLES I Properties of Intermetallic Iron-Platinum II fcc versus fct Lattice Constants for FePt [14] III fcc and fct Lattice Vectors, Basis Atom Positions, and Reciprocal Lattice Vectors IV Possible configurations of Fe and Pt atoms in fcc basis V Quick reference to FePt key temperatures VI Calculated Diffraction Ring Radii for fcc and fct FePt, FePt 3, and Pt. 37 4

5 INTRODUCTION FIG. 1. Hard disk drive, labeled by Microtech.com [1] The demand for electronic information storage rises steadily, outstripping our current capacity. Hard disk drives store most of our electronic data, through a process called magnetic recording. Inside a hard disk drive in a computer, a small head magnetizes the ferromagnetic domains within the surface of the platter. Each magnetized domain corresponds to a logical one or zero, a single bit of information. A ferromagnetic material remains magnetized long after the external magnetic field, like that of the head, has been removed and therefore serves as stable, reliable data storage over long time periods. The quantity of magnetic domains per area, or recording density, limits the capacity of magnetic recording. As computers and per- 5

6 sonal electronic devices shrink and the demand for electronic storage skyrockets, high recording density is increasingly desirable. A clear explanation of magnetic recording and its history can be found here: hard-drive-magnetic-storage-hdd,3005.html. Unfortunately, ferromagnetic materials require a minimum size in order to demonstrate ferromagnetic properties. An otherwise-ferromagnetic material below the minimum size will behave paramagnetically, meaning that it will forget its magnetization in the absence of an external magnetic field. Since paramagnetic materials lack memory, they are useless as long-term magnetic storage mediums. Sadly, the current hard drive platter materials, various cobalt-metal alloys and cobalt-platinum in particular, have exhausted this size limit. In 2010, we could store over 500 GB/in 2.[2] But, we need to do better. High coercivity materials remain ferromagnetic at even smaller sizes, allowing us to increase our storage densities even more. One such promising material is intermetallic iron platinum. However, hard disk drive developers require more information about the properties of this material before they can truly produce effective, long-term storage devices. IRON PLATINUM: EXPECTATIONS AND THEORY Intermetallic FePt is a hard magnetic material, meaning that once magnetized, its magnetization is difficult to change. In fact, Elkins et al. measured the coercivity of some isolated nanoparticles to be as high as 30 koe, [10] indicating that a magnetic field of at least 3 T may be required to change the particles magnetizations. Given roughly equal compositions of Fe and Pt (Fe x Pt 1 x, 0.4 x 0.6), the Fe and Pt atoms form alternating layers along the crystal s c-axis of a tetragonal unit cell, see figure 2(b), exhibiting so-called L1 0 phase structure. The c-axis of the nanoparticle possesses high magnetocrystalline anisotropy, 7x10 6 J/m 3, sufficient 6

7 to thermally stabilize nanoparticle magnetization down to at least 3.5 nm, better than current Co-metal alloys.[8] Rong et al. quantified several size-dependent effects on chemical ordering and magnetic properties in FePt, including coercivity and Curie Temperature.[23] As such, nanoparticle monolayers of intermetallic iron-platinum are anticipated to achieve recording densities of at least 1 TB/in 2.[8] Unfortunately, most iron-platinum synthesis methods yield a paramagnetic relative, A1-structure facecentered cubic FePt alloy, composed of randomly placed Fe and Pt atoms within the lattice structure. Heat treatment is required to convert the material to the useful, ferromagnetic fct L1 0 state. Table I records some useful properties of intermetallic FePt. Property Fe x Pt 1 x, (0.4 x 0.6) Intermetallic structure Names fct, L1 0 Easy axis c, (001) with respect to the conventional cell [19] Lattice constants a = nm, c = nm [14] Magnetic crystallographic 7x106 J/m3 anisotropy constant, K u Magnetization, M s 1140 emu/cm 3 = 1.14x10 10 s A/m 3 [23] Coercivity, H c up to 30 koe reported [10] TABLE I. Properties of Intermetallic Iron-Platinum Face Centered Cubic and Face Centered Tetragonal Structure FePt forms two main crystal structures, face-centered cubic (fcc) and face-centered tetragonal (fct). fcc structure, also called the A1 structure, consists of a cube with sides of length a fcc. Each corner and each face of the cube contains an atom, as seen in figure 2(a). In FePt, each atomic site may hold either iron or platinum - no 7

8 prevailing atomic order dominates. The alloy is paramagnetic and does not possess a strong magnetic axis. In contrast, the fct structure, or L1 0 structure, breaks the cubic symmetry of the fcc structure by altering the length of one of the sides, see figure 2(b). In FePt, one side of length c is 2% shorter than the other two sides of length a fct. Unlike the fcc phase, the Fe and Pt atoms form alternating layers within the crystal lattice in the ordered fct phase. Most important to the hard disk drive engineers, the fct phase is ferromagnetic with the characteristics summarized in table I. Table II gives the lattice constants for the fcc and fct structures. Face-centered Cubic (fcc) Face-centered Tetragonal (fct) a nm nm c a fcc nm TABLE II. fcc versus fct Lattice Constants for FePt [14] fcc and fct Structures in Reciprocal Space A crystal s diffraction pattern corresponds to its Fourier transform, called its reciprocal lattice. Using this approach, the diffraction peaks can be referred to by their corresponding Miller indices, simplifying crystallographic comparison. For FePt, fct constitutes a symmetry break from the fcc structure, clearly reflected in its diffraction pattern, providing an excellent means of distinguishing the FePt phases in situ using the diffraction mode of a transmission electron microscope (TEM). The scattering amplitude of the diffracted beam is given: F = n( r)e i( k k ) r dv, (1) where F is the scattering amplitude, r is the vector from the origin to a given position in the cell, n( r) is the electron number density giving the total electron 8

9 concentration at r due to all atoms in the cell, k is the initial wave vector of the incident beam, and k is the wave vector of the scattered beam. In order to calculate the diffraction pattern for each lattice, we must calculate the positions of atoms in the basis within the lattice, reciprocal lattice vectors, structure factor and the distance to each allowed diffraction peak. The following treatment was derived from Charles Kittel s Introduction to Solid State Physics, 7th Ed. - Chapter 2: Reciprocal Lattice. All calculations are performed with respect to the conventional cell, defined by Kittel to be the unit cell of the simple cubic lattice. Further work includes more careful and complete calculations of the scattering behavior of both lattices and better plots in MATLAB of the results.[17] fcc and fct Lattice Vectors, Basis Atom Positions, and Reciprocal Lattice Vectors (a) Face centered cubic (fcc) lattice (b) Face centered tetragonal (fct) lattice 9

10 Consulting figures 2(a) and 2(b), we can assign atomic coordinates xyz with respect to the lattice vectors for each atom in the basis for both fcc and fct. The coordinates xyz are equivalent to a vector position from the lattice origin, r = x a 1 + y a 2 + z a 3. The basis atoms in the fcc lattice are identified in orange in figure 2(a). For fcc, our lattice vectors are a 1 = aˆx, a 2 = aŷ, and a 3 = aẑ, where a is the lattice constant for the FePt fcc lattice. Referencing figure 2(a) again, atom A s position in the these coordinates is 000, B is 0 1 1, C is 10 1, and D is We can think of the fct lattice as a scaled fcc lattice, where a 1 and a 2 are unaffected and a 3 becomes a 3 = cẑ, so that the positions of atoms along the c-axis pick up a dimensionless scaling factor, c. The constants a and c in fct calculations correspond a to the lattice constants of the FePt fct lattice, as recorded in table II. Next, we need to calculate the reciprocal lattice vectors for both the fcc and fct lattices. Kittel describes the relationship between the lattice vectors and reciprocal lattice vectors in chapter 2.[17] Just as a point xyz in the lattice space corresponds to r = x a 1 + y a 2 + z a 3, a point hkl in reciprocal space is defined G = h b 1 + k b 2 + l b 3. Table III summarizes the lattice details for both fcc and fct, including the reciprocal lattice vectors. 10

11 Face-centered Cubic (fcc) Face-centered Tetragonal (fct) Lattice a 1 = a fccˆx a 1 = a fctˆx Vectors a 2 = a fcc ŷ a 2 = a fct ŷ a 3 = a fcc ẑ a 3 = cẑ A = 000 A = 000 Atomic B = B = c 2a fct Positions C = C = c 2a fct Reciprocal Lattice Vectors D = D = 1 2 b 1 = 2π a fcc ˆx b 2 = 2π a fcc ŷ b 3 = 2π a fcc ẑ b1 = 2π a fct ˆx b2 = 2π a fct ŷ b3 = 2π c ẑ TABLE III. fcc and fct Lattice Vectors, Basis Atom Positions, and Reciprocal Lattice Vectors Structure Factors Following Kittel s derivation in chapter 2, equation 1 can be re-expressed in terms of a sum over the set of reciprocal lattice vectors, G, such that: F = n G e i( G k) r dv, (2) G where k is the difference between the wave vectors of the incident and scattered beam and n G = Vc 1 cell n( r)e i G r dv where V c is the crystal volume. The set of n G are the Fourier coefficients of the periodic electron number density n( r) such that n( r) = G n Ge i G r. If we generalize the scattering amplitude F to an N cell crystal 11

12 and require that the diffraction condition k = G be satisfied, then F G = N n( r)e ig r dv = NS G, (3) cell where S G is the structure factor of the crystal. If a crystal plane (hkl) whose constituent points have reciprocal lattice vectors G = hb 1 + kb 2 + lb 3 produces constructive interference, the structure factor of that plane must be greater than zero. Thus, we can determine the allowed diffraction planes of the fcc and fct crystals by checking their structure factors. The structure factor S G as given in equation 2 is equivalent to the structure factor of a plane, S(hkl), once we take the dot product of G and r: S hkl = j f j e i2π(hx j+ky j +lz j ), (4) for j atoms in the basis with positions x j y j z j, in plane (hkl) and atomic form factor, f j. The MATLAB program SirriDiffraction.m calculates the structure factors of the fcc and fct FePt lattices. In the fct lattice, the atoms are ordered such that atoms A and D are platinum atoms and B and C are iron atoms, following the labeling convention established in figure 2(b). Plugging in the atomic positions described in table III, the structure factor for the fct lattice becomes: S fct (hkl) = f P t + f F e e iπ(k+ c a l) + f P t e iπ(h+k) + f F e e iπ(h+ c a l), (5) where f P t and f F e are the atomic form factors for platinum and iron respectively. In the fcc lattice, however, the atoms are disordered. Each lattice site has an equal probability of containing either an iron or platinum atom. Having required 1:1 ratio between Fe and Pt, the structure factor for the fcc FePt lattice becomes a weighted average of the six possible basis configurations, given in table IV. A, B, C, and D refer to the positions defined in figure 2(a) and table III. 12

13 A B C D Fe Fe Pt Pt Fe Pt Fe Pt Fe Pt Pt Fe Pt Fe Fe Pt Pt Pt Fe Fe Pt Fe Pt Fe TABLE IV. Possible configurations of Fe and Pt atoms in fcc basis Each fcc structure factor for a given configuration takes the form, S fcc (hkl) = f A + f B e iπ(k+l) + f C e iπ(h+k) + f D e iπ(h+l), (6) and all configurations are currently weighted equally in SirriDiffraction.m. If SirriDiffraction.m produces a significant structure factor, then it calculates the corresponding distance to that plane s diffraction peak. Since we observe a collection of FePt crystals in the TEM rather than a single crystal, we see FePt diffraction rings rather than individual points. Therefore, the distance to a plane s diffraction peak corresponds to the radius of its ring. The radius of a diffraction ring of plane (hkl) is given by the magnitude of its reciprocal lattice vector, G = hb 1 + kb 2 + lb 3 : R = G G = h 2 b1 2 + k 2 b l 2 b hkb1 b 2 + 2hlb 1 b 2 + 2klb 2 b 3. For fcc, For fct, (7) R fcc = 2π a fcc h2 + k 2 + l 2. (8) R fct = 2π h a 2 + k 2 + a2 fct fct c 2 l2. (9) 13

14 The calculated radii of the diffraction rings within the first three graphene diffraction rings (R (100) = 29.5nm 1 ; R (120) = 51.1 nm 1 ; R (200) = 59.0nm 1 ) are given in Appendix B. Using MATLAB, we can plot the diffraction rings and observe their relative order, as shown in figures 2 and 3. Further work includes refining the plotting routine, built into SirriDiffraction.m in MATLAB, to reflect the relative strengths of each diffraction ring. A brief note on SirriDiffraction.m - this MATLAB program requires several other programs to run: ASirriDiffraction.m, DiffractionPlotter.m, GrapheneRadius.m, GrapheneRingPlot.m, and RadiusRatio.m. These programs must be in the same directory. SirriDiffraction.m is pre-programed to calculate structure factors and ring radii for fcc and fct FePt. Full details on all available operations can be found in the program s comments. 14

15 FIG. 2. fcc diffraction rings within the first three graphene rings 15

16 FIG. 3. fct diffraction rings within the first three graphene rings The following sections on temperature related, magnetic, and general properties of FePt serve as a guide to present FePt literature thus far explored. The literature reviews are grouped according to topic. As a general rule of thumb, most groups appear to focus on size dependence of the particles properties, extent of ordering after the annealing transition, or making extremely careful assessments of the magnetic properties. Some concentrate on quantifying FePt s structural behavior. 16

17 General Properties of FePt This section concerns literature related to measuring the order parameter of annealed FePt and other structural characteristics. Chen et al. studied the morphology of FePt nanoparticles produced by nanocluster beam technology and chemical deposition, publishing in They found that they could control aspects of the particle shape by tuning the temperature of the nanoparticle-forming chamber. They note a method to control the easy axis of chemically synthesized FePt particles using magnetic fields, which they further refined for morphological control. They took a variety of characterization measurements, predominately at cold temperatures (less than -100 C). Chen et al. also pointed out that some of their nanoparticles may have melted and reformed during the heating process, stating that melted small particles were allowed to cool down slowly, resulting in the thermodynamically stable fct state.[7] Inaba et al. reported successful fcc fct phase transformation of FePt thin films using multiple laser pulses in The properties of the laser determined the effectiveness of the transformation. This has two ramifications: first, it suggests that the anneal time for FePt nanoparticles may be shorter than previously reported. Second, it questions the role of a concentrated electron beam in the TEM during any phases transformations we may observe.[13] Klemmer et al. published a structural examination of fct FePt nanoparticles in They found close agreement between bulk alloy and nanoparticle, unless the sample was iron deficient. The reported lattice constants are similar to those reported by Kang, whose constants were used for the calculations given in this paper. Klemmer et al. also found that the nanoparticle s tetragonality maximized as its composition became more equiatomic. Like Whang et al.[34], Klemmer et al. s paper 17

18 is a good basis from which to work.[18] Laughlin et al. wrote a 2005 summary paper on the crystallographic characteristics of L1 0 magnetic materials, including a valuable contrast of fcc and fct structure. It is a useful overview. Laughlin et al. also point out that the Curie temperature of a material can be affected by atomic ordering, thus T c,fcc > T c,fct.[19] Sun et al. of IBM s research division authored a seminal 2000 paper, Monodisperse FePt Nanoparticles and Ferromagnetic FePt Nanocrystal Superlattices, first presenting the successful synthesis of spread-out FePt nanoparticles by reduction of platinum acetylacetonate and decomposition of iron pentacarbonyl, the basis for the work of Kim et al. and others. Sun et al. reported possible tunable inter particle spacing as well as TEM images and electron diffraction of their new particles. The paper was a breakthrough at the time. Prior to this, size and composition control in the nanoparticle synthesis was largely unknown. The paper, however, is largely outdated. Many, such as Kim et al. and other IBM researchers, have improved on Sun et al. s method. [29] Temperature Related Properties of FePt The hard disk drive industry is very interested in the behavior of heated ferromagnetic materials, particularly of high-coercivity materials like FePt. In fact, Seagate became the first maker of hard drives with storage density greater than 1 TB/in 2 in 2012, using heat-assisted magnetic recording.[25] 18

19 Temperature ( C) Change 400 Kawai et al. in situ FePt film measurements [15] 475 Curie Temperature, T c, of bulk fct FePt [23], [32] Uncoated fcc fct FePt annealing temperature according to Elkins et al. [10] Uncoated fcc fct FePt annealing temperature according to Kim et al. [16] 600 Delalande et al. in situ FePt nanoparticle measurements [8] 750 Magnesium oxide (MgO)-coated fcc fct FePt annealing temperature according to Kim et al. [16] 800 Chen et al. suspect that Fe x Pt 100 x nano particles may begin to melt [7] Kim et al. report sintering of Fe 51 Pt 49 with MgO coats after 6-hr exposure [16] 1300 bulk FePt transitions fct fcc [34] Bulk Fe x Pt 100 x alloys melt [7] C - equiatomic FePt melts [33] 2000 Graphene sublimes [28] MgO coat melts [16] TABLE V. Quick reference to FePt key temperatures 19

20 FePt Binary Phase Diagram FIG. 4. Bulk Iron-Platinum phase diagram, from Whang et al. Whang et al. provide a detailed treatment of the properties of bulk FePt, including figure 4.[34] Figure 4 illustrates the stoichiometric dependence of bulk iron-platinum properties. But, nanoparticle properties differ from the bulk material. Whang s binary phase diagram provides guidance for possible observations and experiments but should not be used to make quantitative predictions. The 1998 Whang paper is, in general, a useful summary of the bulk characteristics of fct FePt. The diagram reports that equiatomic FePt exists in the ordered L1 0 at low temperature, suggesting that it is a more energetically stable state. But the atoms require time to move to their ordered positions. Most synthesis methods, like the 20

21 chemical decomposition described in [16] and used by the Tolbert group, happen too quickly for the atoms to move. As a result, annealing is required to convert the material from fcc to fct. Once the material has transitioned to the fct state, it will be stable and remain ordered, as reflected by figure 4. At high heat, when the atoms become thermally excited, it is possible to convert the material back to fcc from fct. fcc fct Transition: Temperature Dependent Magnetic and Structural Ordering The annealing transition from disordered fcc structure to ordered fct structure in FePt is well studied, although it has never been observed dynamically in nanoparticles. Medwal et al. explored the effect of temperature on the magnetic and structural ordering of nanoparticles in They found that the magnetic properties of the intermetallic depend on the relative concentrations of Fe and Pt. Their 600 C annealing results suggest sintering of the particles, comparable to our observations and reported elsewhere. They used x-ray diffraction (XRD) to distinguish between fcc and fct FePt, although they have nice TEM images and selected-area electron diffractions (SAED) as well. Table 2 lists their ordering parameters as functions of annealing temperature.[21] Thomson et al. published a summary of the thermodynamic processes in FePt with a goal of quantifying their effects on magnetic and structural properties in They provide the bulk fcc and fct Curie temperatures, which is quite suspicious. It is unclear how paramagnetic fcc material may have a Curie Temperature.[32] Varaprasad et al. also explored temperature-dependent magnetic and structural ordering of films of FePt nanoparticles in They focused on granular films for heat-assisted magnetic recording and considered FePt on a variety of substrates, 21

22 including carbon. The growth properties of the granular films are described for each substrate.[33] Zhang et al. studied the synthesis and behavior of FePt nanoparticles on SiO 2 substrate. Zhang figures 1a and 1b give the XRD patterns of the fcc and fct FePt nanoparticles.[36] Curie Temperature A ferromagnetic material behaves paramagnetically above its Curie temperature, T c. While T c for bulk FePt is reasonably well known, it drops for nanoparticles. Several groups have made measurements of T c as a function of particle composition. Bagaria et al. of the University of Alabama presented a poster in 2005 on their Curie temperature measurements of disordered fcc FePt nanoparticles but I never found a related paper.[6] Havorka et al. authored a theoretical treatment of the effect of grain size on T c in FePt in 2012, critical information for the granular magnetic recording media industry. However, they do not quote T c for any FePt compositions.[12] Rong et al. produced two papers, one in 2006 and one in The 2006 paper reported a thorough exploration of size-dependent chemical and magnetic ordering behavior in fct FePt nanoparticles, connecting particle rise with the extent of chemical ordering and a variety of chemical properties, including T c. They examined particles of diameters = 2, 4, 6, 8, and 15 nm annealed using the salt-matrix method to avoid particle aggregation. They noticed that each particle less than 8 nm in diameter was made of a single fct crystal, once annealed. The 15 nm particles were polycrystalline. They reported that particle coercivity increased with particle size (Rong 2006 fig. 4) while magnetization, understandably, drops with decreasing 22

23 particle size (Rong 2006 fig. 5). In accordance with Delalande et al. s findings [8], they did not observe the fcc fct phase transition in the 2 nm particles. They also noted that T c dropped with decreasing particle size, consistent with the finite scaling theory.[23] The 2007 paper focused on T c of annealed FePt nanoparticle systems, carefully relating T c to the particles compositions.[24] Melting Less-well bonded surface atoms on the nanoparticle gain enough energy to melt at lower temperatures compared to the bulk material, dropping the melting point of the material. Chen et al. explain that the decrease in the melting temperature of nanomaterials is a well known phenomenon. The melting point of the FePt alloy is 1500 to 1755 C, while for the small particle, the surface melting may occur at a lower temperature (e.g. 800 C). [7] Since the melting phase transformation temperature is well above the uncoated nanoparticle fcc fct annealing temperature, little quantified research exists concerning the melting point of nanoparticle FePt. However, we are working with MgO coated FePt nanoparticles, whose annealing temperature is 750 C [16], comparable to the suspected melting point of FePt nanoparticles. While the coat s melting point is 2000 C [16], it is not unreasonable that the FePt centers may melt well below that in the event of coat damage. Given this, it is possible that we may observe iron loss through evaporation. Figure 5 shows the expected number of platinum and iron atoms over time at 800 C, using Raoult s Law. 23

24 FIG. 5. Numbers of Fe and Pt atoms as a function of time. The initial total number of atoms in the model is 1.25x10 4, the estimated number of atoms in one 7nm-diameter FePt nanoparticle. Raoult s Law states that the vapor pressure of an ideal solution depends directly on the vapor pressure of each of its constituent components and the mole fraction of each component present in the solution. The total vapor pressure of the system at equilibrium is P total = P Aχ A + P Bχ B +..., (10) where the individual vapor pressure of each component above the solution is P i = P i χ i. P total is the total vapor pressure of the solution, P i is the partial pressure of component i, P i is the vapor pressure of pure component i, and χ i is the mole fraction of component i. Figure 5 was produced by iteratively calculating the mole fractions of Fe and Pt atoms as atoms were lost a rate proportional to their partial vapor pressures. This work forecasts near-total iron depletion within 330 minutes at 24

25 800 C since iron is four orders of magnitude more volatile than platinum. However, many assumptions were made in this model:- - Begin with an equiatomic composition nanoparticle - Assume that the nanoparticles are spherical with surface area equal to 4πr 2 - Treat the radius as constant in time - Maintain constant temperature - Assume that Raoult s Law applies to solid-solid solutions - Assume a loss rate proportional to that component s vapor pressure Proportion established using the Hertz-Knudsen equation. - Assume that the system achieves equilibrium quickly, even as atoms are lost, and that the loss rate mechanism does not vary - Assume that iron and platinum interact weakly, a necessary condition for ideal solutions - Assume that the TEM magnetic field does not affect the system - Assume that the vapor pressures of pure iron and platinum are the same in bulk and in nanoparticles this is not true: the nanoparticles are more volatile than their bulk counterparts since the surface energy increases at small size, reducing the quantity of energy required for vaporization. - Assume that the MgO coating plays no role Future work includes refining the model to account for time-varying radius and the effect of the MgO coat. Magnetic Properties of FePt See table I for a quick reference. Given the application of the material, most groups concentrate on accurately quantifying the magnetic properties of FePt nanoparticles 25

26 of various sizes. Most papers also treat the synthesis of that group s particles. Artemev et al. described the influence of atomic ordering on the magnetic properties of FePd and FePt in They closely compared both intermetallics magnetic properties.[5] Elkins et al. developed dispersed fct FePt nanoparticles with enormous coercivity, 30kOe at room temperature, by annealing them with salt powders at 700 C in 2005.[10] Kang et al. performed HRTEM, XRD, Scherrer Analysis, Nano-energy Dispersive Spectroscopy to describe the microstructure and magnetic alignment properties of fct FePt nanoparticles. They reported, The disordered A1 FePt phase has a fcc structure with a= nm and the L1 0 FePt phase has a chemically ordered fct structure with a= nm and c= nm, which serve as the lattice constants used for our calculations. Kang figures 4a and 4b show self-assembled FePt nanoparticle chains forming along the magnetic field direction.[14] The 2009 work of Kim et al. on synthesizing dispersible ferromagnetic FePt nanoparticles serves as the Tolbert group s synthesis method. They described the creation of dispersible fct-fept nanoparticles in hexane by coating the nanoparticles in magnesium oxide, MgO. The MgO coat prevents aggregation, although Kim et al. did notice sintering at 800 C after six hours exposure.[16] EXPERIMENTS This work aims to assess the properties of the FePt phases dynamically as a function of temperature in order to better prepare hard disk drive engineers to manipulate this material. As such, we propose to observe FePt response to temperature in situ by heating it with graphene in the Titan Transmission Electron Microscope (TEM). 26

27 in situ TEM Experiments by other Groups This section explores other in situ TEM work on FePt. The two main papers are the 2012 Delalande et al. paper titled, L1 0 Ordering of Ultrasmall FePt Nanoparticles Revealed by TEM in situ Annealing and the 2006 Kawai et al. paper titled In Situ Observation of Ordering Process in FePt Films During Annealing in a Transmission Electron Microscope. The other papers, references [22], [30], and [31], support those papers. Reference [11] refers to a conference abstract concerning self-organized FePt nanowires in TEM. The conversion did not work very well, partly because the particles were near the ordering size limit. Delalande et al. observed uncoated 4nm-diameter FePt nanoparticles transition from fcc to fct in the TEM using in situ heating. They verified a transition temperature of 500 C, as reported by others. They believe that the rate of atomic diffusion dominates the ordering process. Their results reflect this as well. They present a sequence of images of different particles taken at time intervals of 7, 17, and 35 minutes at 550 C clearly illustrating that ordering begins on the edges of the particles and proceeds towards the interior. They showed that the process could be completed in minutes at 600 C. They used an Aduro sample holder capable of heating the sample at a rate of 1000 C per ms. They also showed that ultrasmall (<3 nm) FePt nanoparticles could be fully transformed to the fct state.[8] Kawai et al. explored the fcc fct phase transformation process in FePt 200nmfilms through in situ observation while annealing in TEM in They heated their sample to 450 C using a double tilt holder and measured the temperature with a thermocouple. They used a charged-coupled device (CCD) camera and a digital video tape recording (VTR) system to record in situ observations and record grain growth dynamics in the film. They then converted the movies to a series of 27

28 sequential images at 30fps. Their results include excellent observations of real-time grain growth and clear development of fct phase, shown with nano beam diffraction patterns of the (001) zone from a single grain in the film.[15] Both the Delalande and Kawai papers should be kept on hand for reference. Our Experimental Plan We propose to observe temperature-induced phase transitions in FePt in real time using the Titan Transmission Electron Microscope (TEM). Our work aims to provide hard disk drive developers with a complete understanding of FePt s response to heat. We aim to extend the work of Delalande et al. and Kawai et al. by monitoring the entire transformation of single particle in both real and reciprocal space. We hope to observe the contraction of the c-axis and ordering of Fe and Pt atoms within the lattice as it occurs in real time. We also hope to direct nanoparticle alignment using the magnetic field generated by the TEM s electromagnetic lenses. We will heat the nanoparticles using voltage biased graphene. We expect to use the Debye-Waller Effect in graphene, described previously by this group [27], to track the sample temperature. Thus far, we have made two trips to the TEM, on 29 July and 14 August Both TEM trips reveal several things: 1. Our MgO coats are currently compromised or absent. 2. Fe and Pt may be splitting. 3. Particles exhibit lots of movement, making them difficult to image. 4. Particles aggregate and sinter together. I present here the experimental plan moving forward, developed with Ed White, to address concerns raised by those experiments. 28

29 Control Samples FIG. 6. Atomic resolution TEM image of pure Pt on SiN x membrane of 14 August Sample We wish to observe each of the following samples containing a drop of FePt in the TEM in order to isolate the mechanisms by which (A) Mgo and (B) Fe disappear: - a TEM grid, prepared by Laura Schelhas of the Tolbert Group - a chip, before and after etching with Hydrofluoric acid (HF) using the old Teflon holder to secure the sample - a chip, before and after etching with HF using the new Teflon holder - a chip etched prior to depositing the nanoparticles. Each sample should be imaged in TEM and energy dispersive spectroscopy (EDS) should be performed, both on and off the graphene sample. On 14 August, the iron and platinum separated so that chucks of iron could be found on the graphene while essentially pure platinum particles were found on the silicon nitride membrane. EDS of figure 6 revealed it to be primarily platinum with little to none iron signature. 29

30 FIG kev Low Magnification TEM image of 14 August Sample, prepared by Brad Parks Checking for Beam Induced Effects Literature search concerning beam-induced effects in FePt did not yield many results. Lai et al. used ion-beam radiation to drive the fcc fct transition in They found that they could cause the transformation to fct using 2 MeV Heion irradiation. They reported that they deliberately changed the beam current to µa/cm2 scale in order to investigate beam heating effects and energy transfer in FePt 30

31 films. They also compared their results against rapid thermal annealing.[20] In 2012, Sebt et al. reported on the electron flow effect in FePt under heat treatment. They claim that at the FePt nanoparticles become bulk-like at the fcc fct transition temperature, alluding to their tendency to aggregate and sinter. Sebt et al. used electron flux to avoid aggregation and limit particle size to nm at 700 C, still much larger than size limits imposed by other methods.[26] Apart from that, I found some papers (references [3], [4], [9], and [35]) on various beam induced effects, largely for ion or electron beams. The highly active nature of the nanoparticles in the TEM makes them difficult to image. We wish to compare their motion under high beam current as we ramp the voltage across the graphene and then under low beam current under the same ramping conditions. Delalande et al. avoided beam-induced complications by taking static images after long time intervals but we wish to observe the transformations in real time.[8] Kawai et al. make no mention of beam-related issues with a 200 kev current.[15] Compounding our interest is a 14 August result. Figures?? and?? show the same pair of platinum nanoparticles. In figure?? shows our first look at these platinum nanoparticles, imaged with 300 kev electrons. Noting the conspicuous absence of a floral MgO coat, we performed EDS on the pair having condensed the beam on the pair. When we returned to imaging mode, we found that the two particles had sintered together as seen in figure??. We have observed other sintering in our nanoparticles as well, on both the 29 July and 14 August trips. As explained by Kim et al., the MgO coat is intended to prevent sintering behavior while the nanoparticles anneal. However, Kim et al. have observed sintering at 800 C after six hours of exposure.[16] While we don t have six-hour exposure times, we may be working at sufficiently high temperature. Our goal on the 29 July trip was to melt the nanoparticles. One video (movie 8) suggests that we may have at least 31

32 (a) Distinct Pt nanoparticles (b) The same pair of Pt nanoparticles, sintered moments later FIG. 8. A pair of Pt nanoparticles sinters under the TEM s condensed electron beam partially succeeded. On 14 August, we examined the diffraction pattern of a group of particles (movie 5) while biasing the graphene with 2.2V. Figure 9 shows a series of stills of the diffraction pattern from the movie. The diffraction peaks corresponding to FePt rotate in circles at constant radius from the pattern s center, suggesting surface melting. Both of these results may explain the sintering behavior. Another likely explanation supported by observation is damage to the MgO coat. Figure 10 is a still from movie 4 from 14 August. Notice the chewed up appearance of the surface around the dark nanoparticles. The control samples described previously are designed, in part, to address the integrity of the MgO coats. The nanoparticles in figure 10 began to move around quickly on the surface of the sample as we ramped up the voltage across the graphene. 32

33 (a) (b) (c) Intial Note shift in peaks Peaks have rotated again FIG. 9. Stills from the diffraction of multiple FePt nanoparticles on heated graphene substrate 33

34 FIG. 10. Still from TEM video of nanoparticle movement when heated. Note the damaged MgO coats. Proposed Experiment First, we intend to observe a single FePt nanoparticle coated with MgO as it transitions from fcc to fct under the thermal influence of the graphene substrate. Next, we intend to melt it down and observe the recrystallization process. We would also like to explore the importance of integrity in the MgO coat in sintering prevention. Finally, we hope to experimentally verify Raoult s Law at the atomic scale. Movie 8 from the 29 July TEM trip shows a single nanoparticle shrinking as we increased the voltage bias across the graphene. First, the particle s surrounding material, pos- 34

35 sibly a damaged MgO coat, disappears. Compare figures 11(a) and 11(b). Then, the particle suddenly shrinks noticeably to a new, smaller size, as revealed by comparing figures 11(c) and 11(d). While further modeling and experiment are required, this process agrees with the model depicted in figure 5 for iron loss as a function of time. Perhaps we can control a nanoparticle s composition by modulating its temperature. To this end, the diffraction ring radii falling within the first three orders of graphene rings for FePt3 and Pt are included in Appendix B. (a) Initial nanoparticle (b) Surface around the nanoparticle disappears (c) Nanoparticle: Before shrinking (d) Nanoparticle: After shrinking FIG. 11. Stills from 29 July movie 8 showing the shrinking nanoparticle. 35

36 ACKNOWLEDGMENTS Thank you so much to the Regan Lab of UCLA: Chris, Ed, Billy, Alex, Gavin, Jared, Brad and Grant. Many thanks also to Dr. Francoise Queval and the Physics and Astronomy Department of UCLA. Finally, I am forever grateful to the National Science Foundation for sponsoring this work. APPENDIX Appendix A lists the atomic form factors of Fe and Pt at the energies used in the TEM. Appendix B records the diffraction ring radii by allowed plane for fcc and fct FePt, FePt 3, and Pt. Planes are given with respect to the conventional cell and ordered according to increasing radii. A: Atomic Form Factors for Diffraction Calculations Under construction B: Calculated Radii of Diffraction Rings in fcc and fct FePt, FePt 3, and Pt Calculations performed using MATLAB program SirriDiffraction.m. 36

37 Plane fcc FePt (nm 1 ) fct FePt (nm 1 ) FePt 3 (nm 1 ) Pt (nm 1 ) (0 0 1) 16.6 (1 1 0) 23.0 (1 1 1) (2 0 0) (0 0 2) (2 0 1) 36.5 (1 1 2) 40.4 (2 2 0) 46.0 (2 0 2) (2 2 1) 48.9 (3 1 0) 51.5 (3 1 1) (1 1 3) (2 2 2) TABLE VI. Calculated Diffraction Ring Radii for fcc and fct FePt, FePt 3, and Pt hherde@wellesley.edu [1] [2] html 37

38 [3] Abes et al (2003) - Effect of Ion Irradiation on the Structural and Magnetic Properties of Sputtered CoPt Alloy. Materials Science and Engineering C 23 (2003) [4] Alloyeau et al (2009) - Size and Shape Effects on the Order-Disorder Phase Transition in CoPt Nanoparticles. Nature Materials 2009 Vol: 8(12): [5] Artemev et al. (2010) - Influence of Atomic Ordering on the Magnetic Properties of FePd, FePt, and Fe 50 Pd 50x Pt x Alloy Films. Bulletin of the Russian Academy of Sciences: Physics, 2010, Vol. 74, No. 8, pp [6] Bagaria et al. (poster, University of Alabama, 2005) - Curie Temperature Measurements of Disordered fcc-fept Nanoparticles. uploads/2010/07/fall2005_50.pdf [7] Chen et al. (2007) - Microstructure and Direct Ordering of FePt Nanoparticles Produced by Nanocluster Beam Technology. Nanotechnology 18 (2007) (6pp) [8] Delalande et al (2012) - L1 0 Ordering of Ultrasmall FePt Nanoparticles Revealed by TEM In Situ Annealing. J. Phys. Chem. C, 2012, 116 (12), pp [9] Diaz-Droguett et al (abstract, 2008 European Microscopy Conference) - Electron Beam-induced Effects on Copper Nanoparticles- Coarsening and Generation of Twins. EMC 2008, Vol. 2: Materials Science, pp [10] Elkins et al. (2005) - Monodisperse Face-Centred Tetragonal FePt Nanoparticles with Giant Coercivity. J. Phys. D: Appl. Phys. 38 (2005) [11] Garel et al (Abstract, 2012 European Microscopy Conference) - Phase Transitions of Self-Organized FePt Nanoparticles Studied by TEM. /documents/abstracts/abstracts/emc2012_0955.pdf [12] Hovorka et al. (2012) - The Curie Temperature Distribution of FePt Granular Magnetic Recording Media. Appl. Phys. Lett. 101, (2012) [13] Inaba (2010) - The FePt L1 0 Phase Transformation in Thin Films Using Multiple Laser Pulsing. J. Appl. Phys. 107, (2010) 38

39 [14] Kang et al. (2007) - Microstructures and Magnetic Alignment of L1 0 FePt Nanoparticles. J. Appl. Phys. 101, 09J113 (2007) [15] Kawai et al (2006) - In Situ Observation of Ordering Process in FePt Films During Annealing in a Transmission Electron Microscope. J. Appl. Phys. 99, (2006) [16] Kim et al. (2009) - Dispersible Ferromagnetic FePt Nanoparticles. Adv. Mater. 2009, 21, [17] Kittel, Charles. Introduction to Solid State Physics. 7th ed. New York, NY u.a.: Wiley, Print. [18] Klemmer et al. (2002) - Structural Studies of L1 0 FePt Nanoparticles. Appl. Phys. Lett., Vol. 81, No. 12, 16 September 2002 [19] Laughlin et al. (2005) - Crystallographic Aspects of L1 0 Magnetic Materials. Scripta Materialia 53 (2005) [20] Lai et al (2006) - Effects of Ion-Beam Irradiation on the L1 0 Phase Transformation and their Magnetic Properties of FePt and PtMn films. Mater. Res. Soc. Symp. Proc. Vol. 887, Materials Research Society 2006 [21] Medwal et al. (2013) - Temperature-Dependent Magnetic and Structural Ordering of Self-Assembled Magnetic Array of FePt Nanoparticles. J Nanopart Res (2013) 15:1423 [22] Miyazaki et al (2005) - Size Effect on the Ordering of L1 0 FePt Nanoparticles. Phys Rev B 72, (2005) [23] Rong et al. (2006) - Size-Dependent Chemical and Magnetic Ordering in L1 0 FePt Nanoparticles. Adv. Mater. 2006, 18, [24] Rong et al. (2007) - Curie Temperatures of Annealed FePt Nanoparticle Systems. J. Appl. Phys. 101, 09K [25] paving-the-way-for-big-hard-drive-capacity-gains/ 39

40 [26] Sebt et al (2012) - The Effect of Electron Flow on FePt Nanoparticles under Heat Treatment. Phys. Scr. 85 (2012) (5pp) [27] Shevitski et al. (2013) - Dark-Field Transmission Electron Microscopy and the Debye- Waller Factor of Graphene. Phys. Rev. B 87 (2013) [28] Singer et al. (2011) - Single-color pyrometry of individual incandescent multiwalled carbon nanotubes. Phys. Rev. B 84, (2011) [29] Sun et al. (2000) - Monodisperse FePt Nanoparticles and Ferromagnetic FePt Nanocrystal Superlattices. Science Vol 287, 17 March 2000 [30] Takahashi et al (2002) - Ordering Process of Sputtered FePt Films. [31] Takahashi et al (2004) - Size dependence of ordering in FePt nanoparticles. J. Appl. Phys. 95, 2690 (2004) [32] Thomson et al. (2004) - Structural and Magnetic Model of Self-Assembled FePt Nanoparticle Arrays. SLAC-PUB-10450, May 2004 [33] Varaprasad et al. (2013) - Temperature-dependent magnetic and structural ordering of self-assembled magnetic array of FePt nanoparticles. JOM, Vol. 65, No. 7, 2013 [34] Whang et al. (1998) - Ordering, Deformation, and Microstructure in L1 0 Type FePt. Acta mater. Vol. 46, No. 18, pp , 1998 [35] Whoel et al (2012) - Experimental Procedures to Mitigate Electron Beam Induced Artifacts during in situ Fluid Imaging of Nanomaterials. Ultramicroscopy 127 (2013) [36] Zhang et al. (2012) - Synthesis and Characterization of FePt Nanoparticles and FePt Nanoparticle/SiO 2 -Matrix Composite Films. J Sol-Gel Sci Technol (2012) 64: