Materials Transactions , Vol. 47, No. 3 (2006) pp. 677 to 681
Special Issue on Shape Memory Alloys and Their Applications
# 2006 The Japan Institute of Metals
Institute of Metal Physics, Ural Division, Russian Academy of Science,
S. Kovalevskaya Str. 18, Ekaterinburg, 620041 Russia
Using of MoK radiation, on a single crystal of a titanium nickelide intensities of 15 structural and 11 superstructural reflections of the B2phase are measured. Structural factors of scattering for these reflections are calculated, and root-mean-square displacements of atoms of nickel and atoms of titanium from positions of equilibrium are determined. The mean square of displacements of atoms of nickel is equal h u
2 i
Ni
¼ ð 8 : 7 0 : 6 Þ 10
4 nm
2
, atoms of titanium h u
2 i
Ti
¼ ð 3 : 9 0 : 3 Þ 10
4 nm
2
.
(Received September 20, 2005; Accepted November 28, 2005; Published March 15, 2006)
Keywords: titanium nickelide, single crystal, X-ray study, intensity reflections, structural and superstructural reflections, root-mean-square displacements of atoms
1.
The high-temperature B2-phase in alloys of a titanium nickelide (structure CsCl) undergoes martensitic transformations at cooling. The structural state of the B2-phase is characterised by the big value of root-mean-square displacements of atoms concerning position of equilibrium h u
2 i . In different works different values of mean squares of displacements h u s
2 i concerning a crystallographic plane are resulted.
These values change over a wide range: from 1 10
4 till
7 10
4 nm
2
.
1–3)
The difference can be connected both to a measurement technique, and with characteristics of an alloy
(difference in a chemical compound, heat treatment, a different position of temperature of measurement in relation to a martensitic point). Values h u s i determine from measurements of intensity of X-ray lines on polycrystalline samples.
Such measurements usually have a significant error, and this circumstance is affected on accuracy of the obtained results.
Neutron diffraction research, at which measurements of intensity of reflections have much higher accuracy, has given value h u s
2 i ¼ 3 : 1 10 4 nm 2 .
4) In work 4) the conclusion is made, that the mean square of atomic displacement in the B2phase of a titanium nickelide at room temperature approximately five times exceeds this value for normal metals
(copper, iron). At determination h u s
2 i the assumption is made, that atoms of nickel and atoms of titanium are displaced equally about the positions of equilibrium. The purpose of the present work was separate determination of root-mean-square displacements of Ni atoms and Ti atoms.
2.
Introduction
Experimental Procedure
The work was carried out on a single crystal of a titanium nickelide (Ti–50.8 at%Ni), prepared in the Siberian Physicotechnical Institute (Tomsk). The part of single crystal was cut on the plates parallel to (110) plane of the B2-phase. From the plates X-ray diffraction topograms were obtained by method of angular scanning.
5)
Samples for X-ray researches were cut out from the most perfect sections of the plates. In the given work the electropolished sample in the sizes 4
5 mm 2 , having the disorientation on all surface no more than
1 degree, was used. The surface of plate had a deviation from
(110) plane of the B2-phase about 1.5 degrees. The plate was aged at 450 C for 6.5 h. At cooling, according to the X-ray data, phase transition B2 !
R, which began at temperature
45 C and came to the end at 30 C, was observed. The integrated intensity of lines of the B2-phase was measured at
( 90 2 ) C, and this completely excluded a possibility of formation of R-phase.
Measurement of integrated intensities of various reflections was carried out on a diffractometer on which the X-ray tube with a dot projection of focus was established. Height of focus was 0.2 mm, its width was 0.4 mm. The primary beam which have been cut out by collimator, at crossing an axis of a goniometer had height of 0.67 mm and width of 2.87 mm.
The beams reflected from a sample were registered by the scintillation counter before which the filter from zirconium by thickness of 0.18 mm was installed. For removing a researched crystal in various reflecting positions a goniometer attachment was used, allowing to incline a sample and to turn it in the plane. The attachment is equipped with the device for heating a sample.
Measurement of integrated intensity of reflection from the chosen crystallographic plane was carried out at rotation of a crystal with constant speed in the given range of angles and at the motionless position of the counter installed under an angle 2 , where —the Bragg angle. The range of rotation of a crystal was given such that the crystal from not reflecting position has come in reflecting position and has completely left it.
For exact measurements of integrated intensity of reflections from surface of a single crystal on method Bragg 6) it is necessary, that all reflected beam passed completely through a slit of the counter. On height of slit of the counter this condition is carried out in all range of angles of reflections.
On width of the counter this condition to fulfil more difficulty at the big angles of reflection as lines extend. The width of slit of the counter should be increased at increase of the Bragg angle proportionally tg , where —the Bragg angle,
—spectral width of the K doublet. The maximal width of slit was 4 mm. To register completely wider reflections, measurements of these reflections were carried out in parts

678 with step of moving of the counter of 1.27 degrees as 4 mm of slit of the counter cover an angle of 1.27 degrees. We made corrections to the measured values of integrated intensity of reflections on a background, on the contribution of the next reflection of other order, on the width of a sample in the event that the width of sample was less, than 2 : 87 = sin mm.
Mean squares of displacements of atoms in a direction perpendicular to reflecting planes h u s
2 i
Ni and h u s
2 i
Ti are determined from temperature factors which take into account total value of thermal (dynamic) and static displacements of atoms. The temperature factor is included into the structural factor j F j
2
,
7,8) which for the B2-phase can be presented as follows:
( j F j
2
¼ f
Ni exp 8
2 h u s
2 i
Ni sin
2
2
þ f
Ti exp 8
2 h u s
2 i
Ti
)
2 sin 2
2 cos ½ n ð h þ k þ l Þ ; ð 1 Þ where f
Ni and f
Ti
—atomic factors of scattering of atoms Ni and Ti, —length of a wave of X-ray radiation, hkl —indexes of a reflecting plane, n —the order of reflection.
The structural factor for imperfect crystals is determined from the formula for integrated reflective ability from a mosaic crystal:
I = I
0
¼ E != I
0
¼ ð e
4 3
= 4 m
2 c
4 v
2
Þ j F j
2
½ð 1 þ cos
2
2 Þ = sin 2 ; ð 2 Þ where I ¼ E !
—integrated intensity of the reflected beam,
!
—speed of rotation of a crystal, E —the reflected radiation registered during rotation of a sample in which the abovementioned corrections are made, I o
—intensity of the used part of a spectrum of a primary beam, e —charge of electron,
—factor of absorption, m —electron mass, c —speed of light, v —volume of a unit cell.
For registration of several orders of reflections the molybdenum radiation was used. Intensity of K -doublet of a primary beam was equal 23 : 3 10
6 pulse/s. Calculating under the formula
¼
ð = Þ
1
P
P
1
1
A
A
1
1
þ ð = Þ
þ P
2
2
A
2
P
2
A
2
; where ð = Þ
1
Ni, P
1 and P
2 and ð = Þ
2
-mass factors of absorption Ti and
-atomic concentrations Ti and Ni, A
1 and A
2
atomic weight Ti and Ni, -density of titanium nickelide, we obtain ¼ 239 cm 1 for sample from titanium nickelide in the B2-phase. Taking into account, that ¼ 0 : 7107 10 cm, e 4 = m 2 c 4 ¼ 7 : 91 10 26 cm 2 , v ¼ 3 : 016 3 10 24 cm 3
8
, we find
4 m
2 c
4 v
2
= I
0 e
4 3
¼ 1 : 09 s/pulse :
Substituting the calculated value in the eq. (2), we find j F j
2
¼ 1 : 09 E != L p
; where L p
¼ ð 1 þ cos
2
2 Þ = sin 2 .
ð 3 Þ
V. M. Gundyrev and V. I. Zel’dovich
Table 1 Values of obtained from experiment structural factors j F j
2 also calculated under tables of handbook 9 Þ and atomic functions of scattering of X-rays.
hkl
221
442
2
(degree)
41.40
89.97
L p
311 46.00
2.061
622 102.80
1.076
2.363
1.000
320 50.28
1.831
640 116.34
1.336
210
420
30.55
63.59
3.426
1.337
630 104.44
1.097
E !
(pulse/s)
100
200
300
400
13.53
8.313
246.5
27.26
3.909
2110
41.40
2.363
56.24
1.577
1.05
114
500
600
72.19
1.149
89.97
1.000
700 111.13
1.211
800 140.98
2.547
2.97
8.22
1.59
1.88
110
220
19.18
5.758
5240
38.93
2.554
594
330 59.98
1.444
440 83.60
1.019
550 112.84
1.249
79.3
12.2
3.28
111
222
23.55
4.606
48.18
1.939
333 75.50
1.098
444 109.43
1.178
65.5
257
1.49
3.11
0.47
4.17
1.60
8.28
0.66
2.96
22.3
65.1
1.49
992
254
59.9
13.0
2.86
15.5
145
1.48
2.88
j F j
2 f
Ni f
Ti sin
2
2
(nm
2
)
32.3
588
23.09
16.23
17.43
11.85
0.48
13.63
78.9
11.03
9.08
7.65
2.82
8.96
1.43
0.81
9.15
7.74
6.69
5.85
6.65
5.99
2.75
11.0
24.7
44.0
68.7
98.9
5.22
134.7
4.56
175.9
20.45
14.24
14.21
10.50
8.18
6.63
9.49
7.37
5.5
22.0
49.5
6.19
88.0
5.17
137.4
18.75
12.83
12.32
8.33
8.85
6.76
6.50
8.24
33.0
74.2
5.26
131.9
0.25
12.73
4.23
7.03
0.81
13.63
9.02
7.74
8.56
30.2
5.47
120.9
9.08
6.00
24.7
98.9
0.40
11.91
2.41
6.50
8.10
35.7
5.07
142.9
7.09
16.39
11.08
53.0
10.07
7.14
1.48
6.96
13.7
55.0
5.47
123.7
3.
Experimental Results and Discussion
Integrated intensities of reflections place.
8) h 00 , hh 0 and hhh , and also some other was measured by the method stated above.
The structural factor was determined under the eq. (3). The obtained results are submitted in Table 1. Atomic factors of scattering f
Ni and f
Ti
Mirkin’s handbook.
9) are calculated under the tables, taken of
The temperature factor exp ð 8
2 h u s
2 i sin
2
2
Þ , included in the eq. (1) for calculations of influence of displacements of atoms from sites of a lattice on integrated intensity of reflection, is found from a condition, that displacements of atoms are small in comparison with the interplane distance, divided on the order of reflection.
7) However, this temperature factor is true as well at the big displacements of atoms if
Gaussian distribution of density of probabilities of a finding of atoms to distance u from a reflecting plane only takes
Assuming, that displacements of atoms concerning a reflecting plane correspond to Gaussian distribution, it is possible to substitute values j F j
2
, f
Ni
, f
Ti and ð sin
2
Þ = 2 found for different reflections, in the eq. (1) and to result system of the equations from which it is possible to find mean squares of displacements of atoms Ni and Ti concerning a reflecting plane. For cubic crystals the mean square of displacements of the same atoms concerning a crystallographic plane ( h u s
2 i ) is isotropic magnitude. It has allowed to

Root-Mean-Square Displacements of Atoms in the B2-Phase of Titanium Nickelide 679 hkl
110
220
330
440
550
111
222
333
444
500
600
700
800
100
200
300
400
320
640
210
420
630
311
622
221
442
Table 2 Values of D and values of D (see text).
h u s h u s
2 i
Ni
2 i
Ti
¼ 2 :
D
9 10
¼ 1 : 3 10
4
4 nm
2 nm
2
1.09
1.01
0.83
1.03
0.77
1.04
0.79
0.99
1.02
1.05
1.05
1.04
0.90
0.90
0.97
1.52
1.06
3 10
3
1.03
0.50
1.04
0.48
0.90
0.76
0.93
0.97
D h u
¼ s
2
1 i
:
Ni
9
¼ h u s
10
2
4 i
Ti
¼ nm
2
1.37
1.07
20.93
1.21
0.29
1.11
0.03
0.70
1.05
1.17
1.24
1.15
0.80
1.80
1.18
0.43
0.98
29.03
1.00
12.48
1.10
12.80
0.78
2.69
1.09
0.04
solve all systems of the equations written for different reflecting planes, in common. At the joint solution of all equations using program Mathcad we have obtained h u s
2 i
Ni
ð 2 : 9 0 : 2 Þ 10 4 nm 2 and h u s
2 i
Ti
¼ ð 1 : 3 0 : 1 Þ 10
¼
4 nm 2 . From here it is visible, that mean square of displacements of atoms of nickel twice is more, than atoms of the titanium.
In Table 2 values D ¼ j F
0 j
2
= j F
1 j
2
, determining coincidence theoretically calculated on the found values h u s
2 i
Ti structural factors j F
0 j
2 h u s
2 i
Ni and with factors j F
1 j
2
, calculated of integrated intensities of reflections under the eq. (3), are j given for each reflection. For comparison values D ¼
F
0 j
2 = j F
1 j
2 where j F
0 j
2 -theoretically calculated structural factor at the assumption, that root-mean-square displacement of atoms Ni and Ti are identical, are given. In this case at the joint solution of all equations it was received h u s
2 i
Ti
¼ 1 : 9 10 4 h u s
2 i
Ni
¼ nm 2 . For a quantitative estimation of coincidence of calculated values of structural factors with experimentally received, R -factors for all investigated reflections, and also separately for structural and superstructural reflections under the eq. were calculated:
R ¼
X jj F
X j j F
1 jj j F
0 j
:
The obtained results are submitted in Table 3. As can be seen from obtained values R , the structural factors calculated at
Table 3 Values of R -factors.
All reflections
Structural reflections h u s
2 i
Ni h u s
2 i
Ti
¼ 2 : 9 10
¼ 1 : 3 10
4
4 nm
2 nm 2 h u
¼ s
2
1 i
:
Ni
9
¼ h u
10 s
2
4 i
Ti
¼ nm
2
2.8%
13.2%
1.2%
4.4%
Superstructural reflections
13.5%
82.6% h u s
2 i
Ni
¼ 2 : 9 10 4 nm 2 and h u s
2 i
Ti
¼ 1 : 3 10 4 nm 2 have come out much more precisely, than calculated at h u s
2 i
Ni
¼ h u s
2 i
Ti
¼ 1 : 9 10
4 nm
2
. Especially, it concerns
, superstructural reflections.
From the obtained values h u s
2 i
Ni and h u s
2 i
Ti have found p ffiffiffiffiffiffiffiffiffiffiffiffiffi h u s
2 i
Ti p ffiffiffiffiffiffiffiffiffiffiffiffiffi h u s
2 i
Ni
¼ 0 : 017 nm and
¼ 0 : 011 nm. For cubic crystals the mean square of displacements of atoms concerning their position of equilibrium h u 2 i in 3 times is more, than a mean square of displacements of atoms concerning a plane h u s
2 i . Proceeding from this, have found h u 2 h u 2 i
Ti
¼ ð 3 : 9 0 : 3 Þ 10 i
4
Ni
¼ ð nm 2
8 : 7 0 : 6 Þ 10 4 nm 2 and
, and also have calculated the appropriate root-mean-square displacement of atoms Ni and Ti concerning their position of equilibrium: ( 0 : 0295
0 : 0010 ) nm and ( 0 : 0197 0 : 0007 ) nm.
On Fig. 1 calculated dependencies j F j on parameter
ð sin Þ = and experimentally obtained points are given. Lines correspond to calculated values F under the formula (1) at h u s
2 i
Ni
¼ 2 : 9 10
4 nm
2 and h u s
2 i
Ti
¼ 1 : 3 10
4 nm
2
.
The points show the experimental values appropriate to concrete reflections, submitted in Table 1. As can be seen from Fig. 1, for structural reflections good coincidence of experimental points to a calculated curve in all range of changes of values ð sin Þ = is observed. From here it is possible to draw the following conclusions. (1) Accepted for a single crystal of a titanium nickelide the model of ideally mosaic single crystal was correct. Primary and secondary
30
20
10
0
2 4 6 8 nm
-1
10 12 14
λ
Fig. 1 Dependence of structural amplitude j F j on parameter ð sin Þ = .
Lines correspond to calculated values j F j under the eq. (1) at h u s
2 i
Ni
¼ 2 : 9 10
4 nm
2 and h u s
2 i
Ti
¼ 1 : 3 10
4 nm
2
. Points show experimental values: –superstructural reflections, –structural reflections.

680
10
V. M. Gundyrev and V. I. Zel’dovich
25
20
15
10
5
0
2 4 6
(sin )
λ
θ
8 nm
-1
10 12
Fig. 2 Dependence of structural amplitude j F j of superstructural reflections on parameter ð sin Þ = . The continuous line corresponds to calculated values j F j under the eq. (1) at h u s h u s
2 i
Ti values j
¼
F j
1 : 3 10
4 nm
2 under the eq. (1) at h u s
¼ h u s i
Ti nm
2
, the dashed line corresponds to calculated
2 i
Ni
2
2 i
Ni
¼
¼ 1
2
:
:
9
9 10
10
4
4 nm
2 and
. The experimental values j F j are shown by circles.
0
0 2 4 6 8 nm
-1
10 12 14
λ
Fig. 3 Dependencies of coherent scattering by atoms Ni and Ti ( f
Ni and f
Ti
) in view of temperature factors from ð sin Þ = . The continuous curve relates to f
0
Ti
, the dotted one relates to f
0
Ni
.
extinctions were insignificant. Otherwise the first experimental points belonging to reflections (110) and (200), because of a primary and secondary extinction would be much below a calculated curve. However it is not observed.
(2) The carried out measurements and calculations are performed truly, including is correctly measured I o
. We shall notice what to measure intensity of a primary beam there is no necessity as it is possible to find I o in the calculated way from measured intensities of reflections. However comparison calculated I o with measured allows to check all experiment. In this case calculated I o has coincided with measured accurate to one percent. (3) In spite of the big displacement of atoms in the B2-phase of titanium nickelide concerning their position of equilibrium, good coincidence of experimental points to calculated curve is observed nevertheless even at the big values ð sin Þ = for different reflections. It shows that distribution of density of probabilities of a finding of atoms concerning any plane is close to
Gaussian.
On Fig. 2 for superstructural reflections, dependence j F j from ð sin Þ = , calculated under condition of h u s
2 i
Ni h u s
2 i
Ti
¼ is shown by a dashed line. As can be seen, the found experimental points for superstructural reflections do not coincide with this curve, at the same time these points lay close to the continuous curve calculated under condition of h u s
2 i
Ni
¼ 2 : 9 10 4 nm 2 and h u s
2 i
Ti
¼ 1 : 3 10 4 nm 2 .
On exp ½ 1 :
Fig. 3,
0 ð sin
2 the
Þ = 2 calculated and f functions
0
Ni
¼ f
Ni f 0
Ti
¼ f
Ti exp ½ 2 : 3
ð sin
2
Þ = 2 are shown depending on ð sin Þ = . As can be seen from figure, curves are crossed, while atomic functions of scattering f
Ti and f
Ni are not crossed (see Table 1). If rootmean-square displacements would be equal or root-meansquare displacement of atoms of nickel would be less than root-mean-square displacement of atoms of titanium, curves in Fig. 3 would not be crossed and, hence, there would be no minimum near to a point ð sin Þ = ¼ 0 : 55 in Figs. 1 and 2.
However such minimum is experimentally observed. All superstructural reflections, namely (311), (300), (221) and
(320), located near to this point, have is anomalous low intensity. Only provided that h u s
2 i
Ni it is much more h u s
2 i
Ti
, this fact has an explanation. To this condition there correspond the found values h u s h u s
2 i
Ti
¼ 1 : 3 10 4 nm 2
2 i
Ni
¼ 2 : 9 10 4 nm 2 and mean squares of displacement of atoms of nickel and titanium.
As is known, 10) in the B2-phase of a titanium nickelide oscillation of planes (110) in a direction ½ 11 takes place.
The plane (110) consists of alternating rows of ‘‘large’’ atoms
Ti and rows of ‘‘fineer’’ atoms Ni. The rows are parallel to a direction ½ 11 . Above titanium rows in the next planes the same titanium rows, above nickel–nickel settle down.
Because of a difference at a size of atoms, the dominant counteraction to movement of a plane from the direction of the next planes occurs through atoms of titanium. Because of this circumstance, the amplitude of oscillations of rows of atoms Ni should be more, than the amplitude of oscillations of rows of atoms Ti if only to not consider oscillating planes, as absolutely rigid. Thus, from the crystallographic analysis of collective oscillations of atoms in a titanium nickelide, having structure B2, we come to the same conclusion, that oscillations of atoms Ni are more, than oscillations of atoms
Ti.
In work 11) the data under anisotropic temperature factors for the B19 0 -martensite of alloy Ti–49.2 at%Ni are obtained at room temperature, and also their equivalent isotropic values are given. From these data we have determined mean squares of displacement of atoms Ni and Ti, which are given in Table 4, concerning crystallographic planes in the B19 0 phase, and also values h u s
2 i
Ni and h u s
2 i
Ti from equivalent isotropic factors are calculated. From the table it is visible, that the average and maximal values of a mean square of atomic displacements for atoms of nickel are more, than for

Root-Mean-Square Displacements of Atoms in the B2-Phase of Titanium Nickelide
Table 4 Mean squares of displacements h u s
2 i 10
4 nm
2 atoms Ti and Ni concerning crystallographic planes in the B19 0 -martensite of Ti–49.2 at%-
Ni alloy. Mean squares of displacements obtain from equivalent isotropic temperature factors.
11 Þ
Ti
Ni
(100)
0.96
1.66
(010)
0.77
0.40
(001)
1.43
1.57
ð 101
1.30
2.28
Þ (103)
1.14
1.11
Average values
1.06
1.25
The mean squares of displacement obtained from equivalent isotropic temperature factors.
11 Þ atoms of titanium. Further, if to compare the average values, given in Table 4, with the values obtained in the present work h u s
2 i
Ni
¼ 2 : 9 10
4 nm
2 and h u s
2 i
Ti
¼ 1 : 3 10
4 nm
2 for the B2-phase, it is visible, that displacements of atoms in a martensite are less, than in the B2-phase. It corresponds to representation about ‘‘freezing’’ a part of cooperative thermal oscillations at martensitic transformation B2 !
B19 0 .
10)
4.
Conclusions
15 structural and 11 superstructural reflections of the B2phase of single crystal of titanium nickelide from which structural factors for these reflections are determined are given. It is shown, that the single crystal of titanium nickelide can be considered as ideally mosaic concerning scattering
X-rays. Computer data processing under structural factors has allowed to determine mean squares of displacements of atoms of nickel and atoms of titanium from sites of crystal lattice. Values
10
In work results of measurements of integrated intensity of
4 nm 2 h u 2 i
Ni were found.
¼ 8 : 7 10 4 nm 2 and h u 2 i
Ti
¼ 3 : 9
Acknowledgment
Authors are grateful to Prof. Ju. I. Chumljakov for the given single crystal.
REFERENCES
681
1) V. G. Pushin, S. A. Muslov and V. N. Khachin: Fiz. Metal. Metalloved.
64 (1987) 802–808.
2) A. A. Klopotov: Zakonomernosti fazovykh perekhodov v splavakh
TiNi–TiMe i CuPd s B2 sverkhstrukturoi (Laws of Phase Transitions in
Alloys TiNi–TiMe and CuPd with B2 superstructure) (Author’s
Abstract of Dissertation. of Doctor of Physical and Mathematical
Sciences, Tomsk, 2002) pp. 3–32.
3) Ju. P. Mironov, P. G. Erokhin and S. N. Kul’kov: Izvestiya VUZov.
Fizika. (1997) 100–104.
4) E. Z. Valiev, V. I. Zel’dovich, A. E. Teplykh and N. Ju. Frolova: Fiz.
Metal. Metalloved.
93 (2002) 75–79.
5) V. M. Gundyrev, N. V. Belova and V. O. Esin: Vyrashchivanie monokristallov tugoplavkikh i redkikh metallov (Growing Single
Crystals of Refractory and Rare Metals) (Nauka, Moskva, 1973) pp. 121–127.
6) G. S. Zhdanov and Ya. S. Umanskij: Rentgenografiya metallov (X-ray
Diffraction Studies of Metals), Part I (ONTI NKTP of USSR, Moskva,
1937) p. 376.
7) Ya. S. Umanskij, Yu. A. Skakov, A. N. Ivanov and L. N. Rastorguev:
Kristallografiya, pentgenografiya i elektronnaya mikroskopiya (Crystallography, Roentgenography and Electronic Microscopy) (Metallurgiya, Moskva, 1982) p. 631.
8) B. Ya. Pines: Lektsii po structurnomu analizu (Lectures on Structural
Analysis) (Publishing of Kharkov University, Kharkov, 1957) p. 455.
9) L. I. Mirkin: Spravochnik po rentgenostrukturnomu analizu polikristallov (Handbook on X-ray Diffraction Analysis of Polycrystals)
(Fizmatgiz, Moskva, 1961) p. 863.
10) V. E. Naysh, T. V. Novoselova and I. V. Sagaradze: Fiz. Metal.
Metalloved.
80 (1995) 14–27.
11) Y. Kudoh, M. Tokonami, S. Miyazaki and K. Otsuka: Acta Metall.
33
(1985) 2049–2056.