NANoSTRUCTURED MATERIALS VOL. 2, PP. 545-552, 1993 0965-9773/93 $6.00 + .00 COPYRIGHT ©1993 PERGAMON PRESS LTD. ALL RIGHTS RESERVED. PRINTED IN THE USA

H A L L - P E T C H R E L A T I O N IN N A N O C R Y S T A L L I N E

F e - M o - S i - B A L L O Y S

X.D. Liu, Z.Q. Hu and B.Z. Ding State Key Lab. of RSA, Institute of Metal Research, Academia Sinica,

Shenyang 110015, People's Republic of China

(Accepted June 1993)

Abstract---Polycrystalline alloys with grain sizes of 15-200 nm were synthesized by crystallization of an amorphous Fe-Mo-Si-B alloy. Results showed that an inverse Hall-Petch relation between the microhardness and the average grain size is observed when the average grain

size D is less than 45 nm; whereas a normal one is obtained when D is larger than 45 nm. Positron lifetime results indicated that nanovoids in the interfaces greatly influence the magnitude of microhardness of nanocrystalline Fe-Mo-Si-B alloys at D < 45 nm.

INTRODUCTION

Recently, a new category of materials, called nanocrystalline materials, containing ultrafine grains sized from 1 to 100 nm have been developed by Gleiter and his collaborators (1). The tiny crystals give rise to a huge number of interfaces in these materials, which distinguishes them from normal coarse-grained pt)lycrystalline materials or amorphous glasses. Many macroscopic prop- erties of nanocrystalline materials are, therefore, determined by the interfacial structure and properties, and show strong grain size dependence. One of the most significant changes resulting from a reduction in the grain size to the nanometer level is an increase in the strength and hardness, which has been interpreted in terms of the Hall-Petch relationship, ~ = t~o + Kd -l j2 or Hv = Hvo + K'd-1/2 . During the last three years, there have been several reports on the variation of hardness with grain size in nanocrystalline metals or alloys; for example, Cu (2-3), Pd (2-4), Fe (5), Ni (6), Ag (7), TiO2 (8) and Ni-P (9) alloy. Interestingly, an inverse Hall-Petch relation between the microhardness and the average grain size has been reported in Ref. (2, 9.), i.e., microhardness decreases with the reduction of grain size. So far, nanocrystalline materials have been generated by using inert gas condensation (10), ball-milling (11), severe torsional plastic deformation (12), etc. A new method for directly preparing bulk nanocrystalline materials was recently proposed by Lu et al. (13), based on the crystallization of amorphous solids, named the crystallization method. That is, upon heating the amorphous ribbons, wires or powders, crystallites will nucleate and grow within the amorphous matrix. The grain size in the products can be easily controlled by different annealing procedures.

Nanocrystalline Fe-Mo-Si-B alloys, prepared by using the crystallization method as discussed above, are the concern in this paper. Their mechanical properties are presented, and related to the positron lifetime results.

545

546 XD Llu, ZQ Hu ANt) BZ DING

EXPERIMENTAL PROCEDURES

Sample Preparation

Amorphous (Feo.99Moo.01)78Si9B13 (at.%) ribbons with 3-5 mm width and about 27 ~m thickness were prepared by melt spinning. The subsequent annealing treatments, whereby nanocrystaUites are developed, were carried out under an argon atmosphere in a tubular furnace with a temperature stability of+ 3.0 K. The procedures are as follows: 1. The furnace was heated to the required temperature in advance; 2. After finishing annealing the as-annealed samples were extracted immediately from the furnace.

Structure and Property

The as-annealed samples were monitored by x-ray diffraction (XRD, on a Rigaku x-ray diffractometer, Cu Kot radiation) and by transmission electron microscopy (TEM, on a Philips EM 420 microscope) to identify the crystallization phases, as well as to observe the grain morphologies and grain sizes.

A fast-fast coincidence ORTEC system with a 22Na source was employed to record the positron lifetime spectra of the as-quenched and as-annealed samples. The Na source was sandwiched between two stacks of ribbon samples. Each stack is five-layer thick (three pieces in each layer). The measurements of positron lifetimes were conducted at room temperature.

The microhardness Hv measurements were made on a microhardness tester using the pyramidal indenter with a load of 50 g and a test time of 10 s. The samples were polished to remove the flaws in the surfaces before the test.

" ~ e x o

i.,.,.

!

520 620 I

720 T,K

I

820 920

Figure 1. Dynamic DSC curve of the as-quenched Fe-Mo-Si-B alloy at a heating rate of 20 K/min.

HALL-PETCH RELATION IN NANOCRYSTALLINE Fe-Mo-Si-B ALLOYS 547

RESULTS

Two crystallization steps were observed upon heating Fe-Mo-Si-B glass on a differential scanning calorimeter (Perkin-Elmer, DSC-2) at a heating rate of 20 K/min, as in Figure 1. The peak temperatures are 841.0 (Tpl) and 858.0 K (Tp2), respectively. The subsequent crystallization annealing of the as-quenched ribbons was performed at 833-1023 K for I h.

The as-annealed samples were characterized by XRD as shown in Figure 2. The fully crystallized state was verified for all as-annealed samples. From Figure 2, it is very clear that, at 833-913 K, four crystalline phases precipitate. They are (Fe,Mo)3B (bet), (Fe,Mo)23B6 (fcc) and Fe2B (bct) borides, as well as a-Fe(Mo,Si) (bcc) solution. Moreover, with increasing annealing temperature, transformation from metastable (Fe,Mo)23B6 and (Fe,Mo)3B phases into a -Fe and Fe2B occurs, manifested by an increase in the intensities of a-Fe and Fe2B diffraction lines and a simultaneous decrease in the intensities of diffraction lines of the two metastable phases on an XRD pattern (Figure 2b). Due to the co-existence of four crystalline phases inside the crystallized samples, grains of the same structure may be isolated from each other. As a result, grain growth may not occur by short range diffusion of atoms across interfaces, but by a process requiting long range diffusion. This tends to hinder the grain growth, which contributes to keeping the nanocrystalline state. However, no trace of the two metastable phases can be detected at Ta = 1023 K (Figure 2c). At that time, grain growth can occur easily in a possible manner of combining grains of the same structure, as seen by the sharpening of the XRD lines in Figure 2c.

5

3O

I

o.~O ~, o o

0 • A

A 11 " A

CI 0

°° JL_

I I I I I

40 50 60 70 80 20, degree

Figure 2. XRD patterns of the Fe-Mo-Si-B samples annealed at (a) 833 K; (b) 913 K; and (c) 1023 K, for 1 hr.

o ct-Fe (Si,Mo); • (Fe,Mo)23B6; [] (Fe,Mo)3B ; A (Fe,Mo)3Si; [] Fe2B.

548 XD bu, ZQ Hu AND BZ D=NG

TABLE 1 Temperature Dependence of Average Grain Size

Ta,K 833 853 873 893 913 1023

D,nm 15 20 30 45 70 200

By means of the half-maximum width of the broadening XRD lines, the grain size D can be calculated by using the Scherrer equation

= 0.89 k/l]cos0

As analyzed above, four phases appeared in the crystallized samples, leading to an overlapping of diffraction lines and changing of the metastable phases with annealing temperature. Therefore, it was rather difficult to calculate grain size and quantity for every phase. Here, we took the grain size of the t~-Fe(Si,Mo) phase as the average grain size of the sample. Experimental results showed that, after annealing at 833 K for I h, ~Jct-Fe(Si,Mo) Was 15 nm by XRD and D was about 20 nm by TEM observation, as illustrated in Figure 3. The two results are consistent. As Ta > 913 K, was directly determined by TEM. The temperature dependence of average grain size for the crystallized samples are summarized in Table I. Obviously, at elevated temperatures grain growth can occur easily.

Microhardness Hv is closely related to the microstructure of a material. As the nanocrystalline materials are composed of ultrafme particles, which will lead to a large percentage of interfaces, many properties related to the microstructural character are believed to change significantly. For this reason, we measured the relationship between microhardness Hv and the average grain size

of polycrystalline Fe-Mo-Si-B alloys, as shown in Figure 4a. Obviously, at D above ~ = 45 nm, microhardness decreases with increasing in grain size. However, at D below D = 45 nm,

Figure 3. Bright field TEM image of the Fe-Mo-Si-B alloy annealed at 833 K for 1 h.

HALL-PETCH RELATION IN NANOCRYSTALUNE Fe-Mo-Si-B ALLOYS 549

the variation of microhardness with grain size deviates from the above low. This means that there exists a critical grain size, which is 45 nm. At ~ = 45 nm, microhardness is as high as 10.0 + 0.3 GPa, which is about two times the magnitude of that of the amorphous alloy (which is 6.2 + 0.3 GPa).

The Hall-Petch relation (14) is a well-known expression relating the yield stress ~ to the

average grain size ~ of a material, which can be written

Hv = Hvo + f ' D -1/2 (1)

If equation (1) holds, the experimental data normally fall on a straight line with a positive slope

of f '. Figure 4b illustrates the variation of Hv vs ~-1/2. Clearly, two straight lines with both positive and negative slopes are obtained, which can be written as the following linear equations,

Hv (GPa) = 4.28 (GPa) + 36.20 (GPa nmlt2) ~-ir2 (nm-1/2), ~ > 45 nm (2)

= 13.75 (GPa) - 23.77 (GPa nm 1/2) D-lt2(nm-lf2) , D < 45 nm (3)

C~

-,7

0 -l/z, nm-1/z

o o,z o,4 I

10, 0

8,O

10

O 1 °

\ . 1 I I I , z - - I

30 50 90 200 O, nm

Figure 4. Plots of microhardness, Hv, vs the average grain size (a) D, and (b) ~-1/2 for nanocrystalline Fe-Mo-Si-B alloys.

550 XD LIu, ZQ Hu AND BZ DraG

where units for various terms are enclosed within the brackets. Equation (3) reveals that Hall-Petch relationship recorded at large grain sizes cannot be extrapolated to grain sizes of less than 45 nm for polycrystalline Fe-Mo-Si-B alloys. To our knowledge, this is the first report on this kind of material. A similar result was reported by H. Chang et al. (15) on nanocrystalline TiA1 samples produced by the inert gas condensation and consolidation. It is worth mentioning that an inverse Hall-Petch behavior was also found in nanocrystalline Ni-P alloys prepared by the amorphous crystallization (9). Up to now, no satisfactory explanations have been presented for an inverse Hall- Petch behavior.

DISCUSSION

The investigation of Hall-Petch relation in nanocrystalline materials has lately received considerable attention, in that the development of nanostructured materials provides an excellent opportunity to study the deformation mechanism in ultrafme-grained materials. Due to the fact that in an ultrafine-grained material a large number of interfaces exist, for example, in a 5 nm-grained sample the volume percentage of interfaces will be as much as 50%, microhardness may depend not only on the grain size, but other structural parameters, such as grain boundary structure, will influence the magnitude of microhardness Hv. So far, research work on this aspect is still meager.

Positron annihilation (PA) technique is a powerful and promising tool in the study of vacancy-sized defects in solids, and it has been applied to examine the defective structure in nanocrystalline metals and alloys (16,17). It was reported (17) that numerous defects exist in the interfaces of nanophase alloys, and that the subsequent heat lreatment procedures introduce no extra defects to the nanocrystalline alloy produced via amorphous crystallization. Sui et al. (17) concluded that two types of defects, free-volume-sized defect (point defect) and nanovoid (cluster of free volumes), existed in the interface boundaries of nanostructured alloys obtained from the amorphous state. No large voids were observed, and nanovoid was thought to be situated at the intersections of several grains, in which the size is of several missing atoms.

Shown in Table 2 are the positron lifetime components for amorphous and nanocrystalline Fe-Mo-Si-B alloys after the source and background corrections. Clearly, there is only one positron annihilation process in the amorphous sample, i.e. positron annihilation at the quenched-in free volumes. When the nanocrystalline transformation occurs in the amorphous matrix, the positron annihilation behaviors were found to change considerably. Since the grain sizes of the samples listed in Table 2 are much smaller than the mean diffusion length (L += 100 nm) of positrons in a perfect crystal, and no vacancy-like defects were observed in HREM (18), the posilron in the sample may diffuse rapidly across the undisturbed crystals into the interfaces and are Irapped and annihilated in the interface boundaries with high probability. So, the positron lifetimes and their intensities reflect the volume and density of the interfacial defects. From Table 2 it can be seen that the formation of nanocrystaUites within the amorphous matrix leads to a slight decrease of the short-lifetime "q, as well as the development of the intermediate-lifetime'c2. The former may result from the structural relaxation and atomic rearrangement upon crystallization, which means that the point defects in the nanophase alloy have smaller volume than those in the amorphous state, though the point defect in the nanostructured alloy was thought to originate from the quenched-in free volumes in the amorphous (17). The intermediate-lifetime component is normally attributed to positron annihilation at traps, of which the size is several free volumes. With an increase of grain size, the short-lifetime Xl changes slightly. In comparison with "q, x2 and 11/12 change significantly

HALL-PETCH RELATION IN NANOCRYSTALUNE Fe-Mo-Si-B ALLOYS 551

and abnormally with grain size. From 15 to 45 nm, both "c2 and I1/I2 increase with grain size ]5, meaning that nanovoids gather with grain growth at this stage and that the concentration of nanovoid-sized traps declines correspondingly. In reference to (19),"c2 varies from 240 to 290 ps, corresponding to nanovoids containing 5-9 monovacancies. Maximum values of'~2 and 11/I2 were

obtained at D = 45 nm. However, when the average grain size increases further, both "c2 and I1/12 begin to lower, which is similar to that by Sui et al. (17). The long lifetime "c3 and its intensity I3 were ascribed to positrons trapped at very large voids (about 1 pro), which are impossible to exist in the present samples. This conclusion was also supported by TEM observations. Thus, this kind of defects may result from o-Ps formed between the sample and source, etc., instead of within the samples.

The microhardness data of the nanocrystalline Fe-Mo-Si-B alloys are also presented in Table 2 for comparison. It is of great interest that the variation of Hv with grain size exactly conforms with those of'c2 and I1fl2. In the sample with the largest value of I1/12, microhardness reaches the maximum value of 10.0 + 0.3GPa.

As mentioned in Table 2 , two types of interfacial defects, i.e., free-volume-sized (point defect) and nanovoid-sized (free volume cluster) defects, exist in the nanocrystalline Fe-Mo-Si- B alloy. Nanovoids were thought to arise from the aggregation of free volumes during the formation of crystallites and are three dimensional, which lead to large values of'~2. In view of the data in Table 2, one can see that the intensity ratio of the two types of defects 11/I2, which reflects the area ratio of the two types of defects, remarkably affects the magnitude of microhardness Hv of nanocrystalline Fe-Mo-Si-B alloys. The higher the intensity ratio of 11/12, the larger the microhardness. For example, in the case of the 45 nm-grained sample, Ii/12 is as high as 17.0, corresponding to the peak value of Hv (10.0 + 0.3 GPa); whereas at ~ = 15 nm I1/12 is only 10.6, corresponding to much lower value of Hv (8.6 + 0.3GPa). The above result can be explained as follows. In the sample with more nanovoids (which corresponds to lower I1/12) in the interfaces, two adjacent crystallites may be loosely connected, such interfaces possess a poor capacity for plastic deformation upon application of a force. Thus, the sample with relative higher density of nanovoids will give rise to a lower value of microhardness Hv. From the above analysis, it can be concluded that an inverse Hall-Petch relation between Hv and the average grain size D (as shown

in Figure 4b) is due to the fact that at D < 45 nm the reduction in grain size leads to the development of relatively more nanovoids in the interfaces ofnanocrystallineFe-Mo-Si-B alloys, i.e., nanovoids

TABLE 2 PA Results for the As-quenched and Crystallized Samples

SAMPLE

AM

15-Nano

30-Nano

45-Nano

70-Nano

xt,ps

151.2 ± 0.4

139.4 ± 1.5

137.5 + 1.2

137.3 ± 1.3

138.1 + 1.3

"C 2,ps

240 ±12

258 ± 10

282 + 12

272 + 10

IdI2 ~3, ps 13 Hv, GPa

1386±210

10.6 1582 ± 100

15.5 1581 ± 134

17.0 1587 + 143

11.4 1605 ± 136

1.33±0.1

1.25±0.1

1.21±0.2

1.36±0.1

1.21±0.2

6.2±0.3

8.4±0.3

8.6±0.3

10.0±0.3

8.6±0.3

552 XD L=u, ZQ Hu AND BZ D~NG

are dominant. At D > 45 nm, the grain growth will give rise to a shrinkage of interface boundaries, which is expected to be detrimental to microhardness Hv. At that time, grain size may be dominant. Investigation of an abnormal change of the volume and density of nanovoids observed at D < 45 nm in the present alloy system is in progress.

CONCLUSIONS

A critical phenomenon was found in the variation of microhardness, Hv, with respect to the average grain size, D, in polycrystalline Fe-Mo-Si-B alloys. The critical grain size is 45 nm. At this point, Hv is as high as 10.0 + 0.3 GPa. Above it, a normal Hall-Petch relation between Hv and D was obtained; whereas, below it, an inverse one was observed. Positron lifetime results show that the density ratio of the two types of defects exerts considerable influence on the magnitude of microhardness, Hv. It was found that the sample with more nanovoids exhibits a low magnitude of microhardness, Hv, especially as the average grain size is less than 45 nm.

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