UDK 669.27:548.55	ISSN 1580-2949
Original scientific article/Izvirni znanstveni članek	MTAEC9, 48(6)823(2014)
INVESTIGATION OF PHYSICAL PROPERTIES OF TUNGSTEN-BASED SINGLE CRYSTALS USING AN ULTRASONIC METHOD
PREISKAVA FIZIKALNIH LASTNOSTI MONOKRISTALOV NA OSNOVI VOLFRAMA Z METODO ULTRAZVOKA
Katerina Skotnicova1, Valentina M. Kirillova2, Oleg I. Zaporozhets3, Jaromir Drapala1,
Ivo Szurman1
1VŠB - Technical University of Ostrava, Faculty of Metallurgy and Materials Engineering, Department 606 - Regional Materials Science and Technology Centre (RMSTC), 17. listopadu 15, 708 33 Ostrava - Poruba, Czech Republic 2Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences, Leninski prospect 49, 119991 Moscow, Russian
Federation
3G.V. Kurdyumov Institute for Metal Physics, N.A.S.U., 36 Academician Vernadsky Blvd., 252680 Kiev-142, Ukraine
katerina.skotnicova@vsb.cz
Prejem rokopisa - received: 2013-09-27; sprejem za objavo - accepted for publication: 2014-01-09
Using an ultrasonic method, the measurement of longitudinal and transversal velocities v of ultrasonic waves in the major crystallographic directions of pure-tungsten single crystals and tungsten single crystals alloyed with Ta and Mo was performed. Single crystals with a [110] crystallographic orientation were prepared by plasma-arc melting. Crystal density p was also measured. Crystal elastic constants Cij, anisotropy factors A, Young's modulus E, shear modulus G and bulk modulus B for the given crystallographic directions, and the mean values of the longitudinal and transversal velocities of the ultrasound according to the Fochtu-Roisu-Chilly method, Young's modulus, shear modulus, Poisson's ratio and Debye temperature were calculated from the obtained data. The measurement of ultrasound rates was realized by means of a pulse apparatus with a frequency of 10 MHz to 30 MHz. It was found that the alloying of pure tungsten with the elements such as tantalum and molybdenum led to a decrease in the average magnitudes of v, Cij, and B over various crystallographic and polarization directions, as well as the magnitude of p. The effects of the alloying elements on the elastic properties of tungsten crystals were identical. It may be concluded on the basis of the obtained results that the ultrasonic method can be used for the quality control of the purity of tungsten single crystals and tungsten low-alloyed alloys by measuring the attenuation effects of ultrasound waves in various parts of the tested samples.
Keywords: tungsten, single crystal, physical properties, ultrasonic method
Z ultrazvočno metodo je bila izvršena meritev longitudinalne in transverzalne hitrosti v ultrazvočnih valov v glavnih krista-lografskih smereh kristalov čistega volframa in volframovega monokristala, legiranega s Ta in Mo. Monokristali s kristalo-grafsko orientacijo [110] so bili izdelani s taljenjem v plazemskem obloku. Izmerjena je bila gostota p kristala. Iz dobljenih podatkov so bili izračunani: elastična konstanta Cij kristala, faktor anizotropije A, Youngov modul E, strižni modul G in elastični modul pri stiskanju B pri dani kristalografski smeri in glavne vrednosti longitudinalnih in transverzalnih hitrosti ultrazvoka po Fochtu-Roisu-Chillyjevi metodi, Youngov modul, strižni modul, Poissonovo razmerje in Debyejeva temperatura. Meritev hitrosti ultrazvoka je bila izvršena s pulzatorjem s frekvenco od 10 MHz do 30 MHz. Ugotovljeno je, da legiranje čistega volframa z elementi, kot sta tantal in molibden, povzroči zmanjšanje povprečnih veličin v, Cij in B v številnih kristalografskih in polarizacijskih smereh, kot tudi veličino p. Vpliv legirnih elementov na elastične lastnosti kristalov volframa je bil enak. Na podlagi dobljenih rezultatov se lahko sklene, da se ultrazvočna metoda lahko uporabi za kontrolo kvalitete monokristalov volframa in njegovih malo legiranih zlitin z meritvijo oslabitve ultrazvočnih valov v različnih delih preizkušanih vzorcev.
Ključne besede: volfram, monokristal, fizikalne lastnosti, metoda z ultrazvokom
1 INTRODUCTION	a metal. However, at present there are no methods for
quantitative calculations of these constants that would be
The effects of alloying elements and crystallographic	based on the concepts of the electron structure of a metal
orientation on physical properties, particularly the elastic	(Fermi level, Brillouin zone, etc.).
properties of single crystals of refractory metals, widely	In this paper, the results of measuring velocity v of
used for manufacturing cathodes, anodes, blades, nets,	longitudinal and transverse ultrasonic waves propagating
heaters and other parts of electro-vacuum devices, catho-	along the three main crystallographic directions in the
des for thermionic converters, high-power electrical	tungsten-based single crystals with a [110] crystallogra-
contacts, emitters in the detectors of atomic beams, etc.,	phic orientation using a non-destructive ultrasonic
constitute an important area of research1-3. Special focus	method4 are described. Based on the wave velocity and
has been devoted to tungsten-based single crystals due to	density data, crystal elastic constants Cij, anisotropy
their anisotropy that is close (not equal) to unity1,2.	factor A, Young's modulus E, bulk modulus of elasticity
According to the current theory of solids the values	B, shear modulus G, Debye temperature @d and
of elastic constants are related to the electron structure of	Poisson's ratio v of single crystals were calculated.
2 EXPERIMENTAL WORK
Tungsten rods after the second re-melting (99.99 %) with a diameter of 4 mm, and Ta or Mo wires (diameter < 1 mm) were used as the initial materials. Highly pure and perfect single crystals of tungsten with the [110] crystallographic orientation were applied as seed crystals, forming the basis of the relevant alloys. For obtaining single crystals of tungsten alloys, an original re-melted tungsten rod was combined with the wires made of molybdenum or tantalum in the amount corresponding to the calculation of the composition of a particular alloy. The plasma-arc melting15 with a mixture of inert gases - helium and argon (in the volume ratio of 1:5)- was applied for the preparation of these tungsten-based single crystals - W, W-1.5 % Mo and W-1.5 % Ta (the nominal chemical composition). The melting conditions were as follows: the plasma-arc current - 200 A, the voltage between the electrodes (the cathode plasma torch and the grown crystal) - 20 V, the growth rate -1.5 mm/min. The experimental specimens were cut from the beginning of single crystals (near the seed) in the form of cylinders or right-angled parallelepipeds. The X-ray reflection-mode topography (a modified Berg-Barrett technique) and the Ka and Kß radiations produced by a sharp-focus X-ray tube (the focus diameter is 40-50 pm) were applied to determine the angular disorientations of the subgrains in the given single crystals13. The back-reflection Laue method (an X-ray beam perpendicular to the face-end section) was used to determine their crystallographic orientation. The microstructure study was carried out using a light microscope (LM), Olympus GX-51, connected with a digital camera DP12.
The ultrasonic measurements were carried out on a pulsed facility developed at the G. V. Kurdyumov Institute for Metal Physics, N.A.S.U. The working frequency was f = 10-30 MHz. The error of measuring v was 10 4 rel. units for a period 10 ps and it diminished with the lengthening of the period. The density p was measured hydrostatically using the germanium or fused-quartz standards. The measuring error of the absolute density of specimens 10 g did not exceed 10-4 rel. units. The test temperature T was (20 ± 0.5) °C. The elastic constants and parameters were calculated from the velocities of the longitudinal (vl) and transverse (vt) ultrasonic waves and the density magnitudes, using the following well-known relationships applicable to cubic crystals46:
2[110] C11 + C 44 C12
pv
l[ 001 ]
= C11
pv
l[ 110 ]
PVH111 ] ="
C +c + or
' 2 C11 + 2C12 + 4C 44 3
2[001] _ Pvi 110] = C 44
2[1T0] C 11 -C12
PV,l 110 ] ="
(1) (2)
(3)
(4)
(5)
PVA111 ] ="
A =
3
2C
B =
C11 -C 12 C11 + 2C12 3
v =
— h ®D = h^
- _2 (3a' -4) E = pv ,2-^-
^ ' (a' -1)
G = pv^
a' - 2 2( a' -1)
; a = —
9Np
1
/
4nA,
1 2
-r+—T
vv l
(7)
(8)
(9) (10) (11)
(12)
t /
In equations (1) to (7) for the longitudinal or transverse velocities of ultrasonic waves, the subscripts indicate the wave-propagation vectors; the subscript indexes indicate the polarization vectors.
3 RESULTS AND DISCUSSION
The binary systems of W-Ta and W-Mo create ideal types of phase diagrams with unlimited solubility of the components in the liquid and solid states1. Under normal temperatures, the structures of both systems are formed as a result of substitution of the solid solution of tungsten, which may be formed within the concentration interval of the alloying element from 0 % to 100 %. During the investigation of the macrostructure on the surfaces of the single crystals of tungsten, alternating light and dark strips were observed as a result of various etchings of the edges (Figure 1). Some subgrain boundaries of the 1s' order13 were also observed without any additional magnification aids (visually), indicating their relatively high disorientation.
These preliminary results are consistent with the results of the study of the crystal structure with X-ray topography (Table 1). As an example, a topogram taken
Figure 1: Surface morphology of W-1.5 % Ta single crystals Slika 1: Morfologija površine monokristala W-1,5 % Ta
v
2
Figure 2: X-ray topogram taken from the beginning of W-1.5 % Ta single crystal with a [110] growth-axis orientation (cross-section) Slika 2: Rentgenski topogram iz za~etka monokristala W-1,5 % Ta z osjo rasti [110] (pre~ni prerez)
from the beginning of the single-crystalline W-1.5 % Ta alloy is shown in Figure 2. Generally, the fragmentation of the substructure and the misorientation of the sub-grains at the end part of single crystals are higher than at the beginning - there are distinctly visible wide boundaries between the blocks, which, in principle, are characteristic of most methods of single-crystal growth.
Table 1: Structure parameters of tungsten-based single crystals Tabela 1: Parametri strukture monokristalov na osnovi volframa
Sample
W-1.5 Mo
W-1. 5 Ta
W
Disorientation of subgrains (°)
1st order
0.35-1.0
0.1-0.25
0.1-0.2.5
2nd order
0.06-0.2
0.03-0.06
0.1
Size of subgrains (mm)
1st order
2.0-4.0
1.5-3.0
1.0-3.0
2nd order
0.3-0.5
0.3-0.5
0.13-0.55
A single-crystalline structure of tungsten-based alloys was also confirmed during the study of the sections using LOM (Figure 3). The subgrains in the shape of polygons in the cross-section and long columnar subgrains elongated in the direction of growth formed during crystallization due to plasma heating in the longitudinal sections are visible in the photos of these single-crystal microstructures. A lower structural perfection of these single crystals is associated with a considerable disturbance of the melt by the plasma arc, large temperature gradients and the cooling rate of the growing single crystals due to "air rinsing" of their surfaces by the plasma-forming gas.
The data on the longitudinal (Vl) and transverse (vt) velocities of the ultrasonic waves at 20 °C for different crystallographic directions and densities (p) are given in Table 2. Table 3 shows elastic constants and related parameters C11, C44, C12, B, A and 0 calculated from the data given in Table 2. Table 4 includes the average velocities of longitudinal and transverse ultrasonic waves, and the average values of E, G and v. The data on Young's modulus E and shear modulus G for different crystallographic directions are presented in Table 5. It is
evident from the obtained results that in the case of tungsten-based single crystals, as a result of alloying with molybdenum or tantalum, the density slightly decreases (pw = 19.26 g/cm3) in comparison with pure tungsten.
Table 2: Magnitudes of Vl and vt for different crystallographic orientations, and density of tungsten-based single crystals at 20 °C Tabela 2: Veli~ina Vl in vt pri razli~nih kristalografskih orientacijah in gostota monokristalov na osnovi volframa pri 20 °C
Sample
W-1.5 Mo
W-1.5 Ta
W
p/ . (g/cm3)
18.97
19.10
19.26
Vl[ 110]/ (m/s)
5250.1
5235.1
5241.6
v[00'] /
Vt[110]' (m/s)
2893.8
2881.7
2894.4
Vt[110]/ (m/s)
2896.6
2889.3
2879.5
Aniso-tropy
Vt/%
0.095
0.263
0.517
The alloying of tungsten with small amounts of molybdenum or tantalum led to a decrease in elastic coefficients C11, C44, C12 in comparison with single crystals of pure tungsten, while the obtained values of the coefficients for the alloyed samples of single crystals are very
Figure 3: Microstructure of tungsten-based single crystals with a [110] crystallographic orientation: a) W-1.5 % Mo, b) W-1.5 % Ta (cross-section)
Slika 3: Mikrostruktura monokristalov na osnovi volframa s kristalo-grafsko orientacijo [110]: a) W-1,5 % Mo, b) W-1,5 % Ta (pre~ni prerez)
close (similar). Determined elastic coefficients for single crystals of pure tungsten, as well as the values of the speed of ultrasound waves vi and vt correlate very well with the results of the other authors6,7. The average values of the Young's modulus, shear modulus and bulk modulus for single crystals of pure tungsten are also in a very good agreement with the literature data1.
Table 3: Magnitudes of Cij, B, A and Debye temperature 0D of tungsten-based single crystals
Tabela 3: Veli~ine Cij, B, A in Debyejeva temperatura 0D monokristalov na osnovi volframa
Sample	C11/ (GPa)	C12/ (GPa)	C44/ (GPa)	B/ (GPa)	A	Qd/ (K)
W-1.5 Mo	522.4	204.8	159.1	310.7	1.002 (0.2 %)	382.4
W-1.5 Ta	522.5	205.4	159.4	311.1	1.005 (0.5 %)	381.6
W	527.5	208.1	161.3	314.6	1.010 (1 %)	381.6
It is evident from Table 4 that an addition of molybdenum or tantalum led to a decrease in the values of the mentioned moduli. A slight dependence of Young's modulus and shear modulus on the crystallographic direction of the measurement was manifested in all the investigated samples of single crystals (Table 5). The highest values of Young's modulus were determined in the [110] crystallographic direction, while for the shear modulus it was the [111] crystallographic direction.
Table 4: Average values of E, G, vl, Vt and Poisson constant v of tungsten-based single crystals
Tabela 4: Povpre~ne vrednosti E, G, vl, vt in Poissonova konstanta v monokristalov na osnovi volframa
Sample	E/(GPa)	G /(GPa)	v,/(m/s)	v,/(m/s)	v/-
W-1.5 Mo	407.5	159.0	^249.8	^895.5	0.281
W-1.5 Ta	407.7	159.1	5234.3	2886.3	0.281
W	411.9	160.7	5239.9	2888.4	0.282
Table 5: Young's modulus E and shear modulus G for the main cry-stallographic orientation of tungsten-based single crystals Tabela 5: Youngov modul E in strizni modul G za glavne kristalo-grafske orientacije monokristalov na osnovi volframa
Sample	E/(GPa)			G/(GPa)		
	[111]	[100]	[110]	[111]	[100]	[110]
W-1.5 Mo	407.1	407.6	407.8	159.1	159.0	158.9
W-0.5 Ta	406.6	408.0	408.5	159.4	159.0	158.9
W	409.7	412.4	413.4	161.3	160.5	160.2
The obtained results confirm the fact that the aniso-tropy of elastic properties of tungsten approach one1,2. The Poisson constant for individual samples of single
crystals, depending on the ratio between vi and vt, was equal to 0.28 ± 0.001. It may be therefore stated that the amounts of the alloying elements (Mo, Ta) in a concentration of w = 1.5 % did not significantly influence the magnitude of this quantity in comparison with the single crystals of pure tungsten. A similar effect can also be observed when determining Debye temperature Q of these samples, which was found to be (381.8 ± 0.45) °C.
4	CONCLUSIONS
It may be concluded on the basis of the obtained results that a non-destructive ultrasonic method can be used for quality control of the purity and structure of single crystals of tungsten and its low-alloyed alloys, with which we measure the attenuation effects of ultrasound waves in various parts of the tested samples. Using the obtained data on the velocities of longitudinal and transverse ultrasound waves it is possible to determine and assess, using suitable relations, the elastic or physical properties of tungsten low-alloyed alloys, as well as the influence of the alloying elements on the given quantities.
Acknowledgement
This paper was created within project No. CZ.1.05/2.1.00/01.0040 "Regional Materials Science and Technology Centre" within the frame of the operational programme "Research and Development for Innovations" financed by the Structural Funds and the state budget of the Czech Republic and project SP2014/62.
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