- Email: [email protected]
The molybdenum-nitrogen phase diagram
Journal
of the Less-Common
0 Elsevier
Sequoia
58 (1978) 85 - 98 - Printed in the Netherlands
THE MOLYBDENUM-NITROGEN HERMANN
PHASE DIAGRAM
JEHN
Max-Planck-Institut Stuttgart (F. R.G.)
PETER
85
Metals,
S.A., Lausanne
fiir Metallforschung,
Institut
fiir Werkstoffwissenschaften,
D-7000
ETTMAYER
Institut fiir chemische Technologie Wien, A-1060 Wien (Austria)
(Received
August
anorganischer
Stoffe
der Technischen
Universitiit
10, 1977)
Summary In high and low pressure experiments in the MO-N system the solidus line (a + L) and the composition and temperature of the eutectic (L = cr-MO + y-Mo,N) have been determined. MO dissolves 1.08 at.% N at the eutectic temperature of 1860 “C and at the equilibrium pressure of 670 atm (6.7 X 10’ Pa). The eutectic composition is 19 at.% N and the corresponding N content of y-Mo,N is 27 at.% N. The solubility of N, in MO(~) and the liquidus line (a + L)/L have been calculated on the basis of existing data. For y-Mo,N a melting temperature of 2000 “C has been estimated. An MO-N phase diagram is presented and the phases are discussed in detail. Equations for the solubility of N, in solid and liquid MO, the solid solubility limit and the dissociation and plateau pressures are given together with the Gibbs free energy of the corresponding reactions. The special behaviour of the metal-gas system MO-N is additionally treated in ap-c diagram.
1. Introduction The investigations in the molybdenum-nitrogen system published hitherto were mainly limited to certain special problems such as the structure [ 1 - 51 and ranges of homogeneity [ 5, 61 of stable and me&table nitrides, dissociation pressure [ 71 and thermodynamic data [ 8 - lo] of the nitrides, solubility of nitrogen in solid molybdenum at low [ 11 - 151 and high pressures [ 71, solubility limit [ 71 and solubility in liquid molybdenum [ 16 - 171. The phase relationship between p-Mo,N and y-MosN has been clarified [ 5, 61. The pressure-temperature-concentration relations of the nitrogen solubility in solid molybdenum and the solid solubility limit can also be considered as established [ 71. Other data required for a complete description of the molybdenum-nitrogen system (data on the solidus and
86
the liquidus line, the eutectic temperature and composition and further information on the nitrides) are still missing. Experimental investigations in the molybdenum-nitrogen system are made difficult by the high nitrogen pressures necessary to obtain the equilibrium states. The present paper reports the experimental determination of the solidus line (a-MO/(&-MO + L)) and eutectic temperature (eutectic ~-MO-Lr-Mo,N) as well as the calculation of the liquidus line ((~-MO + L)/L). Furthermore, a temperature-concentration phase diagram is presented and the different phases are discussed. In a pressure-concentration diagram the particular behaviour of a metal-gas system is shown.
2. Experimental 3 1. High pressure
autoclave
The high pressure experiments have been performed in an autoclave at pressures up to 300 atm; the apparatus is shown in Fig. 1. Rods or tubes about 30 mm in length are mounted between watercooled copper electrodes and are resistance heated up to the melting point. Further details of the construction of the autoclave are described elsewhere [ 181. The temperature was measured with an optical pyrometer (A = 0.65 pm). The slit in the molybdenum tube samples gave almost black body con-
push
rod 11
out/et cooling water in1
coolrng system ./
water Insulating washer
vie&g
port
Fig. 1. High pressure autoclave, designed for work at temperatures point of the specimens and at pressures up to 250 atm.
up to the melting
ditions. The absorption by the windows and the high pressure gas atmosphere was taken into consideration and corrected according to previous calibration tests 1191. The nitrogen used had a purity of 99.995%. The autoclave was flushed four or five times by charging with nitrogen gas up to about 40 atm before the experimental pressure was adjusted. The remaining small oxygen impurities were removed by the sample itself via the evaporation of the volatile molybdenum oxides which condense on the cooled walls of the autoclave. The reaction periods were chosen in such a manner that at least a 98% equalization of the nitrogen concentration by diffusion was ensured. Taking into account the diffusion coefficients of nitrogen in molybdenum [ 201, periods of a few minutes each were set for each annealing step at temperatures above 1800 “C. Some additional experiments were performed in a further high pressure autoclave for nitrogen pressures up to 800 atm [ 181. 2.2. Low pressure vacuum device The low pressure experiments have been performed in a high vacuum metal apparatus [ 121 chiefly consisting of a water-cooled vacuum chamber, a pumping system and water-cooled copper electrodes. The wire samples were resistance heated and the temperature was also measured pyrometrically using literature values for the spectral emissivity [ 211. After evacuation of the vacuum chamber the pumping system was shut off and high purity nitrogen was admitted via a needle valve until an experimental pressure of 1.3 X 103, 1.3 X lo4 or 6.65 X lo4 Pa (10, 100 or 500 Torr) was attained. 2.3. Samples The high pressure experiments were performed with pieces of molybdenum tubing 5 mm in diameter, 0.3 mm thick and 30 - 35 mm in length. For the low pressure studies, molybdenum wires 1 mm in diameter and about 300 mm in length were used. The impurity contents, according to the producer (Met~lwerk Plansee, Reutte/Austria), were Si < 100, Fe < 50, C < 50, H < 10, N < 10 ppm. Prior to the experiments the samples had been degassed and recrystallized by a high vacuum anneal at 1700 “C and 1.3 X 10m3 Pa (10m5 Torr) for 4 h. 2.4. Procedure Looking at the isobars in the temperature-~oncen~ation phase diagram (schematically shown in Fig. 2) it can be seen that at constant nitrogen pressure the nitrogen concentration in solid molybdenum increases with rising temperature until the solidus line is reached and the sample melts because of the appearance of a liquid phase, In general, a direct experimental determination of the solidus line, which would involve the simul~eous determination of the melting temperature and of the solid solubility of nitrogen in molybdenum given by temperature, concentration and pressure, is not possible. However, using the known relations between pressure, temperature and concentration in the MO-N solid solution [ 71, the nitrogen concentra-
88
concentration
Fig. 2. Increase of the nitrogen concentration in molybdenum during isobaric heating (schematic): 0, preset temperature steps; 0, melting temperature.
tion at the solidus line can be calculated for the experimental melting temperature at the given nitrogen pressure. In order to determine the melting temperature, the tube and wire samples were heated stepwise at constant nitrogen pressure until the samples melted. The stepwise heating procedure was performed in the following manner. The filament temperature of the pyrometer was set at a temperature 30 - 50 “C above the sample temperature. Then the sample was heated up slowly until the image of the filament disappeared; this temperature was maintained for about 5 min. By this procedure the melting temperature could be shown to be between the last temperature step and the preset pyrometer value. In successive experiments with smaller temperature intervals the melting temperature could be determined to within + 30 “C.
3. Experimental
results
3.1. Solidus line In Table 1 the melting temperatures are given as a function of nitrogen pressure. The corresponding nitrogen concentration of the terminal (Ysolid solution is calculated using the p-T-c relation [7] which is valid in the pressure range 0.01-250 atm and at temperatures of 1600 - 2400 “C and which can be extrapolated to some extent. In Fig. 3 the solidus line is shown in the usual temperature versus concentration plot. It can be seen that the melting temperature is decreased markedly by small nitrogen contents corresponding to relatively low nitrogen pressures, e.g. from 2615 “C for pure molybdenum to 2450 “C at 100 Torr Ns/0.046 at.% N in MO (100 Torr = 1.3 X lo4 Pa). At 250 atm N, (2.5 X 10’ Pa) the melting temperature is 1980 ‘C, corresponding to 0.8 at.% N in the molybdenum solid solution. Figure 3 also shows the extrapolation of the solidus line until it meets the
89
TABLE 1 Experimental meiting temperatures and calculated nitrogen concentrations of molybdenum--nitrogen I_Y solid solution Sample
Nz pressure (atm)
Melting point (“C)
Concentration (at.% N)
MO tubing
385 258 250 245 182 118 103 100 50 50 36 20 20 1.5
1920 1980 1990 1980 1970 2080 2060 2050 2110 2100 2140 2220 2220 2355
0.94 0.88 0.89 0.86 0.73 0.74 0.66 0.64 0.51 0.50 0.48 0.39 0.39 0.13
2370 2360 2460 2450 2450 2440 2510 2500
0.092 0.091
MO wire
0.66 0.66 a.13 0.13 0.13 0.13 0.013 0.013
0.047 0.047 0.047 0.046 0.016 0.016
Fig. 3. Sotidus line of the (Ysolid solution in the MO-N system.
solvus line at 1860 “C. The horizontal line represents the eutectic line which in metal-gas systems is defined by the four-phase equilibrium (a. + L + nitride + gas).
Fig. 4. Microstructure of solidified melted material after melting at the solidus temperature (1920 ‘C, 0.94 at.% N, 385 atm) (160x). T,
3.1
%
22QO2000
2600
3.8
1800
I
I
I
I
1.2
1.6
5.0
5.1
3
/
58
6.i0
d//T, K-' Fig. 5. Plateau pressures over the condensed two-phase regions (a + L) and (c\l+ y-MoaN) in the MO-N system.
Figure 4 shows the microstructure of a solidified melted droplet adhering to the unmelted rest of the tube. The solidified droplet has a spongy appearance with large holes. Within the solidified melt as well as within the unmelted molybdenum metal there are nitride precipitations. Evidently, during the melting of the molybdenum metal saturated with nitrogen, the liquid absorbs large amounts of nitrogen which are liberated again during solidification by the formation of nitrogen bubbles. Obviously only a small part of the dissolved nitrogen in the liquid phase can be retained
91
in solution during solidification at pressures below that of the eutectic equilibrium. The nitride precipitations are formed during further cooling because of the supersaturation of the 01solid solution. 3.2. Plateau pressure The nitrogen equilibrium pressure over the condensed two-phase field (a + L) is determined only by temperature and not by the gross composition. It is therefore often characterized as plateau pressure. Its temperature dependence is shown in Fig. 5 in a log p uersus 1/T plot (curve I). With rising temperature the pressure decreases strongly and the curve reaches asymptotically l/T = 3.46 X 10d4 K-l corresponding to the melting point of pure MO (2615 “C). This curve separates the phases Q and L. Furthermore, in Fig. 5 the dissociation pressure of y-MozN nitride is plotted (curve II). It represents the equilibrium pressure over the condensed two-phase field (a + y) and divides the phase fields of cy and y. By extrapolating both curves, the intersection corresponding to the eutectic temperature and pressure is found to be at 1860 “C and about 670 atm (6.7 X lo7 Pa). 3.3. Eu tectic composition In a high pressure (800 atm) autoclave it was possible to melt a molybdenum tube at a nitrogen pressure of 700 atm. At this pressure, which is slightly above the extrapolated eutectic conditions, a liquid phase is observed which upon solidification shows the typical eutectic structure (Fig. 6). The solidified melted droplet has a glossy surface in contrast to the appearance of the melt at sub-eutectic conditions. The etched phase is MO and the light matrix is r-MozN. The evaluation of the microstructure by quantitative metallography (MO, 30%; MoaN, 70% of the area) and the analysis of the nitrogen content of the Mo,N by X-ray determination of the lattice parameters (a = 0.4196 nm, c = 0.3990 nm; 27 at.% N) gives the eutectic composition at about 19 at.% N.
Fig. 6. Microstructure of an MO-N alloy with a eutectic composition (560X).
92
4. Calculation
of the liquidus line
The direct experimental determination of the liquidus line involves the simultaneous determination of the pressure, temperature and composition of the liquid phase. The correlation between melting temperature and pressure has been measured, but attempts to quench the liquid phase without loss of nitrogen were unsuccessful and led to the spongy structure of the solidified melted material (Fig. 4). However, at 700 atm Na compact melted alloys of the eutectic composition could be obtained and the eutectic point was set at 19 at.% N at 1860 “C (eutectic reaction L = ~-MO + r-Mo,N). From measurements of the nitrogen solubility in liquid molybdenum uersus nitrogen pressure [ 16, 171 the Gibbs free energy of solution of gaseous nitrogen in molybdenum has been calculated as A G&es x = 114 220 J (‘/z mol N,)-’ (Dohmke and Frohberg [ 171) and A G.&a = 114 810 J (?h mol Nz)-l (Kozinaet al. [16]) (27 300 and 27 440 cal (‘/z mol Nz)-l, respectively); these results are in very good mutual agreement. No direct information on the enthalpy and entropy of solution is available so far for liquid molybdenum. However, on the basis of the solubility values [ 16, 171 and the equilibrium at the eutectic point and with the assumption of the validity of Sieverts’ law up to the eutectic concentration, to a first approximation the enthalpy and entropy of solution can be calculated to be 14 430 J (% mol N,)-’ and -34.14 J K-l (% mol N,)-‘, respectively. Thus, the Gibbs free energy A G” and the equilibrium constant k, of the reaction %Np = N (in MO(~)) are given, for A G” in J (% mol NO)-l, by AG” = 14420
+ 34.14 T
(for AG” in cal (% mol N,)-I,
(1) AG” = 3450 + 8.16 T is observed)
and
log h, = log cN - ‘/log pNZ = +0.22 - 750/T where cN is in at.%, pNZ in atm; for& in pascals the term has to be replaced by -2.28. The liquidus line can now be calculated by inserting determined plateau pressure in the (CY+ L) region into eqn. the results. The irregularly broken liquidus line in Fig. 3 is to these values.
(2) +0.22 in eqn. (2) the experimentally (2). Table 2 gives drawn according
5. T-c phase diagram
On the basis of the present results for the.solidus and liquidus line, of the solid solubility studies [7] and of nitride phase studies [ 51, the T-c phase diagram given in Fig. 5 can be drawn. The broken lines give tentative phase boundaries which have not been fully established by experiments.
93
TABLE
2
Calculated
liquidus
line concentrations
Temperature (“C)
Pressure (atm)
Concentration (at.%)
1860 1900 2000 2100 2200 2250 2300 2350 2400 2450 2500
660 500 180 60 17 8 3.4 1.3 0.4 0.1 0.013
19.0 16.8 10.4 6.21 3.40 2.37 1.84 0.98 0.55 0.28 0.10
Additionally some isobars representing the equilibrium nitrogen pressure are included. In the following the phases of the MO-N system will be reviewed in detail. 5.1. a Solid solution The b.c.c. molybdenum crystals have a rather low nitrogen solubility, especially below 1000 “C. At higher temperatures, however, the solubility increases markedly and reaches 1.08 at.% N at the eutectic temperature of 1860 “C. The solid solubility limit c~,,,~~ is represented by eqn. (7) (c N,max in at.%, T in kelvins)
log CN,max = 3.69 - 7800/T
(3)
In the (Ysolid solution the nitrogen solubility obeys SieVertS’ law cN 0: dpNZ; cN and temperature T the interdependence of pressure pN2, concentration in at.%, pN2 in atmospheres, T in kelvins) is given by the equation ccN log
CN =
%logp,,
+ 0.875 - 4810/T
(4)
(forp,, in pascals the term +0.875 has to be replaced by -1.627). The isobaric solubility increases with rising temperature, because of the endothermic character of the solution of nitrogen in solid molybdenum, %Nz = N (in ~-MO). At temperatures above the eutectic temperature (L = (Y-MO+ r-Mo,N) the terminal solubility of nitrogen in ~-MO is given by the solidus line determined in the present study.
94
5.2. Liquid
and eutectic
The eutectic temperature of 1860 “C has been obtained from the intersection of the solidus and liquidus line (Fig. 3) or nitride decomposition pressure and plateau pressure (Fig. 5). The experimentally determined eutectic composition is 19 at.% N. The pressure and temperature dependence of the solubility of nitrogen in liquid molybdenum has been calculated (eqn. (2)). By combining nitrogen solubility and plateau pressure the liquidus line has been calculated (Table 2). 5.3. /3- and y-nitride
(Mo2NI + ,)
The compound MozNI_, crystallizes in two modifications: a tetragonal low temperature form fl-MoaN with an ordered array of nitrogen atoms and a cubic high temperature modification r-Mo,N with a random distribution of the interstitial nitrogen atoms in the octahedral voids [ 5, 61. p-Mo,N has a 141 /amd structure with a = 0.420 nm and c = 0.80 nm [ 61. The structure is characterized by a distorted f.c.c. host lattice with an ordered arrangement of nitrogen atoms similar to the nitrogen martensite Fe,,Ns. y-Mo,N belongs to the Bl structure type with a random distribution of 2 f x nitrogen atoms in the unit cell. The y-phase can be retained at room temperature by quenching. The phase fields of /3-MosN and r-Mo,N are separated by a twophase region on the molybdenum-rich side of the homogeneity range. At nitrogen contents above the stoichiometric composition MozN, the phase transition is supposed to be of a diffusionless order-disorder type analogous to other metal-metalloid compounds TzX (T = transition metal, e.g. V, Nb, ‘I a, MO, W; X = metalloid, e.g. C) [22]. At the MO-rich phase boundaries of fl- and r-MosN a three-phase equilibrium must exist (r-MoaN + &MosN + ~-MO); this is thought to be of the peritectoid type. No direct experimental evidence could be obtained for this reaction because of experimental difficulties. Former propositions for the phase diagram [l] cannot now be maintained [ 51. As previously discussed [ 71, the MO-rich phase boundary of y-Mo,N is bent towards lower nitrogen concentrations at higher temperatures. From X-ray measurements the composition of Mo~N~-~ at the eutectic temperature can be set at 27 at.% N. The melting point of Mo,N has not been determined because of the very high equilibrium pressure of nitrogen required. In an estimation on the basis of a value for the entropy of melting of 30 - 40 J K-l mol-’ (7 - 9 cal K-l mol-‘) a melting point of about 2000 “C has been obtained. The pressure-temperature conditions for the formation of Mo2N1_ have been established in the temperature range 950 - 1500 “C in a previous study [ 71. The dissociation pressure of Mo~N~_~ in equilibrium with the a solid solution is represented by the equation log pNZ = 5.63 - 5990/T
(5)
for pNZ in atm; for pNZ expressed in pascals a coefficient of 10.64 has to be introduced instead of 5.63. The corresponding Gibbs free energy of the
95
nitride
formation
according
to the reaction
(2 + X) “MO” + l/z Ns = Mo~+~N (“MO”
is the nitrogen-saturated L%~~+~N
= -57
a-solid solution)
(6) is given by
320 + 53.89 T
where AGbo2 +,N is in J mol-‘. 12.88 T.
For AG” in cal mol-‘,
(7) AG” = -13
700 +
5.4. 6 -Nitride (MoN) Attempts to prepare 6 -MoN with molecular nitrogen at pressures up to 300 atm have not been successful. 6 -MoN could only be obtained by the action of flowing ammonia on molybdenum powder at temperatures between 700 and 1000 ‘C, because of the very high nitrogen potential of flowing ammonia. According to Schijnberg [2] 6 -MoN has an ordered hexagonal structure with a = 0.5725 nm and c = 0.5608 nm, c/a = 0.985, space group P6smmc. The sites of the nitrogen atoms were not given because of their small contribution to the diffracted intensities. Troitskaya and Pinsker [ 31 have studied thin films of MoN by electron diffraction. These films have been obtained by nitriding vapour-deposited molybdenum films in flowing ammonia. Two forms of molybdenum nitride, F ‘-MoN and 6 “-MoN, were revealed; they differ in the arrangement of the nitrogen atoms and the lattice parameters. 5.5. Nitrogen equilibrium pressure In the metal-gas system MO-N, in contrast to systems with nongaseous components, the gas phase has always to be taken into consideration. Therefore, in the T-c diagram (Fig. 7) the isobars play an important role. A certain temperature-concentration value within the phases can only be obtained or is only stable if the corresponding nitrogen pressure exists. Otherwise the alloy will absorb nitrogen or nitrogen will be given off. Because of the importance of the gas phase, metal-gas systems can be fully represented only by a three-dimensional p-T-c diagram [ 231. Thus the T-c diagram in Fig. 7 represents the projection of the spatially running curves of the phase boundaries and isobaric sections onto the T-c plane. Another projection of the MO-rich part of the MO-N system onto the p-c plane is given in Fig. 8 on a logarithmic scale. This diagram illustrates especially the low concentration relations and gives the equilibrium nitrogen pressure as a function of the gross nitrogen concentration of the condensed phases (solid and liquid) and of the temperature. Three-dimensionally, the isotherms lie on planes representing the two-phase equilibria (a + G), (y + G), (L + G) or the three-phase equilibria ((u + y + G), (a + L + G), (L + y + G). The temperature axis has to be thought of as directed into the page and thus, as the projection is seen from lower to higher temperatures, some planes are not directly visible and the isotherms and phase boundaries are shown by broken lines in this region. In the diagram the isotherms are assigned to the
96
Fig.
7. Phase
diagram
of the MO-N
I
103
system
I
-
with isobars.
I
1860
lc
L+7 ---+d
I8
t7
t6
e. h
$ P
t‘
P cN , at. % Fig. 8. Logp--log c diagram of the MO-rich part of the MO-N a+Na;-------,isothermsL+Na;~,plateaupressurecu+~+N2;.......,plateau pressure 01 + L + Na.
system:
-
-
-,
isotherms
97
phase areas by corresponding underlining. A detailed description of the three-dimensional representation of metal-gas systems has been given by Fromm [ 231. In the following the detailed behaviour of the isotherms will be discussed, starting from low nitrogen concentrations. At temperatures below the eutectic temperature, e.g. 1600 ‘C, the isotherm rises within the (Ysolid solution with a slope of 2 according to Sieverts’ law until it reaches the solid solubility limit. There it enters the (a + y) area and runs horizontally (dissociation pressure, equilibrium CY+ y + G) and increases again within the yphase. With increasing temperature in the QIsolid solution the isotherms are shifted to the right, i.e. to higher N concentrations, and in the (a + y) area to higher N, pressures. At temperatures slightly above 1860 “C (the eutectic temperature), e.g. 1900 ‘C, in the a-phase the isotherm ends at the solidus line, enters the (cu + L) area, runs horizontally until it meets the liquidus line and rises in the liquid phase (L) until it reaches the two-phase area (L + y), runs horizontaly once more and rises again within the y-phase. At temperatures above the melting point of y-MoaN (about 2000 “C in the liquid phase) the isotherms are rising continuously (at low concentrations with a slope of 2) after they have passed the (Yand (a + L) area. The high temperature isotherms in the liquid as well as the low temperature isotherms in the (a + y) area are not fully drawn for clarity. The behavior of the isotherms on the nitrogen-rich side of r-Mo,N is not experimentally established and thus their horizontal continuation into y + 6 or y + L cannot be drawn.
References 1 2 3 4 5 6 7 8
G. Hagg, Z. Phys. Chem., Abt. B, 7 (1930) 339. N. Schonberg, Acta Chem. Stand., 8 (1954) 204. N. V. Troistkaya and Z. G. Pinsker, Sov. Phys. Crystallogr., 6 (1961) 34. N. V. Troitskaya and Z. G. Pinsker, Sov. Phys. Crystallogr., 8 (1963) 441. P. Ettmayer, Monatsh. Chem., 101 (1970) 127. J. H. Evans and K. H. Jack, Acta Crystallogr., 10 (1957) 833. H. Jehn and P. Ettmayer, High Temp.- High Pressures, 8 (1976) 83. 0. Kubaschewski and J. A. Caterall, Thermodynamic Data of Alloys, Pergamon Press, Oxford, 1956. 9 A. D. Mah, Rep. BM-RI 5529,196O. 10 B. Neumann, C. Kroger and H. Kunz, Z. Anorg. Chem., 218 (1934) 379. 11 F. S. Norton and A. L. Marshall, Trans. Metall. Sot. AIME, 156 (1944) 351. 12 E. Fromm and H. Jehn, Z. Metallkd., 62 (1971) 372. 13 G. Horz and E. Steinheil, Z. Metallkd., 62 (1971) 849. 14 R. Fraurnfelder, J. Chem. Phys., 48 (1968) 3966. 15 J. H. Evans and B. L. Eyre, Acta Metall., 17 (1969) 1109. 16 L. N. Kozina, A. Y. Revyakin and A. M. Samarin, Dokl. Akad. Nauk SSSR, 184 (1969) 397. 17 H. Dohmke and M. G. Frohberg, Z. Metallkd., 65 (1974) 615. 18 P. Ettmayer, H. Priemer and R. Kieffer, Metal1 (Berlin), 23 (1969) 307. 19 P. Ettmayer, R. Kieffer and F. Hattinger, Metal1 (Berlin), 28 (1974) 1151. 20 H. Jehn and E. Fromm, J. Less-Common Met., 21 (1970) 333. 21 L. Northcott, Molybdenum, Butterworths, London, 1956, p. 26.
98
22 E. Rudy, Compendium of Phase Diagram Data, US Air Force Syst. Command, Wright Patterson Air Force Mater. Lab. Tech. Rep., AFML-TR-652, Part V, Ohio, 1969. 23 E. Fromm, in E. Fromm and E. Gebhardt (eds.), Gase und Kohlenstoff in Metallen, Springer, Berlin, 1976, p. 45.
of the Less-Common
0 Elsevier
Sequoia
58 (1978) 85 - 98 - Printed in the Netherlands
THE MOLYBDENUM-NITROGEN HERMANN
PHASE DIAGRAM
JEHN
Max-Planck-Institut Stuttgart (F. R.G.)
PETER
85
Metals,
S.A., Lausanne
fiir Metallforschung,
Institut
fiir Werkstoffwissenschaften,
D-7000
ETTMAYER
Institut fiir chemische Technologie Wien, A-1060 Wien (Austria)
(Received
August
anorganischer
Stoffe
der Technischen
Universitiit
10, 1977)
Summary In high and low pressure experiments in the MO-N system the solidus line (a + L) and the composition and temperature of the eutectic (L = cr-MO + y-Mo,N) have been determined. MO dissolves 1.08 at.% N at the eutectic temperature of 1860 “C and at the equilibrium pressure of 670 atm (6.7 X 10’ Pa). The eutectic composition is 19 at.% N and the corresponding N content of y-Mo,N is 27 at.% N. The solubility of N, in MO(~) and the liquidus line (a + L)/L have been calculated on the basis of existing data. For y-Mo,N a melting temperature of 2000 “C has been estimated. An MO-N phase diagram is presented and the phases are discussed in detail. Equations for the solubility of N, in solid and liquid MO, the solid solubility limit and the dissociation and plateau pressures are given together with the Gibbs free energy of the corresponding reactions. The special behaviour of the metal-gas system MO-N is additionally treated in ap-c diagram.
1. Introduction The investigations in the molybdenum-nitrogen system published hitherto were mainly limited to certain special problems such as the structure [ 1 - 51 and ranges of homogeneity [ 5, 61 of stable and me&table nitrides, dissociation pressure [ 71 and thermodynamic data [ 8 - lo] of the nitrides, solubility of nitrogen in solid molybdenum at low [ 11 - 151 and high pressures [ 71, solubility limit [ 71 and solubility in liquid molybdenum [ 16 - 171. The phase relationship between p-Mo,N and y-MosN has been clarified [ 5, 61. The pressure-temperature-concentration relations of the nitrogen solubility in solid molybdenum and the solid solubility limit can also be considered as established [ 71. Other data required for a complete description of the molybdenum-nitrogen system (data on the solidus and
86
the liquidus line, the eutectic temperature and composition and further information on the nitrides) are still missing. Experimental investigations in the molybdenum-nitrogen system are made difficult by the high nitrogen pressures necessary to obtain the equilibrium states. The present paper reports the experimental determination of the solidus line (a-MO/(&-MO + L)) and eutectic temperature (eutectic ~-MO-Lr-Mo,N) as well as the calculation of the liquidus line ((~-MO + L)/L). Furthermore, a temperature-concentration phase diagram is presented and the different phases are discussed. In a pressure-concentration diagram the particular behaviour of a metal-gas system is shown.
2. Experimental 3 1. High pressure
autoclave
The high pressure experiments have been performed in an autoclave at pressures up to 300 atm; the apparatus is shown in Fig. 1. Rods or tubes about 30 mm in length are mounted between watercooled copper electrodes and are resistance heated up to the melting point. Further details of the construction of the autoclave are described elsewhere [ 181. The temperature was measured with an optical pyrometer (A = 0.65 pm). The slit in the molybdenum tube samples gave almost black body con-
push
rod 11
out/et cooling water in1
coolrng system ./
water Insulating washer
vie&g
port
Fig. 1. High pressure autoclave, designed for work at temperatures point of the specimens and at pressures up to 250 atm.
up to the melting
ditions. The absorption by the windows and the high pressure gas atmosphere was taken into consideration and corrected according to previous calibration tests 1191. The nitrogen used had a purity of 99.995%. The autoclave was flushed four or five times by charging with nitrogen gas up to about 40 atm before the experimental pressure was adjusted. The remaining small oxygen impurities were removed by the sample itself via the evaporation of the volatile molybdenum oxides which condense on the cooled walls of the autoclave. The reaction periods were chosen in such a manner that at least a 98% equalization of the nitrogen concentration by diffusion was ensured. Taking into account the diffusion coefficients of nitrogen in molybdenum [ 201, periods of a few minutes each were set for each annealing step at temperatures above 1800 “C. Some additional experiments were performed in a further high pressure autoclave for nitrogen pressures up to 800 atm [ 181. 2.2. Low pressure vacuum device The low pressure experiments have been performed in a high vacuum metal apparatus [ 121 chiefly consisting of a water-cooled vacuum chamber, a pumping system and water-cooled copper electrodes. The wire samples were resistance heated and the temperature was also measured pyrometrically using literature values for the spectral emissivity [ 211. After evacuation of the vacuum chamber the pumping system was shut off and high purity nitrogen was admitted via a needle valve until an experimental pressure of 1.3 X 103, 1.3 X lo4 or 6.65 X lo4 Pa (10, 100 or 500 Torr) was attained. 2.3. Samples The high pressure experiments were performed with pieces of molybdenum tubing 5 mm in diameter, 0.3 mm thick and 30 - 35 mm in length. For the low pressure studies, molybdenum wires 1 mm in diameter and about 300 mm in length were used. The impurity contents, according to the producer (Met~lwerk Plansee, Reutte/Austria), were Si < 100, Fe < 50, C < 50, H < 10, N < 10 ppm. Prior to the experiments the samples had been degassed and recrystallized by a high vacuum anneal at 1700 “C and 1.3 X 10m3 Pa (10m5 Torr) for 4 h. 2.4. Procedure Looking at the isobars in the temperature-~oncen~ation phase diagram (schematically shown in Fig. 2) it can be seen that at constant nitrogen pressure the nitrogen concentration in solid molybdenum increases with rising temperature until the solidus line is reached and the sample melts because of the appearance of a liquid phase, In general, a direct experimental determination of the solidus line, which would involve the simul~eous determination of the melting temperature and of the solid solubility of nitrogen in molybdenum given by temperature, concentration and pressure, is not possible. However, using the known relations between pressure, temperature and concentration in the MO-N solid solution [ 71, the nitrogen concentra-
88
concentration
Fig. 2. Increase of the nitrogen concentration in molybdenum during isobaric heating (schematic): 0, preset temperature steps; 0, melting temperature.
tion at the solidus line can be calculated for the experimental melting temperature at the given nitrogen pressure. In order to determine the melting temperature, the tube and wire samples were heated stepwise at constant nitrogen pressure until the samples melted. The stepwise heating procedure was performed in the following manner. The filament temperature of the pyrometer was set at a temperature 30 - 50 “C above the sample temperature. Then the sample was heated up slowly until the image of the filament disappeared; this temperature was maintained for about 5 min. By this procedure the melting temperature could be shown to be between the last temperature step and the preset pyrometer value. In successive experiments with smaller temperature intervals the melting temperature could be determined to within + 30 “C.
3. Experimental
results
3.1. Solidus line In Table 1 the melting temperatures are given as a function of nitrogen pressure. The corresponding nitrogen concentration of the terminal (Ysolid solution is calculated using the p-T-c relation [7] which is valid in the pressure range 0.01-250 atm and at temperatures of 1600 - 2400 “C and which can be extrapolated to some extent. In Fig. 3 the solidus line is shown in the usual temperature versus concentration plot. It can be seen that the melting temperature is decreased markedly by small nitrogen contents corresponding to relatively low nitrogen pressures, e.g. from 2615 “C for pure molybdenum to 2450 “C at 100 Torr Ns/0.046 at.% N in MO (100 Torr = 1.3 X lo4 Pa). At 250 atm N, (2.5 X 10’ Pa) the melting temperature is 1980 ‘C, corresponding to 0.8 at.% N in the molybdenum solid solution. Figure 3 also shows the extrapolation of the solidus line until it meets the
89
TABLE 1 Experimental meiting temperatures and calculated nitrogen concentrations of molybdenum--nitrogen I_Y solid solution Sample
Nz pressure (atm)
Melting point (“C)
Concentration (at.% N)
MO tubing
385 258 250 245 182 118 103 100 50 50 36 20 20 1.5
1920 1980 1990 1980 1970 2080 2060 2050 2110 2100 2140 2220 2220 2355
0.94 0.88 0.89 0.86 0.73 0.74 0.66 0.64 0.51 0.50 0.48 0.39 0.39 0.13
2370 2360 2460 2450 2450 2440 2510 2500
0.092 0.091
MO wire
0.66 0.66 a.13 0.13 0.13 0.13 0.013 0.013
0.047 0.047 0.047 0.046 0.016 0.016
Fig. 3. Sotidus line of the (Ysolid solution in the MO-N system.
solvus line at 1860 “C. The horizontal line represents the eutectic line which in metal-gas systems is defined by the four-phase equilibrium (a. + L + nitride + gas).
Fig. 4. Microstructure of solidified melted material after melting at the solidus temperature (1920 ‘C, 0.94 at.% N, 385 atm) (160x). T,
3.1
%
22QO2000
2600
3.8
1800
I
I
I
I
1.2
1.6
5.0
5.1
3
/
58
6.i0
d//T, K-' Fig. 5. Plateau pressures over the condensed two-phase regions (a + L) and (c\l+ y-MoaN) in the MO-N system.
Figure 4 shows the microstructure of a solidified melted droplet adhering to the unmelted rest of the tube. The solidified droplet has a spongy appearance with large holes. Within the solidified melt as well as within the unmelted molybdenum metal there are nitride precipitations. Evidently, during the melting of the molybdenum metal saturated with nitrogen, the liquid absorbs large amounts of nitrogen which are liberated again during solidification by the formation of nitrogen bubbles. Obviously only a small part of the dissolved nitrogen in the liquid phase can be retained
91
in solution during solidification at pressures below that of the eutectic equilibrium. The nitride precipitations are formed during further cooling because of the supersaturation of the 01solid solution. 3.2. Plateau pressure The nitrogen equilibrium pressure over the condensed two-phase field (a + L) is determined only by temperature and not by the gross composition. It is therefore often characterized as plateau pressure. Its temperature dependence is shown in Fig. 5 in a log p uersus 1/T plot (curve I). With rising temperature the pressure decreases strongly and the curve reaches asymptotically l/T = 3.46 X 10d4 K-l corresponding to the melting point of pure MO (2615 “C). This curve separates the phases Q and L. Furthermore, in Fig. 5 the dissociation pressure of y-MozN nitride is plotted (curve II). It represents the equilibrium pressure over the condensed two-phase field (a + y) and divides the phase fields of cy and y. By extrapolating both curves, the intersection corresponding to the eutectic temperature and pressure is found to be at 1860 “C and about 670 atm (6.7 X lo7 Pa). 3.3. Eu tectic composition In a high pressure (800 atm) autoclave it was possible to melt a molybdenum tube at a nitrogen pressure of 700 atm. At this pressure, which is slightly above the extrapolated eutectic conditions, a liquid phase is observed which upon solidification shows the typical eutectic structure (Fig. 6). The solidified melted droplet has a glossy surface in contrast to the appearance of the melt at sub-eutectic conditions. The etched phase is MO and the light matrix is r-MozN. The evaluation of the microstructure by quantitative metallography (MO, 30%; MoaN, 70% of the area) and the analysis of the nitrogen content of the Mo,N by X-ray determination of the lattice parameters (a = 0.4196 nm, c = 0.3990 nm; 27 at.% N) gives the eutectic composition at about 19 at.% N.
Fig. 6. Microstructure of an MO-N alloy with a eutectic composition (560X).
92
4. Calculation
of the liquidus line
The direct experimental determination of the liquidus line involves the simultaneous determination of the pressure, temperature and composition of the liquid phase. The correlation between melting temperature and pressure has been measured, but attempts to quench the liquid phase without loss of nitrogen were unsuccessful and led to the spongy structure of the solidified melted material (Fig. 4). However, at 700 atm Na compact melted alloys of the eutectic composition could be obtained and the eutectic point was set at 19 at.% N at 1860 “C (eutectic reaction L = ~-MO + r-Mo,N). From measurements of the nitrogen solubility in liquid molybdenum uersus nitrogen pressure [ 16, 171 the Gibbs free energy of solution of gaseous nitrogen in molybdenum has been calculated as A G&es x = 114 220 J (‘/z mol N,)-’ (Dohmke and Frohberg [ 171) and A G.&a = 114 810 J (?h mol Nz)-l (Kozinaet al. [16]) (27 300 and 27 440 cal (‘/z mol Nz)-l, respectively); these results are in very good mutual agreement. No direct information on the enthalpy and entropy of solution is available so far for liquid molybdenum. However, on the basis of the solubility values [ 16, 171 and the equilibrium at the eutectic point and with the assumption of the validity of Sieverts’ law up to the eutectic concentration, to a first approximation the enthalpy and entropy of solution can be calculated to be 14 430 J (% mol N,)-’ and -34.14 J K-l (% mol N,)-‘, respectively. Thus, the Gibbs free energy A G” and the equilibrium constant k, of the reaction %Np = N (in MO(~)) are given, for A G” in J (% mol NO)-l, by AG” = 14420
+ 34.14 T
(for AG” in cal (% mol N,)-I,
(1) AG” = 3450 + 8.16 T is observed)
and
log h, = log cN - ‘/log pNZ = +0.22 - 750/T where cN is in at.%, pNZ in atm; for& in pascals the term has to be replaced by -2.28. The liquidus line can now be calculated by inserting determined plateau pressure in the (CY+ L) region into eqn. the results. The irregularly broken liquidus line in Fig. 3 is to these values.
(2) +0.22 in eqn. (2) the experimentally (2). Table 2 gives drawn according
5. T-c phase diagram
On the basis of the present results for the.solidus and liquidus line, of the solid solubility studies [7] and of nitride phase studies [ 51, the T-c phase diagram given in Fig. 5 can be drawn. The broken lines give tentative phase boundaries which have not been fully established by experiments.
93
TABLE
2
Calculated
liquidus
line concentrations
Temperature (“C)
Pressure (atm)
Concentration (at.%)
1860 1900 2000 2100 2200 2250 2300 2350 2400 2450 2500
660 500 180 60 17 8 3.4 1.3 0.4 0.1 0.013
19.0 16.8 10.4 6.21 3.40 2.37 1.84 0.98 0.55 0.28 0.10
Additionally some isobars representing the equilibrium nitrogen pressure are included. In the following the phases of the MO-N system will be reviewed in detail. 5.1. a Solid solution The b.c.c. molybdenum crystals have a rather low nitrogen solubility, especially below 1000 “C. At higher temperatures, however, the solubility increases markedly and reaches 1.08 at.% N at the eutectic temperature of 1860 “C. The solid solubility limit c~,,,~~ is represented by eqn. (7) (c N,max in at.%, T in kelvins)
log CN,max = 3.69 - 7800/T
(3)
In the (Ysolid solution the nitrogen solubility obeys SieVertS’ law cN 0: dpNZ; cN and temperature T the interdependence of pressure pN2, concentration in at.%, pN2 in atmospheres, T in kelvins) is given by the equation ccN log
CN =
%logp,,
+ 0.875 - 4810/T
(4)
(forp,, in pascals the term +0.875 has to be replaced by -1.627). The isobaric solubility increases with rising temperature, because of the endothermic character of the solution of nitrogen in solid molybdenum, %Nz = N (in ~-MO). At temperatures above the eutectic temperature (L = (Y-MO+ r-Mo,N) the terminal solubility of nitrogen in ~-MO is given by the solidus line determined in the present study.
94
5.2. Liquid
and eutectic
The eutectic temperature of 1860 “C has been obtained from the intersection of the solidus and liquidus line (Fig. 3) or nitride decomposition pressure and plateau pressure (Fig. 5). The experimentally determined eutectic composition is 19 at.% N. The pressure and temperature dependence of the solubility of nitrogen in liquid molybdenum has been calculated (eqn. (2)). By combining nitrogen solubility and plateau pressure the liquidus line has been calculated (Table 2). 5.3. /3- and y-nitride
(Mo2NI + ,)
The compound MozNI_, crystallizes in two modifications: a tetragonal low temperature form fl-MoaN with an ordered array of nitrogen atoms and a cubic high temperature modification r-Mo,N with a random distribution of the interstitial nitrogen atoms in the octahedral voids [ 5, 61. p-Mo,N has a 141 /amd structure with a = 0.420 nm and c = 0.80 nm [ 61. The structure is characterized by a distorted f.c.c. host lattice with an ordered arrangement of nitrogen atoms similar to the nitrogen martensite Fe,,Ns. y-Mo,N belongs to the Bl structure type with a random distribution of 2 f x nitrogen atoms in the unit cell. The y-phase can be retained at room temperature by quenching. The phase fields of /3-MosN and r-Mo,N are separated by a twophase region on the molybdenum-rich side of the homogeneity range. At nitrogen contents above the stoichiometric composition MozN, the phase transition is supposed to be of a diffusionless order-disorder type analogous to other metal-metalloid compounds TzX (T = transition metal, e.g. V, Nb, ‘I a, MO, W; X = metalloid, e.g. C) [22]. At the MO-rich phase boundaries of fl- and r-MosN a three-phase equilibrium must exist (r-MoaN + &MosN + ~-MO); this is thought to be of the peritectoid type. No direct experimental evidence could be obtained for this reaction because of experimental difficulties. Former propositions for the phase diagram [l] cannot now be maintained [ 51. As previously discussed [ 71, the MO-rich phase boundary of y-Mo,N is bent towards lower nitrogen concentrations at higher temperatures. From X-ray measurements the composition of Mo~N~-~ at the eutectic temperature can be set at 27 at.% N. The melting point of Mo,N has not been determined because of the very high equilibrium pressure of nitrogen required. In an estimation on the basis of a value for the entropy of melting of 30 - 40 J K-l mol-’ (7 - 9 cal K-l mol-‘) a melting point of about 2000 “C has been obtained. The pressure-temperature conditions for the formation of Mo2N1_ have been established in the temperature range 950 - 1500 “C in a previous study [ 71. The dissociation pressure of Mo~N~_~ in equilibrium with the a solid solution is represented by the equation log pNZ = 5.63 - 5990/T
(5)
for pNZ in atm; for pNZ expressed in pascals a coefficient of 10.64 has to be introduced instead of 5.63. The corresponding Gibbs free energy of the
95
nitride
formation
according
to the reaction
(2 + X) “MO” + l/z Ns = Mo~+~N (“MO”
is the nitrogen-saturated L%~~+~N
= -57
a-solid solution)
(6) is given by
320 + 53.89 T
where AGbo2 +,N is in J mol-‘. 12.88 T.
For AG” in cal mol-‘,
(7) AG” = -13
700 +
5.4. 6 -Nitride (MoN) Attempts to prepare 6 -MoN with molecular nitrogen at pressures up to 300 atm have not been successful. 6 -MoN could only be obtained by the action of flowing ammonia on molybdenum powder at temperatures between 700 and 1000 ‘C, because of the very high nitrogen potential of flowing ammonia. According to Schijnberg [2] 6 -MoN has an ordered hexagonal structure with a = 0.5725 nm and c = 0.5608 nm, c/a = 0.985, space group P6smmc. The sites of the nitrogen atoms were not given because of their small contribution to the diffracted intensities. Troitskaya and Pinsker [ 31 have studied thin films of MoN by electron diffraction. These films have been obtained by nitriding vapour-deposited molybdenum films in flowing ammonia. Two forms of molybdenum nitride, F ‘-MoN and 6 “-MoN, were revealed; they differ in the arrangement of the nitrogen atoms and the lattice parameters. 5.5. Nitrogen equilibrium pressure In the metal-gas system MO-N, in contrast to systems with nongaseous components, the gas phase has always to be taken into consideration. Therefore, in the T-c diagram (Fig. 7) the isobars play an important role. A certain temperature-concentration value within the phases can only be obtained or is only stable if the corresponding nitrogen pressure exists. Otherwise the alloy will absorb nitrogen or nitrogen will be given off. Because of the importance of the gas phase, metal-gas systems can be fully represented only by a three-dimensional p-T-c diagram [ 231. Thus the T-c diagram in Fig. 7 represents the projection of the spatially running curves of the phase boundaries and isobaric sections onto the T-c plane. Another projection of the MO-rich part of the MO-N system onto the p-c plane is given in Fig. 8 on a logarithmic scale. This diagram illustrates especially the low concentration relations and gives the equilibrium nitrogen pressure as a function of the gross nitrogen concentration of the condensed phases (solid and liquid) and of the temperature. Three-dimensionally, the isotherms lie on planes representing the two-phase equilibria (a + G), (y + G), (L + G) or the three-phase equilibria ((u + y + G), (a + L + G), (L + y + G). The temperature axis has to be thought of as directed into the page and thus, as the projection is seen from lower to higher temperatures, some planes are not directly visible and the isotherms and phase boundaries are shown by broken lines in this region. In the diagram the isotherms are assigned to the
96
Fig.
7. Phase
diagram
of the MO-N
I
103
system
I
-
with isobars.
I
1860
lc
L+7 ---+d
I8
t7
t6
e. h
$ P
t‘
P cN , at. % Fig. 8. Logp--log c diagram of the MO-rich part of the MO-N a+Na;-------,isothermsL+Na;~,plateaupressurecu+~+N2;.......,plateau pressure 01 + L + Na.
system:
-
-
-,
isotherms
97
phase areas by corresponding underlining. A detailed description of the three-dimensional representation of metal-gas systems has been given by Fromm [ 231. In the following the detailed behaviour of the isotherms will be discussed, starting from low nitrogen concentrations. At temperatures below the eutectic temperature, e.g. 1600 ‘C, the isotherm rises within the (Ysolid solution with a slope of 2 according to Sieverts’ law until it reaches the solid solubility limit. There it enters the (a + y) area and runs horizontally (dissociation pressure, equilibrium CY+ y + G) and increases again within the yphase. With increasing temperature in the QIsolid solution the isotherms are shifted to the right, i.e. to higher N concentrations, and in the (a + y) area to higher N, pressures. At temperatures slightly above 1860 “C (the eutectic temperature), e.g. 1900 ‘C, in the a-phase the isotherm ends at the solidus line, enters the (cu + L) area, runs horizontally until it meets the liquidus line and rises in the liquid phase (L) until it reaches the two-phase area (L + y), runs horizontaly once more and rises again within the y-phase. At temperatures above the melting point of y-MoaN (about 2000 “C in the liquid phase) the isotherms are rising continuously (at low concentrations with a slope of 2) after they have passed the (Yand (a + L) area. The high temperature isotherms in the liquid as well as the low temperature isotherms in the (a + y) area are not fully drawn for clarity. The behavior of the isotherms on the nitrogen-rich side of r-Mo,N is not experimentally established and thus their horizontal continuation into y + 6 or y + L cannot be drawn.
References 1 2 3 4 5 6 7 8
G. Hagg, Z. Phys. Chem., Abt. B, 7 (1930) 339. N. Schonberg, Acta Chem. Stand., 8 (1954) 204. N. V. Troistkaya and Z. G. Pinsker, Sov. Phys. Crystallogr., 6 (1961) 34. N. V. Troitskaya and Z. G. Pinsker, Sov. Phys. Crystallogr., 8 (1963) 441. P. Ettmayer, Monatsh. Chem., 101 (1970) 127. J. H. Evans and K. H. Jack, Acta Crystallogr., 10 (1957) 833. H. Jehn and P. Ettmayer, High Temp.- High Pressures, 8 (1976) 83. 0. Kubaschewski and J. A. Caterall, Thermodynamic Data of Alloys, Pergamon Press, Oxford, 1956. 9 A. D. Mah, Rep. BM-RI 5529,196O. 10 B. Neumann, C. Kroger and H. Kunz, Z. Anorg. Chem., 218 (1934) 379. 11 F. S. Norton and A. L. Marshall, Trans. Metall. Sot. AIME, 156 (1944) 351. 12 E. Fromm and H. Jehn, Z. Metallkd., 62 (1971) 372. 13 G. Horz and E. Steinheil, Z. Metallkd., 62 (1971) 849. 14 R. Fraurnfelder, J. Chem. Phys., 48 (1968) 3966. 15 J. H. Evans and B. L. Eyre, Acta Metall., 17 (1969) 1109. 16 L. N. Kozina, A. Y. Revyakin and A. M. Samarin, Dokl. Akad. Nauk SSSR, 184 (1969) 397. 17 H. Dohmke and M. G. Frohberg, Z. Metallkd., 65 (1974) 615. 18 P. Ettmayer, H. Priemer and R. Kieffer, Metal1 (Berlin), 23 (1969) 307. 19 P. Ettmayer, R. Kieffer and F. Hattinger, Metal1 (Berlin), 28 (1974) 1151. 20 H. Jehn and E. Fromm, J. Less-Common Met., 21 (1970) 333. 21 L. Northcott, Molybdenum, Butterworths, London, 1956, p. 26.
98
22 E. Rudy, Compendium of Phase Diagram Data, US Air Force Syst. Command, Wright Patterson Air Force Mater. Lab. Tech. Rep., AFML-TR-652, Part V, Ohio, 1969. 23 E. Fromm, in E. Fromm and E. Gebhardt (eds.), Gase und Kohlenstoff in Metallen, Springer, Berlin, 1976, p. 45.