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Effect of ion irradiation on dielectric and mechanical characteristics of ErFeO3 single crystals
Nuclear Instruments and Methods in Physics Research B 234 (2005) 494–508 www.elsevier.com/locate/nimb
Effect of ion irradiation on dielectric and mechanical characteristics of ErFeO3 single crystals Monita Bhat a, Balwinder Kaur a, Ravi Kumar b, K.K. Bamzai a, P.N. Kotru a,*, B.M. Wanklyn c a
Crystal Growth and Materials Research Laboratory, Department of Physics and Electronics, University of Jammu, Jammu 180006, India b Nuclear Science Centre, New Delhi 110067, India c Department of Physics, Clarendon Laboratory, Oxford University, Oxford OX1 3 PU, UK Received 30 June 2004; received in revised form 17 January 2005 Available online 23 March 2005
Abstract Results of 50 MeV lithium ion irradiation on mechanical and dielectric behaviour of flux grown erbium orthoferrite crystals are reported. It is shown that indentation induced VickerÕs hardness number decreases on irradiation whereas the length of crack induced on indentation increases. Other mechanical parameters including fracture toughness, brittleness index and yield strength are calculated for un-irradiated and irradiated crystals. The change in the values of dielectric constant, dielectric loss and conductivity with temperature and frequency of the applied a.c. field in the range of 1 kHz–10 MHz after irradiation is reported. The dielectric constant versus temperature shows relaxor type of behaviour, irrespective of whether the sample is exposed to ion irradiation or not. 2005 Elsevier B.V. All rights reserved. PACS: 61.80.J; 62.20. M; 77.22.Gm Keywords: ErFeO3 Crystals; Dielectric; Microhardness; Conductivity; Ion irradiation
1. Introduction The modifications induced by using swift heavy ion (SHI) irradiation in magnetic oxides including *
Corresponding author. Tel./fax: +91 191 245 3079. E-mail address: [email protected] (P.N. Kotru).
ferrites is a field of recent interest due to its fundamental importance [1–3]. During SHI irradiation the main parameters for consideration are the electronic stopping power (dE/dx)e, the fluence and the ion velocity. To generate columnar amorphization in the materials, certain threshold value, Seth of electronic energy loss is required. Depending
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.01.119
M. Bhat et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 494–508
on the ion species and its energy, nuclear or electronic loss dominates. The swift heavy ion (SHI) irradiation of solid is known to create controlled point/clusters and columnar defects in materials, which are helpful to establish strain in materials [4–7]. Such type of changes in the materials brought about by irradiation are known to modify the physical and structural properties of the materials. Irradiation with swift heavy ions gives extra tool over the controls on some specific properties of the materials. In the present case, single crystals of ErFeO3 were irradiated with 50 MeV Li3+ ions, which are capable of generating only the point/ clusters of defects. Orthoferrites have the general formula RFeO3 where R is a large trivalent metal ion, such as a rare earth or an Yttrium (Y) ion. They crystallize in a distorted perovskite structure with an orthorhombic unit cell [8]. The high degree of symmetry of these compounds makes them suitable for investigation of their magnetic, optical, mechanical and dielectric properties [9,10]. Rare earth orthoferrite RFeO3 crystals are antiferromagnetic with a weak superboard ferromagnetism and are of both scientific and technical interest in optico-magneto storage, logic events, memory based devices and other related applications [11]. The knowledge of SHI radiation effects on mechanical and dielectric characteristics and modifications caused by the irradiation on the crystals is important from the viewpoint of their technical utility. The microhardness is a mechanical parameter which is strongly related to the structure and composition of the crystalline solids. Microhardness testing is one of the best methods for understanding the mechanical properties of materials such as elastic constants [12], yield strength [13], plasticity [14], hardness anisotropy [15], creep behaviour [16] and fracture behaviour [17]. Indentation induced hardness of erbium orthoferrite crystals has been reported by Sharma et al. [18]. In the present case, authors report the modifications and changes caused due to 50 MeV Li3+ ion irradiation on mechanical and dielectric characteristics of ErFeO3 crystals. The mechanical characteristics include studying effect of lithium ion irradiation on variation of hardness and indentation-induced crack propagation leading to deter-
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mination of the values of fracture toughness and brittleness index. For dielectric characteristics, measurements include dielectric constant and dielectric loss under different frequencies of the applied a.c. field and at different temperatures in the range of 30–550 C on pristine and irradiated crystals of ErFeO3. To the best of our knowledge, there is no such report on the modifications caused by SHI irradiation on microhardness and dielectric behaviour of these crystals.
2. Experimental techniques 2.1. Sample preparation Single crystals of ErFeO3 were grown using PbO–PbF2–B2O3 flux as per the procedure already reported [19]. The addition of B2O3 to the PbO/ PbF2 mixture results in a great improvement in crystal quality and size and twinning is greatly reduced. The major faces developed in these crystals are (1 1 0) and (0 0 1) planes [20]. The grown crystals were thinned to their required sizes according to the range of ion irradiation calculated using SRIM-98 code [21]. 2.2. Indentation tests The selected smooth as-grown surfaces of the crystal were subjected to the static indentation tests at room temperature using a VickerÕs microhardness tester (mhp-100) attached to a large incident light microscope (Neophot-2 of Carl-Zeiss, Germany). Loads ranging from 0.098 to 0.98 N were used for making indentations, keeping time of indentation constant at 10 s in all cases. At least five indentation marks were obtained on each face for the same load, the distance between consecutive marks being kept more than three times the diagonal length of the indentation mark. The diagonal lengths of the indentation mark and crack length were measured, using the micrometer eye-piece at a magnification of ·500. The microhardness value [22] was calculated using the equation, H v ¼ 1:8544P =d 2 N=m2 ;
ð1Þ
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where Hv is the VickerÕs hardness number, P is the applied load (N) and d is the average diagonal length (m) of the indentation mark. 2.3. Experimental error The error on Hv is calculated using the formula, 2
2
DH v ¼ 1:8544½ðDP =yÞ þ ðP DyÞ =y 4
1=2
;
ð2Þ
where y = d2 and Dy = 2dDd; DP, Dy and Dd being errors in P, y and d, respectively.
2.5. Irradiation of samples These crystals were then irradiated with 50 MeV Li3+ ion with fluence value of 5 · 1013 ions/cm2 using 15UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The range of 50 MeV Li3+ ions is calculated using TRIM/ SRIM-98 calculation. The microhardness and dielectric studies were performed on irradiated samples using the above mentioned techniques.
3. Results and discussion 2.4. Dielectric measurements Single crystals of ErFeO3 of desired size were selected for dielectric measurements. Silver paint supplied by Eltecks Corporation, Bangalore was applied on the opposite (1 1 0) faces to make a capacitor for investigation. The sample was then mounted in a specially designed two-terminal sample holder made of stainless steel. The dielectric measurements carried out in the frequency range 103–107 Hz and temperature range 30–550 C, were recorded with the help of an impedance analyzer (LF-4192A model, manufactured by Hewlett Packard (USA)) and further automated in our laboratory by using a computer for data recording, storage and analysis and microprocessor-based furnace. The values of capacitance (C) and dielectric loss (tan d) are read directly from two display panels of the instrument. Knowing the values of capacitance, dielectric constant e 0 was calculated using the relation, e0 ¼ Ct=e0 A ¼ Ct=8:85 10 12 A;
ð3Þ
where C, t and A represent capacitance, sample thickness (in m) and area of the crystal face (m2) respectively. Using the values of dielectric constant e 0 and dielectric loss (tan d), the values of conductivity r were calculated with the help of the following relation: r ¼ x0 e0 e0 tan d;
ð4Þ
where e0 = 8.85 · 10 12 Fm 1, x0 = 2pf, f being the frequency in hertz.
The mechanical and dielectric behaviour of ErFeO3 crystals were studied for both un-irradiated (UIR) and irradiated (IR) crystals and the results are described as follows: 3.1. Load dependence of hardness Fig. 1 shows the variation of microhardness with applied load for both un-irradiated and irradiated single crystals of ErFeO3. The microhardness decreases non-linearly as the applied load increases from 0.098 to 0.98 N for both UIR and IR crystals. The values of microhardness are in quite agreement with already reported values of un-irradiated ErFeO3 crystal [18]. However, it is observed that after irradiating with 50 MeV Li3+ ion beam, the value of Vickers microhardness Hv corresponding to each load decreases. This decrease is not marginal as is very clear from the data available in Table 1. This decrease in the value of microhardness for irradiated crystals is attributed to certain types of amorphization occurring in the material. Tagomori and Iwase [23] and Kuromoto Jr. et al. [24] associate the decrease in enamel microhardness to the presence of deep cracks and to surface fragility for laser irradiated enamel. The relations between load P and diagonal length d are proposed in the literature as follows: Kick’s relation [25];
P ¼ K 1d n;
ð5Þ
where K1 is the standard hardness constant and n is the MeyerÕs index which equals 2 for all indenters and for all geometrically similar impressions.
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creases as the load increases. In low-load regions, the resistance offered by the material may be comparable with the applied load, resulting in a higher value of hardness since indenter penetrates only surface layers. However, at higher loads, the plastic flow of the material may be greater and hence the resistance offered by the material is negligible, thus decreasing the hardness [27]. This type of behaviour is also reported and favoured by several authors [28–31] on the basis of depth penetration of the indenter. Hays and KendallÕs [32] relation is, P W ¼ K 2d 2;
Fig. 1. Graph showing dependence of Hv on applied load for un-irradiated (UIR) and irradiated (IR) crystals.
where K2 is a constant and n = 2 is the logarithmic index. It is based on the assumption that as the load is applied to a specimen, it is partially affected by a smaller resistance pressure W, which is a function of the material being tested and represents the minimum applied load to produce an indentation; load less than W not allowing any plastic deformation. In order to evaluate the function W for a particular solution, Eqs. (5) and (6) may be subtracted to yield W ¼ K 1d n K 2d 2;
Table 1 Difference in the microhardness values of un-irradiated (UIR) and irradiated (IR) ErFeO3 single crystals Load (g)
Load (N)
(Hv)UIR (MPa)
(Hv)IR (MPa)
DHv (MPa)
10 20 30 40 50 60 70 80 90 100
0.098 0.196 0.294 0.392 0.49 0.588 0.686 0.784 0.882 0.98
12923.11 11487.21 10372.29 9771.26 9318.06 8810.10 8652.95 8602.66 8651.01 8643.58
11358.20 10096.18 9077.105 8495.83 8048.99 7732.39 7527.33 7417.60 7391.93 7443.71
1564.91 1391.03 1295.19 1275.43 1269.06 1077.71 1125.62 1185.06 1259.07 1199.87
The equation suggests Hv to be independent of load. That is not true in the present case. In the case of ErFeO3 crystals, values of n are 1.75 and 1.74 for both un-irradiated (UIR) and irradiated (IR) crystals. This supports the concept of Onitsch [26] that for n < 2, the microhardness number de-
ð6Þ
ð7Þ
and d n ¼ K 2 =K 1 d 2 þ W =K 1 :
ð8Þ
A plot of log P against log d for both un-irradiated as well as irradiated samples, (Fig. 2) according to Eq. (5) gives the values of n and K1. K2 and W are calculated from a graph between dn versus d2 as shown in Fig. 3. The values of these constants have been determined by using method of least square fitting using a software program in Fortran language. A plot of log (P W) versus log d as shown in Fig. 4 yields the value of n ffi 2, thereby suggesting the validity of the theory involving concept of resistance pressure (W) proposed by Hays and Kendall for both un-irradiated as well irradiated samples. The data on n, K1, K2 and W thus determined for an un-irradiated and irradiated ErFeO3 crystal is given in Table 2. The application of Hay and KendallÕs law leads to a modified formula of Eq. (1) which gives load independent values of Hv, H v ¼ 1:8544ðP W Þ=d 2 :
ð9Þ
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Fig. 2. A graph of log P versus log d for un-irradiated (UIR) and irradiated (IR) crystals.
Substituting for (P W) from Eq. (6), we have H v ¼ 1:8544K 2 :
Fig. 3. Graph of d n versus d 2 for un-irradiated (UIR) and irradiated (IR) crystals.
thus given are very close to the values calculated on application of Hays and KendallÕs law.
ð10Þ
In the light of this equation, the ‘‘load independent microhardness values’’ for un-irradiated and irradiated crystals are H v ðUIRÞ ¼ 8346 MN=m2 ; H v ðIRÞ ¼ 7162 MN=m2 : This clearly shows that microhardness values decrease after irradiation. One may notice from Fig. 1 that Hv has a rapid fall as the load is increased from 0.098 to 0.98 N. Beyond 0.69 N, the microhardness value achieves saturation and becomes load independent. From the data given through Table 2 as well as the curves, the load independent value of ErFeO3 is around 8650 MN/m2 and 7500 MN/m2 for un-irradiated and irradiated ErFeO3 crystals which is achieved at loads P 0.69 N. The load independent values
3.2. Fracture toughness, brittleness index and yield strength The term toughness may be defined as the property of a material by virtue of which it can absorb maximum energy before fracture takes place. The importance of toughness is in the selection of a material where load exceeds the elastic limit or yield point. The indentation impressions are usually seen associated with cracks at almost all loads on both the un-irradiated and irradiated crystals. However, it is observed that the crack length in case of irradiated crystals is larger than that of the un-irradiated crystals as can be clearly judged from Fig. 5. Thus, presence of deep cracks confirms the decrease in microhardness of the irradiated samples [23].
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Fig. 4. Graph of log (P W) versus log d for un-irradiated (UIR) and irradiated (IR) crystals.
The resistance to fracture indicates the toughness of a material. The cracks developed in a crystal determine the fracture toughness Kc, which in term tells us how fracture stress is applied on a uniform loading. According to Ponton and Rawlings [33], two types of crack systems can develop in a material as a result of indentation. These are radial-median and palmqvist crack systems. Transition from palmqvist to median cracks occurs at a well-defined value [34] of c/a, c being the crack length measured from the centre of the indentation mark to the crack end and a is half the diagonal length of the indentation mark. For c/a P 2.5, the cracks developed are median cracks as shown
499
Fig. 5. Variation of crack length with load for un-irradiated (UIR) and irradiated (IR) crystals.
in Fig. 6(a) and fracture toughness Kc is calculated using the relation [18,33], K c ¼ kP =c3=2 ;
ð11Þ
where the constant k = 1/7 for the Vickers indenter. For c/a < 2.5, the cracks formed during indentation have the configuration of palmqvist cracks as shown in Fig. 6(b) and the fracture toughness may be calculated using the relation [33], K c ¼ kP =al1=2 ;
ð12Þ
where l = c a is the mean palmqvist crack length.
Table 2 Results of microhardness measurements for un-irradiated (UIR) and irradiated (IR) single crystals of ErFeO3 Samples
nk ± Dnk
log K1
K1 (M N/m2)
W (N)
K2 (M N/m2)
Hv = 1.8544 · K2 (M N/m2)
nh ± Dnh
Un-irradiated Irradiated
1.74 ± 0.12 1.72 ± 0.12
2.04 2.07
9019.03 8441.31
0.038 0.042
4500.77 3862.27
8346.22 7162.19
1.91 ± 0.17 1.89 ± 0.17
nk represents value of n on application of Kicks law (P = K1d n). nh represents value of n on application of Hays and KendallÕs law (P W = K1d n).
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2a
2a l
l
2c
c
(b)
(a)
Fig. 6. Geometries of (a) median and (b) Palmqvist crack around Vickers indentation.
In case of both UIR and IR crystals, for a load P 6 70 g (0.69 N) and ratio c/a < 2.5, cracks developed are palmqvist cracks. Eq. (12) is, therefore, used to calculate the fracture toughness Kc. However for P > 70 g (0.69 N), the ratio c/a > 2.5 and hence Eq. (11) is applied in this case for calculating the value of Kc. Table 3 provides data regarding
crack length, nature of cracks, fracture toughness for UIR and IR crystals. From the table, it is clear that the values of fracture toughness decrease after irradiation because of increase in crack length due to amorphization. The nature of variation of Kc with load P for both un-irradiated as well as irradiated ErFeO3 crystals is readily reflected by Fig. 7. The sudden decrease in the value of Kc at loads above 0.6 N for both un-irradiated and irradiated ErFeO3 crystals is clearly seen; the decrease taking place on transition from Palmqvist to median type of cracks. Brittleness is an important property that affects the mechanical behaviour of a material and gives an idea about the fracture induced in a material without any appreciable deformation. The value of brittleness index Bi [11], is calculated using equation, Bi ¼ H v =K c :
ð13Þ
Comparison of data on brittleness index of unirradiated and irradiated crystals leads to interesting results. The brittleness index shows increase in
Table 3 Various values of crack length, fracture toughness, brittleness index and yield strength at different loads for un-irradiated (UIR) and irradiated (IR) ErFeO3 single crystals Hv (MPa)
Crack c
Kc · 106 (N/m
UIR crystal of ErFeO3 10 0.098 20 0.196 30 0.294 40 0.392 50 0.49 60 0.588 70 0.686 80 0.784 90 0.882 100 0.98
12923.1 11487.2 10372.3 9771.26 9318.06 8810.10 8652.95 8602.66 8651.01 8643.58
– 5.23 6.88 8.43 10.20 12.00 13.80 16.30 17.70 19.00
– 6.4 6.42 6.4 6.18 5.95 5.81 1.7 1.69 1.69
IR crystal of ErFeO3 10 0.098 20 0.196 30 0.294 40 0.392 50 0.49 60 0.588 70 0.686 80 0.784 90 0.882 100 0.98
11358.20 10096.2 9077.11 8495.83 8048.99 7732.39 7527.33 7417.60 7391.93 7443.71
– 6.57 8.39 10.20 12.18 14.40 16.10 18.40 20.10 21.50
– 4.93 5.1 5.13 5.02 4.86 4.86 1.42 1.4 1.4
Load
Load in N
3/2
)
Bi (m
1/2
)
Nature of crack
ry (MPa)
– 1794.88 1615.62 1526.76 1507.78 1480.69 1489.32 5060.39 5118.94 5114.54
– Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Median Median Median
4307.70 3829.07 3457.43 3257.09 3106.02 2936.70 2884.32 2867.55 2883.67 2881.19
– 2047.91 1779.82 1656.11 1603.39 1591.03 1548.83 5223.66 5279.95 5316.94
– Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Median Median Median
3786.07 3365.39 3025.70 2831.94 2683.00 2577.46 2509.11 2472.53 2463.98 2481.24
M. Bhat et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 494–508
Fig. 7. Graph of fracture toughness versus load for unirradiated (UIR) and irradiated (IR) crystals.
its value at each load ranging from 0.098 to 0.98 N on irradiation of ErFeO3 crystals. The data is compiled in Table 3 for un-irradiated and irradiated crystals. The dependence of brittleness index on load for un-irradiated and irradiated ErFeO3 crystals is reflected by Fig. 8. The following points are noteworthy: 1. The variation of brittleness index with load is similar for un-irradiated and irradiated crystals, though the value corresponding to each load is different for the two types of samples. 2. As the load increases from 0.098 to 0.98 N, the value of brittleness index decreases with a tendency of achieving saturation at higher loads. However, the value of brittleness index for irradiated ErFeO3 crystal is higher than the un-irradiated one corresponding to each value of load. Thus, irradiation increases the brittleness index of ErFeO3 crystals. 3. There is a sudden jump in the value of brittleness index when the nature of cracks changes
501
Fig. 8. Graph of brittleness index versus load for un-irradiated (UIR) and irradiated (IR) crystals.
from Palmqvist to median type. The transition from Palmqvist to median crack system occurs at loads > 70 g (0.69 N) irrespective of whether the crystal is un-irradiated or irradiated. From the hardness values, the yield strength ry can be calculated [35]. For MeyerÕs index n > 2 the formula applicable is, n 2 Hv 12:5ðn 2Þ ½1 ðn 2Þ : ð14Þ ry ¼ 1 ðn 2Þ 2:9 For n < 2, the above equation reduces to [15], ry ¼ H v =3:
ð15Þ
Since for ErFeO3 crystals n < 2, Eq. (15) can be applied. The values of fracture toughness Kc, brittleness index Bi and yield strength ry in case of UIR and IR crystals are compiled and shown in Table 3. The yield strength also decreases as the load increases in case of both un-irradiated as well irradiated crystals. Since ry is directly proportional to Hv (see Eq. (15)), the dependence of ry on load is similar to that of Hv as is shown in Fig. 9.
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Fig. 9. Dependence of yield strength on load for un-irradiated (UIR) and irradiated (IR) crystals.
3.3. Dielectric properties The variation of dielectric constant e 0 for unirradiated and irradiated ErFeO3 single crystals was studied as a function of an applied a.c. field in the frequency range from 1 kHz to 10 MHz and as a function of temperature in the range of 30–550 C. Figs. 10(a) and (b) shows the dielectric constant as a function of frequency for UIR as well as IR ErFeO3 crystals. At each particular temperature ranging from 30 to 550 C, the dielectric constant shows decrease in its value as the frequency is increased and becomes almost saturated beyond 500 kHz. The decrease in the behaviour of dielectric constant with increasing frequency is the normal behaviour of ferrites and is consistent with the Koops model [36]. After irradiation, at each particular frequency, the value of dielectric constant decreases in the temperature range of 30– 300 C. This decrease in dielectric constant may be due to the decrease in space charge carriers or interfacial polarization in irradiated sample [37]. At 300 C, the values of e 0 for both irradiated
and un-irradiated become almost same whereas above 300 C, the magnitude of e 0 increases for the irradiated crystals as compared to the un-irradiated. This behaviour can be explained on the basis that the mechanism of polarization process in ferrites is similar to that of conduction process. The electronic exchange between Fe ions gives local displacement of electrons in the direction of an applied electric field, which induces polarization in ferrites. The anomaly in the variation of dielectric constant after irradiation is due to the defect creation [38], which results in a collective contribution of p and n type conduction. It is well known that the local displacement of the p type carriers takes part in the polarization in an opposite direction to that of the external field [39,40]. In addition, since the mobility of p type carrier is lower than that of n type carrier, their contribution to polarization decreases more rapidly at lower temperatures thereby reducing the value of e 0 in the case of irradiated samples. After irradiation, below 300 C there is n type conduction and beyond this there is collective contribution of n and p type carriers. The dispersion in the dielectric loss factor (tan d) of irradiated and un-irradiated ErFeO3 samples is shown in Fig. 11. From the figure, it is clear that for low temperatures (6200 C), the dielectric loss is very high in case of un-irradiated samples whereas for higher temperature P300 C, the dielectric loss is higher in case of irradiated sample. The appearance of the peak in the dispersion curves for un-irradiated and irradiated samples satisfies the Koops model and Maxwell–Wagner interfacial polarization. The presence of peaks in the loss factor can be explained on the basis of relative variation of real dielectric constant (e 0 ) and imaginary dielectric constant (e00 ) with frequency [41]. The absence of peak in some curves for tan d in the un-irradiated and irradiated samples may be attributed to the reason that the upper level of frequency used in our studies is too low to show a peak that may occur beyond 10 MHz. The observed variation of dielectric constant with temperature is shown in Figs. 12(a) and (b) for un-irradiated and irradiated ErFeO3 crystals. It was observed that the dielectric constant
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Fig. 10. (a) Dependence of dielectric constant e 0 on frequency at 30–150 C for un-irradiated (UIR) and irradiated (IR) crystals. (b) Dependence of dielectric constant e 0 on frequency at 200–350 C. Inset shows the variation of e 0 with frequency from 400 to 550 C for un-irradiated (UIR) and irradiated (IR) crystals.
increases with increasing temperature, showing anomaly at the transition temperature. The peak height at the transition temperature was observed to decrease with increasing frequency and the dielectric constant peak shifted to lower temperature with increasing frequency, which indicated the relaxational behaviour of the material [42] e.g. for UIR ErFeO3, at 1 kHz the peak value of dielectric constant observed at 480 C is 1284.8 · 103, whereas at, 10 kHz, 100 kHz, 1 MHz, 5 MHz and 10 MHz, the peak values of e 0 as observed at 460, 440, 380, 280 and 260 C are 146.7 · 103, 112.6 · 102, 17.3 · 102, 508.08 and 401.79 respectively. The same anomaly was observed for irradiated crystals of ErFeO3 at 1 kHz; the peak value of dielectric constant being 4070 · 103 at 460 C, whereas at the frequencies of 10 kHz, 100 kHz, 1 MHz,5 MHz and 10 MHz, the peak values of e 0 are 262.26 · 103, 268.75 · 102, 73.4 · 102, 1289.15 and 401.5 as measured at
420, 380, 360, 280 and 220 C respectively. This anomaly is corresponding to a phase change [43], and may be associated to the softening of a vibrational mode called the soft mode [44–47]. For most of the relaxor ferroelectrics, the peak of the dielectric constant shifts to higher temperature with increasing frequency, which has been attributed to decreasing relaxation time with increasing temperature [42]. In case of ErFeO3 crystal, the dielectric constant peak shifts to lower temperature with increasing frequency and seems to be due to the increasing relaxation time with temperature [48]. It is clear from Figs. 12(a) and (b) that there is increase in the value of dielectric constant of irradiated ErFeO3 crystals as compared to the un-irradiated ones at temperatures above 300 C. The drastic increase in dielectric constant is due to ion irradiation which may be correlated to the defects created along the tracks [49] and the structural modifications induced in the surrounding
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Fig. 11. Dependence of the dielectric loss (tan d) on frequency at 30–400 C for un-irradiated (UIR) and irradiated (IR) crystals.
regions [50,51]. By irradiating the crystal with 50 MeV Li3+ ions, the incident heavy ions get embedded in the crystal, lose energy by both the inelastic collisions and the elastic nuclear collisions which are dominant near the end of the range of the implanted ions. The increase in dielectric constant may be due to the disordering of the crystal lattice by the ion beam. Again, for the irradiated samples, there is a shift in the transition peak towards lower temperature for all frequencies. Samara [52] studied this type of shift in the transition temperature using influence of pressure on the dielectric response and phase transitions of PZN-9.5PT. The broad e 0 (T) peaks and strong frequency dispersion on the low temperature side
of the un-irradiated and irradiated samples are the hallmarks of a relaxor phase. Figs. 12(a) and (b) show two transition peaks for the frequencies 1, 10 and 100 kHz and this observation applies to both irradiated as well as un-irradiated samples of ErFeO3 crystals. However, there is only one peak at higher frequencies (P1 MHz), an observation common to both the UIR and IR ErFeO3 crystals. It suggests that the two transition peaks at frequency 6100 kHz and one transition peak at higher frequency >1 MHz is something which is intrinsic to ErFeO3 rather than anything to do with irradiation effects. The higher temperature peak (i.e. the peak above the transition temperature peak) may be due to the space charges getting
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Fig. 12. (a) Plots of the dielectric constant e 0 against temperature at frequencies 1 and 10 kHz for un-irradiated (UIR) and irradiated (IR) crystals. (b) Plots of the dielectric constant e 0 against temperature at frequencies 100 kHz and 1 MHz. Inset shows the variation of e 0 with temperatures at frequencies 5 and 10 MHz for un-irradiated (UIR) and irradiated (IR) crystals.
depleted resulting in a peak at a particular temperature [53]. 3.4. Temperature dependence of a.c. conductivity The plots of a.c. conductivity with temperature of both UIR and IR ErFeO3 crystals are shown in Fig. 13. It is clear from the figure that the conductivity is high for higher frequencies at a given temperature, thus confirming small polaron hopping in the present samples [54–56]. It has been reported that frequency dependence of ra.c is large in ferrimagnetic or in lower temperature region [57]. The same is also observed in case of our samples. The plots are almost linear in the temperature range 100–550 C. Initially, with an increase in temperature, conductivity r seems to remain almost unaffected until 100 C, where the conductivity starts increasing with temperature. The increase in conductivity with temperature is much more at lower frequencies of 6100 kHz, much less at
1 MHz and the least at 10 MHz. The conductivity is observed to be greater at higher frequencies as has been observed in other materials [58–60]. The increased conductivity could be due to a reduction in the space charge polarization at higher frequencies [61]. This is true for both UIR as well as IR samples of ErFeO3 crystals. However, after irradiation, the conductivity decreases in case of irradiated crystals for lower frequencies of 1, 10 kHz, then almost equalizes for 100 kHz and increases at higher frequencies of 1 and 10 MHz because of the conduction mechanism in case of ferrites [62]. This abnormal behaviour after irradiation is attributed to the two types of carriers p and n to the polarization. Since the mobility of p carriers is lower than that of n-carriers, their contribution to polarization will decrease more rapidly at lower frequencies. Thus, we can say that the conduction at lower frequencies is because of n-type carriers only and for higher frequencies (P1 MHz) is due to the collective contribution of p and n type carriers.
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Fig. 13. Variation of conductivity (r) with temperature at different frequencies for un-irradiated (UIR) and irradiated (IR) crystals.
4. Conclusions The irradiation effects of 50 MeV Li3+ ion on mechanical and dielectric properties of ErFeO3 single crystals may be summarized as follows: 1. The microhardness decreases and crack length increases on irradiation. It is attributed to amorphization induced due to irradiation. 2. Irrespective of whether the material is irradiated or not, the microhardness decreases nonlinearly upto 0.686 N and thereafter attains saturation.
3. Single crystals of ErFeO3 show a decreasing trend in the dielectric constant with increase in frequency at all temperatures and almost saturates at higher frequencies which is a normal behaviour of all ferrites. This behaviour is explained on the basis of Koops model for both un-irradiated and irradiated crystals. 4. The variation of dielectric constant with temperature shows anomalous behaviour wherein transition peak shifts towards lower temperature as frequency is increased from 1 kHz to 10 MHz, thereby showing relaxor type of behaviour. After irradiation, the dielectric
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constant e 0 of un-irradiated crystal is relatively larger than irradiated crystal upto 300 C. However, the trend gets reversed after the temperature goes beyond 300 C viz., e 0 for IR crystals is more than UIR ones for temperatures greater than 300 C. Acknowledgements Authors are thankful to the Nuclear Science Centre, New Delhi for providing the ion beam irradiating facility. This work is partially funded by the NSC, New Delhi under UFUP Scheme No. 30312 and forms a part of the Ph.D. programme of one of the authors (MB) under the supervision of Dr. K.K. Bamzai. The author (MB) is thankful to the CSIR for Senior Research Fellowship in the Emeritus Scientist Scheme of the CSIR. The support under ‘‘Emeritus Scientist, CSIR’’ to the corresponding author (PNK) by the Council of Scientific and Industrial Research, New Delhi is duly acknowledged.
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Effect of ion irradiation on dielectric and mechanical characteristics of ErFeO3 single crystals Monita Bhat a, Balwinder Kaur a, Ravi Kumar b, K.K. Bamzai a, P.N. Kotru a,*, B.M. Wanklyn c a
Crystal Growth and Materials Research Laboratory, Department of Physics and Electronics, University of Jammu, Jammu 180006, India b Nuclear Science Centre, New Delhi 110067, India c Department of Physics, Clarendon Laboratory, Oxford University, Oxford OX1 3 PU, UK Received 30 June 2004; received in revised form 17 January 2005 Available online 23 March 2005
Abstract Results of 50 MeV lithium ion irradiation on mechanical and dielectric behaviour of flux grown erbium orthoferrite crystals are reported. It is shown that indentation induced VickerÕs hardness number decreases on irradiation whereas the length of crack induced on indentation increases. Other mechanical parameters including fracture toughness, brittleness index and yield strength are calculated for un-irradiated and irradiated crystals. The change in the values of dielectric constant, dielectric loss and conductivity with temperature and frequency of the applied a.c. field in the range of 1 kHz–10 MHz after irradiation is reported. The dielectric constant versus temperature shows relaxor type of behaviour, irrespective of whether the sample is exposed to ion irradiation or not. 2005 Elsevier B.V. All rights reserved. PACS: 61.80.J; 62.20. M; 77.22.Gm Keywords: ErFeO3 Crystals; Dielectric; Microhardness; Conductivity; Ion irradiation
1. Introduction The modifications induced by using swift heavy ion (SHI) irradiation in magnetic oxides including *
Corresponding author. Tel./fax: +91 191 245 3079. E-mail address: [email protected] (P.N. Kotru).
ferrites is a field of recent interest due to its fundamental importance [1–3]. During SHI irradiation the main parameters for consideration are the electronic stopping power (dE/dx)e, the fluence and the ion velocity. To generate columnar amorphization in the materials, certain threshold value, Seth of electronic energy loss is required. Depending
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.01.119
M. Bhat et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 494–508
on the ion species and its energy, nuclear or electronic loss dominates. The swift heavy ion (SHI) irradiation of solid is known to create controlled point/clusters and columnar defects in materials, which are helpful to establish strain in materials [4–7]. Such type of changes in the materials brought about by irradiation are known to modify the physical and structural properties of the materials. Irradiation with swift heavy ions gives extra tool over the controls on some specific properties of the materials. In the present case, single crystals of ErFeO3 were irradiated with 50 MeV Li3+ ions, which are capable of generating only the point/ clusters of defects. Orthoferrites have the general formula RFeO3 where R is a large trivalent metal ion, such as a rare earth or an Yttrium (Y) ion. They crystallize in a distorted perovskite structure with an orthorhombic unit cell [8]. The high degree of symmetry of these compounds makes them suitable for investigation of their magnetic, optical, mechanical and dielectric properties [9,10]. Rare earth orthoferrite RFeO3 crystals are antiferromagnetic with a weak superboard ferromagnetism and are of both scientific and technical interest in optico-magneto storage, logic events, memory based devices and other related applications [11]. The knowledge of SHI radiation effects on mechanical and dielectric characteristics and modifications caused by the irradiation on the crystals is important from the viewpoint of their technical utility. The microhardness is a mechanical parameter which is strongly related to the structure and composition of the crystalline solids. Microhardness testing is one of the best methods for understanding the mechanical properties of materials such as elastic constants [12], yield strength [13], plasticity [14], hardness anisotropy [15], creep behaviour [16] and fracture behaviour [17]. Indentation induced hardness of erbium orthoferrite crystals has been reported by Sharma et al. [18]. In the present case, authors report the modifications and changes caused due to 50 MeV Li3+ ion irradiation on mechanical and dielectric characteristics of ErFeO3 crystals. The mechanical characteristics include studying effect of lithium ion irradiation on variation of hardness and indentation-induced crack propagation leading to deter-
495
mination of the values of fracture toughness and brittleness index. For dielectric characteristics, measurements include dielectric constant and dielectric loss under different frequencies of the applied a.c. field and at different temperatures in the range of 30–550 C on pristine and irradiated crystals of ErFeO3. To the best of our knowledge, there is no such report on the modifications caused by SHI irradiation on microhardness and dielectric behaviour of these crystals.
2. Experimental techniques 2.1. Sample preparation Single crystals of ErFeO3 were grown using PbO–PbF2–B2O3 flux as per the procedure already reported [19]. The addition of B2O3 to the PbO/ PbF2 mixture results in a great improvement in crystal quality and size and twinning is greatly reduced. The major faces developed in these crystals are (1 1 0) and (0 0 1) planes [20]. The grown crystals were thinned to their required sizes according to the range of ion irradiation calculated using SRIM-98 code [21]. 2.2. Indentation tests The selected smooth as-grown surfaces of the crystal were subjected to the static indentation tests at room temperature using a VickerÕs microhardness tester (mhp-100) attached to a large incident light microscope (Neophot-2 of Carl-Zeiss, Germany). Loads ranging from 0.098 to 0.98 N were used for making indentations, keeping time of indentation constant at 10 s in all cases. At least five indentation marks were obtained on each face for the same load, the distance between consecutive marks being kept more than three times the diagonal length of the indentation mark. The diagonal lengths of the indentation mark and crack length were measured, using the micrometer eye-piece at a magnification of ·500. The microhardness value [22] was calculated using the equation, H v ¼ 1:8544P =d 2 N=m2 ;
ð1Þ
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where Hv is the VickerÕs hardness number, P is the applied load (N) and d is the average diagonal length (m) of the indentation mark. 2.3. Experimental error The error on Hv is calculated using the formula, 2
2
DH v ¼ 1:8544½ðDP =yÞ þ ðP DyÞ =y 4
1=2
;
ð2Þ
where y = d2 and Dy = 2dDd; DP, Dy and Dd being errors in P, y and d, respectively.
2.5. Irradiation of samples These crystals were then irradiated with 50 MeV Li3+ ion with fluence value of 5 · 1013 ions/cm2 using 15UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The range of 50 MeV Li3+ ions is calculated using TRIM/ SRIM-98 calculation. The microhardness and dielectric studies were performed on irradiated samples using the above mentioned techniques.
3. Results and discussion 2.4. Dielectric measurements Single crystals of ErFeO3 of desired size were selected for dielectric measurements. Silver paint supplied by Eltecks Corporation, Bangalore was applied on the opposite (1 1 0) faces to make a capacitor for investigation. The sample was then mounted in a specially designed two-terminal sample holder made of stainless steel. The dielectric measurements carried out in the frequency range 103–107 Hz and temperature range 30–550 C, were recorded with the help of an impedance analyzer (LF-4192A model, manufactured by Hewlett Packard (USA)) and further automated in our laboratory by using a computer for data recording, storage and analysis and microprocessor-based furnace. The values of capacitance (C) and dielectric loss (tan d) are read directly from two display panels of the instrument. Knowing the values of capacitance, dielectric constant e 0 was calculated using the relation, e0 ¼ Ct=e0 A ¼ Ct=8:85 10 12 A;
ð3Þ
where C, t and A represent capacitance, sample thickness (in m) and area of the crystal face (m2) respectively. Using the values of dielectric constant e 0 and dielectric loss (tan d), the values of conductivity r were calculated with the help of the following relation: r ¼ x0 e0 e0 tan d;
ð4Þ
where e0 = 8.85 · 10 12 Fm 1, x0 = 2pf, f being the frequency in hertz.
The mechanical and dielectric behaviour of ErFeO3 crystals were studied for both un-irradiated (UIR) and irradiated (IR) crystals and the results are described as follows: 3.1. Load dependence of hardness Fig. 1 shows the variation of microhardness with applied load for both un-irradiated and irradiated single crystals of ErFeO3. The microhardness decreases non-linearly as the applied load increases from 0.098 to 0.98 N for both UIR and IR crystals. The values of microhardness are in quite agreement with already reported values of un-irradiated ErFeO3 crystal [18]. However, it is observed that after irradiating with 50 MeV Li3+ ion beam, the value of Vickers microhardness Hv corresponding to each load decreases. This decrease is not marginal as is very clear from the data available in Table 1. This decrease in the value of microhardness for irradiated crystals is attributed to certain types of amorphization occurring in the material. Tagomori and Iwase [23] and Kuromoto Jr. et al. [24] associate the decrease in enamel microhardness to the presence of deep cracks and to surface fragility for laser irradiated enamel. The relations between load P and diagonal length d are proposed in the literature as follows: Kick’s relation [25];
P ¼ K 1d n;
ð5Þ
where K1 is the standard hardness constant and n is the MeyerÕs index which equals 2 for all indenters and for all geometrically similar impressions.
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497
creases as the load increases. In low-load regions, the resistance offered by the material may be comparable with the applied load, resulting in a higher value of hardness since indenter penetrates only surface layers. However, at higher loads, the plastic flow of the material may be greater and hence the resistance offered by the material is negligible, thus decreasing the hardness [27]. This type of behaviour is also reported and favoured by several authors [28–31] on the basis of depth penetration of the indenter. Hays and KendallÕs [32] relation is, P W ¼ K 2d 2;
Fig. 1. Graph showing dependence of Hv on applied load for un-irradiated (UIR) and irradiated (IR) crystals.
where K2 is a constant and n = 2 is the logarithmic index. It is based on the assumption that as the load is applied to a specimen, it is partially affected by a smaller resistance pressure W, which is a function of the material being tested and represents the minimum applied load to produce an indentation; load less than W not allowing any plastic deformation. In order to evaluate the function W for a particular solution, Eqs. (5) and (6) may be subtracted to yield W ¼ K 1d n K 2d 2;
Table 1 Difference in the microhardness values of un-irradiated (UIR) and irradiated (IR) ErFeO3 single crystals Load (g)
Load (N)
(Hv)UIR (MPa)
(Hv)IR (MPa)
DHv (MPa)
10 20 30 40 50 60 70 80 90 100
0.098 0.196 0.294 0.392 0.49 0.588 0.686 0.784 0.882 0.98
12923.11 11487.21 10372.29 9771.26 9318.06 8810.10 8652.95 8602.66 8651.01 8643.58
11358.20 10096.18 9077.105 8495.83 8048.99 7732.39 7527.33 7417.60 7391.93 7443.71
1564.91 1391.03 1295.19 1275.43 1269.06 1077.71 1125.62 1185.06 1259.07 1199.87
The equation suggests Hv to be independent of load. That is not true in the present case. In the case of ErFeO3 crystals, values of n are 1.75 and 1.74 for both un-irradiated (UIR) and irradiated (IR) crystals. This supports the concept of Onitsch [26] that for n < 2, the microhardness number de-
ð6Þ
ð7Þ
and d n ¼ K 2 =K 1 d 2 þ W =K 1 :
ð8Þ
A plot of log P against log d for both un-irradiated as well as irradiated samples, (Fig. 2) according to Eq. (5) gives the values of n and K1. K2 and W are calculated from a graph between dn versus d2 as shown in Fig. 3. The values of these constants have been determined by using method of least square fitting using a software program in Fortran language. A plot of log (P W) versus log d as shown in Fig. 4 yields the value of n ffi 2, thereby suggesting the validity of the theory involving concept of resistance pressure (W) proposed by Hays and Kendall for both un-irradiated as well irradiated samples. The data on n, K1, K2 and W thus determined for an un-irradiated and irradiated ErFeO3 crystal is given in Table 2. The application of Hay and KendallÕs law leads to a modified formula of Eq. (1) which gives load independent values of Hv, H v ¼ 1:8544ðP W Þ=d 2 :
ð9Þ
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Fig. 2. A graph of log P versus log d for un-irradiated (UIR) and irradiated (IR) crystals.
Substituting for (P W) from Eq. (6), we have H v ¼ 1:8544K 2 :
Fig. 3. Graph of d n versus d 2 for un-irradiated (UIR) and irradiated (IR) crystals.
thus given are very close to the values calculated on application of Hays and KendallÕs law.
ð10Þ
In the light of this equation, the ‘‘load independent microhardness values’’ for un-irradiated and irradiated crystals are H v ðUIRÞ ¼ 8346 MN=m2 ; H v ðIRÞ ¼ 7162 MN=m2 : This clearly shows that microhardness values decrease after irradiation. One may notice from Fig. 1 that Hv has a rapid fall as the load is increased from 0.098 to 0.98 N. Beyond 0.69 N, the microhardness value achieves saturation and becomes load independent. From the data given through Table 2 as well as the curves, the load independent value of ErFeO3 is around 8650 MN/m2 and 7500 MN/m2 for un-irradiated and irradiated ErFeO3 crystals which is achieved at loads P 0.69 N. The load independent values
3.2. Fracture toughness, brittleness index and yield strength The term toughness may be defined as the property of a material by virtue of which it can absorb maximum energy before fracture takes place. The importance of toughness is in the selection of a material where load exceeds the elastic limit or yield point. The indentation impressions are usually seen associated with cracks at almost all loads on both the un-irradiated and irradiated crystals. However, it is observed that the crack length in case of irradiated crystals is larger than that of the un-irradiated crystals as can be clearly judged from Fig. 5. Thus, presence of deep cracks confirms the decrease in microhardness of the irradiated samples [23].
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Fig. 4. Graph of log (P W) versus log d for un-irradiated (UIR) and irradiated (IR) crystals.
The resistance to fracture indicates the toughness of a material. The cracks developed in a crystal determine the fracture toughness Kc, which in term tells us how fracture stress is applied on a uniform loading. According to Ponton and Rawlings [33], two types of crack systems can develop in a material as a result of indentation. These are radial-median and palmqvist crack systems. Transition from palmqvist to median cracks occurs at a well-defined value [34] of c/a, c being the crack length measured from the centre of the indentation mark to the crack end and a is half the diagonal length of the indentation mark. For c/a P 2.5, the cracks developed are median cracks as shown
499
Fig. 5. Variation of crack length with load for un-irradiated (UIR) and irradiated (IR) crystals.
in Fig. 6(a) and fracture toughness Kc is calculated using the relation [18,33], K c ¼ kP =c3=2 ;
ð11Þ
where the constant k = 1/7 for the Vickers indenter. For c/a < 2.5, the cracks formed during indentation have the configuration of palmqvist cracks as shown in Fig. 6(b) and the fracture toughness may be calculated using the relation [33], K c ¼ kP =al1=2 ;
ð12Þ
where l = c a is the mean palmqvist crack length.
Table 2 Results of microhardness measurements for un-irradiated (UIR) and irradiated (IR) single crystals of ErFeO3 Samples
nk ± Dnk
log K1
K1 (M N/m2)
W (N)
K2 (M N/m2)
Hv = 1.8544 · K2 (M N/m2)
nh ± Dnh
Un-irradiated Irradiated
1.74 ± 0.12 1.72 ± 0.12
2.04 2.07
9019.03 8441.31
0.038 0.042
4500.77 3862.27
8346.22 7162.19
1.91 ± 0.17 1.89 ± 0.17
nk represents value of n on application of Kicks law (P = K1d n). nh represents value of n on application of Hays and KendallÕs law (P W = K1d n).
500
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2a
2a l
l
2c
c
(b)
(a)
Fig. 6. Geometries of (a) median and (b) Palmqvist crack around Vickers indentation.
In case of both UIR and IR crystals, for a load P 6 70 g (0.69 N) and ratio c/a < 2.5, cracks developed are palmqvist cracks. Eq. (12) is, therefore, used to calculate the fracture toughness Kc. However for P > 70 g (0.69 N), the ratio c/a > 2.5 and hence Eq. (11) is applied in this case for calculating the value of Kc. Table 3 provides data regarding
crack length, nature of cracks, fracture toughness for UIR and IR crystals. From the table, it is clear that the values of fracture toughness decrease after irradiation because of increase in crack length due to amorphization. The nature of variation of Kc with load P for both un-irradiated as well as irradiated ErFeO3 crystals is readily reflected by Fig. 7. The sudden decrease in the value of Kc at loads above 0.6 N for both un-irradiated and irradiated ErFeO3 crystals is clearly seen; the decrease taking place on transition from Palmqvist to median type of cracks. Brittleness is an important property that affects the mechanical behaviour of a material and gives an idea about the fracture induced in a material without any appreciable deformation. The value of brittleness index Bi [11], is calculated using equation, Bi ¼ H v =K c :
ð13Þ
Comparison of data on brittleness index of unirradiated and irradiated crystals leads to interesting results. The brittleness index shows increase in
Table 3 Various values of crack length, fracture toughness, brittleness index and yield strength at different loads for un-irradiated (UIR) and irradiated (IR) ErFeO3 single crystals Hv (MPa)
Crack c
Kc · 106 (N/m
UIR crystal of ErFeO3 10 0.098 20 0.196 30 0.294 40 0.392 50 0.49 60 0.588 70 0.686 80 0.784 90 0.882 100 0.98
12923.1 11487.2 10372.3 9771.26 9318.06 8810.10 8652.95 8602.66 8651.01 8643.58
– 5.23 6.88 8.43 10.20 12.00 13.80 16.30 17.70 19.00
– 6.4 6.42 6.4 6.18 5.95 5.81 1.7 1.69 1.69
IR crystal of ErFeO3 10 0.098 20 0.196 30 0.294 40 0.392 50 0.49 60 0.588 70 0.686 80 0.784 90 0.882 100 0.98
11358.20 10096.2 9077.11 8495.83 8048.99 7732.39 7527.33 7417.60 7391.93 7443.71
– 6.57 8.39 10.20 12.18 14.40 16.10 18.40 20.10 21.50
– 4.93 5.1 5.13 5.02 4.86 4.86 1.42 1.4 1.4
Load
Load in N
3/2
)
Bi (m
1/2
)
Nature of crack
ry (MPa)
– 1794.88 1615.62 1526.76 1507.78 1480.69 1489.32 5060.39 5118.94 5114.54
– Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Median Median Median
4307.70 3829.07 3457.43 3257.09 3106.02 2936.70 2884.32 2867.55 2883.67 2881.19
– 2047.91 1779.82 1656.11 1603.39 1591.03 1548.83 5223.66 5279.95 5316.94
– Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Median Median Median
3786.07 3365.39 3025.70 2831.94 2683.00 2577.46 2509.11 2472.53 2463.98 2481.24
M. Bhat et al. / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 494–508
Fig. 7. Graph of fracture toughness versus load for unirradiated (UIR) and irradiated (IR) crystals.
its value at each load ranging from 0.098 to 0.98 N on irradiation of ErFeO3 crystals. The data is compiled in Table 3 for un-irradiated and irradiated crystals. The dependence of brittleness index on load for un-irradiated and irradiated ErFeO3 crystals is reflected by Fig. 8. The following points are noteworthy: 1. The variation of brittleness index with load is similar for un-irradiated and irradiated crystals, though the value corresponding to each load is different for the two types of samples. 2. As the load increases from 0.098 to 0.98 N, the value of brittleness index decreases with a tendency of achieving saturation at higher loads. However, the value of brittleness index for irradiated ErFeO3 crystal is higher than the un-irradiated one corresponding to each value of load. Thus, irradiation increases the brittleness index of ErFeO3 crystals. 3. There is a sudden jump in the value of brittleness index when the nature of cracks changes
501
Fig. 8. Graph of brittleness index versus load for un-irradiated (UIR) and irradiated (IR) crystals.
from Palmqvist to median type. The transition from Palmqvist to median crack system occurs at loads > 70 g (0.69 N) irrespective of whether the crystal is un-irradiated or irradiated. From the hardness values, the yield strength ry can be calculated [35]. For MeyerÕs index n > 2 the formula applicable is, n 2 Hv 12:5ðn 2Þ ½1 ðn 2Þ : ð14Þ ry ¼ 1 ðn 2Þ 2:9 For n < 2, the above equation reduces to [15], ry ¼ H v =3:
ð15Þ
Since for ErFeO3 crystals n < 2, Eq. (15) can be applied. The values of fracture toughness Kc, brittleness index Bi and yield strength ry in case of UIR and IR crystals are compiled and shown in Table 3. The yield strength also decreases as the load increases in case of both un-irradiated as well irradiated crystals. Since ry is directly proportional to Hv (see Eq. (15)), the dependence of ry on load is similar to that of Hv as is shown in Fig. 9.
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Fig. 9. Dependence of yield strength on load for un-irradiated (UIR) and irradiated (IR) crystals.
3.3. Dielectric properties The variation of dielectric constant e 0 for unirradiated and irradiated ErFeO3 single crystals was studied as a function of an applied a.c. field in the frequency range from 1 kHz to 10 MHz and as a function of temperature in the range of 30–550 C. Figs. 10(a) and (b) shows the dielectric constant as a function of frequency for UIR as well as IR ErFeO3 crystals. At each particular temperature ranging from 30 to 550 C, the dielectric constant shows decrease in its value as the frequency is increased and becomes almost saturated beyond 500 kHz. The decrease in the behaviour of dielectric constant with increasing frequency is the normal behaviour of ferrites and is consistent with the Koops model [36]. After irradiation, at each particular frequency, the value of dielectric constant decreases in the temperature range of 30– 300 C. This decrease in dielectric constant may be due to the decrease in space charge carriers or interfacial polarization in irradiated sample [37]. At 300 C, the values of e 0 for both irradiated
and un-irradiated become almost same whereas above 300 C, the magnitude of e 0 increases for the irradiated crystals as compared to the un-irradiated. This behaviour can be explained on the basis that the mechanism of polarization process in ferrites is similar to that of conduction process. The electronic exchange between Fe ions gives local displacement of electrons in the direction of an applied electric field, which induces polarization in ferrites. The anomaly in the variation of dielectric constant after irradiation is due to the defect creation [38], which results in a collective contribution of p and n type conduction. It is well known that the local displacement of the p type carriers takes part in the polarization in an opposite direction to that of the external field [39,40]. In addition, since the mobility of p type carrier is lower than that of n type carrier, their contribution to polarization decreases more rapidly at lower temperatures thereby reducing the value of e 0 in the case of irradiated samples. After irradiation, below 300 C there is n type conduction and beyond this there is collective contribution of n and p type carriers. The dispersion in the dielectric loss factor (tan d) of irradiated and un-irradiated ErFeO3 samples is shown in Fig. 11. From the figure, it is clear that for low temperatures (6200 C), the dielectric loss is very high in case of un-irradiated samples whereas for higher temperature P300 C, the dielectric loss is higher in case of irradiated sample. The appearance of the peak in the dispersion curves for un-irradiated and irradiated samples satisfies the Koops model and Maxwell–Wagner interfacial polarization. The presence of peaks in the loss factor can be explained on the basis of relative variation of real dielectric constant (e 0 ) and imaginary dielectric constant (e00 ) with frequency [41]. The absence of peak in some curves for tan d in the un-irradiated and irradiated samples may be attributed to the reason that the upper level of frequency used in our studies is too low to show a peak that may occur beyond 10 MHz. The observed variation of dielectric constant with temperature is shown in Figs. 12(a) and (b) for un-irradiated and irradiated ErFeO3 crystals. It was observed that the dielectric constant
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503
Fig. 10. (a) Dependence of dielectric constant e 0 on frequency at 30–150 C for un-irradiated (UIR) and irradiated (IR) crystals. (b) Dependence of dielectric constant e 0 on frequency at 200–350 C. Inset shows the variation of e 0 with frequency from 400 to 550 C for un-irradiated (UIR) and irradiated (IR) crystals.
increases with increasing temperature, showing anomaly at the transition temperature. The peak height at the transition temperature was observed to decrease with increasing frequency and the dielectric constant peak shifted to lower temperature with increasing frequency, which indicated the relaxational behaviour of the material [42] e.g. for UIR ErFeO3, at 1 kHz the peak value of dielectric constant observed at 480 C is 1284.8 · 103, whereas at, 10 kHz, 100 kHz, 1 MHz, 5 MHz and 10 MHz, the peak values of e 0 as observed at 460, 440, 380, 280 and 260 C are 146.7 · 103, 112.6 · 102, 17.3 · 102, 508.08 and 401.79 respectively. The same anomaly was observed for irradiated crystals of ErFeO3 at 1 kHz; the peak value of dielectric constant being 4070 · 103 at 460 C, whereas at the frequencies of 10 kHz, 100 kHz, 1 MHz,5 MHz and 10 MHz, the peak values of e 0 are 262.26 · 103, 268.75 · 102, 73.4 · 102, 1289.15 and 401.5 as measured at
420, 380, 360, 280 and 220 C respectively. This anomaly is corresponding to a phase change [43], and may be associated to the softening of a vibrational mode called the soft mode [44–47]. For most of the relaxor ferroelectrics, the peak of the dielectric constant shifts to higher temperature with increasing frequency, which has been attributed to decreasing relaxation time with increasing temperature [42]. In case of ErFeO3 crystal, the dielectric constant peak shifts to lower temperature with increasing frequency and seems to be due to the increasing relaxation time with temperature [48]. It is clear from Figs. 12(a) and (b) that there is increase in the value of dielectric constant of irradiated ErFeO3 crystals as compared to the un-irradiated ones at temperatures above 300 C. The drastic increase in dielectric constant is due to ion irradiation which may be correlated to the defects created along the tracks [49] and the structural modifications induced in the surrounding
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Fig. 11. Dependence of the dielectric loss (tan d) on frequency at 30–400 C for un-irradiated (UIR) and irradiated (IR) crystals.
regions [50,51]. By irradiating the crystal with 50 MeV Li3+ ions, the incident heavy ions get embedded in the crystal, lose energy by both the inelastic collisions and the elastic nuclear collisions which are dominant near the end of the range of the implanted ions. The increase in dielectric constant may be due to the disordering of the crystal lattice by the ion beam. Again, for the irradiated samples, there is a shift in the transition peak towards lower temperature for all frequencies. Samara [52] studied this type of shift in the transition temperature using influence of pressure on the dielectric response and phase transitions of PZN-9.5PT. The broad e 0 (T) peaks and strong frequency dispersion on the low temperature side
of the un-irradiated and irradiated samples are the hallmarks of a relaxor phase. Figs. 12(a) and (b) show two transition peaks for the frequencies 1, 10 and 100 kHz and this observation applies to both irradiated as well as un-irradiated samples of ErFeO3 crystals. However, there is only one peak at higher frequencies (P1 MHz), an observation common to both the UIR and IR ErFeO3 crystals. It suggests that the two transition peaks at frequency 6100 kHz and one transition peak at higher frequency >1 MHz is something which is intrinsic to ErFeO3 rather than anything to do with irradiation effects. The higher temperature peak (i.e. the peak above the transition temperature peak) may be due to the space charges getting
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505
Fig. 12. (a) Plots of the dielectric constant e 0 against temperature at frequencies 1 and 10 kHz for un-irradiated (UIR) and irradiated (IR) crystals. (b) Plots of the dielectric constant e 0 against temperature at frequencies 100 kHz and 1 MHz. Inset shows the variation of e 0 with temperatures at frequencies 5 and 10 MHz for un-irradiated (UIR) and irradiated (IR) crystals.
depleted resulting in a peak at a particular temperature [53]. 3.4. Temperature dependence of a.c. conductivity The plots of a.c. conductivity with temperature of both UIR and IR ErFeO3 crystals are shown in Fig. 13. It is clear from the figure that the conductivity is high for higher frequencies at a given temperature, thus confirming small polaron hopping in the present samples [54–56]. It has been reported that frequency dependence of ra.c is large in ferrimagnetic or in lower temperature region [57]. The same is also observed in case of our samples. The plots are almost linear in the temperature range 100–550 C. Initially, with an increase in temperature, conductivity r seems to remain almost unaffected until 100 C, where the conductivity starts increasing with temperature. The increase in conductivity with temperature is much more at lower frequencies of 6100 kHz, much less at
1 MHz and the least at 10 MHz. The conductivity is observed to be greater at higher frequencies as has been observed in other materials [58–60]. The increased conductivity could be due to a reduction in the space charge polarization at higher frequencies [61]. This is true for both UIR as well as IR samples of ErFeO3 crystals. However, after irradiation, the conductivity decreases in case of irradiated crystals for lower frequencies of 1, 10 kHz, then almost equalizes for 100 kHz and increases at higher frequencies of 1 and 10 MHz because of the conduction mechanism in case of ferrites [62]. This abnormal behaviour after irradiation is attributed to the two types of carriers p and n to the polarization. Since the mobility of p carriers is lower than that of n-carriers, their contribution to polarization will decrease more rapidly at lower frequencies. Thus, we can say that the conduction at lower frequencies is because of n-type carriers only and for higher frequencies (P1 MHz) is due to the collective contribution of p and n type carriers.
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Fig. 13. Variation of conductivity (r) with temperature at different frequencies for un-irradiated (UIR) and irradiated (IR) crystals.
4. Conclusions The irradiation effects of 50 MeV Li3+ ion on mechanical and dielectric properties of ErFeO3 single crystals may be summarized as follows: 1. The microhardness decreases and crack length increases on irradiation. It is attributed to amorphization induced due to irradiation. 2. Irrespective of whether the material is irradiated or not, the microhardness decreases nonlinearly upto 0.686 N and thereafter attains saturation.
3. Single crystals of ErFeO3 show a decreasing trend in the dielectric constant with increase in frequency at all temperatures and almost saturates at higher frequencies which is a normal behaviour of all ferrites. This behaviour is explained on the basis of Koops model for both un-irradiated and irradiated crystals. 4. The variation of dielectric constant with temperature shows anomalous behaviour wherein transition peak shifts towards lower temperature as frequency is increased from 1 kHz to 10 MHz, thereby showing relaxor type of behaviour. After irradiation, the dielectric
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constant e 0 of un-irradiated crystal is relatively larger than irradiated crystal upto 300 C. However, the trend gets reversed after the temperature goes beyond 300 C viz., e 0 for IR crystals is more than UIR ones for temperatures greater than 300 C. Acknowledgements Authors are thankful to the Nuclear Science Centre, New Delhi for providing the ion beam irradiating facility. This work is partially funded by the NSC, New Delhi under UFUP Scheme No. 30312 and forms a part of the Ph.D. programme of one of the authors (MB) under the supervision of Dr. K.K. Bamzai. The author (MB) is thankful to the CSIR for Senior Research Fellowship in the Emeritus Scientist Scheme of the CSIR. The support under ‘‘Emeritus Scientist, CSIR’’ to the corresponding author (PNK) by the Council of Scientific and Industrial Research, New Delhi is duly acknowledged.
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