Thermophysical properties of the intermetallic Mn3MN perovskites II. Heat capacity of manganese zinc nitride: Mn3ZnN and manganese gallium nitride: Mn3GaN

M-1563 J. Chem. Thermodynamics 1983,15, 104-1057

Thermophysical properties of the intermetallic Mn,MN perovskites II. Heat capacity of manganese zinc nitride: Mn,ZnN and manganese gallium nitride: Mn,GaN JOAQUfN GARCfA, JUAN BARTOLOMI?, DOMINGO GONZALEZ, Departamento de Termologia, Fact&ad Universidad de Zaragoza, Spain

de Ciencias,

RAFAEL NAVARRO, Departamento

de Fisica. E. T.S.I.I.,

Universidad de Zaragoza,

Spain

and DANIEL FRUCHART Laboratoire

de Cristallographie,

C.N.R.S.

166X, 38042 Grenoble-Cedex,

(Received 9 February 1983; in revisedform

France

20 April 1983)

Heat-capacity measurements from 5 to 345 K for Mn,ZnN and Mn,GaN are here reported. When one lowers the temperature Mn,ZnN shows two anomalies: the first at TN = (191.4+0.1) K, sharp and narrow, and the second at 7” = (127.510.1) K. The transitions are due to magnetic ordering and lattice expansion, and to magnetic re-ordering and lattice contraction, respectively. Moreover, both transitions have first-order character. Mn,GaN shows only one anomaly at TN = (278.5fO.l) K, sharp and narrow, due to the magnetic ordering and an abrupt lattice contraction. The equilibrium molar thermodynamic properties at 298.15 K are Mn,ZnN Mn,GaN

C, JR 14.56 14.84

%V,YR 18.878 18.772

~KVb-ffXWR 2992.7 2965.2

K

-{G(T)-KX%IRT 8.841 8.827

The analysis of the results below 10 K yields the low-temperature electronic coefficients: y = (0.022+0.001) J.K-‘.rnol-’ for Mn,ZnN and y = (0.038t0.002) J.K-‘.mol-’ for Mn,GaN. The existence of a variation in y in the transition at TA for the Zn compound is clearly derived. For the Ga compound no y change was detected, but an anomalous electronic contribution was noted.

1. Introduction The metallic cubic perovskites Mn,ZnN and Mn,GaN derive from the parent compound Mn,N, (1-3) by substituting the manganese located at the corners of the cube by the divalent metal. Since both Zn and Ga have more electrons than Mn, this change may affect the electronic band structure or its filling, which will be 0021-9614/83/111041+17

%02.00/O

0 1983 Academic Press Inc. (London) Ltd.

1042

J.

GARCiA ET AL.

reflected in the magnetic and structural properties. Since neither Zn nor Ga are magnetic, none of the compounds can support a ferrimagnetic structure, as Mn,N does.t3’ Therefore, the competing interaction effects among the manganese atoms centred at the faces of the cube would be manifested more clearly.“-” Both compounds are cubic for T < 400 K (Pm3m symmetry). At T = 350 K the lattice parameters for Zn and Ga are 395 and 388.5 pm,“,5’ respectively. For both compounds the lattice parameter suffers abrupt changes, but the compounds remain cubic.(‘~*’ When one cools the Zn compound, at TN= 191.4 K the unit cell expands: Au = 1.7 pm, while for 130 K > T > 90 K the unit cell contracts: A(1 = - 2.3 pm. This last transition was a rather diffuse one. For the Ga compound. the unit cell expands: Au = 1.3 pm, at TN = 298 K upon cooling.‘1’2’ Magnetization, magnetic susceptibility, and neutron-diffraction measurements Mn,ZnN”~‘.” orders in a triangular have characterized each compound. antiferromagnetic arrangement (rsl:symmetry) at TN. At TA = 127.5 K it reorders changing to a highly anisotropic quadratic antiferromagnetic magnetically, arrangement. For the latter structure the magnetic cell doubles the chemical lattice. The Mn,GaN”,“’ orders antiferromagnetically at TN (rsp. symmetry); the magnetic structure remains the same down to 4.2 K. In both compounds diffuse neutron scattering was detected in the paramagnetic state,“’ implying localized moments: p(Zn)//c,, = 1.1 and p(Ga)/p” = 1.1 (1~~~Bohr magneton). Finally, for Mn,GaN there is a study of the relative temperature variation of the resistivity.‘5’ which. upon heating, shows a sudden increase at &,. All these experimental facts strongly suggest the existence of interrelated structural, magnetic, and electronic effects at the transitions. indicating, therefore. that a calorimetric study is worthwhile. This study will focus on the nature of the transitions.

2. Experimental The compounds were prepared by solid-state reaction of the non-stoichiometric nitride Mn z+,N, of known composition, with appropriate amounts of pure Mn and Zn or Ga.“,5’ The reactants were finely powdered, thoroughly mixed. and sealed in an evacuated quartz ampoule, which was heated at 1120 K. The purities of the obtained samples were characterized by X-ray diffraction and thermomagnetic measurements.‘5’ Heat-capacity measurements between 5 and 340 K. using the heat-pulse technique, were performed in an adiabatic cryostat.‘“’ For both compounds a goldplated copper sample vessel (laboratory designation J-l) was used. After evacuation of the air from the loaded vessel, about 9 kPa of He was used as exchange gas. The capillary tube used for that operation was finally clipped and sealed with Woods metal. For both compounds, two different calorimetric-vessel loadings were performed; the samples and the addenda used for the different determinations are shown in table 1. The heat capacities of the compounds were obtained by subtracting from the total measured heat capacity the contributions of the empty vessel. previously

HEAT CAPACITY

OF Mn,ZnN

AND Mn,GaN

1043

TABLE 1. Characteristics of the samples and addenda used for the different experiments Experiment I

Experiment II

Mn,ZnN m(sample) Am(copper capillary) Am(Woods metal) AMHe, g) Am(Sn + 50 mass per cent Pb, solder) m(sample) Am(copper capillary) Am(Woods metal) AN-k 4

43.6101 g

44.3316g -9.2 mg

79.1 mg 7.8 mg 0.23 mg

-112.1 mg 0.24 mg 89.7 mg Mn,GaN g 118mg -60.5 mg 0.32 mg 24.4966

Omg 24.3685 g 106.4 mg

199.3 mg 0.32 mg

determined,“’ and small corrections for the addenda. In table 1 are also included the mass differences between filled and empty vessel. 3. Heat capacity and thermodynamic

properties

of Mn,ZnN

The experimental molar heat capacities of Mn,ZnN, listed in chronological order in table 2, are represented in figure 1. The series I to XII correspond to results taken with the usual technique of heat pulses, starting at liquid- or solid-nitrogen temperatures. The series XIII was obtained by the “setback” method: cooling through a temperature interval and giving afterwards a heat pulse which increments the temperature to an extent smaller than the cooling decrement. Therefore, each point involves a cooling and a warming step. In series XIV the sample was cooled from room temperature to 103.4 K and the heat-capacity measurements were taken. The procedure was repeated for series XV but after cooling to 93.6 K. In addition, series XVI and XVII were made using liquid helium as cooling source and series XVIII and XIX correspond to enthalpy determinations. All these series correspond to experiment 1 of table 1. Finally, the series XX to XXII belong to experiment 2, performed after refilling the sample vessel, and were devoted to the study of the lower temperatures. The estimated accuracy is about 6 per cent for T < 14 K and 0.2 per cent for T > 30 K. In the anomalous region the precision decreases due to the steep slope of C,,(T), each point being rather sensitive to the temperature increment used in its measurement. Differences between adjacent measurements give approximately the temperature increment applied. The heat capacity of Mn,ZnN shows two anomalies. Upon cooling, at TN (191.4 +O.l) K a sharp, AC,,,,/R = 65, and narrow, AT = 3 K, peak was detected, corresponding with the transition from paramagnetism to an antiferromagnetic triangular arrangement, together with an abrupt lattice expansion. At TA = (127.5 +O.l) K a second anomaly with AC,, JR = 3.5 and AT x 10 K was also

J. GARCIA

1044 TABLE

TIK

C,.mlR

Series I 49.81 2.729 52.45 3.052 54.86 3.337 66.58 4.703 Series II 77.83 5.956 79.17 6.074 80.48 6.226 81.77 6.345 83.03 6.475 84.27 6.598 Series III 87.75 6.938 90.77 7.212 7.481 93.68 96.50 7.733 99.25 7.985 101.93 8.227 104.53 8.455 107.07 8.684 109.56 8.906 111.98 9.163 114.84 9.510 118.08 9.927 121.20 10.63 124.11 11.94 126.82 13.05 129.47 12.64 132.19 11.95 134.98 11.51 137.82 11.25 140.68 11.09 145.02 11.04 150.78 11.18 156.45 11.33 162.01 11.68 167.46 12.00 Series IV 172.82 12.29 178.04 12.75 183.03 13.98 187.22 21.64 189.91 47.83 191.58 61.51 194.31 18.45 198.85 12.73

2. Experimental

TIK

C,.mlR

Series V 204.07 12.79 209.12 12.87 214.13 12.98 219.10 13.10 224.03 13.22 229.82 13.33 236.18 13.45 242.21 13.53 248.35 13.65 254.60 13.78 260.81 13.90 266.98 14.03 Series VI 274.16 14.17 282.25 14.30 290.3 1 14.43 298.30 14.55 306.28 14.67 321.49 14.85 Series VII 56.95 3.590 59.02 3.840 60.98 4.07 1 63.32 4.344 66.23 4.678 69.27 5.028 74.28 5.559 Series VIII 116.04 9.609 117.18 9.803 118.31 9.959 119.42 10.18 120.51 10.44 121.58 10.78 122.62 11.13 Series IX 123.64 11.68 124.62 12.40 125.57 12.83 126.50 13.10 127.42 13.12 128.35 12.89 129.28 12.59 130.23 12.34 131.47 12.07 133.00 11.75

molar

TIK

heat capacity

C,,mIR

Series X 179.00 12.82 180.96 13.13 182.88 13.68 184.72 14.91 186.04 16.66 186.86 18.92 187.60 21.91 188.26 25.62 188.84 30.64 189.35 36.71 Series XI 189.81 43.55 190.18 52.92 190.51 57.77 190.82 63.03 191.10 67.02 191.38 68.55 191.65 66.48 Series XII 192.12 56.10 192.50 40.14 193.02 26.47 193.73 18.22 194.61 14.05 Series XIII 136.94 10.40 134.99 10.26 133.61 10.19 132.25 10.12 131.36 10.08 130.10 10.01 129.11 9.958 127.76 9.881 126.08 9.790 124.53 9.708 122.95 9.604 121.31 9.516 119.77 9.458 118.76 9.383 118.02 9.345 116.68 9.271 114.86 9.163 113.03 9.044 111.08 8.912 109.18 8.780

ET AL. of Mn,ZnN

TIK

(R = 8.3143 J’K-“mol-‘)

C,,,/R

TIK

c,,,!R

27.64 0.524 112.82 8.986 28.74 0.595 107.22 8.61 1 30.04 0.689 105.28 8.484 31.51 0.800 103.26 8.336 32.81 0.907 100.89 8.167 34.50 1.058 96.44 7.808 1.249 91.51 7.319 36.52 38.82 1.484 87.10 6.879 6.518 41.37 1.754 83.44 1.997 78.85 6.050 43.59 2.226 75.10 5.652 45.58 69.78 5.073 47.75 2.486 Series XIV 50.09 2.761 (After cooling 52.45 3.048 to 103.4 K) 54.85 3.335 104.86 8.469 57.27 3.628 107.70 8.692 59.71 3.919 110.47 8.888 Series XVIII 113.18 9.082 98.23 7.912 115.84 9.268 AH,,, detn. 118.46 9.425 T=99.74K 121.04 9.567 T,‘= 155.84 K 123.58 9.730 A,,,H,/R Series XV = 597.84 K (After cooling 156.92 11.29 to 93.6 K) Series XIX 120.28 9.918 167.98 12.04 122.84 10.32 AH- .,,detn. 125.32 10.87 7;=172.16K 127.73 11.10 r,=204.8 K 130.13 10.95 4s HJR 132.53 10.85 =612.66 K Series XVI 207.60 122.88 16.11 0.097 Series XX 17.30 0.112 6.78 0.024 18.30 0.142 0.029 8.28 19.17 0.156 9.02 0.035 19.95 0.170 9.61 0.037 Series XVII 10.13 0.046 20.48 0.208 0.045 10.75 21.70 0.235 11.44 0.052 22.78 0.277 0.058 12.17 23.76 0.318 13.03 0.062 24.62 0.355 13.96 0.073 25.38 0.399 14.83 0.083 26.40 0.452 15.70 0.094

T/K

C’,,,,!R

16.68 0.113 17.89 0.135 19.24 0.166 20.47 0.202 21.65 0.24 1 22.80 0.287 23.98 0.337 25.35 0.405 Series XXI 7.22 0.027 8.21 0.029 8.99 0.036 9.63 0.038 10.20 0.045 10.87 0.046 11.62 0.052 12.25 0.057 12.83 0.062 13.43 0.069 14.23 0.076 15.08 0.088 16.02 0.102 17.04 0.118 17.97 0.138 18.88 0.158 19.91 0.185 Series XXII 6.05 0.019 7.02 0.025 7.75 0.028 8.35 0.027 9.05 0.037 9.76 0.038 10.54 0.045 11.35 0.046 12.07 0.054 12.78 0.062 13.62 0.070 14.57 0.080 15.41 0.093 16.31 0.106 17.31 0.123 17.55 0.129 18.56 0.151 19.66 0.178

detected, corresponding to a magnetic reorientation to the quadratic-antiferromagnetic structure and to a decrease of the cell parameter.‘1*2*6.7) Both transition temperatures agree with previous determinations by neutron diffraction and magnetic susceptibility. In the neighbourhood of the transitions a detailed study, employing dynamical

HEAT CAPACITY I

OF MnsZnN AND MnsGaN I

I

1045 I

1

0

15

0

5

0

200 250 300 T/K FIGURE 1. Experimental heat capacity of Mn,ZnN between 5 and 350 K. 0, The usual heat points; A, the heat capacity obtained by the “setback” technique, in such a way that the upper pl retained. In the insert the low-temperature points are plotted on an enlarged scale. 0

100

50

150

1 60I

% \ 5 40, 0”

-

-

20

175

I

I

I

I

180

185

190

195

T/K FIGURE 2. Heat capacity of the anomaly at 191.4 K of MnsZnN. 0, Heat pulse results; -, capacity curve deduced from the heating thermogram; - - -, heat-capacity curve obtained fro cooling thermogram.

J. GARCIA

1046

ET AL.

14

I2

8

80

100

I LO 1.' K

140

I ho

FIGURE 3. Heat capacity of the anomaly at 127.5 K of Mn,ZnN. 0, The heat-pulse results; n and A, points obtained after cooling the sample to 103.5 and 93.5 K, respectively; 0, points for the metastable upper phase, as obtained from the “setback” technique; -and - - -. curves deduced from heating and cooling thermograms, respectively.

was performed. Using the methods described elsewhere’lO’ heating and cooling thermograms were made and the temperature rate was z 0.3 mK s ‘. The results for the TN anomaly are plotted in figure 2 together with the discrete c p.m points. The coincidence between the heat capacities measured by the heat pulse-technique and deduced from the heating thermogram was excellent. The C,~, results deduced from the cooling thermogram resemble the heating one in shape and in height, but are displaced downwards by FT = 7.5 K. The same experimental procedure was applied at the anomaly at TA, and in figure 3 results are shown, together with the points from various determinations. Again, the same matching of points from discrete C,,, and heating-thermogram points occurs, with a downward shift of about 6T = 33 K for the cooling thermogram. However, such high thermal hysteresis for the cooling thermogram invalidates some of the approximations involved in the evaluation of C,,, from the thermograms(“’ and, therefore, the dashed line has only qualitative validity. The existence of metastable thermodynamic states shown clearly by the C,,, points of series XIII, indicated that the intermediate phase was retained. Series XIV, obtained after slow cooling of the sample to 103.4 K, had retained most of the intermediate phase. When the sample was slowly cooled further to 93.6 K (series XV) the lowtemperature phase appeared in part, since the results clearly deviate from the other measurements. In any case, C,., always peaks at TA and, therefore, for T > TA the substance is fully converted to the intermediate phase. measurements,

HEAT TABLE

5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 127.6 130 140

0.016 0.041 0.087 0.187 0.378 0.686 1.105 1.606 2.160 2.752 3.953 5.101 6.169 7.145 8.043 8.950 10.305 13.31 12.43 11.11

3. Thermodynamic

0.015 0.032 0.056 0.093 0.153 0.247 0.383 0.563 0.784 1.042 1.650 2.346 3.098 3.882 4.682 5.491 6.321 7.046 7.287 8.147

CAPACITY

functions

0.037 0.172 0.474 1.128 2.497 5.107 9.542 16.292 25.689 37.96 71.51 116.83 173.26 239.90 315.91 400.90 496.31 586.26 617.25 733.2

OF Mn,ZnN

of Mn,ZnN

0.007 0.015 0.024 0.036 0.053 0.077 0.111 0.156 0.213 0.282 0.458 0.677 0.933 1.217 1.523 1.847 2.185 2.452 2.539 2.910

AND

Mn,GaN

(R = 8.3143 J.K-‘.mol-‘;

150 160 170 180 191.4 200 210 220 230 ;z 4: 273.15 280 290 298.15 300 320

11.12 11.61 12.08 13.02 67.46 12.74 12.91 13.12 13.32 13.51 13.69 13.88 14.07 14.13 14.26 14.44 14.56 14.58 14.82

8.909 9.641 10.359 11.071 12.529 13.445 14.070 14.675 15.263 15.834 16.389 16.930 17.457 17.621 17.972 18.476 18.878 18.968 19.917

1047 M = 244.199 g’mol-‘)

843.6 957.1 1075.5 1200.0 1473.4 1651.0 1779.1 1909.2 2041.5 2175.6 2311.7 2449.5 2589.3 2633.7 2731.0 2874.5 2992.7 3019.6 3313.6

3.285 3.659 4.032 4.404 4.831 5.190 5.598 5.997 6.387 6.769 7.142 7.509 7.867 7.979 8.219 8.564 8.841 8.903 9.562

On the other hand, the large hysteresis discussed above explains the diffuse character found for the transition at T,, as detected in X-ray and in magneticsusceptibility measurements.“*3*7) The non-anomalous and anomalous regions were considered separately to obtain the thermodynamic functions. In the non-anomalous regions results were smoothed by fitting appropriate polynomials by the least mean-square method and using Justice’s criteria.“‘) In the anomalous regions the discrete C,,, points together with C,,, obtained from the heating thermogram were treated as above.(12) Temperature intervals with definite C,, curvature were chosen in the fitting procedure to obtain the results listed in table 3. At low temperatures a fit of C,,,/T against T2 was performed and extrapolated to T = 0. Specific determinations of the enthalpy for the first-order transitions at TA and TN were performed, and in table 4 the results are summarized. The enthalpy obtained in the enthalpy-determination series compares with that deduced from the series of discrete points and with the one obtained by numerical integration of the C,,,(T) polynomials. The satisfactory agreement between determined enthalpy and the various calculated values, for both transitions, excludes the presence of nonobserved anomalies in those ranges. From the above calculated enthalpies and entropies, the anomalous values AH and AS were deduced. In order to do this, an estimation of the non-anomalous contribution (base line) was made. Thus, for the transition at TA the series XIII was used to join the points smoothly before and after the transition. On the contrary, since TN is a narrow transition, the base line was obtained by smooth interpolation of c, m above and below TN.The results are given in table 4.

TABLE

4. Enthalpy determination for the transition of Mn,ZnN (a) at & = 191.4 K. Estimation of the anomalous enthalpy and entropy

7;

T

K

K

99.14 100.62 100

155.84 159.26 156

k-4 Series XVIII Series III Numerical integration ~~~. .~~ Enthalpy mean value: Enthalpy base line: Enthalpy Entropy

7;

Series XIX Series IV and V Numerical integration

7; K

172.16 170.18 172

204.8 206.6 205

K))/(R K);/(R

I I

H,(205 K)-H,(l72 .-..-RK

612.66 657.9

615.39 616.86 617.24

K)-H,(172 K)-Hi{156 K)-H,(205

K))/(R K);/(R K);!(R 156 K))/(R

I

I

00

00 o”

K) = K) = KJ =

K)

1.2

K) = 1131.1 &1.X K) = 920.1&1.8

I

clu-

616.51 188.05 326.59

TN)/(R K) =

AH,( = 1.1 1 +O.Ol

AS,(T,);R

00

K) = 596.3* K) = 551.0+

RK

/H,(230K)-H,(l56K);.i(R

,

K)

596.87 595.6 1 596.17

Kl-H,(lCG Kl-H;(lOO

;H,(230 ;H,J230 K)-H,(

of transition: of transition:

K)-H,(lOO RK

591.84 621.59

jHJ205 i&(172

Total enthalpy: Enthalpy base line:

H,(l56

H,,,(q)-H;(T,) ~.-___-.

K

Enthalpy mean value: Numerical integration of the fitted polynomials:

changes

AH,(T,),'(R K) = 45.3i’ T,);R = 0.34kO.O 1

A&,(

(b)

Enthalpy Entropy

H,J7+H,(T,) RK

jH,(l56 iH,(l56

of transition: of transition:

TA = 127.5 K and (b) at

211 k 3.6

1

I

20

00

00 00

Ih

do0 O0 O0

I.2

O0 00

2

O0

(I.8

,p /

0.4

R B”

0

Al

0

IO

20

30

31 5(1

7-/ K FIGURE 4. Experimental heat capacity of Mn,GaN between 5 and 350K. In the insert has been plotted, on an enlarged scale, the low-temperature range. The points of the anomaly, for the sake of clarity, have been reserved for figure 5.

HEAT TABLE T/K

GnlR

Series 48.67 50.85 52.86 55.05 57.46 59.91 62.59 65.30 67.87 70.61 73.51 Series 76.47 79.43 82.51 85.72 88.81 92.06 95.47 98.80 102.37 106.13 109.80 113.52 117.27 120.96 124.59 128.17

I 3.25 1 3.513 3.743 4.008 4.285 4.565 4.858 5.148 5.412 5.681 5.960 II 6.234 6.499 6.768 7.031 7.271 1.527 7.710 8.007 8.231 8.497 8.742 8.991 9.317 9.338 9.474 9.625

5. Experimental T/K

C,.JJR

Series III 131.82 9.800 135.68 9.968 139.87 10.16 143.99 10.34 148.18 10.52 152.46 10.69 156.97 10.86 161.67 11.05 166.31 11.22 Series IV 170.89 11.39 175.96 11.58 181.44 11.77 186.85 11.96 192.16 12.16 197.41 12.32 202.61 12.49 208.10 12.66 213.87 12.84 219.57 13.03 225.22 13.20 230.82 13.35 236.38 13.51 Series V 242.43 13.18 247.85 13.98 253.22 14.17 258.88 14.40

CAPACITY molar T/K

OF Mn,ZnN

heat capacity &JR

264.78 14.81 270.63 16.34 275.64 28.45 278.92 61.39 Series VI 282.83 19.01 288.98 14.91 295.94 14.81 302.71 14.89 309.32 14.91 315.91 14.97 322.44 15.00 328.94 15.05 334.94 15.10 Series VII 6.53 0.040 9.02 0.055 10.56 0.071 11.73 0.085 12.61 0.095 13.31 0.111 14.52 0.131 15.12 0.145 15.73 0.164 16.35 0.180 16.97 0.198 17.59 0.223 18.23 0.244 18.95 0.276

AND

of MnsGaN T/K

C,.,,JR

19.77 20.58 21.45 22.39 23.40 24.45 25.50 26.63 27.87 29.23 30.74 32.69 35.18 37.73 39.93 42.02 44.09 46.45 49.37 52.33 55.28 58.27 Series 268.68 270.53 272.33 274.02 275.52 276.76

0.312 0.353 0.401 0.458 0.528 0.591 0.680 0.771 0.881 1.001 1.152 1.364 1.632 1.919 2.181 2.430 2.678 2.970 3.329 3.680 4.035 4.378 VIII 15.27 15.93 17.21 19.93 25.51 36.21

Mn,GaN

1049

(R = 8.3143 J.K-“mol-‘) T/K

C,, JR

T/K

C,. JR

277.71 53.97 121.93 278.44 70.26 123.01 Series IX 124.06 279.12 63.30 125.10 279.98 39.84 Series 281.26 21.82 115.18 282.95 15.49 115.44 284.82 15.05 115.71 Series X 115.97 AH,,, detn. 116.23 T = 269.80 K 116.49 T,=286.84 K 116.75 Atr,H JR 117.02 =451.75 K 117.28 Series XI 117.55 93.51 7.632 117.82 98.05 7.957 118.08 102.43 8.255 118.34 106.65 8.533 118.59 110.76 8.801 118.85 113.32 8.937 119.11 Series XII 119.37 114.43 9.027 119.64 115.52 9.125 119.91 116.61 9.207 120.17 117.68 9.413 120.42 118.75 9.311 120.68 119.81 9.295 120.86 9.345

9.318 9.386 9.432 9.464 XIII 9.120 9.126 9.105 9.202 9.258 9.230 9.214 9.319 9.427 9.477 9.542 9.432 9.404 9.293 9.250 9.308 9.278 9.278 9.303 9.337 9.322 9.336

4. Heat capacity and thermodynamic properties of Mn,GaN The experimental molar heat capacity of MnsGaN, obtained by the methods described in section 2 has been listed in table 5 and depicted in figure 5. Series I to VI correspond to points taken with the usual technique of heat-pulses using liquidor solid-nitrogen as cooling source. Series VII was made using liquid helium as coolant. Series VIII and IX were devoted to study the anomaly, and series X corresponds to an enthalpy determination. All these series correspond to experiment 1. Finally, series VI to XIII, which belong to experiment 2 performed after refilling the sample vessel, correspond to the study of the small anomaly at T’ = 117.7 K. Although the mass used in the Mn,GaN measurements (see table 1) is almost one half of the mass used in the Mn,ZnN measurements, the accuracy is similar to that estimated for the latter. The Mn,GaN shows two anomalies: the first at T’ = (117.7kO.l) K and the second at TN = (278.5 kO.2) K. The 7” anomaly was provedo3) to be due to the presence of a small amount of MnO, which shows at 118 K a sharp anomaly in c p,m of magnetoelastic origin, associated with the para-to-antiferro-magnetic ordering. (14*15) In the neutron-diffraction experiments this impurity was also

1050

FIGURE 5. Heat capacity of the anomaly deduced from the heating thermogram: obtained for different temperature rates.

J. GARCIA

ET AL.

at 278.5 K of Mn,GaN. 0. Heat-pulse results; - -~, C,,,(T) from cooling thermograms, - ~ -, etc.. C,,, (T) deduced

observed.“’ The anomaly at T, is associated with the paramagnetic to triangular antiferromagnetic transition. together with an expansion of the cell parameter, upon rr, 70. width AT = 4 K, and shape of lowering the temperature. The height AC,JR this anomaly resemble the similar transition in the Mn,ZnN, as expected, because the changes in magnetic arrangement and in the lattice parameter are analogous. The anomaly at TN was studied by means of dynamic measurements, using the same methods as described formerly. The agreement between C,,,(T) deduced from the heating thermogram and the discrete points is good. The C,.,(T) curves deduced from the cooling thermograms were shifted downwards by 6T = 11 K, the peak shape becoming broad and presenting fine structure; the fine structure varies with the cooling rate.‘13’ Five thermograms at cooling rates of 0.55, 0.61, 0.64, 0.08, and 0.36 mK. s- ’ were obtained. A maximum always appeared between 268 and 270 K. The fine structure differences in the C,,,(T) curves deduced from the cooling thermograms might be due to inhomogeneities in the local stoichiometry of the sample, which would cause the hysterical behaviour observed. The existence of inhomogeneities might also explain the differences between TN and 6T of this work and values obtained by magnetic measurements in a purer sample: TN = 298 K and

HEAT TABLE

6. Thermodynamic

functions

K

R

R

RK

5

0.026 0.064 0.143 0.324 0.639 1.080 1.610 2.188 2.788 3.408 4.574 5.613 6.546 7.350 8.070 8.731 9.259 9.694 10.147 10.59

0.025 0.053 0.092 0.155 0.258 0.412 0.618 0.870 1.162 1.488 2.213 2.998 3.809 4.628 5.440 6.241 7.024 7.783 8.518 9.233

0.062 0.283 0.770 1.885 4.236 8.488 15.185 24.669 37.096 52.59 92.53 143.58 204.46 274.04 351.2 435.3 525.3 620.1 719.3 823.0

10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150

CAPACITY

OF Mn,ZnN

of Mn,GaN

RT 0.012 0.025 0.041 0.061 0.089 0.129 0.184 0.253 0.338 0.436 0.671 0.941 1.254 1.583 1.928 2.284 2.647 3.013 3.380 3.746

AND

(R = 8.3143 J.K-“mol-‘,

K 160 170 180 190 200 210 220 230 240 250 260 270 273.15 278.8 280 290 298.15 300 325 335

1051

Mn,GaN M = 248.54 g’mol-‘)

R

R

RK

10.97 11.35 11.71 12.06 12.36 12.73 13.02 13.29 13.68 14.05 14.34 15.64 18.25 72.77 42.51 14.90 14.84 14.84 15.03 15.07

9.929 10.605 11.264 11.906 12.533 13.145 13.744 14.328 14.902 15.47 16.02 16.58 16.78 17.49 17.75 18.36 18.77 18.86 20.06 20.51

930.8 1042.4 1157.7 1276.5 1398.8 1524.2 1653.1 1784.5 1919.3 2058.1 2199.9 2347.8 2400.4 2598.0 2669.8 2844.1 2965.2 2992.6 3365.6 3516.1

RT 4.111 4.473 4.832 5.188 5.188 5.887 6.230 6.570 6.905 7.236 7.563 7.887 7.988 8.171 8.212 8.553 8.827 8.888 9.702 10.018

ST= 13 IL(‘) The validity of this argument is corroborated by the behaviour of the solid solution Mn,-,Ga,N, which shifts the critical temperature downwards to 280 KczT5) for x = 0.05. Prior to obtaining the thermodynamic functions of Mn,GaN, the amount of MnO impurity was evaluated and subtracted from each experimental point of table 5. To evaluate the amount of impurity the regions above and below T’ were smoothly connected, forming a base line. The difference between the measured C,,,(T’) and the estimated value on the base line, gave the size of the anomaly. Using this size and the C,,,(T) value for the pure Mn0,(i4* l 5, a mass of 81 mg of impurity was estimated. This mass of impurity represents corrections to the heat capacity ranging from 0.3 to 0.1 per cent, which were subtracted from the measured C,,(T). With these corrected C,,,(T) values the use of the same methods as for the Mn,ZnN allowed us to obtain the values listed in table 6 for the thermodynamic functions. In addition to the usual heat-capacity and dynamical measurements an enthalpy determination of the anomaly at TN was performed. The results are collected, together with those deduced from the heat-capacity series, in table 7. The agreement between the enthalpy measured and that deduced from the heat-capacity measurements demonstrates that no other anomaly exists. The anomalous enthalpy and entropy associated with the transition at TN was also deduced. The base line for 250 K < T < 300 K was established following the arguments used for the anomaly at T,(Mn,ZnN). Subtracting the base enthalpy or entropy from the total one the anomalous contributions were derived (see table 7). 65

ET AL

J. GARCIA

1052 TABLE

7. Enthalpy

determination for the transition of Mn,GaN at TN = 278.5 K and estimation anomalous molar enthalpy AH,(T,) and entropy AS,(&) changes

7; .-.

T

H,(T,)-H,(T)

K

K

RK

RK

269.80 270

286.84 287

452.57

451.75 451.62

Determination Series XIV Numerical integration Enthalpy mean value: Numerical integration of the fitted polynomials:

[%(27OK)-Hz(250 jH’L(200

Total enthalpy: Enthalpy base line:

{H,(300 (H,(300

Enthalpy Entropy

(H,(287

of transition: of transition:

A&(

KJ-H,(270

H,(287

K)-H,(270

K)-H;,(287

K))/(R K))/(R K))/(R

K) = K) = K) =

K)FN,(250 K)-H;(250

K))/(R K))/(R

K) = 1306.6i K) = 1089.8* K) = 218k3

AH,(T,)/(R T&R = 0.79~0.01

of the

K)

451.7kO.4 289.71 566.19 1.5 1.5

5. Discussion To analyse the different contributions to C,,, (T), the same procedure as in reference 16 (paper I) was followed. The measured points were first converted to C,.,,(T) values. For this purpose, the Nernst-Lindemann relation was used, determining A = cr2Vm/krC&,,(7’) (~1, isobaric expansivity; V,, molar volume; tiT, isothermal compressibility) from experimental values and for each crystallographic phase. The correction to C,,,(T) for temperatures in the magnetically ordered regime was smaller than the experimental error and, therefore, was not performed. In the paramagnetic region the values used were ~(300 K) = 5.2 x lo-” K - ‘, V,,(300 K) = 35.8 cm3.mol-’ for the Zn, and a(300 K) = 6 x 10e5 K-l, Vm(300 K) = 35.6 cm3. mol- ’ for the Ga compounds.‘1*2’ For both compounds K= = 16 TPa-’ (pure Mn)‘17) was used, since no measurements exist. C,,,(300 K) was taken from tables 3 and 6, respectively. The obtained differences, were 0.2R for Zn and 0.27R for Ga, at 300 K, which represent {~,,,(T)-G,,(m 1.4 and 1.8 per cent of C,,,(300 K), respectively. The obtained curves, C,,,(T), are shown in figures 6 and 7 as curves (b). Finally, as in reference 16 all contributions to the heat capacity were assumed to be additive. In both compounds it was assumed that Cr:i = 0 (mag, magnetic) for T < 12 K. Therefore, a linear regression C,,,(T)/T against T2 yielded yqa = (0.022 &O.OOl) J K- ’ . molt ’ (y, electronic coefficient; qa, quadratic antiferromagnet) and On(O) = (4.50+ 10) K for the Zn compound, and jfta = (0.038 +O.OOZ) J. Km2. mol- ’ (ta, triangular antiferromagnet) and On(O) = (400-t 10) K for the Ga analogue [On(O), Debye temperature at T = 01. The values of the obtained y’s and On(O)‘s are of roughly the same size as for the Mn,N. (r6) Moreover, the obtained y’s have higher values than the usual ones for pure 3d metals, indicating the existence of a high density of states near the Fermi level.‘rs) Mn,ZnN

According to what was stated above: c,.,(T)

= ~:,,(T)+~~.,(T)+c~~~~T),

(1)

HEAT CAPACITY

-

I

16 -

OF Mn,ZnN

AND Mn,GaN

I

1053

-1

200 300 T/K FIGURE 6. Analysis of the molar heat capacity of Mn,ZnN. (a), Above 191.4 K, experimental C,,,,(T); (b), deduced C,,,(T); (c), estimated lattice heat capacity CL,,,(T); (d), {C,,,(T)-CL,,(T)]; (e), the hightemperature C;, m term extrapolated to TN. loo

(1, lattice; e, electronic). The most difficult task was to determine C’,,,(T) and for this purpose C?::(T) = 0 and CL,,(T) = ?saT, for T < 60 K, was assumed. Since the system remains cubic, correspondmg states between C\,,( T, Mn,N) and C:,,(T, Mn,ZnN), for T < 60 K, was applied. The scaling factorf = 0.975 coincides with the molar-mass ratio M(Mn,N)/M(Mn,ZnN), and this value for f was extrapolated to 350 K, which gives Cb,,(T, Mn,ZnN) = Ct,,(j7’, Mn,N) (figure 6, curve c). Curve (d) of figure 6 shows {C,,,(T) - C:,,(T)), which represents the electronic and magnetic contributions. For T > TNthe tail of CFf,$(T) would give a decreasing contribution, in such a way that, at high enough temperature, only the electronic contribution would be present. This experimental fact may be inferred from C,,(T) close to TN for other related compounds. For example, for Mn,N(‘*) the tail is very small as well as for Mn,GaC. (ig) In addition, the first order-character of the transition reinforces this tendency. Assuming that for T > 300 K, G::(T) x 0 and C;,,(T) has a linear dependence on the temperature, the electronic coefficient in the paramagnetic (p) phase: yP = (0.033 kO.003) J * Km2 * mol- ‘, was deduced. Taking into account the errors in yqp and yP in the analysis of CC,,,(T), it may be concluded that there exists a change in the density of states near the Fermi level. However, this change cannot be ascribed to a particular transition, because both have first-order character with associated lattice and magnetic variations. Further study of the origin of the change in y can be obtained by the analysis of the anomalous entropies obtained in table 4. The additive hypothesis can be written: A&KJ = {&,,(T,))’ + (AUT,))e + {Wn(T,))““g. (2)

1054

J. GARCIA

ET AL

It is known that (AS,(T,)J-’ = ctAVm/rc,, and that AVm(T,) = 0.62cm3.moll’ and a(T’J = 7 x lop6 K-1.“,2) Due to the lack of +(Mn,ZnN), the tir value at 127 K was estimated from the related compound MnNi, as K~ = 14 TPa-‘.‘20’ Thus a value for {AS,(7”))1/R = (0.04&-0.005) was obtained and equation (2) reduces to (AS,(T’))‘+

{AS,(7”)}m”B = 0.3R.

Applying the same procedure to the anomalous using the a and AV, values at TN namely, = -0.46 cm’. mol- ‘, and the same K= value was obtained. Therefore, equation (2), written (AS,(T,)je

(3)

entropy at TN, A&,,( TN) = 1.11 R, and a( TN) = 2.6 x lo- ’ K - ’ and A V,( TN) as used above, {AS,(T,))i/R = -0.09 for the transition at TN, reduces to

+ (A&,( TN))““” = 1.2R.

(4)

Since there are two equations (3) and (4) but four unknowns, it is impossible to solve for each unknown. Further analysis of the y change problem is possible if the total entropy is considered. Assuming linear behaviour for CeV,m (T) in the different phases, the total entropy at 300 K may be written as S,(300 K) = S;(3OO K)+ASj,+AS;+AS,““Y+

{A&,( TA,)’ + (ASm(TN))‘,

(5)

where S,(300 K) and Sk(300 K), are the total and lattice entropy at 300 K, A% = ~c,aTi + Y,,(T, - TJ + ~~(300 K - TN), refers to the non-anomalous electronic entropy of the low-, T < TA, intermediate-, TA < T < TN, and high-temperature, phases, respectively; TN < T, ASI, = {AS,.& T,)}’ + { A&,,( TN)}’ was previously calculated. Taking into account that (ASJT,))’ = (yla - yqa)TA and (A.‘$,,(TN))’ = (y, - y,,)T,, from (5) the magnetic entropy can be expressed as AS=$g = S,(300 K) - #,,(300 K) - AS!,, - yp x 300 K = (1.5 f 0.2)R.

(6)

This anomalous magnetic entropy can be compared with the upper bound established if localized moments are assumed. In the quadratic antiferromagnetic phase there are manganese atoms with $/pB = 1.03 and others with $‘/pr, = 0.6 in the proportion of l/2.“’ Then, the inequality holds: ASrg/R

< ln( 1 + $/p8) + 2 ln( 1 + $‘/pB) = 1.65.

Therefore, the high value of the magnetic entropy obtained in (6) indicates a considerable localization for the magnetic moments, in agreement with diffuse neutron-scattering experiments in the paramagnetic phase.“’ To obtain individual values for (A&( TA)}mag, {A&( TA)}e, {A&,( TN)}mag, and {A&( TN)je, the ASFg value and equations (3) and (4), in the same framework of equation (5) were used. Due to the evaluation of the anomalous magnetic entropy, it is clear that AS:8 2 {AS,(T,)}m”g+ {AS,(T,)}““*, and if it is assumed that the equality holds, the addition of equations (3) and (4) gives { AS,(T,)}‘+

{AS,(T,)}’

= *0.2R,

HEAT CAPACITY

OF Mn,ZnN

AND Mn,GaN

1055

which implies that yta = (0.055 f 0.025) J * Km2 * mol- ‘. This means that at T’, even considering all possible errors, there is a change in the electronic coefficient. Therefore, using the yna and yt. values, {AS,,,(TA)}e/R = (0.51 kO.38) was obtained, and from (3), {AS,,,(TA))maS/R = -(0.21 kO.38). Consequently, the transition at TA is mainly driven by changes in the electronic band structure. Furthermore, the negative mean value of (AS,,,(TA)}mag agrees with the increase of localized moments with temperature at TA.(I) Following the analysis, using 7,. and yP values, {AS,(T,)}e/R = (0.5kO.55) was obtained, and from (4), {AS,(TN)}mag/R = (1.7 +0.55), which clearly indicate the magnetic origin of the transition at TN. However, considering the errors involved, a zero electronic contribution cannot be excluded. Finally, the reliability of the obtained value for (AS,,,(TN)}mag/R, namely (1.7 + 0.6), is considered. Assuming fully localized magnetic moments for the Mn, an upper bound for {AS,(T,))““~/R is established. The magnetic moments are known,“) p/fig = 1.2, and therefore {AS,(T,)}m”g/R

< 3 ln(1 +p/&

= 2.36.

This last value is comparable with the one obtained above. Mn,GaN

Using equation (1) and neglecting C;::(T) for T < 60 K, it is possible to proceed as for Mn,ZnN. Thus the subtraction of the linear term C’,,,(T) = yta T from Cy, ,(T)

I

16 -

4-

200 T/K FIGURE 7. Heat capacity analysis of Mn,GaN. (a), -.-.-, the lattice estimation, C’“:,,(T); (d), -, the difference {C,,(T)low-temperature electromc contribution: C;,,,(T) = Y,~T. 100

300 C,.,(T); (b), -, C,,,(T); (c) - - -, C;,,(T)}; (e), an extrapolation of the

1056

J. GARCIA

ET AL

gives C).,(T), and the application of corresponding states between C,.,(T, Mn,GaN) and C,,,(T, Mn,N) gives a scaling factor f= 0.8. It is remarkable that f is lower than the ratio of the molar masses M(Mn,N)/ M(Mn,GaN) = 0.976. The use of such a scaling factor gives a negative C;,,,(T) at high temperatures, which invalidates the value. To solve this difficulty a mean value f= 0.97 from f(Mn,ZnN) and from the molar-mass ratio M(Mn,N)/M(Mn,GaN) was used. Curve (c) in figure 7 represents the lattice contribution obtained from C:,,(fT, Mn,N) with the above scaling factor. In the same figure the differences (C,,,(T)-C:.,(T)j are also plotted: curve (d); together with the linear term yta T. curve (e). Curve (d) deserves two comments: (i) between 30 and 80 K, {CeV.m(T)+C~~~(T)) shows a shoulder with a maximum of about 0.8R, located at 50 K. This shoulder might appear as consequence of the lattice-estimation procedure, having no true existence. However, the arguments stated in the previous paragraph, as well as comparison of C,,(Mn,ZnN) and C,,,(Mn,GaN) give enough evidence to lead us to believe that this anomalous contribution is not due to the analysis. None of the usual behaviour for Ct.,,, or C;;; may explain such anomalous contribution; (ii) in the paramagnetic phase, where Cr;,!j,(T) is supposed to be negligible, the low-temperature electronic contribution extrapolated to the high-temperature range is greater than the difference (Cv,& T) - C’\..,( T)).; therefore, the electronic coefficient in the paramagnetic phase yp should be equal to or smaller than the value at low temperature. The presence of the shoulder may be explained in two different ways: one possibility is the existence of an anomaly in the density of states of the conduction band close to the Fermi level. In this case, the thermal population can change significantly the electronic contribution to the heat capacity.‘2’.22’ A second explanation may be found in the recent theoretical treatment of the influence of the spin-fluctuations on the anomalous electronic contributions of weakly ferromagnetic samples.(23,24) It has been shown that C’.,,(T) at low temperatures has a shoulder like that mentioned. Extensive experimentation on magnetic susceptibility and magnetization at high magnetic fields is in progress, to elucidate this particular behaviour. The origin of the transition at TN can be analysed on the basis of the anomalous entropy listed in table 7. AS,(T,)/R = 0.79, and of equation (3). To calculate the anomalous lattice entropy contribution, x=4.2x10-“K-l. Al’,, = -0.36 cm3.moll’, and I+ = 16 TPa- ’ were employed, (l’) leading to (AS,( T,))’ = -0.11 R. Assuming {A&( T,)) e 2 0 a value of AS,( TN)“ag t 0.89R was obtained, which in any case remains lower than the entropy found for a model of fully localized moments: AS,(7’Jmag/R = 2.36. and confirms that the transition is driven mainly by the magnetic interactions. However, it must be remarked that this type of anomaly in C;.m( T). as well as in the magnetic susceptibility, was detected in some palladium’25’ and lanthanide alloys.‘26’ A review of the literature has not given evidence of this behaviour for metallic compounds of the transition elements of the first row.

HEAT CAPACITY

OF Mn,ZnN

AND Mn,GaN

1057

We are indebted to Mr Frank Blunt by his careful and patient reading of the paper. This work was partially supported by the Comisibn Asesora de InvestigacSn Cientifica y TCcnica. REFERENCES I. Fruchart, D. Ph.D. Thesis, C.N.R.S., Grenoble. 1976. 2. L’Heritier, Ph. Ph.D. Thesis, C.N.R.S., Grenoble. 1980. 3. Fruchart, D.; Givord, D.; Convert, P.; L’Heritier, Ph.; Senateur, J. P. J. Magn. & Magn. Mar. 1980, 18-19,490. 4. Bouchaud, J. P.; Fruchart, E.; Lorthioir, G.; Fruchart, R. C.R. Acad. Sci. (Paris) 1966,26X, 640. 5. Bouchaud, J. P. Ann. Chim. 1968, 3, 81. 6. Fruchart, D.; Bertaut, E. F.; Madar, R.; Fruchart, R. J. Phys. 1971, 32C, 876. 1. Madar, R.; Gilles, L.; Rouault, A.; Bouchaud, J. P.; Fruchart, E.; Lorthioir, G.; Fruchart, R. C.R. Acad. Sci. (Paris) 1967, t264, 308. 8. Bertaut, E. F.; Fruchart, D.; Bouchaud, J. P.; Fruchart, R. Solid State Commun. 1968, 6, 251. 9. Burriel, R. Ph.D. Thesis, University of Zaragoza (Spain). 1979. 10. Garcia, J.; Bartolomt, J.; Gonzalez, D.; Navarro, R.; Crama, W. J. J. Chem. Thermodynamics 1983, 15, 1109. 11. Justice, B. H. The Fitab Program, Projet Report COO-1149-143, University of Michigan, Ann Arbor, (U.S.A.). 1969. 12. Since the C,,(T) points obtained from the heating thermogram are quite lengthy, they will be sent on request. 13. Garcia, J.; Navarro, R.; Bartolomt, J.; Burriel, R.; Gonzalez, D.; Fruchart, D. J. Mugn. & Magn.

Mat.

1980,

15-18,

1155.

14. Millar, R. W. J. Am. Chem. Sot. 1928,50, 1875. 15. Todd, S. S.; Bonnickson, D. R. J. Am. Chem. Sot. 1951, 73, 3844. 16. Garcia, J.; Bartolome, J.; Gonzalez, D.; Navarro, R.; Fruchart, D. J. Chem. Thermodynamics 15, 465. 17. Gschneider, K. A. Solid State Physics 1964, 16, 275. 18. Mekata, M.; Haruna, J.; Takaki,.H. J. Phys. Sot. Jpn 1966, 21, 2267. 19. Garcia. J. Ph.D. Thesis. Universitv of Zaraeoza (Snain). 1981. 20. Honda; N.; Tanji, Y.; Nakagawa,*Y. J. Ph;. So>.‘Jpn’l976, 41, 1931. 21. Friedel, J. The Physics of Metals. d-Electrons. Ziman, J. M.: editor. CUP: Cambridge. 1%9. 22. Shim& M.; Katsuki, A. J. Phys. Sot. Jpn 1964, 19, 1740. 23. Makoshi, K.; Moriya, T. J. Phys. Sot. Jpn 1975, 38, 10. 24. Hasegawa, H. J. Phys. Sot. Jpn 1975, 38, 107. 25. Van Dam, J. E. Ph.D. Thesis, Kammerhng Onnes Lab., Leiden (Holland). 1973. 26. Lustfeld, H.; Bringer, A. Solid State Commun. 1978, 28, 119.

1983,